Matters of Time Directionality in Quantum Physics∗ Jean-Christophe Lindner† Department of Physics, Université de Montréal Montréal, QC, Canada 20 August 2020 Abstract This is the second of two reports concerning the issue of time directionality in fundamental theoretical physics. Here a fresh perspective is offered on several aspects of the problem of the interpretation of quantum theory which centers around a reconsideration of the significance of the requirement of time reversal symmetry. Following a critical review of early time-symmetric formulations of quantum mechanics, it is argued that a more consistent approach must overcome the contradictions of the orthodox interpretation that follow from its rejection of scientific realism. It is also shown that the condition of time-reversal invariance provides strong enough a constraint to allow a realist interpretation of quantum theory to satisfy the principle of local causality in the face of quantum entanglement. It is then explained that the existence of a maximum quasiclassical domain can only be predicted to arise and to persist, following measurement, once we consider the problem of the emergence of time in quantum cosmology from the perspective of the solution provided in the preceding report to the problem of the origin of thermodynamic time asymmetry. It is also suggested that in the context of a semi-classical theory of the gravitational field the proposed realist, time-symmetric interpretation of quantum theory would allow the formulation of a satisfactory solution to the problem of objectification. ∗Preprint: philpapers.org/rec/LINMOT-5 †Email address: jean-christophe.lindner@umontreal.ca 1 Contents 1 Introduction 3 2 A simple analogy 9 3 Time-symmetric causality 12 4 Closed causal chains and time travel 20 5 Advanced waves and time asymmetry 30 6 Early interpretations 35 7 The constraint of scientific realism 42 8 Time-symmetric quantum theory 69 9 Quantum entanglement and non-locality 88 10 The quantum measurement problem 99 11 The emergence of time in quantum cosmology 119 12 Universal causal chain and quasiclassicality 132 13 Objectification and the role of gravitation 162 14 Conclusion 180 15 Summary 183 Bibliography 208 Index 211 2 1 Introduction In the preceding report of this series1 I offered original solutions to several outstanding problems in the fields of gravitational physics and cosmology which were all based on an alternative interpretation of the concepts of time reversal and negative energy. Thus, I introduced a generalized, classical theory of gravitation that is consistent with the possibility that elementary particles could exist that would propagate negative energy forward in time. Based on the understanding that it is necessary to distinguish between a fundamental, bidirectional concept of time direction involving elementary particles and the classical, unidirectional concept of time direction associated with thermodynamic irreversibility, I was then led to introduce a more consistent formulation of the time reversal symmetry operation that was shown to be relevant to a description of the fundamental states of matter particles on the quantum gravitational scale. I also showed that the hypothesis that negative energy matter was present alongside positive energy matter in the first instants of the Big Bang allows to satisfactorily explain thermodynamic time asymmetry as being the outcome of a certain condition that must be imposed on this initial state in order that all the elementary particles present in the universe be causally related to one another. But given that the bidirectional concept of time that underlies this approach constitutes a challenge to our traditional conception of causality and the idea that causes always precede their effects, then one of the objectives of the current report is to develop a revised concept of causality that allows to take into account the time-symmetric nature of elementary particle processes. Part of the progress I have achieved concerning this issue actually emerged from an investigation of the significance of certain puzzling aspects of the currently favored interpretation of quantum theory which did not appear to be connected with the issue of time directionality, but which were of interest in their own right. Yet, some of the results I obtained regarding the issue of time directionality in gravitational physics turned out to be necessary for developing a solution to the remaining problems that still stand in the way of a truly consistent interpretation of quantum theory. Thus, in the present 1The document is available as a preprint [1] and it is important to mention that the discussion featured in the present report relies heavily on the developments which were introduced in the first report, so that reading the preceding document should be considered necessary for a proper understanding of the analysis which is the subject of the present one. 3 report I would like to address not only the question of time directionality as it arises in a quantum theoretical context, but also, and more specifically, the important problem of the interpretation of quantum theory itself. I will show, in particular, that it is now possible to provide a realist picture of quantum phenomena that does not violate the principle of local causality, even though it is not incompatible with the consequences of quantum entanglement. This improved understanding will then be used to provide a definitive solution to the quantum measurement problem that allows to explain the emergence and the persistence of a quasiclassical world. Before concluding this discussion I will identify a possible role which gravitation might play in explaining the random character of the unique outcomes of quantum measurement that once again draws its relevance from the preceding developments and that may eventually become an essential element of a fully developed quantum theory of gravitation. In fact, one of the goals of the latter portion of this report is to bring some much needed clarity to the theoretical context in which we are to address the problem of elaborating a theory of the gravitational interaction compatible with the basic principles of quantum theory. In the preceding report I have already shown the essential role played by the discrete spacetime and energymomentum symmetry operations (appropriately redefined and extended to comply with an improved concept of time reversal) in characterizing states of matter at the spatial scale and energy level at which we can expect the gravitational interaction among elementary particles to be as strong as the other known interactions. This was achieved by demonstrating the relevance of those symmetry operations for a definition of the microscopic states of matter that must be taken into consideration in order to provide an appropriate measure of black hole information and entropy. Here I want to show that one of the main consequences of the solutions I will propose to more traditional aspects of the problem of the interpretation of quantum theory is that it becomes clear that an integration of the general theory of relativity to the rest of physics must proceed by first recognizing that in order to formulate a quantum theory of gravitation, it is necessary not to merely integrate quantum principles to our classical theory of the gravitational field, but also to adapt quantum field theory to a general relativistic description of reality at a fundamental level. The approach I have followed in the preceding report consisted in explaining how some specific aspect of a quantum mechanical description of the world, namely the existence of positive and negative energy states which 4 are allowed to propagate both forward and backward in time, changes our understanding of the classical theory of gravitation and allows to improve and simplify its formulation in a way which has decisive consequences for our description of certain phenomena occurring on the cosmological scale. In the present report I will go the opposite way and show how those original insights regarding cosmology shall affect our understanding of quantum physics and open up the way to a more pragmatic approach toward a quantum theory of gravitation. As I mentioned in the preceding document, the level of this discussion is clearly philosophical, despite the fact that it remains very precise in its reference to quantitative aspects and concepts. The particular approach followed here allows me to achieve a broadness of scope that would be impossible to reach using a more conventional methodology. I do recognize that it is unusual in the field of fundamental theoretical physics to formulate exact results in such a way. But even though I would not myself have believed in the pertinence of an approach based on reliance to expert knowledge and rigorous logical analysis of higher level concepts when I began studying physics in a traditional academic environment, I have come to realize that it offers real and significant advantages. If the reader is willing to rely on her own judgment to assert the validity of the outcome of my analysis, it will become pretty obvious to her that despite its originality, the approach adopted here for deriving and communicating those results allows very useful physics to be learned, when the appropriate effort is made to follow the transparent reasoning which I use to demonstrate the consistency and the empirical plausibility of my claims. Some of the most significant contributions I will offer in this report consist in actually showing that there is indeed a problem with some aspects of our current understanding. Two categories of questions I will try to address more specifically are not always distinguished from one another and together constitute the problem of the interpretation of quantum theory. But I will explain why they must in fact be considered as independent questions in need of separate answers. There is thus in effect a problem of interpretation concerning the mathematical framework of quantum theory in general and the distinctive features of quantum physics, which are mainly the use of probability amplitudes instead of classical probabilities (a remark which becomes significant once it is recognized that quantum field theory is a particular instance of statistical mechanics) and the appearance of non-local effects, which are both unavoidable features of physical reality. It is not clear from a tradi5 tional perspective how those aspects are to be understood in a manner that is consistent with so many other well known aspects of reality which would appear to forbid their occurrence. It is commonly believed that the problem here does not have to do with the inappropriateness of our interpretation, but with the inappropriateness of our traditional approach to understanding reality. But if this posture may be legitimate for what concerns probability amplitudes and the existence of quantum interferences in general, I will show that it it not justified for what concerns the problem of non-locality which is actually a question in need of an answer. Thus, answers will be offered to a problem which I call the 'quantum reality problem' and which includes the problem of quantum non-locality as a particular aspect. This problem must be distinguished from the associated problem that is usually referred to as the 'quantum measurement problem'. Those who are not actively working on this particular problem often believe that it too may not be real, or alternatively that it was entirely solved by more recent developments that showed how the evolution of a quantum system is affected as soon as it becomes entangled with certain irreversible processes taking place in its environment. But, as a handful of researchers have already understood, this opinion is not warranted and even though real progress has indeed been achieved in trying to solve the quantum measurement problem and more generally the problem of the emergence of 'quasiclassicality', some related questions remain unanswered and it is precisely those I will address. However, if you happen to be among those who are convinced that there is no longer a problem with quantum measurement, then I would ask you a very simple question: what is the cause of the irreversibility that characterizes the evolution of the environment degrees of freedom with which a quantum system becomes entangled during measurement and which is necessary for explaining decoherence? Clearly, an appropriate answer to that question must be provided before the problem may be considered to have been solved and this is what I have tried to achieve in the previous report. But, as I will explain, that is not the only difficulty. In order to clarify this complex situation I will therefore need to draw on the insights I have gained while solving the problem of the origin of time asymmetry, but I will also have to build on the insights I have gained while solving the quantum reality problem, which illustrates how important it was in effect to first solve that perhaps more intangible problem. It is quite remarkable that in order to answer those two categories of questions it is possible to rely on the most appropriate of the already ex6 isting mathematical frameworks within which quantum physics is currently formulated and it is not necessary to alter the foundations of the theory. I must immediately point out, however, that there is something terribly wrong with the often met remark to the effect that choosing which of the existing interpretations of quantum theory is the correct one is a mere matter of taste given that they are all mathematically equivalent and therefore all constitute equally valid proposals, which all agree with observations. Before any progress can be achieved what needs to be understood is that most interpretations are not equally appropriate, but rather all equally incorrect or incomplete. It would be misleading, therefore, to argue that the problem is that there are too many viable candidates for an interpretation of quantum theory, because in fact none of the currently available proposals is fully consistent, either from a logical viewpoint, or regarding the requirement that the obtained theory be compatible with all observable aspects of physical reality. This state of affairs can only mean one thing and it is that further progress is required to formulate the one interpretation that will meet both of those requirements. I believe that the original results I have unveiled in the preceding report provide some of the missing elements which are required to achieve just such a leap forward in our understanding of quantum physics, which will, at last, allow it to become a fully coherent theory. Before we begin, though, I would like to say a few words about what was one of the essential principles that guided me on developing the revised interpretation of quantum theory that is described in this report. This broad requirement slowly emerged as being unavoidable for a solution to the problems which will be discussed in the following sections. In the preceding report I already emphasized the importance of another essential constraint, which is that of relational definition of the physical attributes of a system. The relevance of this principle follows from the fact that it is not acceptable to refer to aspects of reality that are not part of the universe to which a system belongs in order to define its physical attributes. It is important to understand, however, that the necessity to define the value of physical attributes in a relational way does not imply, as some authors have suggested, that nothing can exist other than the physical reality we observe in our universe. Indeed, it must be clear that what I have found is that there can be no reference, by observers in a given universe, to physical attributes not related to one another by the network of causal relationships belonging to their own universe. But this does not mean that other such ensembles, or universes, cannot exist as logical possibilities, with similar, purely relational and mutu7 ally referring properties, objectively distinct from those existing in another universe. This remark illustrates the importance of a further insight that is at once required by the world view developed in this report and implied by its likely validity. There is in effect a tendency nowadays to designate as metaphysical every aspect of reality which may be impossible to probe through direct observation and to conclude that such aspects are not worth the attention of the scientific community. What I have come to understand is that the self-imposed requirement of systematically characterizing as metaphysical any notion that refers to aspects of physical reality which may not be directly accessible to observation is actually a mild form of solipsism and constitutes one of the most serious obstacle on the way to developing more accurate models in fundamental theoretical physics. In fact, I think that the greatest challenge with which science is currently faced may well be that of surmounting the obstinate refusal to accept as a legitimate object of scientific inquiry what cannot be directly observed by the means of measuring instruments and as physically meaningful what lies outside the limits of observation of a given observer (think of the reality behind event horizons for example). In this particular sense, the success of science might in the end depend on our willingness to adopt a position analogue to scientific realism and opposite to instrumentalism, concerning ultimately the idea that something really exists outside our immediate domain of perception of reality. This requirement is not so different from the original condition of objective reality which was defended by Einstein and which was proposed in an attempt to demonstrate the validity of an approach based on the hypothesis that reality actually exists, even when it is not subjected to direct observation. But given that in the physical sciences objectivity has rather come to characterize any conception of reality that is derived solely from empirical knowledge and observation, then it would not be appropriate to use the term 'objective reality' in order to refer specifically to a reality that is not directly observable under all conditions, even if the nature of this reality was still derived from experimental facts. Thus, I cannot avoid having to speak about a realist conception of reality as being essential to a consistent interpretation of quantum theory, even if that may appear tautological, as there does not exist a more appropriate term to denote this kind of approach. It must be clear, however, that it cannot be required of such a reality that it be classical in nature, despite the fact that it would be characterized as objectively real (in the philosophical sense). Anyhow, I think that this scientific 'realism' 8 must be considered a necessary ingredient for the elaboration of an accurate understanding of the nature of reality at a fundamental level and this is what motivates my position with respect to certain unresolved issues regarding the problem of the interpretation of quantum theory. Such a conviction, however, should not be confused with a belief in the validity of theoretical constructs that have no experimental justification, which does not constitute a desirable position to hold on to and which would actually consist in the exact opposite of the viewpoint I'm defending here. What I'm suggesting, in effect, is that it may sometimes be appropriate to extend the validity of what we know to be true with absolute certainty to a larger domain of reality where this validity may not be directly assessed and not that it would be right to try to extend the domain of validity of a description for which there does not yet exist any empirical evidence. In other words, if we are justified in extrapolating beyond the domain of direct observation, as may be found necessary, principles and notions which we have good reasons to believe are indeed valid, it would be wrong to take advantage of the absence of observational data to try to justify hypotheses which cannot yet be independently corroborated and which may therefore have no validity whatsoever from a scientific viewpoint. Those considerations will have decisive consequences for the formulation of an interpretation of quantum theory that contains no contradiction when considered in the broader context of the representation of reality that emerged from the progress I have already achieved in solving other long-standing problems in the fields of gravitational physics, cosmology, and thermodynamics. 2 A simple analogy One particular event from my early years in elementary school contributed more than any other in developing my awareness of the deep structure of physical reality. I do not remember much about the many events that happened during the period of my life when I was acquiring many of the skills which I'm still using today (like writing and calculating), but I still remember perfectly well that when I was about eight years old my teacher once gave me and each of the other children in my class a few copper wires, an electrical battery, and a tiny light bulb with as a mission to figure out how to produce light using only those components. This may seem like an easy task and most of the kids did, in effect, manage to achieve the assigned objective 9 quite rapidly. Yet, even though I was usually considered a fast learner in most traditional academic disciplines, I really had trouble finding out how to obtain the desired result. I believe that this is because, even as a kid, I always preferred to actually understand things rather than simply be satisfied with learning about the finished answers I was proposed. So, rather than just trying to combine the elements in every possible way and be satisfied once I had accomplished my homework, like the other kids, I tried very hard to understand what the rule could be that would justify that a certain arrangement does in effect produce light. I don't know why I had such an inclination, but it has remained with me all my life as I began to develop an interest in the sciences and learned about the unsolved mysteries of modern physics. What I have since realized, with retrospect, is that somewhere in this simple laboratory experiment was hidden the answer to some of the most enduring problems facing fundamental theoretical physics. The first lesson I retained from this experience with the light bulb and the battery is that there is a polarity to all relevant physical properties. The battery has a positive and a negative pole and so does any light bulb and it is only by taking this aspect into consideration that one is allowed to understand what constitute a successful configuration for producing light. In the preceding report I have discussed at length how this aspect is relevant even in a gravitational context, where the sign of action is the decisive physical property that is involved in determining the attractive or repulsive nature of the gravitational interaction between two particles. I also emphasized the purely relational nature of any polarity, whether it regards the sign of electrical charge or the direction of propagation in time of a particle. Only the difference or the identity of any such property of a system with respect to that of another system has a physical significance. But the most difficult part in devising an electrical setup that works consisted in understanding the role of the wires. What is essential to learn, in effect, is that the experiment can only work if the wires are arranged so as to form a circuit that goes from one pole of the battery into one pole of the light bulb and then back from the opposite pole of same light bulb into the unconnected pole of the same battery. I only realized that this must be so when I carefully examined the light bulb and saw that there is a special kind of wire inside of it that connects the two poles from within, thereby suggesting that for some reason the setup must be closed on itself. But after I came to understand the requirement for the setup to form a closed circuit I was not only faced with the problem of understanding why 10 only such a configuration would produce the desired outcome, but also with the difficulty of understanding what was the role of the battery in allowing light to be produced by the light bulb. In other words, I had trouble understanding in which way the role of the battery could be distinct from that of the light bulb, despite the fact that both components were connected along the same circuit. Only at a relatively late time was I allowed to learn that what the light bulb does from a fundamental viewpoint is simply dissipate the energy that is stored in a useful form in the battery, as a result of the friction that is exerted on the electrical current that flows through the part of the circuit located inside this light bulb. This is a manifestation of the second law of thermodynamics in its purest form. The very objective of producing the circuit is to allow the current to dissipate the energy contained in the battery by producing an enormous number of high entropy light particles that expand out of the system irreversibly. The whole mystery associated with the second law of thermodynamics and the irreversibility of time is contained in this little experiment and with it the solution to the quantum measurement problem. Any circuit that produces a useful result that is observable and which has an effect on its surroundings (the light turns on) must dissipate energy that was originally present in the universe in a well ordered configuration. I will eventually explain what is the essential role of irreversibility in allowing the emergence of the quasiclassical character of reality that is revealed by any process of quantum measurement, but first I would like to point out the profound significance of the property of closure that is imposed on any operational electric circuit. For anyone who works as an electrician the notion of a circuit is omnipresent, but it is also somewhat lost in a practical context where one always works with pairs of polarized wires in which the two branches of a circuit are always contained in a single cable that invariably goes from energy source to appliance over large distances, as if what was involved was one single flow from source to sink, similar to the flow of water inside a pipe. Thus, it is easy to forget that one is always dealing with a closed circuit, however complicated it might be. I believe that what explains some of the difficulties we encounter in quantum physics is that we have always learned to work only with pairs of 'polarized wires' and this is why we fail to understand that what we are dealing with in general is not a single process that unfolds from initial conditions to final measurement, from 'source' to 'sink', but really a closed causal chain similar to the closed electrical circuit of my childhood experiment. 11 It is the fact that, for some reason which will be discussed later, we are always working with portions of a 'closed circuit' which are highly stretched and extended along the unidirectional dimension of time and whose polarized components are constrained to evolve along very similar trajectories, that explains that we have been allowed to ignore the fact that we are actually always dealing with two processes which are the oppositely polarized portions of a causal chain that closes up on itself like a functioning electrical circuit. We always model very long causal chains, similar to electric cables, that extend not along a distance in space, but along the unidirectional dimension of time and for that reason we have never realized that what the polarized character of this causal chain really means is that we are dealing with a 'closed circuit'. I will explain how the simple analogy discussed here can be developed into a rigorous interpretation of experimental facts that allows to provide not only a consistent explanation of the persistence of quasiclassicality, but also a realist and fully intuitive picture of quantum phenomena that reproduces their non-local character without violating the principle of local causality. When we will reach that point it will become possible to actually understand why it is, in effect, that the causal chain associated with the history of the universe as a whole closes up on itself like any electrical circuit that produces light. 3 Time-symmetric causality It is somewhat strange that it is Richard Feynman himself that once remarked that one question he believes to be unanswerable or unscientific is the one that asks why it is that we are allowed to guess from one part of the universe what the rest of it will do? Indeed, it has become pretty clear to me that if this is possible it is simply because things propagate, not just in space, but also in time and, as Feynman himself first understood, not just forward in time, but also backward, from the future toward the past. In fact, this is the essence of causality. The events that form the universe are all related to one another and to nothing else by the network of causal relationships that is established by the propagation of elementary particles between those events across spatial distances and through time, both forward and backward. This is what explains that no part of the universe can be considered independently from any other. The results I have discussed in section 3.9 of [1] regarding the role of the constraint of global entanglement in giving rise to thermodynamic time-asymmetry appear to confirm that such a requirement, regarding the 12 necessary existence of causal relationships established through local contact and propagation, is in effect essential for a consistent description of physical reality. Another significant conclusion from my preceding report that concerns time directionality more specifically is that a distinction must be made between the traditional concept of time direction associated with the thermodynamic arrow of time and a more fundamental concept of time direction which has to do with the direction of propagation in time of elementary particles and which merely distinguishes two opposite directions without favoring one of them in any particular way (under most circumstances). Thus, even at a semi-classical level of description, there already emerges a notion of bidirectional causality more fundamental than the classical, unidirectional concept of causality according to which causes always precede their clearly distinguishable effects in the same unique direction of time. From this more fundamental viewpoint there is no longer an absolute distinction between causes and effects and all that one can meaningfully ask is whether there is a correlation between the occurrence of a certain event and that of another event taking place at a different time, either farther in the past or later in the future (which would affect the probability that one of the events is observed when the other is). Those who have seriously examined the question usually recognize that the idea that we can influence the future, but not the past, is not entirely correct. Indeed, when calculating correlation probabilities we must take into account the effect of the future on the present whenever there are antiparticles in the final state, because antiparticles are most appropriately described as particles propagating from the future. In fact, there appears to be no real distinction at the elementary level of description between the past and the future and despite the fact that the future remains unknown to present observers it is as unique as the past and we are merely discovering what that future is as we progress irreversibly towards it. What we consider to be our control over the future is not a complete illusion, because there are correlations between what we do now and what happens later, but it is no more real than the kind of 'influence' we have on the past, which is made apparent by the very same correlations when they are considered after the events have already happened. As I will explain below, it is merely the absence of information about the future and the fact that all possible futures are allowed to happen (while no such freedom exists for the past, as a consequence of thermodynamic time asymmetry) that makes it look like we only have control 13 over the future, while the future itself appears to exert no influence on the present and the past. But once we realize that the future is only the past of an even more remote future, then it becomes all the more obvious that this is just an illusion. What I'm suggesting, therefore, is that at the level of elementary particles, where thermodynamic time asymmetry is not a meaningful concept, causality is not constrained to always operate from past to future, which means that causes and effects cannot be distinguished based merely on the sign of the time interval between the events they relate. Thus, while it may still be necessary to assume that causes precede their effects, this can actually be achieved in any of the two directions of time in which the particles conveying the effects are propagating. At a fundamental level of description there simply is no restriction regarding the direction in which causality operates and this means that from the unidirectional time viewpoint effects can actually precede their causes. But instead of saying that under certain circumstances causes may actually constitute effects, while effects would become causes it is more appropriate to define causes and effects in a more fundamental bidirectional way, so that effects can propagate either forward or backward in time, but always in the direction in which the particle mediating the process is propagating in time. The absence of absolute distinction between causes and effects does not mean that the relativistic concept of a future light cone clearly distinct from its past equivalent and defining the causal structure of spacetime is wrong. But it does mean that there is no a priori reason to differentiate the structure that arises as a consequence of the limits imposed on the propagation of causal signals in the future from that which would arise as a consequence of the constraints imposed on the possible propagation of causal signals in the past. Yet, it would be incorrect to argue that only correlations exist at a fundamental level of description and that causes cannot be distinguished from their effects in any way, because what the bidirectional, or time-symmetric nature of causality implies is merely that there is no absolute (non-relationally defined) distinction between causes and effects (understood as locally propagated influences of certain events on others), even though a relatively defined notion of time directionality is still involved from a semiclassical perspective that allows to distinguish a direction in the propagation of causal signals. What must be understood is that the only invariably true notion of causality is the time-symmetric, or bidirectional one, while classical, thermody14 namic causality, or unidirectional causality is valid only as a consequence of the existence of the constraint of low entropy that applies on the initial conditions at the Big Bang and is not a fundamental property of nature. In fact, what I have shown in section 3.9 of [1] is that a certain condition of local causality that is not a priori asymmetric in time can be used to explain the observed thermodynamic time asymmetry from which unidirectional time and classical causality emerge. Later on, I will discuss the role played by the constraint of global entanglement (which I previously identified as the ultimate cause of thermodynamic time asymmetry) in constraining classical causality to operate only in the future direction of time. It is already possible, however, to appreciate the fact that the direction of time relative to which entropy grows and information flows is independent from the direction of propagation in time of the particles involved in producing such a change. The direction of propagation in time of an elementary particle, which determines its particle or antiparticle nature, merely allows to assess whether the particle propagates an effect in the past or in the future, while the flow of information is a higher level property that is fixed merely by the macroscopic boundary conditions imposed on a process, regardless of whether it involves particles or antiparticles. Thus, a classical, unidirectional, or thermodynamic causal chain can be differentiated by the fact that it invariably involves a unique event in the past exerting a recognizable effect on multiple spatially separated events in the future2. In this particular sense it transpires that unidirectional causality does in effect always operate from past to future in our universe, as no single event in the future has ever been observed to exert a unique recognizable influence on multiple physically separated events in the past that would actually involve a flow of information from that future time into its past. But, again, this does not mean that a future event cannot influence a past event, merely that such an influence cannot, in effect, occur in a way that 2In fact, as emphasized by Lawrence Sklar [2], it is not always possible to associate the asymmetry that distinguishes causes from effects with the thermodynamic time asymmetry other than by relying on the property of parallelism of the direction of time that allows to 'project' the thermodynamic asymmetry characterizing certain causally related pairs of events onto other pairs of causally related events where the cause is not so easily differentiated from the effect (as in the case of certain mechanical or astronomical processes where friction and dissipation are not manifestly apparent). But this only strengthens the validity of the position I'm defending, to the effect that causality is not by necessity an asymmetric property. 15 would allow the formation of mutually consistent records of the future. It is not causality in the fundamental sense that is asymmetric in time, but the making of records by which it is usually made manifest. This asymmetry has already been recognized as arising from the existence of a thermodynamic arrow of time associated with the continuous decrease of entropy that takes place in the past direction of time. Therefore, the only mystery regarding the apparent absence of causal chains that would run from the future toward the past does not have to do with a real absence of such phenomena, but with the fact that future causes do not exert the same kind of recognizable consequences on the past, as past events exert on future events. The absence of recognizable effects at an earlier time from an event that would have taken place at a later time can always be attributed not to the absence of backward in time causality and to a fundamental character of unidirectionality, but to the fact that entropy always increases only in the future direction of time, while records can only be formed in the direction of time relative to which entropy actually increases. Given that in the preceding report I have explained that the thermodynamic arrow of time is not a fundamental property of nature, but arises from a condition regarding the homogeneity of the initial distribution of matter and radiation energy at the Big Bang (in the presence of anomalously gravitating negative energy matter), then it clearly follows that there is absolutely no rational motive to argue that backward in time causation is forbidden in our universe. Indeed, all the observable properties of naturally occurring processes can be explained without relying on this assumption, while the requirement of a relational description of the direction of propagation in time implies that backward causation must exist at a fundamental level, given that it cannot be distinguished in any absolute way from forward in time causation. I believe that it is again our failure to recognize the full significance of Feynman's description of antiparticles as particles propagating backward in time that is responsible for our ignorance of the necessity (and not just the possibility) of a time-symmetric description of causality in the quantum realm. Once it is understood that there is a requirement for causality to be described in a time-symmetric way (due to the existence of backward in time propagation), then what we are facing is no longer merely the problem of understanding how the future can influence the known past, but really how it can be that a unique future may itself be causally related to this unique past when there is obviously more than one way it can be influenced by 16 those past events. Indeed, the relative nature of the order in time of spacelike separated events, which is implied by the special theory of relativity, means that what appears to be the future for a certain observer is actually the past for a different observer in a different state of motion and therefore if a unique past is causally related to the experienced present, then the future can only be similarly characterized. In a time-symmetric context it is not just the teleological character of backward causation that would need to be justified, but the equivalent teleological character of ordinary forward in time causality. If one insists that there is a problem with the possibility of causally influencing the known past, then one must at least also admit that this problem could not be distinguished from that which would arise from the fact that the past also influences the future, while a unique (even though unpredictable) future is associated with the known unique present. What makes it look like the present state of the universe is not causally related to one particular future is simply the fact that all future states are in principle allowed to be the outcome of random evolution from a given present state (any outcome is possible for future measurements), while not all past states are allowed as 'final' states in the context where the constraint of global entanglement discussed in section 3.9 of [1] exerts a limit on entropy growth in the past. In fact, this is precisely the nature of the difference between what we usually call causality and which relates to the thermodynamic asymmetry of causes and effects and the kind of causality that is involved in a timesymmetric context. Once it is realized that the past and the future are not distinct from a more general perspective, then it clearly follows that if we are willing to accept that the future can be influenced by what happens in the present, as confirmed by our direct experience of reality, then it is also necessary to recognize that the future can itself affect the present and the past just as well, so that imposing final conditions is no less appropriate than imposing initial conditions, as long as these conditions are not those responsible for the observed thermodynamic time asymmetry itself. One commonly encountered misconception regarding backward causation in general, as well as in a quantum context, is that if the future is allowed to causally affect the past, then we can no longer be confident that the past is what it seems to be, because it can be altered by future events. This is usually provided as an argument against backward in time causation because, as everyone knows the past is unique and unalterable and therefore any approach that would allow the future to 'change' the past is certainly based on incorrect assumptions. But what is incorrect with this apparently 17 logically unassailable conclusion is the idea that an alteration of the past would involve changing an observable fact from the past which we already know has occurred, just like we are allowed by our apparent free-will to alter the course of future history. In fact, that is just an inappropriate understanding of the meaning of backward causation, because if an event in the future changes the outcome of an observation in the past, this change is already effected at the moment in the past at which it was observed and the fact is not changed 'again' from an alternative counterfactual at the moment in the future at which its 'cause' occurs. In other words, it is not possible to change history using the kind of time-reversed causal chain that is allowed by fundamental theories. History is the outcome of all causal influences from both the past and the future and is experienced only once as such a globally consistent whole. No known fact is altered or changed by future influences as any change that would be effected would need to have already taken effect at the time at which the fact first occurred. The 'effects' that the future may exert on the past would always be made conspicuous merely through the influence they would have on correlation probabilities established after the fact (when that future itself becomes a known past). Now, it must be clear that the condition imposed on special-relativistic transformations that they should preserve the direction of all time-like intervals (the causal ordering postulate) is not incompatible with the conclusion that backward in time causation must be allowed at a certain level, because all that is required by relativity is that if a causal chain operates from the past toward the future (as we usually assume to always be the case) then the same causal chain cannot be found to operate from the future toward the past as a result of such a transformation. But that does not mean that a distinct causal chain cannot operate from the future onto the past, merely that if such a backward propagating causal chain exists it too cannot be turned into a causal chain propagating in the opposite direction of time, which in this case would be toward the future. In any case, the fact that the causal time of relativity theory is not unidirectional does not itself constitute a problem, because, even in such a context, unidirectionality is allowed to emerge from the global entanglement constraint which imposes a condition of low gravitational entropy at the Big Bang, as I have explained in section 3.9 of [1]. What explains time asymmetry is not a fundamental property of unidirectionality applying to causal chains, but the particular boundary conditions which apply at a certain time in the history of our universe. What makes a flow of information from the future toward the past impossible is not a limi18 tation that would be arbitrarily imposed on the direction in which causality operates, but a distinct constraint that limits the growth of entropy in the direction of time toward the initial Big Bang state. Thus, as long as a causal signal does not propagate faster than the relativistic speed limit it cannot give rise to a violation of the classical, unidirectional principle of causality, whether the signal propagates forward or backward in time. It is not true that the scientific method excludes the possibility that 'final causes' of any kind might exist despite the fact that time-symmetric causality appears to be allowed by relativity, because what can be scientifically demonstrated is merely that entropy does not increase in the past, not that there is no backward in time propagation of effects. What explains that we have become naturally suspicious regarding the possibility that causes could propagate backward in time is only the fact that from a classical perspective it never appeared necessary, or even possible to describe an object or a component of an object as propagating backward in time, while the time asymmetry that characterizes the history of macroscopic systems was always observed to operate from past to future (which made it look like a fundamental requirement). This prejudice remained in effect even when it became clear that backward causation was a necessary assumption in the context where one must recognize that certain particles do propagate backward in time (even though from a unidirectional time viewpoint they are observed as oppositely charged particles propagating forward in time which are involved in the same entropy increasing processes as their ordinary matter counterparts). The teleological problem of time, which is often believed to arise in the context where a unique future is associated with the known present, is not a true problem, but merely follows from the psychological expectation of unidirectional causality that we inherited from our thermodynamically constrained experience of reality and which does not reflect any fundamental limitation. There is no other explanation for the widespread belief that causality must always operate forward in time. What must be understood, then, is that it is not merely the order in which time flows that varies for an antiparticle, but really the fundamental direction in which causes propagate in time. When a particle propagates backward in time, the direction in which it may come to influence other particles is actually reversed and it is merely the thermodynamic arrow of time and the direction in which classical causality operates that remain unchanged. If there is any meaning to be associated with a concept of causality from a fundamental viewpoint, then a reversal of the order in which causality 19 operates must be allowed to occur and future events must be allowed to exert an influence on past events. There cannot be a distinction between causality and the order in which elementary particle processes occur in time, even though this order is a relatively defined property and is only significant in relation to the order in which another such process is unfolding in time. This requirement may perhaps appear doubtful in the context where it seems that many distinct histories, which may involve unobservable subprocesses with variable directions of propagation in time, are required to take place all at once in order to account for the statistics of quantum processes. But I will explain later in this report why this apparent lack of uniqueness of particle trajectories is not an obstacle to a proper understanding of causality as actually depending on the direction of propagation in time of elementary particles. Causal order may be a locally variable property, but it is not arbitrary, even when backward in time causation is allowed. 4 Closed causal chains and time travel As is already apparent from the viewpoint of a semi-classical description, the time-symmetric nature of causality does not merely imply that there is no absolute distinction between causes and effects, it also means that a certain event can all at once influence another event and be influenced by the very same event. In other words, not only is there no absolute difference between causes and effects, but the cause of a certain event can also be an effect of the same event, although this circularity can only be appropriately described in the context of a purely quantum mechanical model of reality such as the one I will propose in a latter portion of this report. It must be clear, though, that the possibility that such closed causal chains may occur does not constitute a valid motive to reject the whole concept of time-symmetric causality and backward in time causation, because, as I will explain, it is possible to provide a consistent description of such phenomena without encountering logical contradictions. Reichenbach's insistence [3] that one must be able to differentiate causes and effects independently from their temporal order if we are to avoid the occurrence of closed causal chains is not totally inappropriate, however, because, as I mentioned in the previous section, the direction in which causal chains propagate is determined locally by the direction of propagation in time of the particles involved and therefore it is not fixed merely by the global time 20 order of causally related events. But, in fact, it is precisely for this reason that closed causal chains are unavoidable and that they must be properly described and interpreted at the most fundamental level. Yet, even at the level where closed causal chains may occur it is certainly necessary to require that no inconsistencies can arise, which would involve an incompatibility between some known present and some known past. What I will eventually explain is that there is actually a requirement for histories not to be self-contradictory and this condition can be satisfied not merely despite the fact that causality also operates backward in time, but as a very consequence of the reality of backward causation. In any case, it is certainly incorrect to argue that there is empirical evidence to the effect that closed causal chains are forbidden, because in the course of elementary particle interactions particle-antiparticle loops are often encountered that constitute just such a phenomenon, which can be adequately described, even from a semi-classical perspective. Once again, I believe that the problem here does not have to do with the possibility that closed causal chains themselves may occur, but rather concerns the hypothesis that classical, unidirectional causality could operate in both the future and the past directions of time along a closed causal chain. I will soon return to this question, but what should be clear already is that it is, in effect, only at the level where unidirectional causality operates that the order of events in time should be absolutely distinguishable and that no closed causal chains would be likely to arise. But, as I have mentioned already, this is a distinct issue, because at the fundamental level, where time-symmetric causality operates, thermodynamic time asymmetry is ineffective and any restriction that would be imposed by the existence of the thermodynamic arrow of time would be irrelevant. One significant outcome of the existence of closed causal chains is that it is not always possible to establish the time order of events in an absolute way, because one event occurring along such a causal chain can be considered to occur both before and after another event occurring along the same chain, even if the events are uniquely ordered from the macroscopic viewpoint of thermodynamic time. The topological order of time is always clear locally along a particle world-line, but globally (even on a small scale) it must be determined in a purely relational way (as dependent on an arbitrarily chosen reference point along a given circular trajectory), like any physically significant property. It is important to realize that the existence of closed causal chains does not 21 introduce additional unpredictability above that which is already assumed to characterize quantum evolution, because the current framework already involves some backward in time propagation (I will further explain in section 8 what motivates the idea that backward causation is involved in determining correlation probabilities in quantum mechanics). But even in a deterministic context, the fact that the present cause of a certain future event could itself be affected by this very same event would imply that it is not possible for the future to be determined by the past alone, because the future itself would be involved in determining the past that determines this very future. Thus, it seems that even in the context of a hidden variables model, backward in time causation would imply that reality must remain fundamentally random and not merely unpredictable due to an absence of knowledge of the exact present state of a system. Of course the simple fact that the cause of a future event can be located not in its past, but in its own future also implies that even when a complete knowledge of the present quantum state of a system and its environment is available, it is not possible to identify all the causes which exert an influence on its evolution, which means that a certain measure of unpredictability is unavoidable that would not be present from a conventional viewpoint. It is usually recognized that the problem which would be raised by what might be called a time travel experience has to do with the fact that such a phenomenon may allow the kind of closed causal chain in which the classical, unidirectional principle of causality would be violated. More specifically, given the assumption that we are free to decide how we influence the future in the context where our evolution is taking place irreversibly toward what would normally be the unknown future, it may appear that a time-traveler arriving from the future would be able to alter the course of a known history in the same way a normally evolving person is allowed to influence the unknown future. The problem here does not only have to do with the fact that we don't know why such unidirectional causality violating evolution is never observed, it also concerns the fact that if we are, in effect, free to influence the course of events taking place along the direction in which our thought processes are functioning, then it would appear that by 'traveling' back in time we might be able to alter a known future and to modify the course of events in a way that would be incompatible with the very possibility that the experience itself might have occurred, thereby giving rise to a time travel paradox. 22 Although time travel has never been observed to occur and therefore remains a purely hypothetical problem for physics, the standard answer to the questions it raises is often believed to be David Deutsch's proposal [4] based on the many-worlds interpretation of quantum mechanics. What Deutsch suggested, basically, is that every time a paradox would be expected to occur that would involve a particle arriving from the future and altering the past conditions that gave rise to the future state that allowed the process to happen, the universe would 'split' into alternative branches where both the initial history (in which the backward propagating particle did not change the future) and its modified version (were the particle does effect a change that would prevent it from having effected this very same change) do occur, but cease to interfere quantum mechanically with one another. Thus, it is proposed that there is an alternative future for every possibility that might be produced as a result of the influence exerted by a future event on a past event through backward causation. I'm not sure what most people make of this description, but the problem I have with it is that I just can't figure out how it actually makes things any better. If we say that a particle arrives from the future and changes the past, then this past must be assumed to have already taken the 'effect' into account and must be such that it allows the said future to occur, as I previously explained. So, how could this future be made different by such an altered past? Clearly the problem with the hypothetical problem of a future 'cause' influencing a past 'effect' only occurs when we assume that there can actually arise inconsistencies or contradictions in the observed historical description of events. But when it is assumed that a particle can arrive from the future and change the past to which it was causally related, it is not possible to say that the future is merely altered from what it 'originally' was by the presence of the particle, because the particle itself could not even have arrived from the future in such an altered version of history. How could one possibly argue that a new future is written in an alternative branch of the universe's history as a result of the arrival of a particle from the future, if the backward propagating influence of that particle did not even occur in this alternative branch of history? What the many-worlds approach purports to show is that inconsistencies and contradictions can actually arise in our historical description of facts, but that this is acceptable, because the future always adapts to the inconsistencies it itself generates. But this is just non-sense, because if a future is such that it influences a given past then this past must be such that it nec23 essarily gives rise to this unique future and this is not made to 'happen' by some hypothetical splitting process taking place at a given arbitrarily chosen moment, it is just how things actually are all along, in both the past and the future. Also, if we are to allow for the existence of other universes then by definition those universes should be causally independent from one another and things happening in one universe should not be allowed to influence what is taking place in another universe. I believe that what is missing from our current understanding is an acknowledgement of the fact that a universe, by necessity, actually consists of a unique ensemble of events causally related to one another and to nothing else (as a consequence of the requirement of relational definition of physical attributes which was discussed in [1]). From such a viewpoint if an event in the past is influenced by the presence of an event in the future then this past event cannot be causally related to a different future, but only to the future that actually influenced it. Thus, it becomes a fundamental requirement for the universe to form a consistent whole, free of internal contradictions. Of course we never experience time travel, so this issue only has to do with elementary particles propagating backward in time and in this realm quantum field theory already does a very good job of consistently describing physical reality and predicting facts. In this particular sense Deutsch's proposal is a solution to a problem that does not exist and this becomes especially obvious in the context where, as I will later explain, the manyworlds interpretation of quantum theory is not required to make sense of the quantum measurement process and can even be understood to have consistency problems of its own (which does not mean that the multiverse concept, as a distinct hypothesis, cannot be considered valid and fully justified). I believe that the strange and convoluted reality that emerges from such a description merely illustrates the kind of complications we would run into if we adopted an interpretation of quantum theory involving such multiple splitting realities present all at once in the same universe. If the many-worlds approach cannot even be made to work in a quantum mechanical context, what motive do we have to invoke it in order to explain problems occurring at a classical level? Consistency requires that if a process happens backward in time, this backward evolving process must in effect evolve backward in the same universe in which it was previously evolving forward, in the sense that it must remain causally related to the same external reality, otherwise nothing at all could be assumed to be causally related to anything else. But, then why is it, in effect, that we never experience time travel if backward in 24 time causation must by necessity be allowed? Does this prohibition have to do with the fact that if it was not in effect, then real contradictions might occur whenever closed causal chains would form? To answer those questions I must first point out that what would really differentiate time travel experiences from the backward in time propagation of elementary particles that is routinely observed in laboratories is the fact that with time travel a macroscopic and thermodynamically constrained system such as a living human being would need to evolve not just in the past direction of time, but with its thermodynamic arrow of time reversed and pointing toward the past instead of the future. From the viewpoint of an observer not part of the process this evolution would be seen as a local violation of the second law of thermodynamics, or the principle that entropy never decreases in the future, because indeed if the time traveler really travels back in time, then as he does so he would not just remember what happened at his past destination, but also what happened in the future (which to him would appear to be the past), thereby allowing information to flow from the future toward the past. But this means that from the viewpoint of a normal observer the processes of memory formation and all the other irreversible processes usually involved in allowing a person to experience time as a unidirectional phenomenon would all appear to function backward for the time traveler, even if the time traveler is not composed of particles (like ordinary antiparticles) usually considered to be propagating backward in time. Yet, for an external observer, the time travel process would be visible at all times while it is taking place, beginning from the point in the past where it 'ceases' and right through to the instant in the future when it 'began' and would thus actually involve the splitting of the time traveler into forward and backward evolving copies and the later merging of the backward evolving copy with the original process. At this point it is necessary to recall the discussion from section 3.9 of [1] concerning the origin of thermodynamic time asymmetry in a universe like ours. There, I explained that it is the inescapable nature of the constraint of global entanglement (which must be imposed in order to allow relationships of causality to be established between all elementary particles in the universe) that explains the parallel nature of thermodynamic time asymmetry (there does not coexist opposite thermodynamic arrows of time in different regions of the same universe), even for temporarily isolated branch systems. Thus, in a universe in which negative energy matter is necessarily present (for reasons I explained in chapter 1 of my preceding report) gravitational entropy 25 (and therefore all entropy) must be continuously decreasing as we approach the instant in the past (which corresponds with the very first instant of the Big Bang) where the global entanglement of all elementary particles is effected, because otherwise certain particles would not be allowed to be in contact with other particles present in the universe at the Planck time. Thus, all macroscopic systems must evolve with decreasing entropy in the past direction of time, because all matter particles without any possible exception must become entangled with the rest of the matter in the universe if they actually constitute elements of that universe. Of course the point here is that if time travel is never experienced or observed, it is not because backward in time causation is impossible at a fundamental level, but merely because entropy must be continuously decreasing in the past and only in the past (because no global entanglement constraint applies to the future), which means that the conditions necessary for the thermodynamic arrow of time to be experienced backward are not merely unlikely, they are actually forbidden for all practical purpose. Unidirectional causality only operates from the past toward the future, because it would take a very significant fluctuation for entropy to temporarily decrease in the future from a present state of non-maximum entropy, but given that this would be required for time travel to occur, then it is possible to understand why we never experience time backward. Indeed, classical, unidirectional causality is reflected in the fact that it would take only a little change in the past to allow a present event not to have occurred, while it would in general require enormous changes in the future for some present event not to have occurred. This asymmetry is precisely what is enforced by the global entanglement constraint when it is assumed that causal relationships must exist between all elementary particles in the universe. For time travel to be possible this thermodynamic time-asymmetry would need to be reversed locally for the whole duration of the process and the unlikeliness of such an evolution is responsible for the fact that time travel is virtually impossible, at least as a controlled phenomenon. Therefore, it is not possible in practice to be involved in a closed causal chain while remembering what occurred at a later time (no information can be transferred from the future toward the past), even if this restriction does not affect the possibility for microscopic systems to be involved in such causal chains, as long as global consistency is preserved (I will explain in section 8 how this condition is enforced at the fundamental level). This means that so-called 'knowledge' paradoxes are also unlikely to occur. It was suggested 26 in effect that if time travel was possible there could arise situations where some valuable piece of information (say a beautiful treatise about the physics of time directionality) would be brought from the future that would not have existed before it arrived from that future, but which would nevertheless become available as a result of the process, so that it can later be brought back to the present, thereby raising questions as to its origin. But given that what would be required for such a paradox to occur is a sustained local decrease of entropy toward the future, then it follows that the creation of information out of nothing in such a way would be as unlikely as the possibility that it materializes out of chaos by pure chance alone, which again is not fundamentally impossible, but merely ridiculously unlikely. Thus, from my viewpoint, despite the fact that backward causation is allowed to occur it is not possible for information to be created out of nothing, which certainly agrees with what I have written concerning the conservation of information in chapters 2 and 3 of [1]. It is, therefore, possible to understand that even in the absence of closed causal chains what prevents violations of the classical, unidirectional principle of causality is actually the global entanglement constraint that restricts the growth of entropy in the past direction of time and this is clearly a constraint of irreversibility that is not imposed at a fundamental level, but that emerges from the particular boundary conditions which apply to the initial Big Bang state. The frequently encountered remark to the effect that objects can move in any direction of space, but not in any direction of time (at least when they are restricted to not move faster than light particles in a vacuum), is only true in the sense that it is not possible to reverse a macroscopic system's thermodynamic arrow of time; it does not mean that an object cannot propagate backward in time under appropriate conditions. If it was not for the constraint that is responsible for the diminution of entropy in the past, all evolution would be symmetric with respect to the direction of time at all levels and there would be no way for information to flow from either the past or the future, as all systems would remain in a state of thermal equilibrium (if that was possible) and no record making process would ever be allowed to take place. Only under such conditions would it be possible to directly appreciate the fact that the future is not fundamentally different from the past. What is important to understand is that not only would entropy be observed to decrease in the future during a hypothetical time travel phenomenon (which would require it to increase in the past), but the process 27 would remain observable all along as an entropy diminishing process taking place forward in time, even after a hypothetical time travel paradox would have been produced. Indeed, an observer which would be evolving backward in time from a thermodynamic viewpoint would still be causally influenced by the events taking place at the moment of unidirectional time which would appear to him as the present, so that he would again observe the same sequence of events (even though from a different perspective) as when he was evolving as a normal observer, but in the reverse order. Therefore, it would be impossible to assume that the process did not occur, once it would have actually exerted its influence on the past. It just cannot be assumed that the future would be changed at the precise moment when a time travel paradox would have occurred if this change does in effect arise as a consequence of an influence of the future on the past. What makes the paradoxes themselves impossible, however, is not the requirement of entropy growth in the past, but the very same constraints that would forbid the occurrence of a contradiction from a fundamental viewpoint, as when elementary particles are propagating backward in time without being involved in anti-thermodynamic evolution. In this particular sense it is true that the problem of time travel can be fully resolved only in a quantum mechanical context, but as I previously indicated (and for reasons that will be discussed only later) this does not mean that one must invoke the hypothetical splitting branches of a many-wolds interpretation of quantum theory. In any case, it is now possible to appreciate that what makes time travel itself impossible is not the fact that it may allow forbidden contradictions to occur, but really the improbability of observing processes for which entropy decreases in the future. But, even if one was allowed to travel back in time as a result of a phenomenal fluctuation, one would not be allowed to alter one's own future when one would resume normal forward in time evolution, even if that is unexpected from our everyday viewpoint. Even under such conditions there would necessarily occur events that would enforce global consistency and this would happen despite the fact that under normal conditions we seem to be free to modify the future at will. It is simply the fact that we are used to experience the future as unknowable in advance that explains that it appears doubtful that we would not be able to alter the course of reality3. We usually 3In order to understand how global consistency can be obeyed even under such circumstances it may help to notice that if knowledge about some future was to become available 28 have no factual knowledge about the future and this is why we never run into the possibility of making a decision that would alter a known fact about the future. The global consistency requirement appears to have unexpected consequences merely because we are not used to experience a reality in which we would have available information about what has not yet occurred. We are accustomed to observe that present actions exert an influence on the probability that such or such a future occurs, but this is only a reflection of the fact that there exist correlations between the past and the future which are the result of both forward and backward in time propagated influences and it does not mean that the future is not unique. It is merely the fact that all possibilities are usually allowed for the future, while only a subset of them is allowed for the past (as a result of the constraint of entropy diminution) that justifies the impression we all share of being able to exert a certain control over the future which does not apply for the past. From a fundamental viewpoint the future is not different from the past (even if it cannot be determined in advance) and we do know that the past cannot be changed from what it already is. If we are not used to remember the future and if we are never confronted with the limitations to free-will which exist as a result of the global consistency requirement it is simply due to the fact that information does not usually flow from the future toward the past. This is probably the most important lesson that can be learned from the study of hypothetical time travel experiences in the context of timesymmetric causality: we are causally related to one unique past. But this is also true for the future. We live in an unpredictable universe and while it is certainly true that what we choose to do now has an effect on what will happen tomorrow, based on the most rational explanation of both classical and quantum mechanical phenomena it is necessary to recognize that we are causally related to only one such future and even if we were to obtain in advance knowledge about what this unique future actually is, events would have to unfold in such a way that the consistency of history would remain inviolable. to a given observer, a prediction of her actions would have to take into account the fact that the prediction itself can influence the outcome. 29 5 Advanced waves and time asymmetry Since Maxwell introduced his electromagnetic wave equations more than a hundred fifty years ago it has been known that there exist both retarded and advanced solutions to those equations (this is equivalent to say that Maxwell's equations do not distinguish the future from the past). The retarded solutions describe the propagation of positive energy electromagnetic waves leaving a point source and spreading into a growing volume of space as time passes. The usually rejected advanced solutions, on the other hand, would describe the propagation of electromagnetic waves of opposite energy sign leaving a point source and spreading into a growing volume of space in the past direction of time. This is usually described as the hypothetical phenomenon of a spherical and concentric positive energy light wave converging on a point source in the future direction of time4. From this equivalent viewpoint it is obvious that the advanced solutions represent a kind of process that cannot occur, as from the unidirectional time viewpoint one never observes light waves, or indeed any kind of waves, converging on a 'source' just to be absorbed by this source. But while this observation reassures our commonsense expectations, the fact that the phenomenon described here never occurs, while there is no a priori reason why it couldn't happen, still constitutes a profound mystery from a theoretical perspective. It is usually recognized, in effect, that if a valid theory describes a certain phenomenon and there is no good motive to assume that this phenomenon should be forbidden, then its occurrence is compulsory. It is not enough to argue that what prevents the hypothetical phenomenon of a radio wave produced by multiple sources in the environment converging in perfect spherical symmetry and with perfectly correlated phases onto a transmitter where it would be absorbed, is the unlikeliness of the phenomenon, because as I emphasized in chapter 3 of my preceding report this is precisely what we 'observe' to occur in the past direction of time and this evolution is clearly not the outcome of the singular nature of present conditions. Given arbitrary initial conditions what we should expect to observe are waves that would be diverging in the past, just like they do 4The positive value of the energy of this converging wave, which allows the 'source' to gain energy as a result of the absorption process, arises from the fact that, as I explained in [1], a negative energy photon propagating backward in time is always observed as a positive energy photon propagating forward in time, while a negative energy photon propagating forward in time would not even be allowed to interact with ordinary matter. 30 in the future, because this is in fact the most likely evolution when only the present conditions are fixed, even if from the unidirectional time viewpoint such a process would appear unlikely. If it is considered natural for certain electromagnetic waves to spread outward in the future, despite the fact that this means that they converge on their source in the past, then it should naturally be expected that certain electromagnetic waves would spread outward in the past, even if that means they would converge on their source in the future. Therefore, what remains unexplained is the asymmetry of the situation in which waves do not spread outward in the past while they do so in the future of some arbitrarily chosen initial state. The problem discussed here is all the more significant given that it is not restricted to Maxwell's theory. Indeed, there exist advanced solutions to all relativistically invariant wave equations, including the equation that describes the propagation of electrons in quantum field theory. Once again this is a problem that Feynman visited, but apparently failed to solve. What he and John Wheeler proposed was a theory [5] that would have allowed advanced electromagnetic waves to be produced on an equal basis with retarded waves, but to be canceled out through destructive interference, as a consequence of the difference in opacity that seems to characterize the far past and the far future of our universe. According to this model, retarded and advanced electromagnetic waves are always produced together in equal proportions and propagate in the future and the past respectively. But when the retarded wave is absorbed in the future the absorbing process itself triggers the emission of an additional retarded wave of identical amplitude which is completely out of phase with the original retarded wave, thereby erasing all traces of this additional retarded wave. At the same time the absorber also produces an advanced wave and if certain conditions are met this advanced wave only serves to strengthen the retarded wave produced by the source through constructive interference, while it also conspires to cancel out the advanced wave originally emitted by the same source through destructive interference, which may allow to explain the fact that it is not observed. The problem is that this theory requires that there is more absorption in the future than in the past, while that would appear unlikely in the context where the universe is expanding in the future direction of time. Other theories based on similar assumptions (see for example [6, 7, 8]) and which tried to overcome the problems encountered by Feynman and Wheeler through various alternative hypotheses (for example by assuming that the Big Bang acts as a reflector of all advanced radiation) have apparently also 31 failed to produce a satisfactory solution to the problem of advanced waves. It seems that whenever it is not independently assumed that for some unknown reason a fundamental asymmetry exists in the interaction of matter with radiation that would differentiate the far past from the far future, the desired outcome is never obtained. In other words, the only way to reproduce the observed time asymmetry that characterizes wavelike processes in our universe using such a model is by postulating that some asymmetry exists which is responsible for reducing or increasing the amount of interference that takes place either in the past or in the future. But given that no convincing explanation exists that would justify this assumption, then it is apparent that it merely amounts to assume the very outcome we would like to explain. From the difficulties encountered with this kind of approach it has become pretty clear that it is not possible to explain the absence of advanced waves as being a mere consequence of hypothetical interference effects. I was only able to understand what explains the absence of advanced waves when I began considering the quantum aspect of this hypothetical phenomenon. Indeed, I already knew that backward in time propagation was possible for elementary particles and therefore it seemed to me that what was not allowed was not really backward propagation itself, but merely the spreading of a backward propagating wave into an increasingly larger region of space. I also knew that there was a requirement, imposed by the constraint of global entanglement which I had recently uncovered, that backward in time evolution be such that it gives rise to a continuous decrease of gravitational entropy in the past. But, as elegantly explained by Olivier Costa de Beauregard [9], there is a certain equivalence between entropy increase and wave retardation which is implied by Planck's definition of entropy and which arises from the quantized nature of electromagnetic radiation. Thus, in a quantum mechanical context, entropy necessarily rises when an electromagnetic wave spreads into a larger volume of space, because at any given time the photons associated with an expanding wave front can be detected anywhere on its growing surface. In fact, given that from the viewpoint of relativistic quantum field theory any wavelike phenomenon is associated with the propagation of some elementary particle, it follows that entropy increase is always associated with wave retardation, while the observation of advanced waves would always imply that a decrease of entropy has taken place in the future direction of time. From my bidirectional time viewpoint this is equivalent to say that entropy would need to increase in the past for an advanced wave to spread as it propagates backward. But this is precisely 32 what is forbidden by the constraint which I previously identified as being responsible for thermodynamic time asymmetry. What is also unexpected from a thermodynamic viewpoint is the fact that from the unidirectional time viewpoint the existence of advanced waves would seem to allow work to be generated out of nothing, when radiative energy would converge on a 'source'. But the existence of advanced waves would also make possible the transmission of information from the present or the future toward the past. It is natural to expect, therefore, that this kind of process should be prevented from occurring by the same condition that explains thermodynamic time asymmetry. It must be clear, however, that simply invoking the classical (unidirectional) principle of causality does not allow to solve the problem of the absence of advanced waves, because, in the above discussed context, saying that there always exists a unique preferred direction in time for the propagation of effects merely amounts to restate the problem of advanced waves (which is also known as the problem of the electromagnetic arrow of time) without explaining why such a restriction is indeed observed to apply. In fact, the previously discussed phenomenon of time travel, as I have redefined it, would be one particular instance of backward in time communication of the kind that would be allowed by the existence of advanced electromagnetic waves and therefore a solution to the problem of advanced waves would definitely rule out time travel. Now, I mentioned in section 3 that the causal structure of spacetime is not incompatible with the concept of backward in time causation, given that with every event is associated both a future and a past light cone, which reflect the existence of a speed limit imposed on the propagation of causal signals in either the future or the past. But it should also be clear by now that there is a difference between the kind of backward in time causation that may occur as a consequence of the propagation of an elementary particle backward in time and the kind of causality we experience in a purely classical context and which is known to operate only forward in time. Thus, while it is not observationally forbidden for an electron to propagate backward in time, an explanation of cosmological time asymmetry based on the global entanglement constraint would not allow this propagation to occur in such a way that the area over which the electron could potentially be found to be at an earlier time would be growing continuously along with the twodimensional boundary of the past light cone. But this is precisely the kind of evolution that an advanced wave would describe from a quantum mechanical viewpoint and therefore what explains that advanced waves are absent is the 33 constraint of global entanglement I have identified in section 3.9 of [1], which enforces a continuous decrease of entropy in the past, as a consequence of the requirement that there exist causal relationships between all the elementary particles which are present in the expanding universe. Our failure to observe advanced waves must not, therefore, be interpreted as an indication that backward in time propagation, or backward in time causation are forbidden, but rather as evidence that only a small subset of potentially available states is available as 'final' conditions for backward propagating particles. This means that the statistical predictions obtained using quantum theory for the evolution of a large number of identically prepared physical systems are not valid in the past direction of time and this is what explains that electromagnetic waves, as particular instances of wave functions, are never observed in their advanced form. In such a context it becomes apparent that the only true virtue of the Feynman-Wheeler absorber theory (aside from the fact that it was one of the first models which actually took the problem of advanced waves seriously) is that it sought to deduce the absence of advanced waves from boundary conditions imposed on the universe at large, instead of requiring that timeasymmetry be imposed at a fundamental level, which could only be satisfied by assuming that backward in time propagation is impossible. In any case, even if absorber theory had conveniently solved the problem of advanced waves, this solution would have remained problematic, because it would not have allowed to explain the origin of thermodynamic time asymmetry in a more general context (when quantum interferences are absent). From my viewpoint the fact that there also exist advanced solutions to Dirac's relativistic equation for the electron allows to confirm the validity of the conclusion that the absence of advanced waves does not preclude backward in time propagation, because, while it is not possible to assess whether a given photon propagates forward or backward in time, in the case of electrons it is possible to differentiate a forward in time propagating particle from a backward in time propagating particle, given that from a unidirectional time perspective such an electron is observed as a positron with its positive electric charge. Therefore, if we do observe positrons it means that the irrelevance of advanced solutions cannot arise from the unphysical nature of backward in time propagating particles and must in effect be the outcome of the global entanglement constraint. 34 6 Early interpretations To begin the portion of this report that deals with quantum aspects of reality more specifically I would like to first describe what constitutes the distinctive characteristic of the revised interpretation of quantum theory I will propose. What I had already understood, even before I was able to solve the problem of advanced waves, is that the processes that constitute the essence of our experience of reality are all mirrored by similar processes which obey the same observable macroscopic conditions, but which take place once again in the opposite chronological order in a portion of history that must be assumed independent from the viewpoint of local causality. The hypothesis that history does not occur only once, but must happen a second time in the reverse order may appear arbitrary and unnecessary given that we know of only one history, but, as I will explain, this proposition is actually made unavoidable by some of the most fundamental principles of physics and also reflects the basic mathematical structure of quantum theory. Even though I was not motivated only by the desire to produce a time-symmetric theory when I began developing this original approach, the final outcome does share a certain property of time symmetry with some early interpretations of quantum theory which are based on the hypothesis that there must be an equivalence between initial and final conditions. Given that most of those early time-symmetric interpretations constitute more or less elaborate (and more or less inappropriate) quantum versions of the original absorber theory discussed in the preceding section, then one may say that absorber theory is their common ancestor. In this respect it is apparent that those time-symmetric quantum theories also share some of the above discussed weaknesses of the original, classical theory. I believe that part of what explains that this kind of approach is usually considered to have failed to produce a consistent interpretation of quantum theory, despite the many advantages it offers (and which will be discussed below), is the fact that absorber theory itself is considered a failure. As a result, many generations of physicists were inoculated against time-symmetric approaches in general, even though a few well-informed specialists have recognized that the requirement of time symmetry is essential to a consistent interpretation of quantum theory. But it is also clear that this is not the only reason why the early attempts at formulating a time-symmetric version of quantum theory did not succeed, because, as I came to understand, they also contain hypotheses and constructs that make them inconsistent and inadequate as a 35 representation of quantum reality. One of the first interpretation of quantum theory that sought to accommodate the requirement of time symmetry was that proposed by John Cramer [10] as an outcome of his work on the problem of advanced waves. As such, it contains hypotheses which are very similar to those of the original absorber theory which I have identified as problematic. But its most important defect in my opinion is that, despite the fact that it is proposed as an alternative time-symmetric model, it actually involves a fundamental time asymmetry that is incompatible with this basic requirement. What Cramer proposed, basically, was that a kind of 'handshake' process takes place whenever a quantum particle is emitted by a source and then propagates a certain distance before being absorbed by a detector. We may consider, for example, the traditional double slit experiment in which a particle must go from source to detector by passing through the slits. It is known that an accurate estimation of the probability for such a process to occur must take into account the existence of interferences between the individual probability amplitudes associated with each of the paths through which the particle is allowed to go whenever both slits are open. What Cramer's handshake process involves is the emission of a classical wave acting as an 'offer', which is assumed to be sent by the source forward in time and which is allowed to propagate without constraint (it is assumed to go through both slits all at once), followed by the production of another such wave that would constitute its 'confirmation' and which would be sent by the detector backward in time (toward the initial emission event) upon absorption of the offer wave. The most problematic aspect of this description from my viewpoint is the fact that the confirmation wave must follow an evolution that is restricted to be compatible with the macroscopic constraints which would have existed if the particle (not the offer wave) had been restricted to follow the unique classical path it is assumed to actually have taken as it propagated forward in time (the confirmation wave only comes back through one of the two open slits)5. It is difficult to see how the advanced wave could be submitted to macroscopic constraints which differ from those that apply to the retarded wave in the context where the observed macroscopic conditions of the experiment 5In fact, Cramer assumes that this handshake is actually repeated several times for any single quantum process and is responsible for the transfer of energy and other conserved quantities which take place during the process, but we may ignore this problematic aspect of the handshake process if it simplifies the discussion. 36 are fixed once and for all. But what is even more incomprehensible with this interpretation is that the evolution of the 'confirmation' wave is actually required to reflect the fact that the particle took a certain path (say the upper slit), while the evolution of the 'offer' wave would not be allowed to reflect the same fact (passage through both slits would initially be allowed). This is how time asymmetry is reintroduced in the model as a means to allow a unique, classically well-defined history to correspond with the process, despite the fact that the statistics of this quantum process can only be explained by assuming that the particle is not restricted to follow a unique path. Of course, even if those problems did not exist, there would still be a difficulty associated with the fact that this approach requires the existence of both classical waves and classical particles (constrained to follow unique trajectories by those classical waves), while it is known that both concepts (which are shared by certain classical hidden variables theories) are problematic in quantum field theory. I believe that the source of the problems affecting Cramer's transactional interpretation of quantum theory is to be found in the fact that it assumes that the retarded and advanced waves are actually propagating in the same portion of history, because this is why it needs to be required that the quantum particle submitted to the constraint of those classical waves goes through only one slit, corresponding to this unique history, which in turn requires a certain fundamental temporal asymmetry to be introduced in the theory, in violation of the time-symmetric nature of its equations. Also, the fact that, as a particular instance of (quantum mechanical) absorber theory, Cramer's framework appears to require genuine wave emission and absorption to take place in the course of all quantum processes, may be problematic, because there are situations where quantum measurements are performed without interaction. Those difficulties are more significant than the additional problem that would arise in the context where it is not obvious from the viewpoint of Cramer's theory when it is exactly that the handshake would be initiated while the particle is propagating along its classical path. Indeed, if the handshake was to be completed when the particle reaches one of the two open slits, then the process would always be that which we expect to occur when one is allowed to observe through which slit the particle goes and under such conditions the particle would follow a quasiclassical trajectory (interferences would be absent), which is contrary to observation. Thus, there may be a difficulty associated with the apparent arbitrariness of the choice of which macroscopic conditions are necessary to trigger a hand37 shake (do we have to wait for an observer to become aware of the outcome as John Von Neumann once proposed?). But this is in fact the same quantum measurement problem as may affect a more traditional interpretation and therefore we are allowed to assume that any solution to this problem that would be proposed in a more conventional context would also apply to the transactional interpretation. This is an important point, because this difficulty is sometimes proposed as an argument against all time-symmetric approaches to quantum theory, while when it is properly understood it no longer stands out as a problem that is specific to time-symmetric models. Of course it would not be appropriate either to assume that Cramer's theory is equivalent to standard quantum theory, as its author suggested, because ordinary quantum mechanics does not explicitly involve advanced waves, while they are required to exist by the transactional interpretation. In fact, when the inadequacy of the boundary conditions that give rise to the destructive interference effects that would allow advanced waves to go unnoticed is recognized, the theory no longer even agrees with observation, which certainly makes it different from standard quantum mechanics. What I'm suggesting that we retain from those alternative, semi-classical interpretations is the notion that the squaring of the wave function which allows to obtain the probability of a process is made necessary as a consequence of the fact that, somehow, two histories are involved in any quantum process. I believe that this is what explains that it is merely by multiplying the probability amplitudes associated with each of those paired processes that we can obtain (under appropriate conditions) the probability for the entire process to occur. Indeed, the squaring of the wave function (which is necessary to obtain the probability of a process) involves taking the complex conjugate of the probability amplitude associated with one history before multiplying it with the probability amplitude associated with another history and it is known that taking the complex conjugate is equivalent to reversing the direction of time for those equations that describe the changes taking place in the quantum state of a system. Therefore, one of the most basic aspects of the mathematical framework of quantum theory already contains in embryonic form the requirement that each process be described as a history that unfolds forward and then backward in time for some mysterious reason. This otherwise puzzling requirement has been transformed by modern interpretations into a condition, imposed (without any real justification) on certain pairs of minimally coarsegrained histories, that they provide the probability of occurrence of a 'consis38 tent' history, but in the process it seems that the most important aspect of this requirement, which is the fact that the two histories forming such pairs take place in opposite directions of time, was lost and with it the important insight we should have learned from early time-symmetric interpretations of quantum theory. At this point it is important to mention that a more pragmatic approach to achieve symmetry with respect to the direction of time in quantum mechanics had already been proposed by Aharonov, Bergmann and Lebowitz [11] (see also [12] for a more recent review) long before Cramer introduced his transactional interpretation. Unlike the transactional interpretation this formulation of quantum mechanics really is mathematically equivalent to the standard theory, but it does not seek to explain the time asymmetry of boundary conditions and merely suggests that two state vectors are required to describe the state of a quantum system. One state vector contains all the information obtained from past measurements (as in the standard interpretation) and the other contains all the information that will be obtained concerning the same system in the future. Between measurements those two state vectors follow a 'unitary' evolution toward the future and toward the past respectively6. What this means is that there is no longer a preference for the past over the future in determining the current state of a system (a system can be submitted to both preand post selection, although the post selection is only apparent after a future measurement has actually been performed). Of course there is a natural reluctance to recognize that it might be possible for a state vector to be determined by what 'happened' in the future instead of what happened in the past, but this is merely a consequence of the previously discussed prejudice toward a unidirectional conception of causality which we inherited from our thermodynamically constrained experience of reality and does not rest on any rationally formulated argument. It must be clear that despite the equivalence between the two-state vector formalism and standard quantum theory, it has been shown that post selection, or the effect of a future measurement on the past state of a system, is not an optional feature of quantum theory, but arises even in the simplest and most conventional of quantum mechanical experiments. Indeed, in 6I use the term 'unitary' to denote the deterministic evolution of the wave function or state vector that takes place in the absence of a change in the observational constraints applied on a quantum system, because using the term 'deterministic' would be misleading in the context where I will argue that the evolution of the system itself always takes place randomly. 39 certain interferometer experiments which bear enormous resemblance to the classical double slit experiment and which will be discussed in section 9, the choice of performing either a measurement that determines through which path a photon went on its way to the detector, or a measurement that reveals the quantum interferences attributable to the presence of two possible paths can be delayed to long after the particle has actually traveled most of the distance to the detector and it does in effect influence what the particle did back when it was just leaving the source. The reality of such post selection effects has therefore been experimentally confirmed and contrarily to what is sometimes suggested it is not possible to assume that no post selection occurs as long as we reject a realist interpretation of quantum phenomena (because it is not possible to reject such an interpretation, as I will explain later). Thus, somehow, the path taken by a photon can be influenced by a measurement that takes place long after the actual process is over7. Only a time-symmetric approach to quantum theory that recognizes the existence of a backward evolving state allows to explain those facts while remaining within the confines of the principle of local causality. Now, even though some of the originators of the two-state vector formulation of quantum theory are hesitant to assume the reality of the backward evolving state that enters the formalism, it is clearly possible to assume that we are indeed dealing with a distinct state that evolves somewhat independently from the forward propagating state, but which is subjected to the same macroscopic experimental conditions. What I'm proposing is that in order to go beyond early time-symmetric models one must in effect recognize that a whole history unfolds backward in time, whose elements are not in causal contact with those of the history that unfolds forward in time. Indeed, I believe that in order to accommodate the requirement of time symmetry it is not enough to assume that semi-classical waves are propagating backward in time in the same portion of history, because, as I have already explained, advanced waves are forbidden to exist by the constraint of global entanglement that gives rise to time asymmetry in our universe. The problem here usually is that, even though two kinds of Schrödinger equation appear to exist which would allow to describe the propagation of the wave function in 7It should be clear that I'm not suggesting that post selection would allow information to flow from the future, or that it would allow one to change an observable fact from the past which has already been established. For reasons I have already mentioned, backward causation, as would occur in the context of a consistent time-symmetric interpretation of quantum theory, is incompatible with both of those conclusions. 40 either the future or the past, only the equation that describes the evolution of the retarded portion of the wave function is retained given that retarded waves are the only ones which are allowed to evolve without constraint and this is why it is usually considered appropriate to take into account only the state vector that evolves forward in time in order to obtain the probability of a whole process, even if this process may actually involve a pair of histories occurring in opposite chronological orders. But once it is understood that this limitation is not a fundamental property of the wave function itself, but arises as a consequence of the requirement of diminishing entropy imposed on all past evolution by the global entanglement constraint that applies to the initial Big Bang state, then the two-state vector formalism becomes not only acceptable (as it does not require the existence of advanced waves), but actually essential to accommodate time symmetry in a quantum mechanical context. In fact, given that the direction of time in which any process unfolds is a relatively defined property, the state vector that is determined by future measurement conditions (the postselected state vector) could also be considered, as a matter of convention, to be that which was determined by past conditions, while the state vector which would otherwise be assumed to be determined by past measurement conditions (the ordinary state vector) may be considered as that which actually evolves back in time 'after' having been determined by future conditions, as long as the other state vector is in effect assumed to be that which evolves forward in time. Therefore, we would not be better off by assuming that only past conditions can determine the evolution of the state vector, because this could also be understood to mean that only future conditions can determine the same evolution, which would be an even worse conclusion from a conventional perspective. I may add that an explanation of thermodynamic time asymmetry of the kind I have proposed in section 3.9 of [1] does not only render plausible the hypothesis that every quantum process is complemented by a backward evolving counterpart, but actually seems to require the existence of two histories evolving in opposite chronological order, because otherwise it would be difficult to explain what enforces the then unique, classical history, which we are free to consider as evolving toward the past, to take place with continuously decreasing entropy. But once it is recognized that there necessarily exists at least one history that unfolds from the past toward the future (as one needs to assume in the context of a time-symmetric interpretation), then it becomes possible to explain the thermodynamic arrow of time as being the 41 consequence of the initial condition of low gravitational entropy imposed on the initial Big Bang state by the global entanglement constraint, because the evolution of at least one state vector is then determined by past conditions. In fact, this is a general requirement that would apply to all processes in the context where global consistency is required, because from a quantum mechanical viewpoint the consistency of past events with future events can only be fulfilled when those future events are also allowed to influence past events, as I will explain in section 12. Once this is understood it is easy to see how a relativistically invariant model based on the sum-over-histories approach can be formulated that embodies the explicit time symmetry of the two-state vector formalism by assuming that every quantum process involves both a conventional history (evolving without apparent constraint in the future direction of time) and a possibly distinct time-reversed history evolving independently (from the viewpoint of local causality) toward a state of lower entropy in the past direction of time. This is an issue I will discuss more specifically in section 8, but before I can do that I must first explain why it is that a model involving two unique, but partly unobservable histories unfolding in opposite directions of time (instead of two wave functions propagating in opposite directions of time) is not merely possible, but actually constitutes an essential requirement of a fully consistent realist interpretation of quantum theory, despite the fact that what is usually assumed to be required in order to obtain the appropriate statistics is that all possible paths are followed all at once in one single portion of history for any given process. 7 The constraint of scientific realism It has often been argued that the counterintuitive aspect of quantum theory is not a real problem and merely indicates that there is a limit to what one can intuitively understand. It would then be incorrect to assume that the fact that there appears to be something incomprehensible with the current interpretation of the theory is due to the inadequacy of this interpretation. I would like to suggest, however, that this argument is invalid. In order to see what is wrong with this long-standing viewpoint let's first suppose that we humans are in effect too dumb to understand quantum theory. The argument would then be that only some artificial superintelligence from the future would eventually be able to overcome those limitations and to properly 42 understand the significance of the empirically derived mathematical framework of quantum theory. Such a superintelligence would therefore succeed at gaining a proper understanding of physical reality in a way that is simply impossible for us to achieve due to the inherent limitations of our primitive intellect. But what does that mean in concrete terms? When you carefully think about this question it becomes obvious that the only thing that could happen is that this superintelligence would then have developed a better interpretation of quantum theory, because if the current mathematical framework is in effect appropriate to describe physical reality, then the only progress that could be achieved would have to arise at the level of interpretation. You do not have to be superintelligent to understand that and yet this is precisely what we fail to take into account when we suggest that the problem we experience while trying to make sense of quantum theory merely reflects the fact that it is not possible for our brains to understand the theory. I believe that the lack of intelligibility of our current understanding of quantum theory is not a fantastic new property of the universe which we happen to have discovered. It is a failure that originates in the inappropriateness of the current interpretation and if this difficulty may be a consequence of the inadequacy of certain concepts we inherited from our human experience of the world, it is also a problem that can be solved using our human intellect, as long as we do recognize that there is indeed a problem and that it deserves our attention. But those who still doubt the importance of a proper interpretation of quantum theory should take notice of the fact that without interpretation it would not even be clear that the theory is about probabilities of measurement outcomes, as this is indeed an aspect that only came to be understood after the mathematics of the theory (regarding the Schrödinger formulation in particular) had already been developed. Now, it must be clear that quantum theory is in effect counterintuitive and that it cannot be reduced to a classical view of the world by using the freedom we may have to interpret experimental facts and the current mathematical framework of the theory. Physical reality cannot be such as it was conceived at the epoch of Isaac Newton. Classical waves (which are not mere manifestations of quantum interference) and classical particles (which would allow violations of the constraints imposed by the uncertainty principle) are gone and they will never form part of a consistent theory about the fundamental structure of reality ever again. But that does not mean that everything else is possible. What is not allowed of a rational understanding 43 of physical reality is inconsistency. The problem is that all known interpretations of quantum theory do contain inconsistencies. Thus, either they contradict themselves, or else they do not agree with certain facts concerning that portion of reality which can be directly observed. This is usually understood by well-informed authors who recognize that the best that we can do in the present context is to pick as our necessarily inaccurate standpoint the interpretation which may be the least problematic for the kind of problem we are working on. What I have come to realize is that while some new conceptual elements (which have never been considered before) are necessary to formulate a fully consistent, but straightforward interpretation of quantum theory (which actually constitutes a more accurate theory), it is also necessary to reject many of the outlandish concepts that came to be associated with a quantum mechanical description of reality. Thus, I believe that the concept of history or the concept of reality itself must be simplified to once again be allowed to agree with the most basic empirical evidence, concerning in particular the uniqueness of facts and the particle nature of physical reality. The problem here is that it is often believed that the notion of an elementary particle propagating along a unique trajectory is incompatible with the 'complexity' which characterizes the quantum state of a system. But, as best understood by Richard Feynman, given the right formulation of quantum theory, not only is it unnecessary to reject the existence of elementary particles, or even to deny the relevance of the concept of trajectory, but it becomes imperative to recognize that those concepts actually form the substance of reality at the level where we are currently allowed to perform experiments. I think that it is important to emphasize, therefore, that even though common sense is not always a good guide for judging the validity of a physical theory, as the development of quantum mechanics itself illustrates, it would not be wise to conclude from this that more intuitive models are inappropriate and are necessarily ruled out by the apparent awkwardness of experimental facts, or that our direct experience of reality is irrelevant as a guide for elaborating a consistent interpretation of quantum theory. We must keep in mind that classical physics itself once involved quite unintuitive concepts which turned out to be inappropriate, like action at a distance, or which are fully explainable only in the context of a more adequate quantum mechanical description of reality, like the principle of least action. Thus, I believe that, in the end, quantum reality will not be more difficult to visualize than classical reality, but will rather be more comprehensible, because 44 it will be more consistent from a logical viewpoint. In any case, I believe that I'm justified in adopting a more intuitive approach given that the persistent problems which we are dealing with here have to do precisely with the apparent impossibility to provide a consistent, but also understandable representation of reality. However, instead of entering into a sterile debate about which of the ontological or the epistemological viewpoint8 constitutes a better approach to interpret quantum theory, I will concentrate on explaining what the elements of an empirically accurate approach actually are that allow to reach consistency with the least amount of arbitrary hypotheses (I believe one does not need any). To begin this discussion it would be appropriate to point out that the most radical of those deficient approaches which were once proposed in order to make sense of quantum theory is certainly that which is called quantum logic. It was suggested, in effect, that the logic that applies to physical reality may not be the ordinary Boolean logic with which we interpret ordinary facts, but some alternative logic emerging from the apparently contradictory nature of certain conclusions made on the basis of a strict adherence to the rules which govern quantum reality. But while it is now recognized that such an approach would go too far as a tentative to adapt our mode of thinking to the reality of the quantum world, the fact that at a certain epoch quantum logic was considered to constitute a viable candidate for a solution to the problem of interpretation is quite indicative, I believe, of the extent to which we have deviated from the true objective of science, which is to understand facts by adapting and generalizing our physical laws and concepts to fit new experimental facts, in order precisely to avoid having to change the rules of logic with which we analyze and understand reality. The best example of such an adaptation is of course the shift to Riemannian spacetime that was brought about by relativity theory as a means to retain the validity of the concept of space in view of the equivalence of acceleration and gravitation. Indeed, if we were to reject Einstein's theory of gravitation, the only way we could retain the validity of the concept of 8The debate concerning interpretation has always centered around the problem of deciding whether the wave function that allows to derive the quantum statistics of a process is a real 'entity' or whether it merely provides the sum of all knowledge about what a (real) system is doing, which I believe is pointless, as the wave function definitely is a 'real' aspect of reality, but it is an aspect that does in effect concern empirical knowledge. The approach I will follow may actually be considered to allow a reconciliation of those two apparently incompatible viewpoints. 45 physical space would be by altering the rules by which we formulate logical arguments, such as would be necessary to argue that despite all the evidence the Earth is flat. What the whole history of physics tells us is that it is always appropriate to use logical coherence as a means to constrain our representations of reality and as a guide to assess the validity of our assumptions, while the rules of logic themselves are rather like the rules of the game and can only be altered at the expense of invalidating most of everything else we have learned. But the mere fact that quantum logicians were never able to dispense themselves from the need to use ordinary logic in order to reason about their own alternative system is quite indicative of the failure of their approach. I think that this is a particularly good example of the difficulties which the currently favored interpretations of quantum theory are facing as they stretch the notion of consistency while trying to adapt to some perceived requirement of the mathematical framework of the theory, by going so far as actually allowing for contradictory accounts of factual aspects of the world. I will return to this question later in this section. Not so long ago it was suggested that certain difficulties that emerged as a result of the development of quantum field theory may indicate that the concept of an elementary particle is no longer relevant to fundamental theoretical physics. One of those 'difficulties' would have to do with the fact that, due to quantum uncertainty, particles can no longer be considered to be localized in space, as would seem to be necessary for the particle concept itself to make sense. Actually, in a relativistic context it seems that the very fact that a particle is localized may depend on the state of motion of the observer which is assessing this fact, given that a particle's wavelength varies as a function of its relative velocity. Another aspect of the quantum mechanical description of reality which would appear to constitute a serious challenge for the particle concept is quantum entanglement and the demonstration that what one particle does may under certain conditions depend on what another particle is doing at the exact same time in a remote location (relative to a given reference system), thereby apparently implying that only the ensemble consisting of the two particles taken together has physical significance. Finally, an additional difficulty arises from the fact that, due to the fluctuating nature of the quantum vacuum, the very reality of a particle's existence may be called into question, because, even in empty space, particles would appear to be present. This problem is particularly severe in the context of a semi-classical approach where the effects of acceleration 46 and spacetime curvature on the quantum vacuum are taken into account and the presence of real (observable) particles becomes an observer dependent property. While I will not immediately address the issue of quantum entanglement, the conclusion I have reached is that, despite the difficulties mentioned here, the elementary particle concept is still viable in quantum field theory. In the reminder of this section I will provide arguments to the effect that a realist description of physical processes based on the concept of particle trajectory is still desirable even in the context where quantum interference involving multiple position states must be assumed to constitute an essential aspect of reality. What emerges from this reflection is that it might be incorrect to suggest that particles cannot be localized in any way, because it may well be that particles in a pure momentum state do follow unique, but unobservable trajectories in a certain sense which is merely incompatible with the classical concept of trajectory. In such a context the fact that the 'wave packet' which is sometimes associated with the position state of a particle can be more or less localized in space, depending on the state of motion of the observer which measures this position, would not mean that a particle can actually be more or less 'real', because such a variation would merely be a reflection of the dependence of the macroscopic conditions which constrain the non-classical trajectory of the particle on the choice of a particular reference system. But a detailed description of the realist picture of quantum processes that allows to articulate those considerations will only be provided in section 8. In any case, I believe that the only real problem here is the general confusion that surrounds the question of deciding what it is exactly that remains acceptable about the particle concept in a quantum field theoretical context, because all attempts at completely disposing of this essential concept have failed to provide a sensible alternative conception of the nature of physical reality at the most elementary level. What I would like to immediately emphasize, though, is that in light of the developments already introduced in chapter 1 of my preceding report it is possible to conclude that vacuum fluctuations, far from constituting a problem for the elementary particle concept, actually allow to provide a more consistent definition of what a matter particle really is. Indeed, I have explained in [1] that positive energy bodies must be considered to arise from an absence of negative energy in the fluctuating vacuum, that is to say, in the distribution of virtual particles that contribute negatively to the maximum measure of vacuum energy density (while negative energy bodies arise 47 from a similar absence of positive vacuum energy). It therefore appears that the distinction between real particles and the virtual particles present in the vacuum is not as significant as one might imagine, given that the presence of real particles is actually equivalent to an absence of virtual particles in the quantum vacuum. But it was also made very clear in section 3.7 of the preceding report that despite the fluctuating nature of the vacuum there is a clear distinction between matter (or radiation) energy and vacuum energy which is reflected in the absence of contribution to gravitational entropy by a uniform distribution of vacuum energy. On the basis of those developments it becomes relatively straightforward to provide a clear and unambiguous definition of when it is that matter is present in a vacuum, that would also apply for accelerating observers or in the presence of very strong local gravitational fields (such as those present in the vicinity of a black hole) and therefore the difficulties identified above would now appear to be rather insignificant. But, in my opinion, one of the most powerful argument that can be used to support the idea that the elementary particle concept still constitutes a necessary and viable element of a consistent interpretation of quantum theory (when it is allowed to obey the limitations imposed by the uncertainty principle) is the observation that even in the context where it may seem to be the least appropriate to hypothesize about the usefulness of elementary particles, it nevertheless turns out that this assumption allows to explain in a surprisingly simple way certain key aspects of the processes involved. What I'm talking about is the use of virtual particles as the mediators of elementary particle interactions. The fact that it would be very difficult to explain certain properties of those interactions, like their range and their strength, without assuming that the interactions themselves are actually mediated by particles, even if those particles cannot have classically well-defined energy states, is indicative of the usefulness and indeed of the necessity of assuming that from a material perspective quantum fields actually consists of particles that propagate between interaction events9. The problem we may have in relation to this conclusion is that even if particles do exist as real physical entities, then it would seem that it is not possible to attribute a unique position state to those particles at all times 9Feynman himself insisted that the concept of an external field becomes relevant merely in the context where the motion of a particle depends on a probability amplitude to interact with the particles mediating this field that varies only with the particle's position at a certain time, as may arise when a large number of such interactions take place over a relatively short period of time. 48 in the context where it is known that many different trajectories must be taken into account in order to obtain the right transition probability for a particle in a given momentum eigenstate. This is why so many people prefer to assume that the wave function, despite its immaterial nature, may constitute reality itself; a hypothesis which raises difficulties of its own in the context where it must be recognized that this reality would be submitted by the act of measurement to discontinuous changes that may violate the spirit of relativity theory and the principle of local causality. In any case, it must be clear that the wavelike nature of quantum processes is simply a consequence of the fact that the probability amplitudes that must be used in the calculation of transition probabilities are subject to periodic evolution and there is no sense in saying that a particle sometimes evolves as a particle and sometimes as a wave, because the wavelike property is already wellunderstood as being a property of processes which always involve particles and the problem really has to do with the apparent impossibility to attribute a definite location to those particles under general circumstances. What I will explain, however, is that we have not yet exhausted all possibilities and that a realist interpretation of quantum theory that involves elementary particles can still be formulated that would be compatible with the current mathematical framework of quantum field theory (if we allow for a slightly more elaborate particle concept, while still rejecting the contradictory notion of wave-particle duality). I believe that it is indeed possible to assume that a unique history of some kind is taking place even for what regards the physical attribute of a system that is not under observation. This is a conclusion that would obviously contradict the orthodox interpretation of quantum theory, at least under its original form, given that according to the conventional doctrine there is no sense in speaking about the state of some physical attribute when no measurement has been effected to actually determine what this state is at a given time. But if we recognize that the elementary particle concept is essential to a consistent interpretation of quantum theory then it seems that we have no choice but to recognize that the current interpretation of the theory is incomplete, because it does not provide a clear and unambiguous description of what happens when the position of such a system is not under direct observation. Of course certain modern interpretations, such as the consistent histories interpretation of quantum theory, go some way into providing a more realist picture of quantum phenomena, but they also appear to be incomplete, given precisely that they allow reality to be described only under particular circumstances, which are 49 determined by a certain more or less arbitrary criterion of consistency and also due to the fact that despite their more appropriate handling of the measurement problem they still fail to explain the emergence and the persistence of a quasiclassical world, as I will explain in section 10. In the introduction to this report I mentioned that I believe that it is essential to adopt a realist interpretation of quantum phenomena if we are to avoid deviating into a solipsist and idealist view of reality according to which nothing would really exist aside from your own mind (if that could ever be found possible). This is particularly important in the context where the only thing that may be considered undeniable about reality is precisely that it is real. The problem is that the adjective 'real' is usually assumed to be the characteristic of something that exists as a fact rather than as a mere possibility and therefore the characterization of quantum reality as actually being real would appear to exclude the possibility that this reality may not always consist of observable facts. Thus, it is important to emphasize that what I have in mind here is the scientific concept of realism according to which it would be deemed appropriate to seek to describe the actual ways by which certain physical processes can occur, even when it is not possible to determine the specific path which is followed in the course of any one particular process. But in the context of the preceding discussion it would also appear desirable to apply the criterion of physical reality not to the wave function itself, as is usually proposed, but rather to the elementary particle trajectories that enter the sum-over-histories formulation of quantum theory. The hypothesis would then be that it is appropriate to assume that, even in between position measurements, elementary particles follow real and to a certain extent unique (but not classically well-defined) trajectories in spacetime, despite the fact that those trajectories must, as a matter of principle, remain mere potentialities. I believe that one of the clearest indication to the effect that quantum theory is not incompatible with a realist conception of phenomena, even when what is assumed to be real is not the wave function itself, is the fact that, despite its probabilistic nature, under appropriate circumstances quantum theory allows to predict the outcome of certain measurements with absolute certainty (think about measuring the momentum state of a particle soon after it was prepared to be in an eigenstate of this observable). If it is possible, at least under particular circumstances, to tell with perfect certainty what the state of some dynamic attribute of a quantum system was prior to measurement, then it may not be definitely ruled out that even when the 50 various alternative states available to a system interfere quantum mechanically with one another, the unobserved attribute of the system could exist in a definite, unique, but unknown state, which would be compatible with the constraints imposed by a subsequent measurement. Of course this is what is usually believed to be ruled out by the fact that all possible histories must be put to contribution in order to derive the right probability for a process to occur (that which is obtained by repeating the experiment a large number of times), which appears to be incompatible with the hypothesis that the system would have occupied one unique state of that unobserved attribute all along. Thus, despite being intuitively appealing, the hypothesis that a unique history exists at all levels of description, in the sense that even the unobserved attributes of a system always exist in a unique state, would appear to be invalidated by experimental results, given that it does not allow to predict the right correlation probabilities. Faced with those difficulties one usually concludes that it is not possible to retain a realist description of quantum phenomena that would involve elementary particle trajectories if one recognizes that there do arise quantum interferences involving the multiple spacetime paths which are all at once available to a quantum system. Thus, what one normally assumes is that reality simply cannot be unique in any way between measurements and that the question of what happens to unobserved attributes is simply meaningless from a scientific viewpoint, as originally proposed by Bohr and Heisenberg and as apparently required by the existence of quantum interferences. But, if one recognizes that the uniqueness of history is a fact that cannot be rejected, one may alternatively propose that quantum interferences are not indicative of the fact that multiple trajectories must be taken into consideration simultaneously, but rather arise as a consequence of the existence of hidden and explicitly non-local, but otherwise classically well-behaved influences that would determine the course of a conventional history involving otherwise ordinary objects. Without entering into the details of each proposal it is clear that they are both unsatisfactory, precisely because they both involve assumptions that contradict one key aspect of physical reality (either the uniqueness of history as an observational requirement, or the absence of instantly propagated causal influences as a theoretical requirement). But it must be clear that, despite what is commonly believed, the first proposal is just as problematic as its alternative counterpart, even if it was favored by the originators of quantum mechanics on the basis of the fact that it involves fewer arbitrary assumptions. 51 It always appeared preferable, in effect, to avoid postulating the existence of classical hidden variables, given that any model based on such a requirement would necessarily involve complex mechanisms of an unobservable nature whose validity could never be empirically confirmed. Yet, the argument that it is the non-locality of the hidden variables models that makes them unacceptable is not very satisfactory. Indeed, if one recognizes that there must necessarily be a reality of some kind, then the only known alternative to assuming the existence of hidden variables would be to consider the wave function as this reality and this means that explicit non-locality would also constitute an aspect of the orthodox interpretation, because the wave function is also a non-local entity which is subject to non-local changes, as would occur in the course of certain measurements. Thus, it would appear that the only alternative to an explicitly non-local theory, potentially involving complicated arbitrary constructs whose validity would remain unconfirmed, actually amounts to assume that reality is not real. This is obviously a simple assumption, but I'm not willing to accept that it would be mere scientific progress to consider it as a valid assumption about physical reality. One must come to recognize that such a position is not progress, but simple non-sense of the most scientifically objectionable kind. If a physical reality exists, then I believe that what is certainly the most basic property that would need to characterize this reality is that it is, in effect, real. This must be considered an essential consistency requirement and neglecting it would again amount to allow a logical contradiction to stand at the basis of our interpretation of the most fundamental of all physical theories. Therefore, I suggest that one of the crucial points that cannot be neglected in trying to produce a consistent interpretation of quantum theory is that the unique outcome of measurements is indicative of the uniqueness of the history that takes place in between measurements, even for what regards those dynamic attributes that are not subjected to direct observation. The existence of definite causal relationships between all elements of the universe must be understood to actually require that every element of this physical reality is indeed involved in only one such history in any one particular universe. The right interpretation must therefore emerge from a combination of two apparently incompatible requirements which are provided on the one hand by this condition of uniqueness of history and on the other by the necessity to allow quantum interferences to occur between the many distinct possibilities that may exist for the unobservable aspects of this unique history, even as may affect a single quantum process that is not repeated many times. It is 52 the description of reality we are considering that must adapt to those two requirements if we are to avoid having to alter the rules of logic to accommodate their simultaneous fulfillment. But I do agree with Copenhagenists that this must not be achieved by postulating the existence of arbitrary, hidden influences propagated at superluminal velocities, because from all that we know the principle of local causality provides as real a constraint on our description of physical reality as the existence of quantum interferences. In fact, I have come to understand that the debate between Copenhagenists and classical hidden variables theorists is not as meaningful as one might assume, because the only hidden variables models that may allow to retain agreement with observational data are those that postulate that the hidden influences would remain unobservable and indeterminate as a matter of principle, even when they evolve deterministically (ignorance of the exact state does not arise from a practical limitation that could eventually be overcome, as in conventional statistical mechanics). Thus, even though such classical hidden variables models would contradict the orthodox postulate of objective indefiniteness, the fact that the hidden variables could never become part of experimental knowledge means that those models do not require a rejection of the concept of objective chance and would not allow to circumvent quantum indeterminacy (associated with unpredictability). It would therefore appear that it is really just the naive classical definiteness of the state of the non-local object which is assumed to govern the behavior of quantum particles that is problematic with those hidden variables models, given that it necessarily requires the existence arbitrary mechanisms of a conspiratorial nature to achieve agreement with observational data. The real problem for current (classical) hidden variables theories would then be that instead of enhancing the domain of validity of the quantum mechanical state, as an improved realist interpretation of quantum theory should enable to achieve, they just allow to perhaps reproduce the empirically confirmed predictions of the theory through some unnatural and complicated contortion of reality that make them even less appealing than the currently favored traditional approach. But before I elaborate on what kind of physical reality might agree with the two basic requirements identified above (uniqueness of history and local causality) it is important to mention that the requirement that there exists a unique reality is different from Einstein's proposal that reality should be independent from whether or not a certain parameter is being observed, which assumes more than just a unique reality and which is irreconcilable with 53 the mathematical framework of quantum theory. We must recognize as an established fact that quantum reality is not independent from experimental conditions, even if it might be possible to assume that conjugate physical attributes like position and momentum can simultaneously possess unique (even though partly unobservable) values in a certain sense, because, as I already explained, this unique reality must also give rise to quantum interferences among multiple states and it is only the physical attribute that is under direct observation at a given time, or in the course of a certain process that is free of interferences. Assuming that reality is independent from experimental conditions would require that quantum interferences be absent altogether, which is certainly not compatible with any plausible interpretation of quantum theory. If the values taken by conjugate observables cannot be determined at the same time with an arbitrarily high degree of precision it is precisely because the macroscopic constraints necessary to determine the exact state of those physical attributes cannot be realized all at the same time for the same process, while it is those macroscopic constraints (associated with the existence of records) that determine which physical observable is not subject to quantum interferences (for reasons I will discuss in section 12). Thus, even though I believe that it is necessary to assume that a unique reality actually exists, regardless of whether it is being observed or not, I also think that it must be recognized that this reality does not evolve independently from the macroscopic physical conditions necessary for an experimental determination of its actual state. Furthermore, it should be clear that the hypothesis that there exists a unique reality of some sort does not impose on quantum particles (say negatively charged, positive energy electrons propagating forward in time) that they be distinct individually, even when they possess the same static attributes. What we must ask ourselves, therefore, is what the unobservable reality actually is if it does not conform to a classical representation in terms of simple, identifiable objects. Quantum theory, from the viewpoint of its current interpretation, is not so much an answer to the problem of the fundamental nature of reality, as a constraint that must be obeyed by any realist description of physical phenomena. At this point it is necessary to mention that I do know that from the viewpoint of someone who has been introduced to quantum mechanics in the conventional way, the requirements discussed above may appear irreconcilable, as the formalism of the theory itself seems to be indissociable from the Copenhagen interpretation, while the traditional definition of a quantum 54 state would appear to be totally incompatible with a realist interpretation that would involve a unique history. It is only when one begins studying relativistic quantum field theory, that one is introduced to Feynman's method and the sum-over-histories formalism, at which point one has already been conditioned to believe that it is not possible to visualize quantum processes as involving unique histories of some sort, while in fact this is precisely what the sum-over-histories approach suggests and from a certain viewpoint even requires10. In this particular sense I was lucky, because I first learned of quantum theory by reading about the problem of interpretation and Feynman's original approach, while I became familiar with the conventional formalism of quantum mechanics only later on, which means that rather than being critical of the reality of Feynman's histories, I was rather critical of the conventional interpretation. I believe that this uncommon course is what allowed me to see more clearly how it can be that each independent elementary particle process consists of a unique (even though partly unobservable) history, despite the fact that there always arises interference effects between the multiple histories which are allowed by the macroscopic experimental conditions of the process. What I would like to explain, therefore, is why it is necessary to assume that the multiple unique histories depicted in Feynman's diagrams correspond more than is usually recognized to the actual reality behind all quantum phenomena. I believe that it is merely the fact that no truly acceptable realist interpretation of quantum theory has ever been proposed that motivates the widespread belief that the multiple histories described by Feynman diagrams do not relate to anything actually occurring (must be considered purely fictitious) and merely constitute useful computational apparatus, despite the obvious similarity between the processes so described and the actual reality we experience. It has become very clear to me that what this formalism provides is nothing but a description of what is actually going on which we are not able to directly observe concerning some dynamic physical attribute of a quantum system. Even ignoring the arguments provided so far concerning the relevance of the concept of elementary particle in quantum field theory, 10It is important to note that even a conventional formulation of quantum mechanics like Heisenberg's matrix mechanics can be interpreted as involving a summation over a series of intermediate unobserved or 'virtual' processes and it is significant that some of the originators of quantum theory were in effect open to such an interpretation (perhaps because they were not told by others how they should interpret their own theory) even though they did not see how it could be made truly viable. 55 I think that one must recognize that it is very unlikely that such an essential concept as the individual paths entering a sum-over-histories formulation of quantum theory could happen to be intuitively significant simply by chance, without being related to what actually goes on in between measurements of the observable concerned. Perhaps that instead of insisting that our experience of reality is not a reliable guide for judging the value of certain hypotheses concerning unobservable aspects of this very same reality, we should instead try to figure out how the phenomena that cannot be directly observed can be described in a way that would agree more with what we do know about physical reality. It is remarkable in this regard that while Feynman himself believed that quantum reality involves particles and only particles, he also said that there is no way to explain or to understand what happens to those particles, even during the most simple of quantum processes, because it is not possible to assume that a particle in a given momentum state goes one way or another in space, so that it may be preferable to give up trying to create a model of what is actually happening. I believe that this shows how deeply the philosophy behind the Copenhagen interpretation of quantum theory has become ingrained in our conception of reality, because if one person might have been allowed to understand what is the reality behind all quantum phenomena it should certainly have been Feynman and it is clear that his failure is in part attributable to the fact that, despite his remarkable insights, as all physicists of his generation he adhered to the notion that a realist representation of quantum phenomena is not possible. But if those difficulties have been allowed to persist to this day it is merely because we still do not understand the profound meaning of quantum strangeness and remain ignorant of the fact that quantum phenomena can be visualized. What remains to explain, therefore, is how it is that one and only one of the histories which can be depicted using Feynman diagrams may correspond to what really happens in the course of a specific quantum process11, 11I must mention that I'm aware that a method called 'unitarity' is often used as a shortcut for the determination of quantum probabilities that constitutes a modification of Feynman's original approach, but this alternative technique does not require assuming that the original sum-over-histories formulation of quantum theory is not fundamentally the most accurate and it remains that the summation over all possible histories is more representative of what really goes on at a fundamental level, even if from a practical viewpoint it may be even less appropriate than the alternative approach for performing certain calculations under particular circumstances. 56 despite the fact that it is not possible to attribute to a quantum particle the properties of a classical object and in particular to simultaneously determine both its momentum and its position with an arbitrarily high degree of precision. For that purpose it is necessary to point out that there is something highly problematic with the conventional viewpoint provided by Bohr's complementarity principle. What Bohr suggested, in effect, is not just that the conditions necessary for the measurement of a certain dynamic attribute is incompatible with those necessary for the measurement of its conjugate counterpart, but really that the concepts of momentum and position, for example, constitute mutually exclusive representations of a quantum object (like an elementary particle) and that it does not even make sense to try to apply them simultaneously. If one was to hold on to such a viewpoint, then, clearly, a realist description of phenomena based on the sum-over-histories formulation of quantum theory would become impossible to achieve. But, in fact, there is absolutely no reason to assume that the indefiniteness of the state of some unobserved attribute of a quantum system cannot be the consequence of a mere incompatibility between the macroscopic conditions necessary for the measurement of one dynamic attribute and those necessary for a measurement of its conjugate counterpart. When one understands the true nature of the constraints which allow decoherence to take place and to rapidly eliminate quantum interferences for the physical attribute that is subjected to measurement (an issue I will address only in section 12), it appears quite plausible that quantum indefiniteness actually arises as a consequence of this practical (but fundamental) limitation. Therefore, it is not a priori impossible for a quantum particle which is known to be in a pure momentum state to follow a unique, but observationally undetermined trajectory in space and only the existence of quantum interferences involving multiple distinct trajectories would appear to contradict this conclusion. There is certainly something true in Heisenberg's statement to the effect that the progress made through the elaboration of quantum theory was obtained at the price of having to abandon the possibility of visualizing natural phenomena in a way that is directly comprehensible in the context of our conventional way of thinking. However, I would insist that what is inappropriate is not the requirement that it should be possible to visualize physical reality, but the requirement that this reality in effect be similar in every way to what it appeared to be before experiments began revealing the existence of quantum interferences between alternative potential histories. In order to progress toward this legitimate objective of visualizing quantum reality we 57 may again consider the classical double slit experiment. What can be learned using this simple, but very general experimental arrangement is that despite the fact that we are always dealing with discrete, localized particles, interferences, similar to those which can be observed when what is propagating is a classical wave, must be assumed to occur whenever a particle is allowed to propagate between a source and a detector through more that one possible path without giving rise to the formation of a permanent record that would indicate through which trajectory the particle actually went. Even though such interferences become apparent only in the statistical distribution of measurement results, which is known to depend on the differences between the length of the possible paths along which a particle can propagate before its position is detected, the interference must be considered to take place even in the course of a single process involving the propagation of one unique particle (because such processes also obey the rules of quantum theory). The problem, then, is to figure out how it is possible for a localized particle to give rise to those interferences involving distinct potential paths if, as a particle, it must necessarily propagate in space by going through a definite, yet unobservable trajectory. Stated in such a way this aspect of the problem of interpretation appears at once very simple and quite irresolvable. But it took me a very considerable amount of time to simply realize that this is in effect how the problem must be stated, as this is not how most people see things. Indeed, it is not usually assumed that the particle, as a particle, must necessarily go through a single trajectory or through any trajectory at all, as this would immediately appear to give rise to an unavoidable contradiction, because 'obviously' a particle cannot go through one trajectory and produce interference effects which involve multiple distinct trajectories. Anyone arguing that this is not necessarily the case would merely be a nostalgic of classical reality that does not accept the 'undeniable' strangeness of reality unveiled by the observation of quantum phenomena. Such an approach to the problem of interpretation would necessarily have to deviate into classical hidden variables and non-local causality. But in fact, that is not the case. Not only is it possible to visualize what is going on when one acknowledges the validity of those premises, but this is the only way to arrive at an interpretation of all quantum phenomena that does not involve any arbitrary and undesirable assumptions that would either conflict with the observed uniqueness of experimental facts, or contradict one another (as when one speaks of a 'probability wave' going through both slits all at once, which then 'becomes' a particle when its posi58 tion is detected), therefore implicitly or explicitly requiring an alteration of the conventional rules of logic. It is important to understand that while it is usually believed that logical contradictions may arise when one insists on requiring a realist interpretation of quantum theory, those contradictions are merely a consequence of holding on to a conventional, or naive conception of reality, according to which it might be possible to obtain simultaneous experimental knowledge about the state of all physical attributes of a quantum system. Indeed, it is usually believed that one cannot assume that all dynamic attributes of a system could be in a unique state at all times without assuming that a precise knowledge of the state of those dynamic attributes would be available (which would violate the uncertainty principle). But, once one recognizes that only the second assumption is inadequate and could give rise to factual contradictions, while an absence of knowledge concerning the state of some dynamic attribute that is not subjected to measurement may actually allow one to assume, without contradiction, that this attribute is in what would appear to be two unique, even though possibly different states all at once (in a certain sense which will be clarified later), then it becomes possible for a realist interpretation to be formulated that is not logically inconsistent. In the present context it would therefore appear that the fact that a purely phenomenological model of reality (such as that which constitutes the core of the orthodox interpretation of quantum theory) may appear to be better suited than a realist model for explaining certain observations is merely a consequence of the fact that a realist model cannot be applied to quantum phenomena as they are traditionally described, but only becomes appropriate in the context of a time-symmetric description of those phenomena. Following Einstein, I believe that one must be ready to take an intuitive leap and to derive, based on available experimental data, general postulates that may not always be immediately confirmed through direct observation, but which allow to better model the reality underlying those empirical facts. For what regards the problem of the interpretation of quantum theory this intuitive leap would actually consist in assuming that the particles involved in the description of elementary quantum processes are in effect real and that they are taking part in one unique history of some kind. Once this is recognized to be a legitimate and necessary requirement, the difficulty would then consist in understanding how such a realist description of reality could be made compatible with both the observational constraint imposed by the existence of quantum interferences and the theoretical constraint of a time-symmetric 59 conception of causality. I think that one cannot be satisfied with assuming that what explains the existence of quantum interferences is the 'fact' that a particle doesn't follow a unique path and actually propagates from emission to detection by simultaneously following, at once, all possible trajectories. I believe that the notion that all the available paths are actually followed together in the course of any single quantum process occurring in a given universe actually constitutes one of those strange aspects of quantum reality (as it is usually conceived) which are not merely unexpected, yet unavoidable, but which remain strange because they actually conflict with certain factual aspects of reality. What is quite amazing is that even though such a notion is only slightly different from the usually rejected viewpoint according to which a particle may go partly through one slit and partly through the other (in a double slit experiment), it is sometimes considered to provide an appropriate depiction of quantum reality. But if one recognizes that such a representation is indeed incompatible with a realist interpretation of quantum phenomena that would not reject the empirical evidence for the uniqueness of historical facts, it remains that one must take into account, in the determination of transition probabilities, any possible trajectory which is allowed by the macroscopic conditions which are in effect while those transitions are taking place. In order to accommodate this fact what is sometimes assumed (as I briefly mentioned in section 6) is that a single unique process may actually always involve two interfering histories which, for some reason, would share the same observational conditions. But, it remains to explain what justifies this assumption (which would still appear to conflict with the uniqueness of historical fact) and why it can be expected to give rise to the kind of classically well-defined reality we do experience. It is certainly true that one of the criteria that allows one to judge the validity of an alternative conception of reality involving unobservable theoretical constructs is its usefulness for producing accurate predictions of experimental phenomena, but this is precisely why the currently favored interpretation must be rejected. Indeed, I believe that if the notion that all histories occur all at once in the same universe is incompatible with the experimentally derived uniqueness of historical facts (in the context where the tentative solution to the quantum measurement problem that is provided by a 'many-worlds' approach is recognized to be ineffective, as I will argue in section 10), then it must be rejected in favor of a conception of reality that does not require this uniqueness to be a mere illusion. The problem, how60 ever, has always been that it would appear that the only realist alternative to such an interpretation would require assuming that the wave function itself is the reality, because in the context where quantum interference is possible for unobserved attributes, this mathematical object (the state vector in general) does not merely provide a probability distribution for the position of a particle in a definite momentum state, but may involve superpositions of position states with complex-number weighting coefficients, which means that position may sometimes appear to constitute an inappropriate element of physical reality (of course the same is true for momentum under distinct experimental conditions). But, while this is not necessarily inadequate from a mathematical viewpoint it remains unsatisfactory from a physical viewpoint, especially in the context where this wave function can be subjected to discontinuous changes that would violate the principle of local causality whenever the potentialities involved are actualized, as I previously mentioned. I believe that it is merely the fact that we fail to correctly visualize what is going on in between position measurements (for instance) that makes it look like physical reality cannot involve a unique history of some kind and needs to be replaced by some weird picture which actually deviates from a conventional representation to the point where reality itself looks unreal, in the sense that the proposed picture is not only incompatible with observable aspects of reality, but also with the logical consistency which is known to apply under more general circumstances. What holds the key to a better understanding of quantum reality is the acknowledgement that what can be known about a quantum system does not allow one to tell everything about what it does, even though, as a matter of principle, no better knowledge is available. Such a standpoint is the only alternative that is available when one considers it inappropriate to assume that dynamic attributes simply do not exist when they are not those concerning which direct observational knowledge is available. Although the approach I favor may at first seem problematic, it is actually much simpler to apply than its logical alternative, because the idea that a dynamic attribute does not exist when it is not subject to observation cannot be adapted to the case where such an attribute is only known to an intermediary level of precision, because, clearly, either an attribute exist or it doesn't, while it is undeniable that the state of any attribute can be determined with more or less precision by the appropriate measurement, as long as an inversely proportional uncertainty applies to its conjugate counterpart. If at least it was possible to speak of certain quantum systems as 61 definitely being observed, while other systems would not, then it might perhaps make sense to assume that what is measured is real and what is not measured doesn't exist, but in fact there is always something that is known with arbitrarily high precision about a physical system as long as it remains causally related to the rest of the universe (this is what is implied by the linearity of Hilbert space) and it is merely the conjugate dynamic attribute of this system which is then undetermined, so that if one chooses to follow the orthodox approach one is forced to somehow ascribe both reality and absence of reality to the same physical system, which again constitutes a logical contradiction. Thus, despite what one is usually encouraged to believe, it seems necessary to assume (particularly if one wants to avoid having to consider the possibility of a reality created through observation) that two systems prepared in the same quantum state may evolve differently at the level of the dynamic physical attributes whose states are not determined by the macroscopic conditions of an experiment. I believe that this is what explains that a subsequent measurement of those originally undetermined attributes may produce outcomes that differ from one system to the other and if this is correct it would mean that it is inappropriate to assume that it is the act of measurement itself that introduces randomness into our description of quantum phenomena. The more consistent approach I will propose therefore allows physical systems which are described by the same wave function to actually be different at a certain unfathomable level, even if the wave function still provides the most complete description of what can be experimentally determined about a quantum system. From that perspective it becomes apparent that there is something very problematic with the conventional interpretation whenever post selection is involved in the determination of which physical attribute of a system is actually measured (as would occur in the context of the delayed choice experiments discussed in section 6). Indeed, if one assumes that only measured attributes are real then it would mean that what is real at the present moment depends on what choice will be made in the future regarding which attributes are to be measured. This is so embarrassing that it is usually considered to support the view that quantum theory is not about reality at all, but about the outcome of measurements, while in fact what the reality of post selection illustrates is rather the awkwardness of the conventional interpretation of quantum theory in the context of which it would be impossible to explain the outcome of all measurements without assuming that certain 62 influences do exist that can propagate faster than is allowed by the principle of local causality. Once the necessity of a realist approach is recognized, all that one must avoid is taking the easy way out and postulate that there exist hidden variables of a classical kind that would require explicit violations of local causality as a consequence of trying to reproduce in too simplistic (but actually quite complicated) a way the interference effects between multiple position states. In order to achieve a realist description of quantum phenomena that does not contradict other essential aspects of reality it is necessary to first understand that the most significant difference between the sum-over-histories formulation of quantum theory and the statistical mechanics of classical systems with a large number of independent degrees of freedom has to do with the existence of the quantum phase that gives rise to interferences among the different possible histories involved and which is attributable to the use of probability amplitudes instead of classical probabilities as elements of the summation process. From that viewpoint what needs to be explained is how it is possible for a particle to follow a path along which all of its conjugate dynamic attributes have unique values at all times, despite the fact that the many trajectories which can be followed by the attribute that is not directly observed would seem to interfere with one another, as if no definite trajectory was ever followed. At this point it may still appear justified to reject this possibility, but once the requirement of a time-symmetric description will be taken into consideration, it will appear that it is as clearly inappropriate to refuse to admit the existence of those unique trajectories, as it would be to refuse to recognize the existence of elementary particles themselves. John Von Neumann was certainly right when he claimed to have demonstrated that the ordinary reality of everyday objects cannot apply to quantum particles if those objects are to obey the principle of local causality. But, as I will explain, that does not necessarily mean that we need to reject the notion that particles always follow a unique trajectory of some kind (in the space of their unobserved attribute), if we allow for this trajectory to remain unknown under all conditions and to conform to the requirements of a time-symmetric conception of causality. If the sum-over-histories formulation really constitutes a fundamentally different formulation of quantum theory that cannot be derived from earlier formulations by a simple mathematical transformation, as is usually understood, then one cannot reject the possibility that it is only by considering the reality it describes for what it is that we can begin to understand quantum 63 theory. From that perspective it is certainly incorrect to argue, as many authors do, that quantum theory is only about the probability of measurement results and does not tell us anything about what goes on in between measurements. If the most adequate and generalizable of quantum mechanical formalisms does involve a certain description of what happens in between observations, then it would seem that it is merely our failure to understand why it is exactly that this description is relevant from a physical viewpoint that motivates our rejection of this realist picture of phenomena as not being indicative of anything true. In any case, one must keep in mind that the widespread opinion that what the sum-over-histories formalism indicates is that all paths are followed all at once in the course of any single process is not an unavoidable conclusion and that it cannot be claimed that no other choice exists for a realist description of quantum phenomena. What I will explain is that it is still possible, in effect, to assume that a quantum particle must merely be allowed to take any of the available paths, but that it does not actually go through all paths in the course of one single process. It is not true that we are confined to contradictory assessments of reality and that it is necessary to assume that quantum theory is about particles and yet that it is not about unique particle histories. What I would like to emphasize is that it is not the hypothesis of a unique and variable (but unobservable) history which is incompatible with experimental facts, but rather the usually preferred hypothesis that similarly prepared systems always evolve in identical ways in between measurements. Indeed, it is clearly the measurement results which are characterized as unique and variable, while it is merely our current assumptions regarding what remains unobservable which may turn out to be inappropriate. Yet, it must be clear that I'm not claiming that the mathematical framework of quantum theory is incomplete, because I do recognize that it is not possible to provide a more accurate description of the state of a system than is allowed by the uncertainty principle, so that even if it is real, the exact unique history of an unobserved dynamic attribute remains a mere potentiality for any specific process. As I mentioned above, experimental knowledge of both the exact momentum and the exact position of a particle is not allowed by the basic structure of quantum theory. In the language of the consistent histories interpretation of quantum mechanics one would say that the simultaneous determination of a particle's momentum and position can only take place on decoherent 'branches' of history, which from my viewpoint actually means that it cannot occur at all, because this would require distinct macro64 scopic constraints to exist together simultaneously (for the same system) and if one wants to preserve the character of uniqueness of physical reality, then, obviously, one cannot argue that one set of mutually exclusive macroscopic constraints exist at the same time as a different one. In a more conventional interpretation one may seek to accommodate the uniqueness of measurement results in light of the existence of quantum interferences between the multiple possible histories by postulating that all histories actually occur all at once in the same universe, but that it is precisely the decoherence effect that allows observed reality to appear unique, given that it requires the interferences between different states of a dynamic attribute to vanish very rapidly upon a measurement of this physical attribute. But it is a positive development that from the viewpoint of a model such as the one I will propose, decoherence can only achieve the goal of giving rise to a quasiclassical world if we do indeed require the existence of a unique history of some kind, as I will explain in section 12. In such a context it would appear that once the dust has settled, no valid argument actually remains that would support the validity of the hypothesis that all histories are followed at the same time in the same universe as different coexisting and interfering 'branches'. Thus, by assimilating what I believe to be the only appropriate interpretation of quantum phenomena, we will go from a situation where it is necessary to assume that either there is no reality at all between measurements, or else that all histories are followed all at once, to a situation where it is no longer possible or necessary to embrace such logically inconsistent viewpoints and where we are allowed to once again conceive of a universe as involving one single and unique history of some kind, which in effect constitutes an essential element of the definition of what a universe actually is. What emerges from those considerations is that it is the very notion that decoherence merely allows to eliminate the interferences between many coexisting 'branches' of history that makes quantum entanglement problematic, given that it requires the existence of explicitly non-local influences to enforce the selection of one branch over another following measurement, while this is in effect a global phenomenon. I know that many people do not agree with that, because they assume that the multiple branches of history are causally independent from one another, as if they actually consisted of different universes. But the problem, once again, is that there is a logical contradiction here, because we cannot assume that we are dealing with truly independent branches, while those branches would nevertheless be assumed 65 to exist in the same universe (so that they can interfere with one another). A lot of crazy things have been said concerning why those two assumptions may not be incompatible with one another, but in the end one must recognize that the simple truth is that there is a contradiction and if the branches interfere prior to a measurement, then there must exist non-local influences propagated faster than the relativistic speed limit to enforce the global consistency of measurement outcomes at multiple remote locations in the presence of quantum entanglement, when it is assumed that all possible histories are indeed followed together in the absence of measurement. Thus, it is not absolutely true that the non-locality associated with quantum entanglement cannot be used to demonstrate that a realist picture of quantum phenomena might be more viable than one of the alternative interpretations, as Einstein tried to achieve. It is telling, therefore, that it is quantum entanglement which is usually assumed to forbid a realist description of quantum phenomena. Indeed, the violation of Bell's inequality by the results of multiple different experiments which have actually been performed on pairs of entangled elementary particles proves that a naive concept of reality according to which all dynamic physical attributes are in a unique classical state at all times could not be considered valid unless this reality explicitly involves non-local influences. In fact, what was shown by the experiments in which a violation of Bell's inequality occurs is that reality is in effect non-local, but that does not necessarily mean that explicitly non-local influences must exist that would propagate faster than the relativistic speed limit, because this property may instead be a simple reflection of the fact that the basic structure of reality is richer than we usually assume, particularly with regards to time directionality and causality. Given that quantum entanglement is made manifest through quantum interference, the non-locality that is discussed here is not different from that I have already identified as emerging whenever one assumes that the wave function itself constitutes physical reality. I believe that what this actually means is that it is not the uniqueness of history which is problematic, but the notion that quantum non-locality must necessarily involve a violation of the causal structure of spacetime which is otherwise imposed by relativity theory. I have already emphasized in the discussion about time-symmetric causality from section 3, that backward in time causation is not forbidden by relativity theory. But it should be clear that backward causation, even when it is restricted to operate in accordance with the principle of local causality, 66 may actually give rise to non-local correlations. The important point here is that the existence of such correlations would not allow faster-than-light communication, given that the backward propagated influences are also submitted to the constraint of diminishing entropy in the past that is imposed by the constraint of global entanglement and in such a context information is only allowed to flow from the past toward the future and never in the opposite direction. Amazingly, this is precisely the property that is observed to be obeyed by the non-local correlations which have been experimentally demonstrated to occur in the course of certain quantum phenomena, as a result of entanglement. I believe that this is not just a coincidence, but that it actually confirms what I have said concerning the time-symmetric nature of causality and the crucial role played by this property in a quantum mechanical context. If this is the true origin of quantum non-locality, then it would mean that the only non-local influences which are ruled out are those that would occur through a violation of the principle of local causality attributable to fasterthan-light propagation (which would allow faster-than-light communication and therefore also the flow of information from the future toward the past), while the non-locality that follows from backward in time causation would actually be a fact which we were traditionally allowed to ignore only because it does not allow signals or information to be communicated instantaneously (due precisely to the origin of this non-locality) and therefore can only be revealed through subtle correlations of otherwise random outcomes of measurements performed on carefully entangled quantum systems. What should be clear, in any case, is that the observed absence of backward in time signaling need not be a consequence of the inadequacy of a realist time-symmetric interpretation of quantum theory, as it can also be a consequence of the effectiveness of the constraints which were identified in section 3.9 of [1] and that give rise to the thermodynamic arrow of time under more general circumstances. Only if this was not possible would the backward in time causation that may be involved in giving rise to quantum non-locality be allowed to violate the principle of local causality that is enforced by relativity theory. It is not appropriate to conclude that the experiments which have revealed the non-local nature of quantum phenomena have proven that those phenomena are irreconcilable with any commonsense interpretation of the theory. What must be abandoned is not scientific realism, but the traditional interpretation of quantum theory which forces us to reject the principle of local causality and to return to a conception of reality that would involve instantaneous 67 action at a distance. It is important to note in this regard that it is the locality assumption that would allow one to conclude, based on the results of certain recently performed experiments [13] involving multiple entangled photons, that there may coexist many mutually incompatible accounts about what constitutes a known, or observationally confirmed fact. Those experimental results, which involve the violation of certain inequalities similar to, but distinct from the conventional Bell's inequality, were initially assumed to support the claim that reality is a relative notion (and therefore that it may not be objective), which would appear to confirm the relevance of the relational interpretation of quantum theory. But once we recognize that non-locality is not optional and that it was actually shown, by even more straightforward methods, to itself constitute an unavoidable aspect of reality, then the inappropriateness of the radical conclusions which were drawn based on the results of the above discussed experiments (regarding the lack of objectivity of observationally derived facts) becomes all the more obvious, even aside from the fact that they would (once again) have given rise to logical contradictions. Thus, it should be clear that the assumption that the experimental results obtained in one part of such an experimental setup cannot influence, or be correlated non-locally with those obtained in a remote part of the same setup is incorrect and it is only when we are not willing to take this aspect into consideration that those experiments seem to imply that reality is not objective and that the truth of certain experimentally established facts which happened in the very same universe may be an observer dependent aspect of reality. I believe that this only shows how important it is to recognize that locality is not a property of physical reality, even if causal influences are always constrained to propagate slower than the relativistic speed limit imposed by their associated light cone, either forward or backward in time. What I have tried to make clear in this section is that it is highly preferable to adopt a realist interpretation of quantum phenomena, because all alternative proposals involve logical contradictions at one point or another and those difficulties are always attributable precisely to a rejection of scientific realism. What is unsatisfactory, however, is the absence of a realist interpretation that would agree with the multiple specific constraints imposed by the mathematical structure of quantum theory, like non-locality or quantum interference (more generally). I believe that if the orthodox interpretation of quantum theory is still preferred by most researchers in the field despite the fact that it requires rejecting scientific realism, it is because something 68 essential is missing from all known realist interpretations that could make one of them acceptable. The problem to which I will now turn, therefore, is that of explaining in an intuitively satisfactory, but logically consistent way, without rejecting as mere illusion the uniqueness of historical facts, why it is that the probability amplitudes associated with the many trajectories available to a quantum particle interfere with one another when its position state is not under direct observation, as if the particle actually followed several different trajectories all at once in the course of one single process. It is here that it will finally be shown that despite what is usually believed this is not an impossible task. 8 Time-symmetric quantum theory It is quite amazing that one single requirement allows to satisfy all at once both the condition of scientific realism in face of quantum interference or state superposition and the principle of local causality in face of quantum entanglement. This requirement is that of time-symmetric causality. There should be no doubt, indeed, that the only way one can avoid having to conclude that there exist non-local influences propagating faster than the relativistic speed limit in the context of a realist description of quantum phenomena is by assuming that certain causal influences actually propagate backward in time. But it is usually believed that such backward causation would be even more problematic than explicit non-locality. Yet, it is difficult for me to understand what could be worse than an outright rejection of relativity theory and the principle of local causality, or what could be more difficult a task than rebuilding quantum physics from the ground up while trying to provide a consistent classical hidden variables theory that would allow to match all empirical constraints by postulating explicitly non-local influences. But what is even more significant is that, as I have explained in sections 3, 4, and 5 the alternative of a time-symmetric conception of causality, far from being undesirable, actually constitutes an essential development in the context where there can be no fundamental distinction between the past and the future at the most fundamental level of description. What must be understood is that backward in time causation is not necessarily problematic, even if the finality it involves may appear unnatural from the viewpoint of our conventional, unidirectional experience of time. First of all, in a universe where entropy cannot grow in the past, backward 69 in time causation would not allow us to tell the future in advance. But, as I already explained, it is also clear that backward causation does not allow one to change a known fact from the past. Classical causality, or the pairing of the distinction between causes and effects with the thermodynamic distinction between past and future only comes into play at a macroscopic level where time asymmetry emerges from the constraint imposed by the presence of negative energy matter on the initial Big Bang state at which global entanglement must take place. In other words, our experience of classical, unidirectional causality is not necessarily incompatible with backward causation, as long as the effects which are propagated backward in time do not give rise to the kind of backward in time signaling that would require entropy to grow in the past. Now, I previously mentioned that what quantum entanglement appears to allow is precisely the kind of non-local correlations that would arise from such backward in time propagation of effects, which is required to occur with ever decreasing entropy in the past and which, for that reason, is not allowed to give rise to faster than light communication, as would ordinary non-local influences of the classical, hidden variables type. A consistent interpretation of quantum theory would be one that naturally agrees with this limitation in all situations, rather than merely require it based on the fact that no violations of the principle of local causality have ever been observed to take place in the course of any measurement on entangled systems. If this is correct then we need to ask how it is exactly that such backward causation is allowed to take place in the context where the only particles we know about that do propagate backward in time are antimatter particles, while it has never been shown that such particles are necessarily involved in the experiments which reveal the existence of non-local correlations. What I have come to understand is that, in fact, such time-symmetry is precisely what the mathematical structure of quantum theory naturally requires, as my discussion of the two-state vector formalism from section 6 emphasized. Indeed, as I previously explained, a mathematically equivalent formulation of quantum theory is possible that involves two state vectors, one of which provides the state of a system as determined by past measurements, and the other the state of the same system as will be determined by future measurements. In between measurements those two state vectors evolve in a conventional 'unitary' manner, in the future following a past measurement, and in the past preceding a future measurement. Of course, this is not a realist representation of quantum phenomena, as we are still dealing with 70 wave functions, but at least it shows that a formulation can be provided that allows to reproduce all the predictions of quantum theory (sometimes more naturally than even the standard theory) while taking into account the requirement of a time-symmetric description of quantum reality (whatever this reality turns out to be). One clear advantage of such an approach is that it allows the timesymmetry that is implicit in the original theory to be preserved even when non-local correlations exist and the order in time of two measurements performed on a pair of entangled particles is dependent on the state of motion of an observer. Indeed, when the chronological order of two measurements taking place at space-like separated events is an observer dependent property, a process of state vector reduction which may appear to be triggered by a measurement performed on one entangled particle from the viewpoint of a certain observer, would appear to be triggered by the measurement performed on its entangled counterpart for a different observer. But it would be problematic to have to choose one or the other of two such measurements as being the cause of the outcome of the other measurement if it was not also possible to assume that it is this other measurement that is the cause of the outcome of the first one, because, in such a case at least, there is no objective criterion that would allow one to tell which event is the cause and which is the effect. Yet, from the viewpoint of the conventional approach it would appear that it is necessarily the event that happens first that is the cause of the other event, even if this first event actually happens later from the viewpoint of a different observer. In the context of a time-symmetric formulation of quantum theory, however, the fact that future measurements are allowed to influence the present state of a system means that a certain reciprocity is allowed between the measurement that influences and the measurement that is influenced (both measurements exert an influence on the outcome of their remote counterpart). In other words, it is no longer necessary to assume that there exists an absolute distinction between a cause and its effect from a purely quantum mechanical viewpoint and this actually allows to avoid the contradiction that would otherwise emerge when we are dealing with measurements performed at space-like separated locations on entangled systems. What one must retain is that if it was not for the existence of backward in time causation, then a clear distinction would need to exist between the causes of state vector reduction and their effects, even when we are dealing with entangled particles, but given that in such a case this distinction would 71 be an observer dependent property, then it would appear that the spirit of relativity theory would be violated, even if it would be impossible to say exactly what distinguishes the cause from its effect, because from a traditional viewpoint this distinction would indeed be required to exist. The fact that in all known situations where non-local correlations may arise, backward in time signaling is not allowed to occur, clearly shows that unidirectional causality is not involved in the determination of the outcome of the second of two measurements performed on a pair of entangled particles, because if it was involved then there would be no reason not to expect backward in time signaling to occur, at least in some reference systems. From such a viewpoint it would appear that the prevalent belief that causality must always operate forward in time is motivated by expectations similar in nature to those which originally motivated the formulation of the Lorentz transformation (the contraction of physical objects in motion relative to absolute space), because imposing a unidirectional conception of causality in the context of quantum non-locality amounts to postulate a property of reality which, even if it did pertain to the physical world, would be required to have absolutely no distinguishable effect on it. Now, even though the two-state vector formulation of quantum mechanics represents a step forward, the fact that it still does not provide a realist picture of quantum phenomena that would fully accommodate the particle concept and the requirement of a unique history of some kind means that it cannot be the final answer to the problem of interpretation. Clearly something essential is still missing and it is only after much questioning and while trying to figure out how the two-state vector formalism could be generalized to agree with the sum-over-histories formulation of quantum theory that I was able to obtain a truly consistent, realist picture of quantum phenomena. I have become convinced, in effect, that the bold intuitive leap which I previously suggested one must be ready to take to achieve a more realist interpretation of quantum theory actually consists in recognizing that what we are dealing with here is a set of two unique histories (involving unique particle trajectories) unfolding in opposite directions of time without directly interacting with one another in any way. In such a context what matters is not really the direction of propagation in time of the particles involved in those processes, but an overall direction of time that only differs in a relationally defined way, such that if the two histories were to be otherwise identical they would still differ in that the direction of propagation in time of all the particles involved would be opposite 72 for those two histories. But in fact it is not possible to differentiate in any absolute way initial causes from final 'causes' and it is only the difference between the directions of time in which the two histories unfold that has physical meaning and this relationship must be preserved even when the processes actually occurring in the course of those two histories differ in ways not forbidden by the macroscopic experimental conditions imposed on those processes. The important point here is that the path followed by a quantum system in the space of its unobserved dynamic attributes must in effect be allowed to differ for the retarded and the advanced portions of a process (the ordinary process and its time-reverse counterpart). What really happens, therefore, to a photon on its way to a detector in the double slit experiment (see figure 1) is not that it passes through both slits all at once, but that it has the possibility to pass through any one of the two open slits in both the retarded and the advanced portions of the same process (when the actual trajectory remains observationally undetermined), which therefore requires that both paths be taken into account in the determination of transition probabilities for any given process, even though a photon only ever goes through one particular slit in the retarded portion of history and then again through one particular (but possibly different) slit in the advanced portion of history. It is simple to verify that those assumptions allow to reproduce the predictions of the standard theory in any specific and possibly more complex situation (I will explain below why this should indeed be expected). It is merely the fact that we do not observe the actual trajectory followed by the photon that makes it necessary to consider both possibilities all at once for any single process, given that under such conditions this trajectory can be different for the retarded and the advanced portions of the process. But this does not necessarily mean that the trajectory is actually different for the two histories, only that it can be and, as I will explain below, this is sufficient a motive for requiring that both trajectories be considered to contribute to the estimation of transition probabilities. Any one history still involves a particle following a unique, unobservable trajectory, only, each process involves both a retarded history and an advanced history (a pair of histories taking place in opposite directions of time) and which are only required to share the same macroscopic experimental constraints. Those histories are therefore allowed to differ in all aspects which are not constrained to a particular subset of possibilities by the observable 'macroscopic' conditions (the paths can differ as long as no permanent record of those differences ever becomes available) 73 S S S S D D D D 2 1 t 2 1 t 2 1 t 2 1 t  : XXXXzXXXX y9 XXXXzXXXX : 9y  : XXXXzXXXX9XXX XyXX XX XXXXzXXXX : X XXXy XXX X9 Figure 1: The four possible combined retarded and advanced histories of a double slit or simple interferometer experiment, with one source S and one position detector D, when the actual trajectory of the quantum particle remains unknown. The direction of the arrows corresponds to the flow of time. When the actual trajectory of the particle is subject to experimental determination only the first two combined histories remain possible and the two trajectories no longer interfere, as the retarded and the advanced histories must be the same for any complete process. 74 and this is why the many different possible paths available to a quantum system interfere with one another and must therefore be taken into account in the determination of the probability for the complete process (comprising those two histories) to occur. It is remarkable that if it was not for the fact that probability amplitudes, unlike conventional probabilities, involve periodic variations which can interfere constructively or destructively, then it would be impossible to deduce the existence of the advanced portion of a process (which may actually be any one of the two histories), because it is the periodic or wavelike aspect of probability amplitudes which allows the retarded and advanced portions of history to interfere when the dynamic attributes involved are not subjected to direct experimental determination. The greater consistency of the viewpoint proposed here is apparent in the fact that it is no longer necessary to assume that when the path followed by a particle is not observed the object actually behaves as if it was a different entity (a classical wave), because the interferences which are made conspicuous in the statistical distribution of measurement results can be explained without requiring one to assume that the particle behaves differently when its position is not observed. What changes when a different dynamic attribute is submitted to direct observation is merely the macroscopic conditions imposed on a process, while the particles involved still follow unique, but unknown, and possibly different trajectories in the retarded and the advanced portions of history that unfold in the space of the unobserved attribute. It is only when a particle is constrained by the experimental conditions to follow a certain definite path (when a record of the actual slit through which the particle went is available) that interferences are absent for the dynamic attribute involved, because in such a case the particle must follow the same path during both the retarded and the advanced portions of history. It would therefore be incorrect to maintain that it is not possible to visualize what occurs to a photon as it propagates from source to detector in a double slit experiment when its trajectory is not observed. It is not nonsense to speak of the passage of the photon through one particular slit, even when this trajectory remains experimentally undetermined, as long as one recognizes that the actual trajectory can be different for the retarded and advanced portions of the process. From this viewpoint what looks rather absurd is the conventional assumption that an elementary particle whose trajectory is undetermined follows at once all possible paths. When it is properly understood, quantum theory is no longer as unsettling as it used to be (this 75 comment will become even more apposite when other essential aspects of this approach are discussed which allow to justify its inevitability). From the viewpoint of the interpretation of quantum theory proposed here there would no longer arise logical contradictions in the description of the state of a system when a certain dynamic attribute of the system is in a state of superposition (which is always the case for at least one physical attribute). We may consider for example an electron whose spin has been measured to be up along the horizontal axis. Under such conditions the spin of this electron along the vertical axis must be considered undetermined. But it is well known that this cannot be understood to mean that the spin of the electron is either up along the horizontal axis and up along the vertical axis, or else up along the horizontal axis and down along the vertical axis, as one might consider appropriate from a classical perspective. Whenever one tries to experimentally confirm the apparently indisputable validity of this legitimate hypothesis the results one obtains show that it cannot be true. It may therefore appear that whenever an electron is in a definite state of spin relative to the horizontal axis, its spin state along the vertical axis, if it is real, must be such that it cannot be described without violating the conventional rules of logic, because it would seem to be allowed to point along two mutually exclusive directions all at once, which from a realist viewpoint does in effect constitute a contradiction. But once it is understood that two independent histories are involved in any single process then it becomes clear that what the results of the discussed experiments mean is not that the vertical spin of the electron is in no state at all (which would require rejecting the possibility of a realist description of quantum phenomena), or that it is at once in all possible states (which would require rejecting the conventional rules of logic), but merely that while its vertical spin state in the retarded portion of history can be either up or down, the same vertical spin state can also be either up or down in the advanced portion of history, which means that four different combinations of states are allowed, thereby contradicting the hypothesis that this vertical state can only be either up or down and nothing else for any single process, or at any single time (which actually consists of two different times that must simply correspond with one another for the retarded and advanced portions of history, as I will later explain). It is therefore possible to assume that the spin of an electron along any axis is always in a unique, but unobservable state in any one portion of history, even though it is not in a unique state for any process (when a process 76 is adequately considered to involve both a retarded and an advanced portion), as experiments confirm. Thus, if those experiments with electrons, as well as more decisive observations of the same kind, do show that quantum strangeness is unavoidable, it would be incorrect to assume that what they demonstrate is that a realist interpretation of quantum theory is impossible and that there cannot be an unique reality of some kind behind the observed phenomena. Indeed, the contradictions which are encountered in the context of a conventional realist interpretation are only made apparent in the statistical distribution of measurement results and always concern physical attributes which actually remain unobserved, while it is precisely at this level that the alternative interpretation proposed here differs from the conventional theory. But given that this realist interpretation of quantum theory allows non-local correlations to arise from backward in time causation, even in the absence of non-local influences, then it also appears inappropriate to argue, as is often done, that only a rejection of scientific realism (the idea that there must exist an 'objective' reality between measurements) may allow to avoid the conclusion that quantum non-locality is a real phenomenon that arises from instantaneous action at a distance. Quantum non-locality is not an illusion, but action at a distance can be avoided, even in a realist interpretation (I will return to this question in the following section). It is the fact that, traditionally, time-symmetric interpretations of quantum theory involved classical wavelike phenomena that made them undesirable as realist interpretations. But once the dual nature of the state vector is understood to be a consequence of the existence of two actual histories in which particles propagate once through any of the available paths and then again through any of those same available paths, but in the opposite direction of time, then the time-symmetric nature of quantum reality becomes a more significant asset given that it allows to reproduce the statistics of quantum measurement processes and to explain interference effects involving distinct paths while naturally providing a picture of quantum reality that satisfies the requirements of scientific realism. Of course the reality unveiled here is not classical, because it involves probability amplitudes instead of classical probabilities and it requires the existence of an unobserved counterpart to every conventional process (because we really experience only one of the two portions of history at any single time). But then, what we are dealing with is quantum reality and not classical reality and only consistency provides an unavoidable criterion for judging the validity of any representation of reality. If quantum strangeness itself cannot be avoided then there must certainly 77 remain some unexpected element in any empirically accurate model. In fact, it appears that it is the remaining 'incomprehensible' aspects of quantum reality that make the theory truly consistent in a way that would be impossible classically and, as such, they are certainly not undesirable. As I explained in the preceding section, consistency merely dictates that physical reality must in effect be real and therefore unique in some particular way, but it does not a priori constrain this reality to conform to some preconceived criteria of appropriateness we may believe should apply, that would be based on an experience of physical reality which is restricted to a subset of experimental conditions, namely those where quantum interference and time symmetry are usually unapparent. What's more, I'm not suggesting that two processes are taking place in parallel that could differ from one another in an observable way, in violation of the uniqueness of historical facts, but merely and precisely that there is a counterpart to history which, even if possibly distinct from its time-reverse version at the level of intricate details, would nevertheless remain identical from the viewpoint of its observable macroscopic features, even though it would still be required to exist in order to explain certain observable features of reality (the interferences). Therefore, what constitutes a decisive advantage of the time-symmetric interpretation of quantum theory proposed here (over the usually favored approach according to which all paths are followed together all at once in one single portion of history) is that it naturally agrees with the observation that all results of quantum measurements are in effect unique, so that it is no longer necessary to try to provide an independent explanation (such as the hypothetical splitting process of a many-worlds interpretation) for why all potentialities are not actualized all at once, as would appear to be required if all histories actually occurred all at once, as is usually assumed. It seems that the error that is made in the context of most current interpretations of quantum theory is that we fail to recognize that if we were to take into account the existence of the advanced portion of every quantum process it would simply no longer be necessary to assume that all paths from either the retarded or the advanced portion of history are somehow being followed all at once, because the simple fact that the advanced portion of the process can be different from the retarded portion while still obeying the macroscopic constraints of the experiment, is sufficient to guarantee that it is only when all possible paths are taken into consideration that the right predictions concerning the probability of occurrence of the whole process will be obtained. Those considerations are also valid in the case where we are 78 dealing with an entirely predictable outcome involving one single event (like the non-arrival of a photon at a detector located in one of the dark regions of an interference pattern), even if such a time-symmetric process cannot involve all interfering paths all at once (but merely two of them), because in the context where probability amplitudes are involved it is possible for the probability of one single event to be null, or for the event to be absolutely certain given that the presence of phase interferences allows a complete history (composed of a retarded and an advanced portion) to contribute negatively to the final probability of a process and as I will explain below this actually allows all the different alternatives to contribute to the probability of one single process. Another advantage of such a realist time-symmetric interpretation is that it allows to enforce the global consistency of factual aspects of the world in a way that is particularly significant in the case of entangled systems. Indeed, if one is to assume that the retarded and the advanced portions of history share the same macroscopic conditions (a hypothesis whose validity will be justified in section 12), then the result of a measurement performed on one of two entangled particles must be compatible with both the experimental conditions of this measurement and those of any measurement that may eventually be performed on the other particle, because in any reference system (from the viewpoint of any observer) there is as much causal influence from the first measurement on the second, as there is from that second measurement on the first, due to the existence of both forward and backward propagated causal influences. What is apparent here, therefore, is that a quantum mechanical description of reality involves some form of causal circularity of the kind that would arise if time travel was a possibility. But, as I mentioned in section 4, the only problem that may arise in the context where such closed causal chains would be considered a possibility does not have to do with the absence of free-will that they would perhaps render manifest (which is significant merely from the viewpoint of our conventional, unidirectional experience of time), but with the hypothesis that global consistency (the idea that all facts must agree with one another under all circumstances) could be violated. What remains to understand, therefore, is how it is exactly that this requirement is enforced at the level of time-symmetric quantum mechanical processes. It should be clear, first of all, that quantum theory does appear to be the appropriate framework for implementing global consistency, as it already allows to appropriately handle the closed causal chains occurring as a re79 sult of the existence of antiparticles as negative energy particles propagating backward in time. Thus, the usual approach to estimating the probability for a process to occur, which amounts to sum up the probability amplitudes for all possible ways by which a process can occur and then to take the square of this complex number, appears to allow global consistency to be predicted, only, it is not completely clear why, in effect, such an annoying procedure allows to produce consistency in the context where backward causation would be assumed to constitute an unavoidable aspect of a quantum mechanical description of reality. To understand what is going on, it is necessary to first recognize that a complete quantum process (one to which can be attributed a certain probability) actually consists in the combination of a retarded history unfolding from a given past state toward a given future state through one particular unobservable path forward in time, followed by an advanced history unfolding from the same future state toward the same past state through another particular and still unobservable path backward in time, or vice versa (as it may be the advanced history that is 'followed' by the retarded history backward in time). Thus, it is essential that the two possible segments of history, which are unfolding in opposite directions of time, be combined to actually give rise to one complete time-symmetric process to which can indeed be assigned a definite classical probability (instead of a mere probability amplitude). It would then be by adding the probabilities for all such combined, time-symmetric processes which are compatible with the observable past and future experimental conditions that we would obtain the final correlation probability. Now, even though such a procedure can be shown to produce transition probabilities equivalent to those of the conventional approach under similar circumstances, the problem is that it is not always possible to obtain meaningful results from such a procedure, unless one limits the scope of the questions that can be asked concerning the history of a system and its environment by adopting a suitable coarse-graining. It is only under such conditions (when certain details are ignored about the processes which are described) that classically meaningful probabilities can be obtained for various alternative histories. In the context of the conventional, modern interpretation of quantum theory (the consistent histories interpretation) what this would be assumed to mean is that when described with a maximum level of detail certain histories are simply nonsense and cannot be considered to actually occur as real physical phenomena. This would be the case, for example, of the history of 80 a photon as it goes from source to detector in the conventional double slit experiment, when the particular path taken by the particle is not subjected to direct observation, because it seems that one cannot define a classically meaningful probability for any such a history. But I believe that this selfimposed and somewhat arbitrary restriction concerning what can be considered real of reality itself is not appropriate and arises merely because we do not understand the profound significance of those apparently inconsistent probabilities, which only emerges when they are considered in the context of a fully time-symmetric conception of reality. It must be clear that what I find problematic about the formalism of consistent histories is the restriction that is usually imposed regarding what can be meaningfully described of quantum reality, not the logic of the conclusion made in the context of the conventional interpretation of quantum theory concerning what can be classically described of quantum reality (which histories can be assigned classically meaningful probabilities) and under which circumstances. What I'm trying to explain is that the criterion of decoherence which is imposed on families of coarse-grained histories in the context of the consistent histories interpretation of quantum theory is not really a criterion for assessing what is consistent of reality, but merely a criterion for assessing what is classically well-defined of this reality. I believe that it is incorrect to argue that common sense logic (conventional logic) is increasingly less adequate for describing reality when we consider increasingly smaller scales, even though it is certainly true that the probability that various alternative histories interfere with one another rises as those histories are being described with an increasing amount of detail (using a finer coarse-graining). Clearly either conventional logic applies or it doesn't and one cannot try to justify how nonsense could be made acceptable by relying on the confused notion of complementarity (the apparent freedom to describe the same reality with mutually incompatible concepts). The problem with this conventional interpretation of quantum strangeness is that it would cease to provide a logically consistent picture of reality12 precisely on the scale where the unconventional phenomena we may want to understand are occurring (the quantum scale). But this difficulty arises merely when we fail to understand that conventional logic applies not to 12It must be clear that my use of the term 'consistency' does not have the meaning it has in the context of the consistent interpretation of quantum theory where it refers merely to the classical definiteness of a history. 81 the observed phenomena themselves, but to the unobservable, unique reality which consists in each of the two portions of history that unfold in opposite directions of time for every process on any scale. The fact that conventional logic still applies on the classical scale, even from a more traditional viewpoint can therefore be understood to result not from the fact that reality is only consistent on such a scale, but from the fact that the two time-reversed portions of history must always be the same on such a scale (for reasons I will explain in section 12). Anyhow, what is usually considered undesirable of the probabilities that may sometimes be obtained for a combined pair of histories is that they can assume negative values, or normalized values larger than one. I believe that one can only begin to understand why the existence of negative probabilities in the intermediary stages of the estimation of a final transition probability is not catastrophic when one recognizes that it is precisely the circularity of all quantum causal chains (that follows from the existence of an advanced portion to every quantum process) that enforces the consistency of the present with a given future (while the retarded portion enforces the consistency of this future with the known present, as is usually understood). In the context where one must take into account the existence of quantum interferences it appears necessary, in effect, to impose on the quantum phase that it returns to a value that is as close to its initial value as possible after a complete, time-symmetric process has occurred (once forward and once backward in time) if this unobservable parameter is to have any physical significance. Of course this initial value can be any arbitrarily chosen one, as only changes to the phase and the amplitude of the wave function, occurring as a result of the evolution that takes place during the retarded and advanced portions of a process, are significant. In other words, if the phase was originally π radiant it cannot end up being 2π radiant (if the amplitude of the wave function remains unchanged) after a complete time-symmetric process has taken place, otherwise a contradiction would have occurred, as those two phases are the perfect opposite of one another and therefore correspond to two maximally distinct unobservable initial conditions (of the phase itself) which can only belong to two mutually exclusive instances of physical reality. In the present context, probabilities larger than one merely constitute another facet of the same problem, because, as Feynman pointed out [14], a greater than one probability for a given process to occur is equivalent to a negative probability that the same process will not occur. What I'm suggesting, then, is that whenever the probability for a process to occur in one 82 specific way is negative one must assume that if the process would occur in this specific way it would diminish the chances that the observable macroscopic conditions which would have actually given rise to it existed in the first place, thereby making the sum of probabilities for all the possible ways the process could occur smaller than it would otherwise be, given that it would make the initial conditions themselves less likely to have occurred (because the probability that the process would occur in such a way would decrease the likelihood that the process may occur in any possible way instead of increasing it as is usually the case). Thus, when a pair of minimally coarse-grained histories (composed of both a retarded and an advanced portion) has a negative probability of occurrence, this can be interpreted as diminishing the chances that the process involved may occur by following any possible path (even those for which there is no destructive interference). Likewise, when the probability for an individual pair of minimally coarse-grained histories to occur is larger than one, this can be interpreted as decreasing the chances that alternative initial conditions existed, which is another way to say that it would actually increase the chances that the actual initial conditions that gave rise to this history did indeed occur. Thus, one cannot just speak about a reduction or an increase in the probability that some future outcome is realized when some past conditions are observed, but also about a reduction or an increase in the probability that a given set of initial conditions could be observed to occur whenever a given set of future conditions are satisfied. Those additional contributions to the conventional measures of transition probability are dependent only on the degree of compatibility between the unobservable initial quantum phase and the quantum phase that is obtained as a result of the phase change that occurs in the course of the whole time-symmetric process (the combination of a retarded and an advanced history). From this viewpoint, therefore, a process is allowed to influence the very probability that certain boundary conditions necessary for its occurrence may be found to exist, not just in the future, but in the past as well. In the context of a time-symmetric interpretation of quantum theory it should actually be expected that such effects would arise given that there is necessarily as much influence of the future on the past as there is of the past on the future, which forbids the initial macroscopic conditions to be determined independently from what happens in the unknown future. What transpires therefore is that when the retarded and advanced portions of the history of a given unobserved physical attribute are such that 83 they require changes to the quantum phase that would not allow it to return to its initial value (as would occur when the phases associated with the two possible paths in a double slit experiment interfere destructively), then one must assume that the probability that those very initial conditions themselves could be observed to occur is reduced in proportion to the magnitude of this contradiction and given that those initial conditions have 'already' occurred then the pair of minimally coarse-grained histories with which is associated a negative probability would merely contribute to reduce the probability that the process is actually observed to take place following any possible paths forward and backward in time. As a result, even though the probability that a given history is observed to occur must in effect be a positive number smaller or equal to one, any unobserved portion of history that contributes to determine this final probability could have a negative probability of occurrence, or a probability larger than one and still be describable as consistently as any other portion of history. The proposed interpretation, therefore, does not require to reject as meaningless the histories with which are associated negative probabilities, as those time-symmetric processes can be interpreted in a realist way and do not differ fundamentally from other time-symmetric histories (occurring once forward and then backward in time), given that they do contribute in a meaningful way to establish the final, positive transition probabilities for a given sufficiently coarse-grained (macroscopic) history to occur. It is merely the fact that negative probabilities can only arise when quantum interferences are actually present, while in general interferences are only apparent when the actual path followed by a quantum system is not subjected to direct observation, that explains that we appear to be justified to assume that negative probabilities cannot arise and must be physically meaningless, because it is true that the validity of theoretical estimates regarding the probability that such individual portions of history occur cannot be confirmed through direct observation, as a matter of principle. Once again, it is merely the fact that our experience of reality is limited to the portion of it that is directly accessible to our senses that explains that we have never experienced negative probabilities and that we view them with suspicion, as if the histories they characterize could not be real. What I have explained is that this self-imposed limitation concerning the scope of a realist description of quantum phenomena is not necessary and once this is understood, then all the histories that contribute to establish the statistics of quantum processes can be given the status of physical reality as required. 84 Thus, the occurrence of negative probabilities in the context of the realist, time-symmetric interpretation of quantum theory I'm proposing should not be considered a problem all by itself, because it can be assigned a clear meaning as long as those negative values do not show up in the final results of the estimation of a transition probability for an observed history. In fact, even from a purely formal perspective, the proposed approach may be considered more adequate than the traditional method, given that it always involves only the summation of real probabilities (real but possibly negative numbers) instead of probability amplitudes (complex numbers with no independent physical meaning). In any case, it is now apparent that the most important weakness of early time-symmetric quantum models (such as Cramer's transactional theory discussed in section 6) is that they required assuming that the advanced waves which are part of a complete 'handshake' process propagate backward in time in the same portion of history as that in which the retarded waves propagate forward in time, instead of occurring as part of an independent segment of history, which would forbid any interaction with the processes taking place in the retarded segment13. It is important, therefore, to understand that even though the retarded and advanced portions of history share macroscopic experimental conditions and even though their durations also correspond to a certain extent, they do not take place simultaneously (even in the opposite order) in the same segment of history (how this can actually be made reasonable will be discussed in section 12). It is precisely the fact that we are dealing with two different portions of history that allows the principle of local causality to be observed despite the fact that the model proposed allows non-local correlations to arise, because, in effect, the particles which are propagating in one of those two portions of history do not interact with those which are propagating at the corresponding moment in the time-reversed portion of history. As a result, this alternative approach allows to do away with the advanced waves as real classical waves and this means that, contrarily to the early time-symmetric models, the interpretation of quantum theory proposed here is not a particular instance of classical 13For those reasons the time-symmetric interpretation of quantum theory proposed here cannot form the basis of a solution to the problem of advanced waves, because in the present case we are not dealing with advanced propagation as it could be observed to occur in the same portion of history and this shows again that the problem of the absence of advanced waves must be considered independently from the problem of the interpretation of quantum theory. 85 hidden variables theory. This is certainly a suitable characteristic of the proposed model because, as I previously mentioned, it is now understood that in order to reproduce the results of certain experiments in which quantum entanglement is involved (the EPR-type experiments which will be discussed in the following section), classical hidden variables would need to violate the principle of local causality, which would require the existence of complex and highly unnatural mechanisms. I believe that a similar unnatural coordination of influences, now affecting experimental conditions, would be required if we were to assume instead that quantum non-locality is an illusion attributable to what has been called absolute determinism, or the idea that every choice of measurement is determined in advance as a consequence of deterministic evolution. It is clear to me, indeed, that from a physical viewpoint this latter proposal merely constitutes the same classical hidden variables theory in disguise, because in the absence of non-local influences the puzzling predetermination which it requires would remain unexplained and this means that the hypothesis would simply be inadequate. What adds to the difficulties facing all such interpretations is that it was experimentally demonstrated not so long ago [15] that the classical hidden variables hypothesis is in fact incompatible with the results of certain measurements that can be performed on a single quantum object, for which entanglement is irrelevant. Basically, what those experiments are designed to achieve is a measurement of five pairs of attributes of a photon that is in a state of superposition of three position states. When the experiments are performed it emerges that the statistical distribution of measurement results is incompatible with what is allowed in the case where classical hidden variables (of the naive realist kind) determine the outcome of those measurements, because the choice of which pairs of attributes are to be measured affects the outcome of the measurements. What those results were immediately assumed to imply is that what is not measured of a quantum system cannot be considered to exist independently. But it must be clear that, in this particular case, just as in the cases where quantum entanglement is involved, what has really been demonstrated is not that there cannot exist a unique reality in between measurements, but that this unique reality cannot be of a classical kind (it cannot involve only a unique retarded history for the unobserved physical attributes). I have already explained, however, why reality cannot be uniquely characterized, in the classical sense, in between measurements and those devel86 opments clearly show that it is not necessary to reject the hypothesis of a unique reality for the retarded and advanced portions of a process, regardless of whether a physical attribute is being measured or not. In the case at hand it seems that what is happening is that the different possible measurements are affecting the constraints which are exerted on the unobserved retarded and advanced portions of history and are thus allowed to give rise to different patterns of interference for some related physical attributes, as also occurs in the case of entangled systems (more about this in the following section). But the conclusion that there is no reality independent of what is revealed by measurements is not made unavoidable by those experiments, even if it is certainly true that this reality cannot be classical and must be conceived of in accordance with the requirements of time-symmetric causality. It is also the fact that reality is not classical, even though it is unique in a certain sense, that allows to explain the otherwise puzzling thought experiments proposed by Yakir Aharonov, Jeff Tollaksen, Sandu Popescu and their colleagues [16]. Those experiments involve sending three electrons on two possible paths in an interferometer and then effecting some post selection (see section 6) on some of the electrons to influence their past states backward in time and in the process give rise to quantum correlations between the states of the electrons involved. What is remarkable here is that according to quantum theory even if you send three electrons at a time in the interferometer, no two electrons will ever appear to have gone through the same arm of the interferometer during any single trial, as if it was possible for three electrons to simultaneously go through two possible paths without any two electrons ever going through the same path. But the paradox associated with such a thought experiment only arises when we fail to understand the fact that the trajectory of the electrons is only unique in the sense discussed above. What would be proved by those experiments (if they were actually performed) is merely that when none of the particles are directly observed to follow one path, then no pair of particles can in effect be determined to follow the same path classically, that is, for both the retarded and the advanced portions of the process. But this does not mean that a given pair of particles may not be following the same unobservable paths during either the retarded or the advanced portions of the process, as long as those trajectories actually remain unobserved, which is precisely the outcome of the condition imposed on the final state in the experiments discussed here. No three particles can go through two different paths without two going through the same path, 87 only, particles can go through no specific path during the complete timesymmetric process and obviously if no particle goes through a single path from a classical viewpoint, then no pair of particles can go through a single path either (from the same viewpoint), even if from a realist time-symmetric viewpoint there are always at least two particles following the same unique, but unobservable path either forward or backward in time. Finally, it is also important to mention that even though the energy signs of the particles present in the advanced portion of history considered here are well-defined relative to the energy signs of the particles present in the retarded portion of history, in the sense that any positive energy particle that is observed to be propagating forward in time would be related by the observable macroscopic conditions to a negative energy particle propagating backward in time (those assumptions will be justified in section 12), this does not mean that all the particles present in the retarded portion of history would have positive energy signs, while those present in the advanced portion of history would have negative energy signs. In fact, in each of the two corresponding segments of history there may be both positive and negative energy particles propagating in any direction of time and all that we can assess is that the positive energy particles which are observed to propagate forward in time in one of the two portions of history must have negative energy as they are observed to propagate backward in time in the corresponding time-reverse portion of history. It should be clear, therefore, that there is no correspondence between the particles present in the advanced portion of history that is required to exist by the time-symmetric formulation of quantum theory discussed here and the unobserved negative action particles whose properties were described in chapter 1 of [1] and which actually propagate in the same segment of history as ordinary positive action particles, even though they also have their own counterparts in the advanced portion of history, as any other matter component. 9 Quantum entanglement and non-locality Before I get onto the quantum measurement problem and share the most significant insights I have gained while working on the problem of the interpretation of quantum theory I would like to return to the important question of the viability of a realist description of quantum phenomena in the context of the existence of non-local correlations. It is possible, in effect, to apply 88 the interpretation which was developed in the preceding section to provide a realist and yet locally causal description of the processes taking place in the course of an experiment of the Einstein-Podolsky-Rosen type involving pairs of entangled photons. What I will explain is that the experimentally confirmed violation of Bell's inequality does not make unavoidable the conclusion that instantaneous action at a distance must be an integral aspect of any realist interpretation, in the sense that we are still allowed to assume that no influence can propagate faster than the relativistic speed limit in the course of the retarded and advanced portions of history, when those histories are conceived as taking place independently at two different epochs. The fact that I'm allowed to actually explain the existence of non-local correlations in such a way is significant, because, contrarily to what is often believed, quantum non-locality is not only unexplainable from a classical perspective, it is not explainable at all in the context of the conventional interpretation of quantum theory. To help visualize the phenomenon of quantum non-locality we may consider, for example, a simple interferometer experiment where the source, instead of emitting one photon in one direction, would emit a pair of entangled photons which would be allowed to travel in opposite directions along one or another of two possible trajectories in each of which they would meet a mirror that would direct them toward a unique detector that would allow to determine either the presence of interferences between the two paths available to a given photon (by simply detecting the arrival of the photon), or the exact path a photon took on its way to the detector (through a measurement of the photon's angle of impact). What's particular with such an interferometer experiment is that when we choose to measure the angle of impact of one of the two photons we also inevitably determine which path the other photon took in its own otherwise independent part of the experiment, so that even if we try to measure interferences between the two paths available to this other photon we do not observe any. This correspondence is made unavoidable by the fact that when the angle of impact of the first photon is determined, the angle of impact of the second photon must be the exact opposite of that of the first photon in order that momentum be conserved in the initial state. Thus, it is only when we choose not to determine the exact path taken by any of the two photons that we are in effect allowed to observe the presence of interferences between the two paths available to each of them. From this perspective it is apparent that when we are dealing with entangled systems (when the phases associated with the propagation of two 89 otherwise independent systems have become entangled as a result of local contact) the choice of whether to measure an angle of impact or the presence of interferences between multiple paths is not made locally, but constitute a global property of the experiment, because whenever an angle of impact is measured for one of the entangled photons it is no longer possible to measure interferences between the multiple paths available to the other photon. All that must be understood is that what enforces the global character of this choice of measurement is the existence of an advanced portion of history. Indeed, whenever we choose to determine the exact path taken by one of the two photons, the result of any measurement performed on the other photon must reflect that choice, because the effect of the measurement performed in the future on the first photon propagates backward in time (through the advanced portion of the first process) to the initial entangled state and then forward in time (through the retarded portion of the second process) to affect the measurement result performed on the second photon, even when this measurement is separated from the measurement performed on the first photon by a space-like interval. It must be clear that this backward causation does not determine what the result of one particular measurement is whenever a measurement is performed on the other particle (this is the outcome of conservation laws), it only determines if interferences can actually be observed at any of the two detectors. Indeed, you may recall my earlier discussion regarding the fact that in the context of the proposed realist time-symmetric interpretation of quantum theory it becomes possible for the observable macroscopic conditions imposed on a quantum process in both the past and the future to be influenced by the very process itself. What I have explained is that those conditions should allow the quantum phase to get back to a value as close to its initial unobservable value as possible after a complete time-symmetric process has occurred (once forward and once backward in time) if the conditions necessary for the process to happen are to themselves be allowed to have occurred in the first place. When the outcome of a complete time-symmetric process along one possible trajectory results in a final phase that is interfering destructively with the initial phase, then negative probabilities arise (with an amplitude determined by the phase shift involved) which contribute to decrease the final measurable probability that the observed process actually occurs by following any of the possible trajectories available to it, because the probability that the (initial and final) conditions necessary for the process to occur in such a way are satisfied is then itself reduced. 90 But it is exactly in such a way that non-local influences are conveyed between the two particles forming an entangled pair in the experiments discussed above, because under such conditions interference effects observed at one location (on one particle) depend on the experimental conditions observed at a different location (on a different particle), simply because the phase changes which arise in the course of those processes are occurring as a result of the boundary conditions applying on the complete time-symmetric process and not just on some portion of it associated only with one or another particle. What those experiments (during which a violation of Bell's inequality is observed to occur) have revealed is that it is possible to demonstrate the existence of such non-local correlations which cannot be attributed merely to the conditions imposed by conservation principles on the total momentum (or polarization state) of the two entangled photons in the context where they are created by pair in the initial state (which merely requires that one photon goes through the upper path when the other goes through the lower path). In any case, as soon as the angle of impact of a photon is measured at one or the other detector in the experiment described above, then it is no longer possible to measure interferences between the two possible trajectories for any of the two photons, because the retarded and the advanced trajectories are then exactly the same in all possible cases and for each photon, which means that there is no phase change for a complete time-symmetric process. If it seemed impossible from a conventional viewpoint to assume that the photons propagated along a unique trajectory prior to such a measurement, it is because the measurement is what determines whether interferences will be observed or not for both particles and when interferences are indeed present the trajectories of the two photons are no longer well-defined from a classical viewpoint, which has always been interpreted to mean that there is nothing we can say of reality under such conditions. But what emerges from the more consistent perspective adopted here is that it does appear possible to assume that each photon follows a unique, causally independent trajectory as it propagates toward its detector, from the moment when it is emitted by the source and right up to the moment when a measurement is performed on it, contrarily to what would appear to be allowed according to the orthodox interpretation of quantum theory, only, it turns out that in certain cases (when interferences are present) this unique trajectory can be different for the retarded and the advanced portions of the propagation process, so that it cannot be argued that the photons are always in a classically well-defined 91 position state as they propagate toward their detectors. What happens, therefore, is that the presence or the absence of quantum interferences between the multiple trajectories available to one of the two entangled photons as it propagates toward its detector is determined by the choice of which measurement is performed on the second photon in the future, as a consequence of the existence of the backward in time propagating influences attributable to the advanced portion of the history of this second photon. Thus, the trajectory of the first photon must already be either classically well-defined or quantum mechanically superposed right from the moment when the particle emerges from the initial entangled state, in order that those conditions actually agree with the observational constraint set by any measurement that could be performed on the second photon in the future. Any measurement performed on the first photon itself must, therefore, agree with the constraints set by the choice of which measurement is performed on the second photon in the future. But, given that there is also an advanced portion of history that is experienced by the first photon, then the classical or superposed nature of the trajectory followed by its entangled counterpart as it propagates in the future toward its own detector is also required to agree with the choice of measurement that is to be performed on the first photon itself in the future. As a result, even if the experimental conditions that determine which attribute will be measured by the detectors are changed once the photons have already been emitted, the initial retarded and advanced states will already be such as to reflect that future change and will evolve in accordance with those altered conditions, because the initial retarded states of the two entangled photons are influenced by the choice of measurements performed at each detector in the future (through the advanced portion of the processes). Thus, the whole experimental setup with which the photons will interact in both the past and the future determines what is allowed to happen to both of them, even as they just leave the source in the forward propagating version of history, before they interact with a detector. It should be clear, therefore, that the measurement that is performed on any one particular photon cannot alone and in every circumstance determine what happens to both photons, as one must assume from a conventional viewpoint, because unidirectional causality is not involved in conveying the influence that propagates along the advanced portions of the processes, from each future measurement back into the initial entangled state. There is no additional complexity involved here (no information carrying 92 signal needs to be sent backward in time). Each measurement determines the state of a photon at the moment when this measurement takes place, but this choice of measurement also influences the state of the photon as it reaches the source in the advanced portion of history, just as when a past state influences a future state, only now backward in time and without entropy increase. But, given that in the above discussed experiments this past state is an entangled state which results in the two photons sharing a common phase, then it follows that the past state of the first photon is also causally influenced by the choice of measurement performed on the second photon in the future, in a way that is not that different from the usual manner by which influences are propagated forward in time, except that information cannot be carried by the effects so produced, given that entropy cannot rise as the causal influences propagate in the past direction of time. This is all made unavoidable in the context where the retarded portion of history experienced by any of the two photons must share the same observational constraints as apply to the advanced portion of history that is also experienced by any of the two photons (for reasons I will discuss in section 12). What this shows, is that instead of insisting that the wave function may not be real, or that it merely represents the state of knowledge of one particular observer which must be actualized on contact with information from another, previously independent observer (as one postulates in the context of an interpretation of quantum theory such as 'QBism'), we should instead recognize that the wave function does provide our best account of the exact quantum state of a system at any time, but that there are two such states (associated with two actual histories), one of which is evolving forward in time and the other of which is evolving backward in time. In such a context the fact that the wave function may sometimes appear to be a subjective property, dependent on whether information concerning the conditions of a future measurement to be performed on a system is available or not, can be seen to be a mere consequence of the fact that we cannot know in advance what the backward in time evolving state is before we obtain information about that future measurement, even though it already affects the present state of the system. The adequacy of this viewpoint appears to have been confirmed by the fact that the process of actualization of quantum potentialities is now understood to be the consequence of concrete changes that take place in the environment with which a system becomes correlated under very specific conditions (those responsible for triggering decoherence), thereby contradicting the hypothesis that it might be a subjective phenomenon. 93 In any case, what must be understood concerning the interferometer experiment discussed above is that the unique trajectories of the entangled photons are only required to be made identical in the retarded and advanced portions of history for the two photons when it is the angle of impact of the photon that is measured at one or the other of the two detectors and not the interferences. Indeed, even if what happens at the source is influenced through backward causation by what occurs at the detectors, if the two detectors are set to determine merely the presence of quantum interferences, the measurement performed by the second detector cannot determine the trajectory that was not determined by the first one and neither is the measurement performed by the first detector allowed to determine the trajectory that was not determined by the second one, given that neither of those two measurements allow to determine through which slit one of the photons went on the way to its detector and this must be reflected in the unobservable and interfering nature of the trajectories of both photons as they propagate between the source and the detectors in the retarded and advanced portions of history. Thus, if one of the two photons in an EPR experiment of the kind described above is found to have traveled along one particular path as a result of the choice of measurement performed on it, then both photons will propagate along one particular path during both the retarded portion of history (away from the source) and the advanced portion of history (toward the source). It is only when none of the two photons in an entangled pair is experimentally determined to have traveled along one or another of the two possible paths (as a result of the choice of measurement to be performed on both particles) that it can no longer be assumed that the trajectory of both photons is classically well-defined and in such a case interferences between the multiple possible trajectories would indeed arise. This does not mean, however, that the two photons would not have unique and corresponding trajectories (when one photon goes through the upper path, the other photon must necessarily go through the lower path) in both the retarded and the advanced portions of the process, merely that those trajectories would remain unobservable and could be different for the same photon in the two portions of history. For any type of EPR experiment it is only the attribute of a particle that is correlated to that of the other particle by the conservation principles applying on the initial state (which in the example discussed here would always be the one-parameter angle of impact associated with the momentum direction of the photon) that must necessarily be classically determined for one particle 94 when it is so determined for the other particle. As I mentioned above, what justifies the widespread belief that the unobserved attribute of the photons in an EPR experiment were in no state at all before at least one of the two measurements was performed is simply the fact that when neither detectors are set to measure the correlated attribute, interferences between multiple intermediary states can arise which cannot be classically described. But once we recognize the influence exerted by the advanced portion of the processes involved, then it once again becomes possible to consider that the photons follow unique trajectories at all times in both the retarded and the advanced portions of any one particular history, even when it is not the correlated attribute (the angle of impact) which is measured at any of the two detectors. This is certainly appropriate given that it is not possible, in general, to tell which of two measurements (on one or the other photon) determines the time at which the intermediary states could be considered to no longer interfere and to actually become real14. The only requirement, therefore, is that there is always a correspondence between the trajectories followed by the two photons in both portions of history (such as if one photon goes through the upper path, then the other must go through the lower path), as we are in effect dealing with correlated states, but unless it is the state of the correlated attribute that is actually measured at one of the two detectors it is not possible, as a matter of principle, to tell what those corresponding trajectories really are in any particular case. What's interesting is that once the validity of this viewpoint is recognized it follows that the idea that the concept of a localized particle may no longer be valid in the presence of quantum entanglement and that it should be replaced by a holistic concept of reality at a fundamental level is no longer justified and actually loses most of its appeal. At this point it is necessary to mention that I'm perfectly aware of the fact that Murray Gell-Mann (among others) once argued that the idea that EPR-type experiments imply a certain form of non-locality is merely a distor14This is easier to understand in the context of EPR-type experiments involving pairs of linearly polarized photons where it is merely the difference between the angles of polarization which are measured by the two detectors that determines if there are interferences or not. The fact that in the experiment describe above one of the detectors may appear to be privileged in determining the presence or the absence of interferences at both detectors when only one of the detectors measures the state of the correlated attribute should not be considered to undermine the validity of the hypothesis that the classical definiteness of the trajectories is in general determined by the configuration of both detectors. 95 tion of reality, because (so he argued) what occurs when the angle of impact is measured for one of the two photons is merely that we find ourselves in one particular 'branch' of history where both photons happen to follow a definite trajectory. What is problematic here, however, is not merely the fact that such an explanation would depend on the validity of the contradictory notion that a photon goes at once through all available paths (in many 'branches' of the same history until a 'splitting' process takes place and all potentialities are actualized all at once, but presumably no longer interfere with one another), the real difficulty has to do with the fact that from such a viewpoint unnatural coincidences would still be observed that would remain unexplained, because the choice of which measurement is to be performed on one of the two photons affects the outcome of measurements performed on the other photon in a given 'branch' of the universe's history and it is not possible to explain how even such a coordination of measurement results would occur in a certain branch of history where the global outcome would in effect be observed. The truth is that this rejection of quantum non-locality is equivalent to the absolute deterministic view discussed in the preceding section, given that it requires one to assume that it is possible for preexisting correlations to exist which are not attributable to any locally propagated causal influence. It is quite ironical, therefore, that is was suggested that this viewpoint constitutes an alternative to classical action at a distance, because, as I previously explained, in the context of a realist interpretation absolute determinism is actually a form of classical hidden variables theory. It is now possible to be more specific regarding why it is that we would not be justified to assume that local causality is violated when a state vector is reduced in a more general context, as when a photon is emitted by a source, whose propagation is described by an expanding spherical wave function, and its presence is detected in one particular location, thereby affecting the wave function over the entire volume. I believe that if the conclusion that the principle of local causality is violated under such conditions is not unavoidable, even when we acknowledge the fact that the wave function always provides the most accurate description of the state of a quantum system, it is because this phenomenon can be described using the same realist, time-symmetric approach which I used to explain the origin of quantum non-locality as it arises in the case of entangled systems and which involves two histories (independent from the viewpoint of local causality) unfolding in opposite directions of time. What happens is that the spreading wave function allows to accurately 96 describe the results of any measurement that would reveal the existence of interferences between the multiple paths through which a photon might have traveled as its position remained unobserved and this requires that the wave function does indeed provide the most accurate account of the situation before a position measurement is performed, but only as long as such a measurement is not, in effect, performed, because under such conditions the retarded and advanced portions of the propagation process might take place along different paths. However, if a position measurement is effected at some point (before an interference measurement is performed on the same photon), then the trajectory of the photon can nevertheless be considered to have been unique and well-defined (to a certain extent) all the way back to the emission process given that in such a case the advanced portion of the process enforces the right trajectory (that which agrees with the future measurement) to be followed as a result of its backward in time causal influence. Now, given that what I'm proposing is a time-symmetric interpretation of quantum theory, it is important to mention that in such a context there must exist a time-reverse analog to ordinary quantum entanglement which can be shown to actually give rise to non-local correlations arising from post selection (the phenomenon discussed in section 6 by which the future state vector in a two-state vector formulation of quantum theory is allowed to influence the evolution of a quantum system backward in time). Thus, even in the apparent absence of ordinary quantum entanglement established through local contact in the past, it should be possible to observe the existence of nonlocal correlations of the same type as arise in a more conventional context when it is a future state that is entangled in a certain way as a result of post selection. From my viewpoint the fact that those correlations do not allow faster-than-light communication can once again be explained as being a consequence of the fact that the constraint of global entanglement discussed in section 3.9 of [1] requires entropy to decrease in the past for all macroscopic processes which are occurring in the same universe, which means that no causal signal can propagate toward the future and then backward in time to a distant location, as a result of post selection, even if causality does operate both forward and backward in time at a more fundamental level. But, despite what one might be tempted to believe, the possibility that such future entanglement may arise does not mean that every measurement result obtained at the present moment must be correlated to every other measurement result obtained at remote locations as a result of post selection, because contrarily to the situation we have in the far past, most elementary 97 particles present in the remote future are not in contact with one another at any point and therefore, even if those effects do exist, they should not be as commonplace as the effects arising from ordinary, past entanglement. In fact, the very significance of the cosmological constraint of global entanglement is that every particle of matter or radiation in the universe must have been entangled with at least one other particle, which was itself entangled with another particle, and so on, in the maximum density state of the Big Bang. But no such a condition exists for the future (especially in the presence of negative energy matter, for reasons I have explained in section 3.9 of [1]) and given that we would be justified to expect that no low-gravitational-entropy Big Crunch will ever occur, then it would seem appropriate to conclude that future entanglement is not as essential a requirement for the universe as the existence of a globally entangled state from which all matter emerged in the past. It is now possible to reflect back on the traditional positions regarding the significance of EPR-type experiments. If we consider first of all the orthodox view and Bohr's position, it amounted to consider that the detection of the angle of impact of one of the two photons (that which happens first) is the only cause of the reduction of the state vector (we would now say the decoherence process) that takes place at one or the other detector. The problem with this viewpoint is that if the wave function is considered to be a real entity, then instantaneous action at a distance appears to be required, which is why the orthodox interpretation retreated into its idealist position, according to which it simply does not make sense to speak about a reality behind observed phenomena (which may allow to avoid the conclusion that this reality is non-local). The position held by Einstein and the advocates of a realist approach was that this rejection of scientific realism is not acceptable and that quantum theory must simply be wrong or incomplete, given that it appears to require instantaneous action at a distance when the consequence of a measurement on one of the two photons spreads to its entangled counterpart. Basically, then, one position required assuming that there is no reality, while the other required assuming that there is no entanglement. I believe that both positions were inappropriate in some way, but also accurate in a distinct way15. Clearly quantum theory and quantum entanglement are 15It has been argued by some of the originators of the consistent histories interpretation of quantum theory that Einstein was misguided in trying to uphold a certain requirement of scientific realism to which the conventional interpretation of the theory does not conform, because it must be the theory that determines what is true of reality, even when it appears 98 there to stay, but what I have tried to explain is that scientific realism is not optional either and can be accommodated without requiring instantaneous action at a distance, when time-symmetric causality is recognized to be an essential aspect of this physical reality. 10 The quantum measurement problem It is usually recognized that the two main conceptual difficulties with which we are faced when trying to formulate a consistent interpretation of quantum theory are the existence of non-local correlations and the absence of an objective criterion for judging when it is that the multiple interfering potentialities characterizing the state of some unobserved dynamic attribute of a quantum system are actualized to a given definite value, as happens when a measurement of this attribute is performed. In the preceding sections I have offered a viable solution to the problem of quantum non-locality in the context of a realist interpretation of quantum theory based on the requirement of time-symmetric causality. But while progress was achieved in the last few decades in identifying the conditions necessary for the decoherence process to occur, it remains that we haven't yet been able to determine exactly what is responsible for the persistence of quasiclassicality that is observed to characterize the evolution of quantum systems when they become entangled with their environment following a measurement. The currently favored approach proposed for solving the quantum measurement problem plays a role that is much the same as the late nineteenthcentury approaches for solving the problem of the origin of thermodynamic time asymmetry through the use of statistical methods. Indeed, at some point Boltzmann thought that he had solved the problem of the origin of the arrow of time, because he had achieved significant progress in identifying its true origin. But as we now understand it appears that he had not really provided a satisfactory explanation and that the remaining difficulties had not even been clearly identified. Today it is widely believed that the problem to require contradictory descriptions of it to be valid together at the same time, as when we are trying to determine which of two measurements is responsible for determining the state of a pair of entangled particles. But I believe that it is rather this position which is misguided and this precisely because it constitutes an attempt at limiting what can be consistently described of reality based on practical limitations which are attributable merely to the inadequacy or the incompleteness of the proposed interpretation. 99 of quantum measurement has been solved by the recent advances achieved in identifying the conditions necessary for the phenomenon of decoherence to occur, while in fact this is not entirely correct, precisely because the consequences of thermodynamic time-asymmetry on quantum evolution haven't yet been properly assimilated. This is the problem I will attempt to circumscribe in this section and to which I will be able to provide a satisfactory solution in section 12. This will allow me to confirm, once again, that a realist approach, according to which there must exist a unique reality of some kind, independently from whether or not a system is being observed, is not incompatible with the empirical evidence that singles out quantum measurement as the necessary condition for the factual definiteness of reality. Traditionally the quantum measurement problem had to do with the difficulty we were experiencing in trying to identify the exact nature of the conditions that give rise to the actualization of quantum potentialities. In fact, the linearity of the equation that describes the evolution of the state vector made it difficult to understand how it could be that quantum interferences are in effect allowed to vanish for the dynamic attribute of a system under observation, so that they can give rise to a definite set of outcomes to which meaningful probabilities can be ascribed. Thus, there appeared to be a conflict between observations, which indicate that quantum potentialities are actualized to definite non-interfering outcomes following what we call a measurement, and the theory itself, which seems to require quantum superposition of states to persist indefinitely. From a conventional perspective it would appear that when each possible outcome of a quantum process becomes correlated with one possible state of a measuring device, if the quantum system was in a state of superposition of the observable concerned at the time when this correlation was established then the whole measuring device should also be found in a state of superposition following the moment at which the interaction took place. One of the earliest attempt at solving this measurement problem became the actual justification for the conventional interpretation of quantum theory according to which interferences arise because all possible histories occur all at once in the same universe as different 'branches' of history. What was proposed by Hugh Everett III is that there is no actualization process, but that the superposed macroscopic states of a measuring apparatus which result from its correlation with the interfering states of a quantum system are themselves occurring simultaneously in parallel versions of history, while for some reason a 'splitting' occurs following measurement, which is responsible 100 for the fact that the multiple branches of history no longer interfere with one another. The difficulty with this proposal, however, does not have to do only with the fact that it would involve logical contradictions in the context of a realist interpretation of quantum phenomena (a particle could be in one location as well as in another, in the very same portion of history), it also has to do with the fact that if all branches are followed together then there is no a priori reason why there could not be branches where a measuring device is in a state of superposition of macroscopic observables. But it is also contradictory to suggest that no actualization process takes place, while it is recognized that a splitting of branches is required to eliminate interferences following a measurement. Nevertheless, the idea endured and was later revived when it was discovered that under specific conditions the phenomenon of decoherence must give rise to a diagonalization of the reduced density operator in the basis of the attribute under measurement, which would appear to legitimate the splitting hypothesis. But, if there should be no doubt that the discovery of decoherence itself was a step in the right direction, this does not mean that the hypothesis that there may exist many continuously 'splitting' branches of history in the very same universe has been confirmed. Indeed, given that decoherence does not require the existence of those multiple branches of history, it appears that the only value that there might be in Everett's original proposal is not in providing a solution to the quantum measurement problem, but in allowing one to avoid having to explain the uniqueness of measurement results. Indeed, it is usually recognized that the only adequate purpose of the multiple branches hypothesis would be to allow one to avoid having to postulate the existence of distinct dynamical laws that would apply only during processes that can be qualified as measurements, given that when all possible histories occur all at once it may not be necessary to explain why it is that one unique measurement result is actualized among the many different potentialities, even in the context where one would consider it necessary to assume that the different histories are happening all at once in the absence of measurement (given that they are known to interfere with one another under such conditions). Thus, it is argued that when all the superposed states of some physical attribute are assumed to be actualized together in different splitting 'branches' of the same history, there no longer needs to be a cause (of unknown origin) that would give rise to the one particular outcome that is actually observed following measurement. But I do not find this argument 101 very useful, because what it would really mean is simply that we need many distinct causes for the many different outcomes, instead of one single cause for the one outcome that is actually observed. Anyhow, given that I have already argued, based on more general considerations, that it is not really necessary in order to explain the existence of quantum interferences to assume that all histories are followed all at once in the course of each and every quantum process, then it would appear that it is preferable to recognize that the unique reality we do observe during measurements is a reflection of the uniqueness of the non-classical (timesymmetric) reality that exists in between measurements, instead of trying to argue that there must be a multiplicity of measurement results, which we do not observe, that would correspond with a multiplicity of histories, which we cannot observe, in between measurements. Thus, what must be clear is that the uniqueness of measurement results is not less, but rather more problematic when one assumes that all trajectories are followed all at once when a physical attribute is not subject to measurement, which is a hypothesis that is actually necessary only in the context of this many-worlds interpretation itself. But what's even more significant is that, as I will explain below, it appears that decoherence is not sufficient to predict that what was measured remains in a definite quasiclassical state for which interferences between macroscopic attributes of a measuring device are absent and therefore it seems that we should still expect that in some of those hypothetical branches, macroscopic state superpositions would develop at some point. What I find most difficult to accept regarding the many-worlds interpretation, however, is the fact that we are required to believe that the unique character of reality that we do observe on a classical scale is just an illusion, while we are also expected to assume that the hypothesis of a multiplicity of coexisting branches of history, which has never been directly confirmed by any observation, is valid under all circumstances. In other words, we are required to assume that what we see is not the true reality, while what is a mere hypothesis that cannot yet be observationally confirmed must be considered true, even though it is clearly incompatible with what we do know about reality. It must be clear that it is not possible to assume that the existence of interferences between the multiple paths available to a quantum system simply means that in between measurements a system goes through one path in one universe and through another path in another universe, because if that was the case then we should not in fact observe interferences in any one particular universe, because by definition universes must be assumed 102 independent from the viewpoint of causality. But, it is also difficult to conceive that following a measurement an observer present in one of the multiple branches of history would not be allowed to perceive what happens in the other branches, while those branches would under ordinary circumstances be allowed to interfere with one another, thereby implying that they actually exist all at once in the very same universe. Here, again, a lot of silly things have been said to try to justify how it can be that those two requirements do not contradict one another, but in the end one must recognize that this constitutes a basic inconsistency of the many-worlds interpretation of quantum theory that invalidates it as a solution to the problem of quantum measurement. It is merely because this objection is so simple that it has avoided the attention of the most knowledgeable experts, who usually prefer to concentrate their efforts on more complex and more challenging issues. Those criticisms, however, must not be understood to mean that the hypothesis of a multiplicity of universes existing independently from one another is wrong, because in fact there may be good reasons to recognize the validity of this clearly distinct hypothesis (which is not dependent on the validity of the many-worlds interpretation of quantum theory) in the context where the weak anthropic principle appears to constitute the only possible explanation for certain otherwise unlikely properties of our universe. Thus, while it may not be possible to reject the hypothesis that an infinity of causally independent universes exist in parallel, it must be clear that the idea that many interfering branches exist in the same portion of the universe's history is a distinct hypothesis which is certainly not as unavoidable. But if a multitude of realities are to be allowed to interfere with one another so as to explain quantum state superposition, then they must definitely be present all at once in the same portion of the universe's history and therefore cannot constitute different universes, as is often suggested. Personally, I always felt that the whole idea that there may exist multiple parallel branches of history in the same universe, but that it is only when those alternative branches should become observable (following measurement of a physical attribute initially in a state of quantum superposition) that they actually 'split' and become totally independent (as a result of decoherence), therefore precluding a confirmation of their existence, has all the characteristics of a conspiracy theory and this only reinforces my conviction that the many-worlds interpretation is not good science. A truly appropriate solution to the problem of quantum measurement would then need to be based on 103 the hypothesis that reality is unique in a certain way, even in between measurements, which is the only way one could avoid having to appeal to the problematic splitting branches hypothesis in order to explain the uniqueness of measurement results. I'm aware, though, that it has been argued by Heinz Dieter Zeh [17] that the multiple branches hypothesis may be unavoidable if one does not want to have to modify quantum theory, because this hypothesis allows all possibilities to be actualized all at once as different branches, which is the only way one can avoid having to assume that a unique state of such an unobserved attribute existed before decoherence took place, that would merely have been revealed by the measurement. Indeed, it is known that, for various reasons, a quantum measurement cannot be considered to simply consist in acquiring knowledge about the unique preexisting state of an unobserved attribute. But I have explained in section 8 that the only reason why it is impossible to assume that a unique reality existed before a measurement was performed on some unobserved attribute of a quantum system is the fact that we usually assume a unique reality to be unique in the classical sense, while in fact the unique reality that would characterize a quantum process (in the absence of measurement on a certain dynamic attribute) is of a time-symmetric nature and involves both a unique retarded state and a unique and possibly different advanced state at all times, which guarantees the consistency of past evolution with any future measurement and which requires all possible intermediary states to contribute to the final probability amplitude, so that the future measurement does not allow to reveal a unique classical path through which the system would have propagated16. It is therefore simply the fact that under such circumstances the future measurement also exerts an influence on the past state preceding it (as when a system is submitted to post selection) that forbids one from assuming that a unique classical state existed in the past, independent from what hap16Contrarily to what Zeh suggests in another publication [18], the fact that there would exist a unique but unknown state prior to measurement of an unobserved attribute does not violate the condition imposed by the Von Neumann equation (the quantum mechanical generalization of Liouville's equation) that ensemble entropy should not decrease during measurement, because this conclusion would only be valid based on the hypothesis that the unknown but definite state would actually be a classical (hidden variables) state, while in a time-symmetric context when information about a measured attribute is obtained, information concerning its conjugate counterpart is lost, which allows information to be conserved. 104 pened during measurement. But it must be clear once again that this does not prevent a unique state from having actually existed at all times in both portions of history and therefore the conclusion that the unique character of measurement results can only be explained by postulating that all histories are followed all at once (in the same universe) cannot be considered valid. In any case, if reality was not of the unique time-symmetric type and the decoherent branches hypothesis was assumed to alone provide a solution to the quantum measurement problem, then an alternative explanation of quantum non-locality would have to be found, as it cannot be provided by Everett's interpretation and this is an additional difficulty for the conventional approach. Thus, I think that I have explained sufficiently clearly why it is that the frequently stated conclusion that it is just as difficult to provide decisive arguments in favor of the many-worlds interpretation, as it is to provide arguments that would invalidate the idea is not well founded, because the hypothetical, multiple branches of history are not necessary, or even adequate to explain quantum strangeness, while they also do not appear to be required to solve the quantum measurement problem (especially in the context where it is recognized that the splitting process would not, all by itself, allow one to avoid the difficulty associated with the non-local aspect of state-vector reduction). Now, some theoreticians worry about the fact that decoherence would seem to be insufficient to solve the problem of the actualization of quantum potentialities when we are considering the system under observation to be the universe as a whole (as becomes necessary in a quantum cosmological context). The problem they see is that in such a case there would be no outside environment degrees of freedom to effect decoherence, while this is known to be a requirement under ordinary conditions. What constitutes a more serious difficulty, however, is that from the viewpoint of the currently favored approach (the consistent histories interpretation of quantum theory) decoherence is insufficient to explain the persistence of quasiclassicality not just in the cosmological case, but even under more general circumstances and on a much smaller scale, as was first pointed out by Fay Dowker and Adrian Kent [19]. But this is not just a consequence of the fact that (ignoring my own contribution) we do not yet have a valid explanation for the irreversibility that characterizes the processes which give rise to decoherence, it rather appears to be a basic insufficiency of the current approach, which does not allow to predict that classical behavior would persist following decoherence, even when irreversibility is assumed to characterize the evolution of the en105 vironment degrees of freedom without explanation, due to some boundary condition of low entropy that presumably apply to the initial state of the universe at the Big Bang (I will return to this question below). The desired solution to the quantum measurement problem, therefore, must allow to predict the emergence of quasiclassicality not just on the cosmological scale, but also on the much smaller scale of measuring devices, where the conventional approach is insufficient as well. In any case, it is my intention to demonstrate that it is not necessary in order to explain the nature of the outcomes of quantum measurement to postulate the existence of distinct (perhaps fundamentally irreversible) evolution laws that would apply only during a process that could in effect be characterized as a measurement. Thus, if I do agree with the most knowledgeable authors that quantum theory, as it is currently interpreted, fails to explain the persistence of quasiclassicality that is observed to follow any measurement, I do not believe that what is required in order to address this difficulty is a modification of the basic mathematical framework of the theory that would need to apply whenever measurements are performed, as was once proposed. We cannot reject a requirement like that of time symmetry, whose value has been sufficiently demonstrated, to seek a solution in terms of fundamentally irreversible physical laws when there is no evidence that such a choice is absolutely essential for a solution to the problem of the emergence and the persistence of quasiclassicality. I still believe that it is at the level of interpretation that the appropriate solution will emerge that will allow us to solve the remaining difficulties surrounding quantum measurement. As I will explain in section 12, what the current theory needs is not so much a modification of its structure, as an extension of its meaning. It must be recognized, however, that the distinctive feature of all processes that can be characterized as effecting a measurement is indeed irreversibility. A quantum measurement is nothing but the entanglement of a particular state of some attribute of a quantum system with some distinguishable macroscopic property of its environment whose future evolution is irreversibly influenced by this particular event. The fact that no quantum interference is ever observed for irreversibly evolving systems indicates that the non-superposed nature of measurement results is related to the irreversible character of the measurement process. Thus, decoherence itself (literally the loss of phase coherence) can only occur when there is entanglement of an attribute of a microscopic system with some irreversibly evolving (entropy increasing) processes taking place in its environment (usually involving dissi106 pation), so that the phase relations that could have given rise to interferences become delocalized and are assumed to no longer be accessible to observation, as is already well understood. In fact, the ultimate manifestation of irreversibility appears to be decoherence itself. It should not be unexpected, therefore, that all measurements involve the formation of a record, given that for a record of some past event to form, entropy must be growing in the future. Indeed, the formation of a record merely consists in the production of multiple persistent and somewhat independent effects in the future, which all emerge as an outcome of one single identifiable cause in the past and this is undoubtedly a process that is asymmetric with respect to the direction of time. What this means is that there is something very tangible occurring when a quantum measurement is performed and therefore, if it is true that our knowledge of a quantum system changes when quantum potentialities are actualized, it would not be appropriate to assume that the changes which are taking place in the course of a measurement are merely subjective, because following measurement the observed attribute is no longer unique merely in a time-symmetric quantum way, but acquires the same unique value in both the retarded and the advanced portions of history. It is not difficult, in effect, to show that irreversibility is essential for a measurement to occur, while the mere complexity, or the large number of independent degrees of freedom of a macroscopic system with which an quantum system may become entangled, alone is not sufficient a condition for triggering a measurement. Indeed, it is apparent in the formalism of quantum field theory that there is a near infinite amount of structure that must be taken into account in estimating the probability amplitude of any process, as is apparent in the fact that additional fermion loops and radiative correction terms arise at every level of approximation on shorter scales. If we were to consider this small scale complexity to provide the conditions for quantum measurement to take place then it should be the case that the world would be quasiclassical down to a much smaller scale, given that all the complexity that is present at higher energies (and which can only be ignored as a result of the validity of the renormalization procedure) would allow measurement to take place long before a quantum system even has the chance to become entangled with a macroscopic system17. The situation 17I have provided strong arguments in section 3.7 of [1] to the effect that in the absence of matter there can be no persistent microscopic structure in the distribution of vacuum 107 here is similar (but not identical) to what would happen in the case where a quantum particle is embedded in an environment which is in a state of static thermal equilibrium, where nothing appears to change. In such a case the predictions of quantum theory would not merely apply as much for the future as for the past, they would not apply at all, because there would be no measurement, that is to say, no irreversible process of amplification of alternative microscopic states. From this we can only conclude that the defining characteristic of the processes that allow quantum measurement to happen is not merely their complexity, but really their irreversibility. This asymmetry must not be confused with that which also characterizes the otherwise time-reversible 'unitary' evolution that takes place in between measurements and which is made conspicuous by the fact that the predictions of quantum theory are only valid for future evolution. Indeed, the impossibility to accurately 'predict' the past arises as a consequence of the fact that only a subset of states can be actualized in the past due to the constraint of diminishing entropy that exist for this direction of time and which also applies to classical evolution. It is the fact that no such a constraint applies on future evolution that allows predictions of future transition probabilities to be valid, while predictions of transition to past states do not apply in general. In section 3.9 of [1] I explained that this constraint arises from the requirement that there exist relations of causality between all particles present in the expanding universe, which in the presence of negative energy matter implies that the initial state at the Big Bang was characterized by a condition of minimum gravitational entropy from which all later irreversibility follows. But while the time asymmetry that characterizes all measurement processes has the same origin, it is a distinct phenomenon that usually operates on a much faster time scale and that does in effect give rise to a reduction of the state vector. Yet, it is appropriate to remark that it is the global entanglement constraint unveiled in the preceding report that actually explains the fact that decoherence is allowed to occur, which is necessary (even though not entirely sufficient) to explain the persistence of the quasiclassical nature of history that follows quantum measurements. In fact, this is the only explanation of time asymmetry that allows to deduce (rather energy and this means that no record of what takes place in the vacuum on smaller scales can exist unless we directly reveal the existence of those processes by entangling them with irreversibly evolving degrees of freedom which leave persistent traces of their occurrence, which allows to confirm that the complexity of virtual processes cannot be considered sufficient as a condition for quantum measurement to take place 108 than merely assume) that decoherence always occurs in one and the same direction of time for all measurement processes (as is required for the logical consistency of history according to Roland Omnès [20]), as decoherence itself does not a priori favor one direction of time over the other. It is the fact that the wave function associated with the evolution of a quantum system is itself observed to evolve irreversibly during a measurement that differentiates this evolution from that which occurs in between measurements. When a measurement takes place and the state vector is reduced, the time symmetry and the deterministic nature of the evolution of the wave function no longer applies. But in the context of a realist interpretation of quantum theory this cannot be understood to mean that it is the evolution that takes place in the course of a measurement which is alone responsible for giving rise to the unpredictability of quantum phenomena, as is sometimes proposed. If the state of a quantum system is unique, in the time-symmetric sense, before a measurement is performed, as I previously argued one must recognize, then it certainly cannot be assumed that the randomness of its evolution is merely a consequence of the events that take place during the subsequent measurement and it becomes necessary to admit that it is the unobserved paths followed forward and backward in time by the system as it approaches or emerges from the event at which a measurement is performed that is randomly determined and which explains the unpredictability of the outcome of this measurement. It must be clear, in any case, that the randomness of quantum processes, like their uniqueness, is not an illusion that emerges from the fact that an observer may be unable to perceive the evolution that supposedly takes place all at once in multiple branches of history that would exist together in one single universe, as is sometimes suggested in the context of a many-worlds interpretation. Randomness is a fact of the reality we experience that becomes perfectly acceptable in the context of a time-symmetric formulation of quantum theory where the deterministically evolving wave function is not reality itself and there exists a unique history of some kind, even in between measurements. Thus, if randomness appears to take place only during measurements it is simply because it is only as a result of processes which can be characterized as measurements that the uniqueness of reality (in the time-symmetric sense) is made apparent, while it is only at the level of individual histories that reality may be observe to vary unpredictably. But quantum evolution must be understood to always be random, even though in the absence of new measurement, or when the macroscopic constraints applying on a system remain 109 unchanged, the state vector evolves deterministically. Once again, therefore, it seems that it is incorrect to assume that a fundamental distinction must exist between the 'unitary' evolution that takes place in between measurements and the evolution that characterizes a process during which quantum potentialities are actualized and this means that it should be possible to explain the quasiclassical nature of the evolution that follows a quantum measurement while remaining within the confines of the current mathematical framework of quantum theory. The difference between observed and unobserved evolution is real, but only because the conditions under which there is an absence of knowledge provide a quantum system with more freedom regarding what it is allowed to do as it randomly evolves. It also transpires that the standard account regarding the distinction between those situations in which a measurement takes place and those in which the usual 'unitary' evolution law applies is somewhat misleading, because in fact a quantum system is always in a state where at least one dynamic attribute (as unnatural as it may be) is in a classically well-defined state, even though this means that the conjugate attribute is completely undetermined. This is a very important fact that is often overlooked and which actually holds the key to a solution to the remaining issues that prevent the formulation of a satisfactory explanation of the persistence of quasiclassicality. When a measurement is performed all that really happens is that the state of a system changes in such a way that an attribute (say position) which was in a state of quantum superposition the moment before, becomes classically well-defined the moment after, while its conjugate attribute (say momentum), which was classically well-defined initially, actually becomes quantum mechanically superposed. In such a context it would certainly be inappropriate to argue that a fundamental change occurs in the course of a process that can be qualified as a measurement, even though it is clear that some constraint, not present before the process took place, does in effect become significant for the future evolution of the attribute of the system which is subjected to measurement (I will have more to say concerning this issue in section 12). Now, the modern formulation of quantum theory is usually considered to be that of consistent histories, which was developed in three steps by Robert Griffiths [21], Roland Omnès [22], and Murray Gell-Mann and James Hartle [23]. From this formalism emerges an interpretation according to which it is merely the fact that one may choose to ignore certain aspects of reality, and submit them to a summation process, that allows one to obtain meaningful 110 probabilities (which are positive and which add up to one) for the possible histories of a quantum system which has become entangled with the summedover portion of reality. It would then merely be the fact that one may choose to ignore what goes on in the environment with which a system has become entangled that would allow one to find the system to be in a mixed quantum state instead of a pure quantum state for which interferences would be observed. More specifically, what the formalism of consistent histories provides is a criterion for judging when it is that sufficiently coarse-grained histories are obtained (by ignoring certain details of the historical description of reality) which do not interfere with one another and which can therefore be attributed meaningful probabilities. Interestingly, the manner by which this is achieved is by considering pairs of coarse-grained histories (consisting of sets of alternative fine-grained histories whose ignored details are allowed to differ in any possible way) which are subjected to decoherence and between which there are virtually no interferences. When those conditions are satisfied, a meaningful probability for the process so described to occur can be obtained by applying the usual rule which consists in multiplying the probability amplitude for a history with the complex conjugate of the amplitude for the same coarse-grained history. But no interpretation is given for why it might be necessary to consider pairs of coarse-grained histories rather than single histories, even though this appears to be required from a mathematical viewpoint. I believe that the formalism of consistent histories must be considered an essential element of an appropriate and fully satisfactory interpretation of quantum theory, even if only because it constitutes the basis of the only solution to the quantum measurement problem that would apply even on a cosmological scale where no external environment degrees of freedom exists that would, according to a more conventional theory, be required to give rise to decoherence. It is incorrect, therefore, to argue that the universe cannot decohere because no environment exists that would be outside the universe, because if decoherence is an outcome of temporal irreversibility, then there is enough opportunity for decoherence to occur on a much smaller scale. Indeed, what the formalism of consistent histories allows is a more appropriate definition of quantum measurement as taking place continuously over the entire duration of a process rather than at one particular event, as becomes possible when the environment degrees of freedom which are left out of the description of the process evolve irreversibly, thereby allowing decoherence to arise. One of the advantages of such a viewpoint is that it is 111 easier to see how it can be that the simple possibility for an event to happen allows a measurement to be performed even if this event does not happen (as in the case of interaction-free measurements), because when something is in effect allowed to happen we simply are in a situation where one specific set of macroscopic experimental constraints exists throughout the duration of a process which would not exist otherwise, while different constraints mean a different measurement not an absence of measurement. But while the consistent histories approach is certainly well motivated all by itself, given that it allows one to avoid having to refer to classical observers and measuring devices that would not be describable using the formalism of quantum theory, it appears to be insufficient to predict the emergence of a classical world (a maximum quasiclassical domain). It is as if decoherence alone was not enough constraining a condition to guarantee an absence of quantum interferences between all the coarse-grained histories to which it may give rise, while no criterion currently exists to select as physically relevant only those future histories which actually describe a quasiclassical evolution. As was the case with the original many-worlds interpretation of quantum theory, it is not possible to avoid the conclusion that in the course of certain otherwise 'consistent' histories, a macroscopic measuring device may end up in a superposition of states after becoming entangled with a quantum system. The problem here does not merely have to do with the previously discussed lack of motive for justifying the application of the criterion of 'consistency' that is attributed to families of coarse-grained histories and according to which certain histories would simply be meaningless given that classically meaningful probabilities cannot be assigned to them. Indeed, I have already mentioned that it appears preferable to allow our conception of reality to adapt to the fact that classical probability theory does not always apply, instead of trying to limit what may be appropriate of this reality through some arbitrary condition that only serves to accommodate a criterion of consistency that should instead apply to a more appropriate, realist, timesymmetric description. Thus, I believe that it is important not to commit the error of enforcing consistency at the price of rejecting a realist interpretation of facts, which would simply contribute to perpetuate the difficulties which are known to affect the description of reality that was provided by the original Copenhagen interpretation. What should be recognized as nonsense is not the hypothesis that a photon follows a unique but unobservable trajectory of some kind in between 112 measurements, but the decree that we should not even try to describe reality in situations where we do not yet know how to make sense of it. This reflexion is especially relevant given that in a quantum mechanical context we are always dealing with probabilistic inferences, which means that even histories which we may expect to be 'consistent' might in some rare circumstances turn out to be 'nonsense', which is certainly indicative of the arbitrariness of the restrictions imposed by the consistent histories interpretation of quantum theory on our concept of reality. Therefore, to achieve further progress regarding the issue of quantum measurement one must first realize that in face of the experimental evidence from which quantum theory emerged, the desire to restrict the application of the criterion of logical consistency to aspects of reality which behave in conformity with classical expectations is just as irrational as the desire to uphold determinism. The additional issue we need to consider, however, is more pragmatic. It has to do with the fact that in the absence of a stronger and more specific constraint there would be histories which could be characterized as 'consistent', but which would not remain quasiclassical as time goes, following decoherence. This is the problem discussed in [19] and which I have mentioned earlier in this section. As Dowker and Kent explain, predictions only become possible, within the formalism of consistent histories, once a set of histories, the physically relevant set, formulated using a specific choice of dynamic attributes and a particular choice of coarse-graining, has been selected whose elements can then be attributed meaningful probabilities. But in a quantum mechanical context there appears to be total freedom over the choice of which dynamic attributes are used to specify the exact state of our physical systems and what elements of reality can be ignored and summed-over, and this is where the problem originates, because when no criterion exists to limit those choices, most 'consistent' histories do not remain quasiclassical in the future, even if they were so characterized in the past. Thus, the criterion of 'consistency' appears to be insufficient to predict the persistence of the quasiclassical nature of history. In fact, it seems that it would not even allow one to assume that the past itself must have been classical up to the present moment, despite the fact that the existence of mutually consistent records of a unique past appears to indicate that this condition was met across the whole observable universe as far back in time as one can tell. What remains problematic with the current approach, therefore, is the absence of a criterion within the interpretation itself for choosing the appropriate, physically relevant set which would allow to describe the quasiclassical world we do 113 experience. What was originally proposed by Murray Gell-Mann and James Hartle is that if we perceive a quasiclassical world it is because, as observers, we have evolved to take advantage of only those formulations of history according to which the world does in effect remain quasiclassical. The problem is that it appears that in the absence of a criterion for justifying the selection of the appropriate, physically relevant set of histories, the above mentioned results imply that the most likely explanation for the fact that one experiences a quasiclassical world would require one to reject all evidence of past quasiclassicality and all expectations of future quasiclassicality as being mere illusions and to satisfy oneself with having 'explained' why it is that at the present moment one experiences what merely looks like a world that could have been quasiclassical on a global scale during most of its history, even though that would not be the case. But I have already explained why such solipsist explanations, which require one to assume that one's current state of awareness is all that truly exists (classically), are not acceptable in general from the viewpoint of scientific realism and if there is one situation where this criticism would definitely need to apply it is certainly here. It seems to me that if such an approach is still considered by some to constitute a valid explanation of the quasiclassical character of reality it is merely because we cannot see how the remaining issues facing the current state-of-the-art interpretation of quantum theory could be resolved, so that we have come to believe that the solution may be that there is no problem after all, as long as we consider the world in the 'appropriate' way. But, if we really want to explain something, then clearly we must identify the constraint that allows to select the physically relevant set of histories in which quasiclassicality is experienced by all observers, because the only alternative would be to retreat into a paranoid vision of reality where all that exists is the impression of a persistent quasiclassical reality, despite the fact that there would be absolutely no reason for why such an impression should be experienced (which is the real problem). I believe that what those difficulties illustrate is the incorrectness of the basic assumption that no logically consistent interpretation exists for the interfering fine-grained histories which actually constitute the most fundamental elements of the consistent histories formulation of quantum theory. It is significant in this context that certain specialists have proposed a weaker and more general form of consistency conditions [24] that merely amounts to impose that the probabilities of coarse-grained histories be posi114 tive while still satisfying the usual probability sum rules. Those generalized 'consistency' conditions result in a formalism that is time-reversal invariant (which from my viewpoint is certainly a desirable property) and which selects sets of histories called linearly positive histories that include consistent histories as a subset of possibilities. Once this is recognized as a viable approach, however, one may be tempted to go one step further and simply allow negative probabilities as well, by considering the most complete sets of histories that would include all sets of linearly positive histories as a subset. If such an even more complete generalization was never considered viable it is obviously due to the fact that negative probabilities cannot be classically interpreted and therefore appear meaningless and undesirable. Yet, Roberth Griffiths, suggested that it might be desirable to try to provide an interpretation of the probabilities which are known to arise when we consider histories that do not satisfy the 'consistency' criterion. Dowker and Kent themselves insist that there would be no logical contradiction in using an 'inconsistent' set of histories if a criterion existed that would allow one to select from it the physically relevant set and it was found that it allows a logically consistent description of historical facts on a sufficiently 'large' scale. The problem is that in the current context the 'consistency' criterion appears to be necessary for selecting sets of coarse-grained histories that do not interfere with one another, as required by observations, while no satisfactory interpretation exists for negative probabilities. But in the context where we still need to identify the constraint that allows to choose the physically relevant set, it cannot be ruled out that it might be this condition which enables to generate a historical description of reality that naturally satisfies both the criterion of 'consistency' and that of persistent quasiclassicality. I have already suggested that in the more appropriate context of a realist, time-symmetric interpretation of quantum theory, logical consistency (in the general sense) would rather need to be satisfied by the unique retarded and advanced portions of history. But I also explained that from such a perspective an adequate interpretation of negative probabilities can be formulated that would confine them to unobservable aspects of physically allowed processes. Thus, if a criterion can be found for the selection of a set of histories that is not a priori 'consistent', but that would nevertheless allow both the quasiclassical character of reality and the logical consistency of its historical description to naturally emerge on the appropriate scale, then we may finally obtain a satisfactory extension of the current formalism that would allow to solve the quantum measurement problem. 115 In fact, there may exist another motive for recognizing that an additional constraint is necessary to explain the quasiclassical nature of reality that is observed on a sufficiently irreversible scale. It was, in effect, pointed out by Roger Penrose and apparently also by John Bell and Bernard d'Espagnat that the current explanation for the reduction of the state vector through decoherence is dependent on the hypothesis that it is not possible to reveal the existence of quantum interferences involving the detailed configuration of the degrees of freedom of that part of the environment which has become entangled with a quantum system. But there is presently no valid reason to assume that such an unlikely procedure could not be carried out at some point in the future (even without deliberate intervention) and this means that the current explanation for the disappearance of quantum interferences following measurement is merely valid based on the assumption that the practical limitations that may prevent the observation of interferences between macroscopic states will never be overturned. Given that the existence of practical limitations to unveil superposition of macroscopic states through manipulation of the delocalized environment degrees of freedom has been shown by Roland Omnès to be necessary for the validity of the factual definiteness of reality and the applicability of the conventional rules of logic, it is certainly significant that Omnès himself has argued that one cannot definitely rule out the possibility that such an unlikely evolution could happen, but that given that it would mean that the world would no longer be 'consistent', then he prefers to simply assume that the low probabilities involved require the decoherence process to be definitive in principle. In the context of a conventional many-worlds interpretation we would certainly be justified to assume that this condition needs to be fulfilled as if it was not the case, then we should be observing all possible macroscopic states to exist all at once in the same portion of history, which does not only illustrate the absurdity of the multiple branches hypothesis, but also the necessity of providing a satisfactory explanation for the absolute irreversibility of the decoherence process. Of course we do observe an absence of interferences between alternative coarse-grained histories past a certain level of irreversibility of the ignored (summed-over) portions of a process18 and this may appear to confirm the validity of the assumption that the practical limitations discussed here can18It was once suggested that quantum interferences between alternative states are actually always allowed to occur regardless of the size of the system under observation, or the degree of irreversibility of its evolution, but that if the existence of such interferences can 116 not be overcome. But we must recognize that we have at present no reason, from a theoretical viewpoint, to assume that such an unlikely reversal of fortune could not happen at some point in the future, because even if there is only an infinitesimal chance that it does, given an infinite amount of time it should eventually happen and in such a case the consequences would be felt right now (this is made unavoidable in the context where the time-symmetric nature of quantum evolution allows future measurements to exert a causal influence on past evolution). Even if such a phenomenon was to occur only once on a large scale, we should actually observe its consequences in the fact that the usual assumption to the effect that there is no state superposition following measurement would no longer allow our prediction of transition probabilities to match observations, therefore indicating that the conventional hypothesis is incorrect. The fact that we usually do not observe such a disagreement means that the assumption that the decoherence process is in general truly irreversible is appropriate even if it is not at present entirely justified. A satisfactory solution to the problem of quantum measurement should therefore allow one to gain confidence that once decoherence has occurred there is no chance that it may somehow be overturned at any time in the future, which would allow to justify attributing the status of established facts to measurement results. In any case, the often encountered statement to the effect that quantum theory has never been proven wrong, which would seem to invalidate the claim that the currently favored interpretation is incomplete, can no longer be considered accurate, given that in the context of the developments discussed above it seems that what the theory predicts is an absence of quasiclassicality in both the future and the past and this is clearly in violation with what we do observe (for the past) and with what we have very good reasons to expect to observe (for the future). Therefore, a solution to the quantum measurement problem, the central problem of the interpretation of quantum theory, cannot merely consist in assuming that elementary particles acquire reality as a consequence of interaction with another part of reality (presumably a measuring device) as was originally proposed by the founders of quantum mechanics and as is still considered appropriate by advocates of be ignored it is simply because they would be too difficult to reveal in the case of macroscopic systems. But it is usually recognized that this is not a valid proposal, because in fact nothing would be easier to distinguish than interferences between two different states of a pointer on a measuring device, given that this would necessarily be apparent in the statistical distribution of subsequent measurement results. 117 the relational interpretation of quantum theory. What I have tried to explain in this and the preceding sections is that it is not necessary and not appropriate, or even possible to assume that no unique reality of some kind exists for a quantum system in between interactions with a measuring device. The difficulty to explain the emergence of quasiclassicality cannot be considered to mean that the theory only allows to describe how quantum systems interact with the rest of the world, as if this was a requirement of a relational description of reality. In fact, as I will soon explain, it rather appears that a satisfactory solution to the quantum measurement problem actually requires considering that a well-defined and in some way unique, but unobservable reality does exist between measurements. Particles do not become real through interactions, and the uniqueness of reality which is observed during measurements is not an effect that propagates as a result of further interaction, because even if that was considered to be true, the emergence of quasiclassicality would remain unexplained. It is not our intuition that this is absurd that is at fault, it is the orthodox interpretation and the insistence that we should not attempt to describe reality when it is not observed (which is never truly the case in fact). What emerges from all those considerations is that, as undesirable as it may once have appeared, there seems to be something unavoidable with John Von Neumann's conclusion that something essential (even though not necessarily fundamental) must differentiate a quantum system from the measuring apparatus and observer who effect a measurement on this system. Unless we are to allow for grossly inaccurate predictions, it is necessary to explain what justifies this distinction. But, even though this difference can be recognized to have something to do with time irreversibility, and must come into effect following decoherence, its exact nature remains unidentified from the viewpoint of all known interpretations. What explains that Von Neumann's conclusion was never taken seriously is certainly his early proposal that the dividing line between superposed system and observing system may be determined by the level at which consciousness occurs, which could perhaps explain that human observers never experience quantum interferences. Indeed, any reference to such qualitative aspects of physical reality as a degree of consciousness, or a level of cerebral development as a possible cause of state vector reduction is properly viewed with extreme suspicion by any physicist with a minimum level of cerebral development, while in fact such a reference is not necessary for the validity of Von Neumann's conclusion. Once again a perfectly valid deduction was ignored as a consequence of being associated with question118 able assumptions which are not essential to its validity. But, if this is the truth, then it remains to identify what this distinguishing property really is and why it has the decisive consequences it is observed to have in the context where the basic mathematical framework of quantum theory is assumed to be valid under all circumstances. This is the task I will try to accomplish once I have clarified the role played by time in the most fundamental of quantum mechanical frameworks. 11 The emergence of time in quantum cosmology When considering possible solutions to the quantum measurement problem and an explanation for the emergence of a quasiclassical world what one must first decide is whether quantum theory needs to be replaced by a better theory or whether the current framework is adequate to deal with those apparently insoluble difficulties. What I have been led to conclude is that quantum theory is indeed incomplete and that it must be supplemented with new conceptual elements if it is to be made fully consistent with what we already know of physical reality that currently appears to conflict with its predictions. But, as I already mentioned, this does not mean that the current mathematical framework of quantum theory (under its most appropriate form) must be rejected, or that the progress already achieved at providing a better interpretation of the theory has become useless. It is, in effect, by building on earlier developments towards a time-symmetric formulation of quantum theory that I will be able to address the remaining difficulties affecting the consistent histories interpretation and to finally explain the quasiclassical nature of reality. For that purpose, however, it is necessary to first examine to what extent time itself can still be assumed to constitute a meaningful concept in quantum cosmology and to explain how it is allowed to emerge from a fundamental theory in which it may only be present in embryonic form. This has been made unavoidable by certain developments that took place in the field of quantum gravitation which appear to imply that the notion of a universal time variable may no longer be relevant to a fundamental description of reality, whether on the Planck scale or on the cosmological scale. Even though it was first suggested that time may be irrelevant to cos119 mology only when the first tentative quantum mechanical descriptions of the universe as a whole were introduced, the perceived difficulty is actually also present in classical cosmology. Indeed, it would appear desirable from both a practical and a theoretical viewpoint to formulate the general theory of relativity as a dynamical theory which seeks to describe the evolution in time of the curvature of three-dimensional space, given that such an approach can be more easily extended to a background independent quantum mechanical theory. But in a general relativistic context, when it is recognized that all the meaningful physical attributes of a universe must be defined in a purely relational way, without reference to any absolutely defined, external parameter, it transpires that any slicing of spacetime into three-dimensional space-like hypersurfaces and a time dimension (any particular choice of foliation) is equivalent to any other. A general relativistic description of the dynamics of the universe as a whole, therefore, does not allow to identify one particular dimension from among the four dimensions of spacetime as being that of time, given that the gravitational field equations remain valid regardless of the choice of a particular signature for the metric of spacetime. An additional difficulty arises due to the fact that the universe, as a particular instance of isolated system, must have an invariant total energy19, which would appear to imply that no meaningful change can take place on the cosmological scale, as if time was, in effect, irrelevant. It seems that a similar conclusion would have to be drawn about the status of time in canonical quantum cosmology, where the same arbitrariness in the choice of a particular foliation and the same absence of change to the energy content of the universe would now apply to the many different histories of extended three-dimensional space-like hypersurfaces which must be allowed to interfere with one another quantum mechanically. This is reflected in the fact that the most straightforward interpretation of the Wheeler-DeWitt equation (the equation that would allow to determine the wave function of the universe) requires assuming that it is similar in form to the stationary Schrödinger equation, while time is notoriously absent from such an equation. It is sometimes suggested that what those difficulties demonstrate is that the 19I have provided arguments in section 3.5 of [1] to the effect that the energy of the universe (just like its momentum and its angular momentum) must actually be null (even when space is assumed to be flat on the largest scale) if no characterization of the physical properties of the universe is to refer to external or metaphysical elements of reality, because a positive or negative energy for the universe as a whole would allow to identify a particular direction in time as being of absolute (non-relational) significance. 120 hypothesis that time exists as a unique dimension distinct from the other three dimensions of space is incorrect. It should be clear, however, that the absence of change on a global scale, which is attributed to the fact that the universe has a fixed value of energy, does not mean that time is not a meaningful concept for relating the changes taking place in one part of the universe with those occurring in another part, as long as we are actually dealing with different portions of the same universe, because it is not required of local subsystems that they have invariant energies as a consistency requirement and therefore change can certainly be observed to take place on an intermediary scale. In other words, even if we were to assume that time is irrelevant on a global scale, this could not be understood to mean that it has no clear significance locally for observers evolving along a particular trajectory within the universe. What's important to recognize is precisely that, from a cosmological viewpoint, time, as a dimension distinct from space, has meaning only as a relationally defined physical quantity which allows to relate various local measures of change, thereby enabling any particular observer to provide a unique description of the various processes taking place across the entire universe (or within his associated causal horizon). Thus, it is an exaggeration to suggest that time does not constitute a meaningful concept in quantum cosmology, because it can actually be given clear meaning as a local parameter to which can be related in various, but well defined ways other such local measures of change throughout the universe20. But to show that a conventional notion of time is not irrelevant to our description of reality on the cosmological scale one must first explain how time is in effect allowed to differentiate itself from the other three dimensions of spacetime, despite the fact that all four dimensions are kept on an equal footing and are required to be equivalent from a fundamental viewpoint by relativity theory. It is regarding this particular issue that I will contribute the most significant insights. Two points must be taken into account in order to explain the existence of a uniquely significant slicing of four-dimensional spacetime into threedimensional space-like hypersurfaces that would consistently select one sin20In this particular sense, the idea that a null value of energy for the universe as a whole would be indicative that time does not exist is no more reasonable than the idea that the null momentum of the universe (relative to the global inertial reference system determined by the average state of motion of matter in the universe) would be indicative that space does not exist, which is so obviously inadequate a hypothesis that no one has ever suggested it could apply. 121 gle dimension as being that of time. First, it needs to be recognized that there must exist unique relationships of causality between the various local elements of an extended four-dimensional universe. Second, it must be recognized that at the fundamental quantum gravitational level it is possible for the principle of local causality to be enforced by postulating the existence of an element of directionality in the causal structure of spin foams, which actually constitutes an embryonic element of time directionality (one original proposal made along those lines can be found in [25], but this concept arises more naturally in the causal sets approach to quantum gravity). Once this is recognized then it becomes possible for a metric of spacetime with a unique signature to emerge that singles out one particular direction of four-dimensional spacetime as being that which is associated with the dimension of time across an entire space-like hypersurface (throughout the universe), because the homogeneity of the initial matter distribution at the Big Bang arises precisely as a consequence of imposing a constraint of global entanglement uniformly over that entire slice of spacetime and this constraint is actually a condition for the existence of causal relationships between all elements of the universe which are present in this initial state. Indeed, what distinguishes time from the other dimensions of space in a relativistic context is merely the choice of a particular signature for the metric of spacetime, which is imposed on solutions of the gravitational field equations. But what this distinction provides is merely a separation of spacetime into past and future light cones, which is really a requirement of local causality. Thus, if the signature of the metric was different and causality still operated uniformly, but along another dimension of spacetime we would simply call this dimension time, while the other three dimensions would then all be analogous to space. In fact, given that general relativity involves local variations of the light cone structure one may say that what is produced as a result of spacetime curvature or the presence of local gravitation fields attributable to the presence of matter are merely smooth local alterations of the direction in which causality operates. All that is required by the global entanglement constraint is that at least one spacelike hypersurface exists over which the embryonic quantum gravitational element of time directionality is oriented in the same direction of spacetime in all locations, thereby consistently imparting on classical spacetime a unique signature that is shared throughout the universe. The point of the above argument is that, in the context of the explanation I have proposed in section 3.9 of [1] for the homogeneity of the initial dis122 tribution of matter energy and the existence of the thermodynamic arrow of time, the direction of spacetime in which causality operates is allowed to be the same initially over an entire three-dimensional space-like hypersurface, simply because the constraint of global entanglement is a condition for the existence of causal relationships between all elementary particles present in the initial Big Bang state and by its very nature such a constraint must apply uniformly over an entire spacelike hypersurface, right down to the quantum gravitational scale (the Planck scale), so that it actually requires the embryonic element of time directionality that is present in the causal structure of spin foams to be uniformly oriented over the entire spin network initially and this is what explains that the direction in which time is flowing is still mostly the same over all of space today (except in the presence of strong local gravitational fields), as necessary for the emergence of a universal time variable. This is a significant result, because when a constraint of global entanglement is imposed on the initial Big Bang state in the presence of negative energy matter particles, a strong limit is imposed on early fluctuations in the density of matter, which means that local variations in the light cone structure that determine how proper time intervals vary over the extended space-like hypersurfaces are virtually absent, so that time flows uniformly over all space, as would be the case by default in a Newtonian context. This argument would therefore appear to provide the basis for a satisfactory solution to one of the last major unsolved issues still facing the most appropriate of current tentative quantum gravitation theories, which is the question of how it is possible for a universal time variable to emerge from the timeless equations of the theory. Thus, it would no longer be necessary to appeal to anthropic arguments to explain not only the observed time asymmetry and the unidirectional nature of causality, but really the very existence of a universal time variable. Even though from a classical perspective relativity theory does not a priori require that there is a preference for one particular dimension of fourdimensional space over the others, the condition that there should exist causal relationships between all parts of that undifferentiated four-dimensional reality (between all the events taking place in it) implies that one direction in four-dimensional space is singled out uniformly as being that along which causal influences are propagated in the emerging spacetime and this is what gives rise to time as the continuous and uniformly flowing variable we are accustomed to experience on a macroscopic scale. The validity of the hypothesis 123 that there does emerge such a singular time dimension in four-dimensional spacetime is what legitimizes a formulation of quantum cosmology as having to do with the dynamics of extended three-dimensional space-like hypersurfaces whose histories can be described as unique trajectories in superspace (the configuration space of those three-dimensional objects). What is remarkable is that the viability of such a description is in fact a necessary condition for the elaboration of a consistent explanation of the quasiclassical nature of reality which emerges under conditions where irreversibility is a characteristic of the processes involved, as I will explain in the following section. The problem that there was originally with the proposal that quantum cosmology has to do with the dynamics of extended three-dimensional spacelike hypersurfaces is that the introduction of a fundamental element of causality in quantum gravitation requires a decomposition into positive and negative energy solutions, as in conventional relativistic quantum field theory, and it was not clear how this could be achieved. But progress has been achieved regarding those issues, as discussed in [25] and it cannot be excluded that such an approach may even allow the derivation of a global measure of change that would apply on the cosmological scale (despite the fact the universe has a null constant value of energy). In fact, I'm deeply convinced that it is because we are still ignoring the possibilities offered by the generalized, classical theory of gravitation I have introduced in the first chapter of [1] and which allows a consistent integration of the concept of negative energy matter into the general theory of relativity, that we are still experiencing difficulties with the issue of the decomposition into opposite energy solutions that is necessary for implementing causality into the spin foam formulation of quantum gravitation. The fact that such a decomposition (which from my viewpoint is a reflection of the existence of an embryonic element of time directionality) is made unavoidable in the context where local causality itself cannot be overlooked is certainly a strong enough motive to conclude that those requirements cannot themselves be ignored. But if local causality is, in effect, a decisive constraint, then time itself necessarily constitutes a meaningful parameter in quantum cosmology, even on a global scale, because the separation of four-dimensional spacetime into three dimensions of space and one uniformly pointing dimension of time appears to be the defining character of a world that obeys the principle of local causality in the presence of negative energy matter. One must be careful, however, when considering a quantum mechanical 124 theory that purports to describe the whole universe, because from a realist viewpoint it may not be appropriate to describe the universe by using a deterministically evolving wave function extending over all space. Indeed, by doing so we would commit the same error as we do in the classical theory of relating all past and future three-dimensional space-like hypersurfaces in a predetermined way to some arbitrarily chosen present state, which makes it look like everything about history is resumed in one single stationary state. In a more realistic situation the whole history would not be determined from knowledge of one particular state and following each local measurement the state of the universe would need to be actualized, which would reveal the random nature of the history that actually takes place and the absence of predetermined relationships between the multiple extended three-dimensional spaces forming a history, which in turn illustrates the relevance of time and more specifically of causality in establishing the actual relationships. Even in the context where a unique future is assumed to exist in the same way a unique past does, there is no rational motive to argue that time, as a measure of change, becomes an irrelevant notion, because such a conclusion would only be valid if we ignored the element of randomness that exists from a quantum mechanical viewpoint (particularly in the context of the existence of closed causal chains) and if we neglected the constraint imposed by the necessary existence of causal relationships between all parts of the universe, which singles out the state of maximum matter density of the Big Bang as a state of minimum gravitational entropy from which all future evolution is taking place irreversibly, as I explained in section 3.9 of [1]. In any case, it must be clear that despite what is sometimes suggested, it is not true that time, or even space do not exist at all in canonical quantum gravity. Indeed, a certain embryonic notion of space is clearly present in the structure of spin networks which allows classical space to emerge naturally when a sufficiently large number of fundamental, discrete elements of structure are combined according to purely quantum rules. Furthermore, even in such a context we are still dealing with four-dimensional boundary conditions and this is certainly indicative of the relevance of time, even if this parameter may not explicitly appear in the equations which allow to determine the correlation probabilities associated with those four-dimensional boundary conditions. Actually, the mere fact that even in a quantum gravitational context we are still speaking about local changes occurring in the configuration of spin networks means that an additional degree of freedom must, as a fundamental requirement, be allowed to emerge which relates those local 125 changes with one another. The problem that there was originally is simply that in the absence of a constraint of global entanglement no universal time variable was allowed to emerge, because no unique direction would exist that would be associated with this degree of freedom and along which events could be sequentially ordered into some kind of universal causal chain. When the most essential aspect of time is understood to be causality, however, then the most appropriate of the current fundamental theories do allow a certain notion of history to emerge as a result of the fact that causal relationships must apply uniformly in one particular dimension over at least one extended spin network configuration in the presence of negative energy matter and for this reason alone those extended configurations may be considered to constitute the dynamic elements of quantum cosmology. However, in my opinion, what would definitely invalidate a truly timeless quantum theory of gravitation is precisely the fact that such a theory would be incompatible with the existence of a fundamental time direction degree of freedom (such as revealed in particular by violations of time reversal symmetry T ), while I have shown in chapters 1 and 2 of [1] that such a property is essential to a consistent description of physical reality in a semi-classical context. Indeed, once it is recognized that in quantum field theory the propagation of elementary particles may take place along any of two opposite directions of time, independently from the constraints imposed by thermodynamic irreversibility, then a conflict emerges with the timeless viewpoint given that if there is no time, then obviously there cannot be a fundamental direction in time, because any relationship of time directionality must necessarily involve a sequence of events related to one another following a definite and unique order, even when the classical spacetime structure in which those events are embedded is assumed to emerge from the combination of discrete elements. Given the nature of the arguments which are usually proposed to support the conclusion that time is irrelevant in quantum cosmology and therefore may not even exist, it would seem that solipsism is once again to blame for misleading even some of the most brilliant thinkers into this theoretical dead-end. Indeed, what a rejection of time would require us to assume is that there can be change and that all changes can be related to one another by the use of a reference system we call time, but that this is not enough to conclude that this reference system is the reflection of something real. Thus, while we are allowed to recognize the emergence of a certain variable, distinct from spatial position, which is useful for comparing various local 126 measures of change involving one or another physical attribute, and while the assumption that such a variable exists is undeniably useful and allows to simplify our description of reality, the fact that it is not possible to directly measure any changes relative to that additional variable itself and the fact that this variable may no longer be relevant under the most extreme conditions (on the small scale of distance characteristic of quantum gravitation) would mean that it cannot be considered a real physical property even under more ordinary circumstances. All arguments against the existence of time as a meaningful concept in quantum cosmology involve such an element of solipsism. Time does not exist because it cannot be subjected to direct observation, or be the object of some measurement that would confirm that it is real. But that is just a perfect example of the kind of irrational conclusion one can draw based on such considerations, because what can be more obvious in fact, from our experience of physical reality, than the existence of change and the reality of time? Now, it has been argued that it might be possible for time to emerge as a mere thermodynamic phenomenon, despite the fact that it would not really exist from a fundamental viewpoint. What I'm talking about is the concept of 'thermal time' according to which the passage of time would actually be an illusion attributable to the fact that the irreversible time of our conscious experience appears to always be associated with heat dissipation, which would appear to single out one particular physical variable as that relative to which energy remains unchanged, while in fact there would be nothing significant from a fundamental viewpoint with a time variable derived in such a way. But the problem with this proposal is that there is in fact plenty of evidence for the relevance of a more conventional notion of time at the level of elementary particles where irreversibility is not a defining characteristic. Of course the fact that there would be no preferred direction of time in the absence of heat dissipation is not completely irrelevant to the problem of the existence of a classical spacetime continuum (given that dissipation is necessary to an understanding of the decoherent nature of space and time as I shall explain), but it is not that significant either, because we are not merely trying to decide whether unidirectional time is a valid concept, but with deciding if the whole concept of time is in effect irrelevant to a description of physical reality. However, if thermodynamics was the ultimate explanation for the existence of time it would not be necessary to wait until we begin to explore reality on the quantum gravitational scale to witness an absence of time, because many phenomena are known to exist on a much larger scale that do 127 not involve any irreversibility and yet they are still describable using space and time coordinates21. It is important to point out that if we were to assume that time really doesn't exist, even on a macroscopic scale, we would then be left with having to conceive of the present moment as just one independent, stationary state among many possible states devoid of any causal relationships with one another. It was in effect suggested by Julian Barbour that such causally independent, stationary states may not be incompatible with our perception of the passage of time if we assume that all that we really experience are instantaneous states of consciousness which might be more appropriately described as memory states. But the problem here, again, is that even if such an explanation of consciousness as a state rather than as a process was possible (which I believe may not really be the case22) you would then have no explanation for the fact that the present state of the universe in which the state of your consciousness is contained is one which is characterized by the existence of a large number of mutually consistent records of a unique lower entropy past, while such a configuration would not likely be chosen in a random trial out of all the possibilities which would appear to exist for an instantaneous present state. The fact that what can be characterized as long-term records are usually preserved in what appears to be the most stable structures, while short-term memories are usually preserved in more rapidly changing structures would also remain unexplained from a timeless universe perspective. There were many attempts at trying to explain why such present states as revealed by our personal experience of reality may not really be unexplainable, even when one assumes that all that exists in the universe is an extended space without any time. But in the end one must recognize that those proposals are inadequate and that the unlikeliness of the observed con21In the context where a satisfactory solution to the problem of the origin of thermodynamic time asymmetry that is not based on the weak anthropic principle is now available (this was the subject of section 3.9 of [1]), the fact that the thermal time hypothesis may appear suitable to an explanation of cosmological time-asymmetry based on a certain interpretation of entropy growth as a purely subjective, observer dependent phenomenon would no longer constitute a potential advantage of a timeless interpretation of quantum cosmology. 22Memory, as well as other basic mental faculties, are not really static events, but rather processes which require a certain duration to be experienced and if there is no duration what one should expect to experience is not one ever lasting memory, but nothing at all, which is certainly not compatible with my own experience of reality at least. 128 figuration remains a complete mystery unless one is ready to assume that what one actually observes is not really indicative of the existence of a lower entropy past, even though there is absolutely no rational motive (even of an anthropic nature) to legitimate the validity of such a conclusion. Of course if it had actually been demonstrated without doubt that time does not exist, then we may have no choice but to assume that everything is such a strange and deceptive illusion, but this is not true and the only reasonable conclusion we are allowed to draw from our observations is that the present state of the universe, regardless of how it is defined, must be related to one single past history through the existence of unique (but not predetermined) causal relationships unfolding back in time to the state of low gravitational entropy that allows to explain the existence, in the present state, of mutually consistent records of a unique past. It is usually recognized, in fact, that all that one may reasonably argue concerning time as a quantum gravitational concept is that it is the continuity of its flow and the existence of a unique spacetime metric signature which do not apply at the most fundamental level. Thus, if at some point there was such a strong desire to do away with time it is perhaps only due to the fact that we were unable to explain the singular character of time as a dimension of spacetime, because we did not understand the profound significance of the existence of a uniform distribution of matter energy at the Big Bang, which allowed me to explain the near uniformity of the direction of propagation of causal influences in spacetime and therefore of the flow of time. But the fact that we did not benefit from the guidance of the generalized theory of gravitation which I have introduced in the first chapter of [1] also complicated the task of implementing an appropriate decomposition of the solutions of the equations of canonical quantum gravity into positive and negative energy terms, which I believe is the source of the difficulties we still experience in trying to integrate time and causality into our most fundamental theory of gravitation. In such a context it was rather convenient to simply assume that time does not exist at all given that, like space itself, time is not present in its classical form on the most fundamental scale. But it must be clear that if time, or more specifically causality, did not exist under any form at a fundamental level, then what we should definitely not experience is a dimension of time distinct from the other dimensions of space. Now, despite the fact that I have criticized Julian Barbour's suggestion that our experience of the passage of time may not be incompatible with a timeless description of reality, I must recognize that he, more than anybody 129 else, is responsible for having convinced me of the validity of the concept of simultaneity hyperplanes, or more generally of space-like hypersurfaces as the basic building blocks of a dynamical theory of space that would be relevant to quantum cosmology. The only problem I have with Barbour's interpretation has to do with his insistence that those global states of the universe as a whole should not be related to one another causally (should not be considered to form a unique causal chain or to take part in a unique history). But in fact this is not a requirement of a dynamical approach to quantum cosmology and, as I have explained above, it would rather seem that there do exist unique causal relationships between those properly defined global states, despite the fact that there appears to be a lot of freedom in how spacetime can be sliced into such space-like hypersurfaces. We may, therefore, retain as valid the concept that the present state of the universe as a whole, including that of its gravitational field or spacetime curvature, can be defined over one such space-like hypersurface, which may be represented as a point in the appropriate configuration space (say the superspace of canonical quantum cosmology), while the time variable would enter the picture as the position along the actual trajectory followed by the global state in this configuration space. This becomes a valid proposal in the context where we now have a valid explanation for how it can be that one given spacetime dimension is uniformly singled out as that along which local causality is allowed to operate (as reflected in the uniqueness of the signature that must be assigned to the metric of spacetime) and to constitute a physically significant constraint that is not shared by the other three dimensions of space, even in a general relativistic context. To be honest I have to mention that the conclusion that a universe's history can always be represented as a path in the configuration space of three-dimensional space-like hypersurfaces is dependent on the hypothesis that any solution of the gravitational field equations that contains closed time-like curves (which would make conventional time travel experiences a reality) can be excluded. Usually this is recognized to be possible merely if we assume without reason that the second law of thermodynamics is valid under all conditions. But given the explanation I have provided in section 3.9 of [1] for the existence of the thermodynamic arrow of time, the conclusion that closed time-like curves cannot naturally arise actually becomes unavoidable. Indeed, under such circumstances the constraint that gives rise to thermodynamic time asymmetry must always operate in the same unique direction of time and invariably have as a consequence the diminution of en130 tropy in the particular direction of time that points toward the initial state of minimum gravitational entropy of the Big Bang, as a requirement for the existence of causal relationships between the various elements of the universe. Therefore, a universe could not even exist as a causally interrelated ensemble of space-like separated physical elements if it did not satisfy this unidirectionality constraint as a result of the presence of a closed time-like curve for which the direction of entropy diminution could not be well defined and this means that such closed time-like curves are actually forbidden. From my viewpoint it would therefore appear that it is always possible to represent the universe and its entire history as some monotonic foliation of space-like hypersurfaces, that is to say, as a path in superspace. It is, therefore, the existence of a unique direction in spacetime along which causal influences must propagate that allows histories to be parametrized by a universal time variable (associated with a particular slicing into space-like hypersurfaces) and that enables a description of the whole universe and its gravitational field as evolving with respect to this time variable, thereby legitimating the notion of history as consisting in an ensemble of causally related global states, that is to say, a universal causal chain. What I have shown is that the absence of a fundamental distinction between time and the other three dimensions of spacetime, which is an essential feature of relativity theory, does not constitute an insurmountable obstacle to achieving this objective, so that we are no longer justified to conclude that time is altogether absent in quantum cosmology. This is certainly a significant result for the elaboration of a solution to the problem of the interpretation of quantum theory, given that the existence of classical space and time is actually required by conventional quantum theory for the description of histories in the context where the various macroscopic experimental conditions which are shared by both the retarded and the advanced portions of a quantum process must be defined over one unique and classically well-defined spacetime continuum. Thus, spacetime itself must be assumed to be decoherent under conditions where a history can be consistently defined, which means that quasiclassicality must already apply to the gravitational field in order that decoherence be observed at a higher level in the observed attributes of conventional quantum systems. This again illustrates the fact that a continuous and spatially uniform notion of time must be allowed to emerge from a quantum theory of gravi131 tation23 before ordinary quantum processes can be appropriately described and conventional quantum theory itself can become a valid representation of reality with clear and precise meaning at the most fundamental level. The problem of the emergence of time in quantum cosmology must therefore be recognized as constituting one particular aspect of the more general problem of the nature of the conditions necessary for the emergence of a quasiclassical world. What this means is that in order to obtain a satisfactory interpretation of quantum theory one must first examine in which way gravitation and the curvature of space could be subjected to the same time-symmetric description as would apply to more conventional physical attributes under ordinary conditions. Achieving such an objective will allow me to identify additional constraints from which both the decoherent nature of spacetime and the persistence of quasiclassicality that characterizes all observed aspects of physical processes can be expected to arise, even in the context where quantum theory is assumed to be valid under all circumstances. What those considerations will demonstrate is that it is not just general relativity which is really a theory of the universe as a whole, as is usually recognized, but that quantum theory, from the viewpoint of its most accurate interpretation, is also essentially a cosmological theory. 12 Universal causal chain and quasiclassicality We are now finally in position to examine how it is exactly that quantum theory can be extended so as to become fully consistent from both a logical and an experimental viewpoint. It is here that all the progress achieved in [1] as well as in the preceding portions of the present report in providing a better understanding of so many aspects of physical theory associated with time directionality will converge to produce their most significant outcome: a logically consistent interpretation of quantum theory that is valid at absolutely all levels of description. It is certainly a positive development already that in the preceding section I have been able to conclude that time is still 23Of course even on the astronomical scale the spatial uniformity of the flow of time is only an approximation, because the metric properties of space and time are influenced by the presence of matter and by the inhomogeneities which are present in the negative energy matter distribution, which means that even from the viewpoint of the approach favored here there is still no universally valid measure of the passage of time. 132 relevant to a description of our universe in a quantum mechanical context. What I have proposed more specifically is that it is possible to define the state of the universe (at least for what regards its gravitational field or intrinsic space curvature) as consisting of a single point in superspace that specifies, all at once, the ensemble of relationships which exist between each and every one of its local subsystems over a particular three-dimensional slice of spacetime. From such a viewpoint the role of time emerges quite straightforwardly as being that of relating those global states of the universe to one another into some kind of universal causal chain, while establishing the sequential (chronological) order of events. What's remarkable is that the existing mathematical framework by which this particular approach can be formalized, which originates in the ADM formalism [26], allows history itself to be described as one particular trajectory in superspace [27, 28, 29]. Time, therefore, must be conceived as the global variable to which are related the multiple local measures of change that take place as the state of the universe evolves along such a trajectory in superspace. This allows to fulfill Reichenbach's vision of time as reducing, under its most essential form, to a certain concept of causal chain which allows to establish and maintain the invariant local topological ordering properties of spacetime, even when its metric properties are subject to local variations. From my viewpoint, however, it would not be appropriate to consider a traditional concept of causal chain that would involve irreversibility at a fundamental level, as Reichenbach contemplated, because irreversibility is a property that must rather emerge from the particular boundary conditions which existed at the Big Bang. In any case, it must be clear that it is the network of local relationships that varies as we move along a trajectory in superspace, because from the viewpoint of its total measure of energy the universe, as the ultimate isolated system, would appear to remain in the same state without any change actually taking place (this is what motivates the unsubstantiated claim that time may not be relevant to quantum cosmology, as I explained in section 11). It must also be emphasized that what is provided by the concept of spacelike hypersurface is not a unique and absolutely defined characterization of reality, because even when a universal time variable is allowed to emerge there exist many equivalent ways by which spacetime can be sliced into three-dimensional spacelike hypersurfaces, which would appear to require a history of the universe to consists not in a unique trajectory in superspace, but rather in a given surface in the same infinite-dimensional 133 configuration space, formed of the many equivalent trajectories which are associated with the same unique history of spatial curvature. What must be clear, though, is that even if many equivalent possibilities exist for such a trajectory, they all provide alternative descriptions of the same causal chain, to which corresponds one unique history. Once again, the arbitrariness that surrounds the choice of a suitable slicing of spacetime must not be considered to reflect the irrelevance of time for a description of the dynamics of space on the cosmological scale, as it is merely a reflexion its local and relational nature. Now, from the perspective of the developments introduced in the first portion of this report, it would appear that a quantum mechanical description of the universe as a whole cannot merely involve adjoining a wave function to some boundary conditions defined over superspace, under the assumption that every possible history compatible with those conditions happen all at once as different branches in the same universe. The purpose of a quantum cosmology would rather be to estimate the probability of observing a global state of the universe (a point in superspace with which is associated a certain matter distribution and a certain curvature of space) when another such global state has been observed at a certain time in the past, by summing-up the (positive and negative) probabilities associated with all the different ways by which those two points can be joined together as a result of the global state of the universe evolving once forward and once backward in time along two possibly distinct trajectories in superspace for which even the local curvature of space could differ, as long as those differences remain unobservable. Here again we face the mystery of the existence of two interfering histories occurring in parallel, which would appear to merely complicate the causal chain picture of the universe's history by actually requiring bidirectional causality to operate in opposite directions along two otherwise similar portions of history. From a conventional viewpoint, even though this aspect of a quantum mechanical description of the universe is certainly convenient, given that it allows to explain quantum non-locality, it nevertheless remains unexplained. In order to begin to understand why this dual character of quantum reality is not as arbitrary and superfluous as it may seem, one must first examine how it is that causality would operate if there was no advanced portion to the history of the universe. It only became clear to me what the organizing principle is that allows to clarify this situation when I began working on the problem of time travel and closed causal chains. It is at this point that I realized that if the history 134 of the universe was described by one universal causal chain freely unfolding in the appropriate configuration space along the direction corresponding to unidirectional time, there would need to be external causes that would determine how the universe began to get going along the particular trajectory over which it is found to have propagated. This is a very important point, as an external cause is precisely what must be considered forbidden by the constraint of relational definition of the physical attributes of the universe, which basically implies that there should be no 'first cause' that would need to be attributed to some external agent that is not part of the causal structure of the universe itself and that may not be governed by the same physical laws24. The reader may recall the problem associated with so-called knowledge paradoxes that would arise from the viewpoint of unidirectional time when a time traveler would take a copy of some complex and highly valuable work of art, which happens to exist in the future, back to a time in the past before which it did not yet exist, thereby allowing it to be created instantaneously, without any apparent cause, so that the invention is allowed to exist in the future, which is necessary if it is to be brought back in time. I have explained in section 4 that such a phenomenon is not impossible in principle, but is simply very unlikely to occur, given that it would actually require entropy to increase in the past direction of time, while the time traveler would be in the process of bringing back information from the future, which would constitute a violation of the second law of thermodynamics, because it would involve a decrease of entropy in the future. What can be learned from such a thought experiment is that if the phenomenon described here is extremely unlikely, it would not, however, constitute a violation of fundamental time-symmetric causality, because it would only involve a diminution of entropy that would be apparent from a unidirectional time viewpoint, but would not require a real discontinuity in the flow of information along the direction in which the time traveler would be progressing in time. Indeed, as I explained in section 3 it must be recognized that there is no absolute difference between causes and effects at a fundamental level and this means that the future can influence the past just as much as the past is allowed to influence the future, even in the same por24The same inconsistency would arise if the condition of continuity of the flow of time along a particle world-line which was introduced in section 2.10 of [1] was allowed to be violated and therefore this constraint can be understood to really be a condition for the local continuity of all causal processes. 135 tion of history (as long as no inconsistency develops), which is what actually happens when an elementary particle is propagating backward in time (in which case it behaves as an antiparticle). But if the present state of the universe was determined by a certain cause (located either in the past or in the future) that is not itself determined by an earlier or later cause that also belongs to the universe itself, but that would be necessary to set the universe on its course in one particular trajectory of the configuration space (with which is associated one particular structure and one particular information content), then a real problem would emerge, because under such conditions bidirectional causality would definitely be violated. But how could one avoid the conclusion that there needs to exist an initial input, however remote it may be located in the past (or indeed in the future), that would causally determine the structure of the spin network that now exists and that contains the detailed information about the extended three-dimensional spacelike hypersurface that constitutes the point along the universal causal chain we call the present? I believe that the truth is that we have no choice and that we must admit that a certain hypothesis, which may at first appear gratuitous and arbitrary, actually constitutes an absolutely essential condition that needs to be imposed if our quantum mechanical description of reality is to be free of logical inconsistencies when it is applied to a description of the universe as a whole. It is at this very precise point that quantum theory ceases to be baffling and that its most incomprehensible aspects become essential elements of a fully comprehensible representation of reality. What emerges from the original perspective developed in this report is that the history of the universe is nothing but a closed causal chain of enormous proportions that unfolds in its configuration space. There is no first cause. The initial impetus that sets the universe on its course is provided by the universe itself, as all later states of the universe also constitute earlier states along this closed, universal causal chain. The universe truly brings itself into existence by providing the cause of its own present condition as being nothing but a remote effect of this very same present condition. Perhaps that you remember my earlier discussion of the closed circuit analogy from section 2. What I explained is that most electrical circuits are really closed circuits and if they may not seem so under ordinary circumstances it is simply because the circuits are usually extended in one particular direction and can only be recognized for what they really are by the fact that the cables in which they are confined are always composed of pairs of polar136 ized wires which betrays the fact that this unique path that seems to extend from source to sink is actually formed of the two branches of a closed circuit in which the current flows in opposite directions. Well, I believe that one must come to accept as unavoidable that this is what is described by the quantum mechanical version of the history of our universe. It is a closed trajectory in superspace that is stretched to universal proportion along the direction relative to which unidirectional time unfolds, as allowed by the solution I have provided in the previous section to the problem of the origin of the differentiation between space and time. What I suggested in the previous section is that the existence of a time dimension distinct from the other three dimensions of space is an outcome of applying to the initial maximum density state of the Big Bang a constraint of global entanglement, as a requirement for the existence of relationships of local causality on the quantum gravitational scale for the universe as a whole, which has for consequence that the same unique direction in spacetime is selected throughout the universe for the propagation of causal signals. But such a distinction between space and time (which is made apparent by the unique signature that must be attributed to the metric of spacetime) is what allows a description of the history of the universe as consisting of a trajectory in superspace. What a quantum mechanical description of the same reality allows, then, is for this trajectory to be a 'polarized' version of history, in the sense that it actually consists of two parallel histories which share the same observable macroscopic conditions and whose corresponding elements are being propagated in opposite directions of time. But while this pairing of history and this polarization would remain a complete mystery from a conventional viewpoint, in the context of the above discussion it becomes a natural and essential feature of physical reality that should actually have been expected all along, if only we had recognized that logical consistency is not an optional requirement. Indeed, if causality is of any relevance to cosmology it is certainly due to the fact that it imposes two essential conditions on the universe in order that it be allowed to simply exist in any possible way. The first of those two conditions is that all elementary particles present in the universe must be causally related to one another as a result of having been in local contact with one another at least once in the history of the universe. As I explained in section 3.9 of [1] this must be considered necessary in order that all particles be allowed to actually consist of different elements of the same universe. The existence of such a condition, which is responsible for the low gravitational entropy of 137 the initial state of maximum matter density of the Big Bang, is what allows me to assume that the history of the universe is in effect described by one unique trajectory in superspace rather than by multiple unrelated trajectories which would really constitute the histories of many different universes not causally related to one another. But, as I just mentioned, this global entanglement constraint is also responsible for the fact that time actually exists as a dimension distinct from the other three dimensions of space, which is responsible for giving rise to the very causal structure of spacetime. What's more I will argue below that this condition is also necessary to explain the classical nature of reality, under conditions where a dynamic attribute of a quantum system becomes entangled with irreversibly evolving degrees of freedom of the environment in which the system evolves. The second condition would then be that which I have just identified and which is that the universe must be self-determined from the viewpoint of causality. This can be satisfied when the history of the universe consists of a closed causal chain in its appropriate configuration space, which requires the universe to eventually return to the exact same (but partly unobservable) state in which it currently is, as it evolves along a particular trajectory in this configuration space. This condition is what explains that it is necessary, in order to obtain the right correlation probabilities, to take into account the existence of two otherwise independent histories evolving in opposite directions of time, which is the distinctive feature of the realist, time-symmetric interpretation of quantum theory developed in this report. What defines a universe, therefore, is not just the fact that all of its constituent elements are causally related to one another despite the spatial distances that separates them following the expansion of space, but also the fact that the momentary global configurations of those local elements are all causally related to one another and to nothing else (they from a unique causal chain). Indeed, when history consists of a closed trajectory in the space of all possible configurations, every single global state can be in local 'contact' with both a preceding and a succeeding state and this is what allows all global states to be causally related to one another, regardless of the distance that separates them in time. Thus, the multiverse is not merely the ensemble of all possible, causally independent universes (those which would be characterized by distinct values of their physical attributes at arbitrarily chosen times), it is really the ensemble of all possible, universal causal chains which exist as inequivalent closed trajectories in superspace. What is essential to grasp is that, despite what would seem to be implied 138 by the progress that had already been achieved towards the elaboration of a consistent time-symmetric interpretation of quantum theory, even though there appears to be two causally independent, but interfering histories to every process, from a cosmological viewpoint there is only one history, but it feeds back on itself so as to form a closed causal chain which, for some reason to be discussed below, goes through observationally indistinguishable trajectories once forward and then once backward along the particular direction of superspace that corresponds to unidirectional time. Thus, there is no quantum system in a state of superposition, going at once and in the same universe through all possible histories. There is one unique history, the details of which remain in part unobservable to any observer, that unfolds as a closed causal chain in its appropriate configuration space, subject to the condition that all observable properties of this history be shared by the two portions of it which are stretched along this direction of the configuration space which we call time. But it is in effect only in this particular sense that we may assume history to be unique, because the uniqueness of the history that unfolds relative to unidirectional time is merely a consequence of the fact that both the retarded and the advanced segments of history must share the same observable macroscopic conditions and are submitted to a constraint of diminishing entropy that operates in the same unique direction of superspace (at least for this portion of history that unfolds on one side in time of the Big Bang), even though this is not the direction in which the advanced portion of history is being propagated. This interpretation allows to explain the fact that the interfering realities are not in local causal contact with one another, because even if the two portions of history share the same macroscopic conditions, they do not really happen at the same epoch and therefore the particles present in the retarded portion of a process cannot interact with those which are present in the advanced portion of what only appears to be the same process. As a result, it is no longer necessary to assume as an a priori hypothesis that particles from different histories do not interact with one another in order to avoid the contradiction that emerges in the context of a more conventional approach when it is assumed that all branches of reality coexist in the same portion of the universe's history. It must be clear that while this approach allows the state of the universe specified by a particular point along the configuration space trajectory to be characterized by simultaneously well-defined values of conjugate attributes, observable data would still be subjected to quantum indeterminacy, because 139 no observer that is part of the universe can determine the exact states of both a dynamic attribute and its conjugate counterpart by imposing one particular set of experimental constraints. Thus, when position is determined with arbitrarily good accuracy, momentum becomes totally undetermined, even if there always exists a definite momentum state that corresponds to the relevant point on the configuration space trajectory and this is reflected in the fact that the unobserved attribute is allowed to have completely different, interfering values in the retarded and the advanced portions of history. The only difference between this situation and that which would appear to exist from a more conventional quantum mechanical viewpoint is that it can now be assumed that there does exist a unique reality in each portion of history for the unobserved attribute associated with a given set of observational constraints, even though this reality can differ for the retarded and the advanced portions of history and cannot as a matter of principle be subjected to direct experimental knowledge. But despite the enormous clarification and simplification which are made possible by the adoption of such a viewpoint, it would remain to explain why it is exactly that we are allowed to expect that the curvature of space, as well as other experimentally determined macroscopic conditions, do not differ much, most of the time, for those two portions of history, that is to say, we still need to explain why it is that under normal circumstances a unique classical spacetime and a unique classical trajectory are shared by the particle propagation processes which unfold in the retarded and advanced portions of history, as required if the conventional mathematical framework of quantum theory is to be compatible with what is observed on a sufficiently large scale. As I previously mentioned, this is a particular aspect of the quantum measurement problem, or the problem of the origin of the quasiclassical nature of observed reality. Actually, as I will explain below, it is the fact that the history of our universe consists of one single, closed trajectory in superspace that allows quasiclassicality to naturally emerge as a property of the physical world under appropriate conditions and therefore it will be apparent that the fact that our world is in effect classical on a sufficiently large scale allows to confirm the validity of the hypothesis that the history of the universe constitutes a circular process that feeds back on itself. Thus, if it was not for the closed, or circular nature of quantum mechanical history we would really need to assume that for some reason two independent, quantum mechanically interfering processes are taking place at the same time, all the time, despite the 140 fact that it would then be impossible to explain why it is that the retarded and advanced portions of a process actually share the same experimental conditions (because the criterion of consistency specified by the consistent histories interpretation of quantum theory is insufficient to achieve such an outcome, as I explained in section 10). One thing should be clear already, though, and it is that if the history of the universe consists of a closed causal chain, then the retarded and advanced trajectories in superspace must be smoothly joined at some point in what appears to be the future from the viewpoint of unidirectional time and also at a certain point in what appears to be the past from the same unidirectional time viewpoint. As a result, no two points on the universal causal chain can be absolutely characterized as 'earlier' or 'later'. But it is also clear that the directions of propagation in time along two corresponding segments of the closed causal chain (those which appear to be in the same macroscopic state at a given instant of time) have significance merely as relationally defined properties (only the difference between those two directions has physical meaning), because no direction of propagation can be attributed absolute significance. Thus, the direction of time associated with one or another portion of history along the universal causal chain is not a direction in configuration space, but a relationally defined property of the universal causal chain itself. Yet, the growth of (gravitational) entropy does allow for the existence of an objectively defined direction of time, to which can be compared the direction of propagation along a given segment of the universal causal chain and it is from the viewpoint of this unidirectional time parameter that the universal causal chain would eventually appear to close and time would come to an end. Now, it may appear that the hypothesis that the superspace trajectories associated with the retarded and advanced portions of history must be smoothly joined at a certain point in the future could never be proven right, given that from the unidirectional time viewpoint the closure of the universal causal chain cannot be observed unless it has already occurred, in which case we would no longer be there to acknowledge this fact. But, as I mentioned above, the validity of the theoretical requirement of closure can actually be confirmed by the observation that reality is of a quasiclassical nature, for reasons I will soon explain. The existence of such an end of time, however, must be distinguished from that which would occur as a result of an interruption of the trajectory of the universal causal chain in superspace, which despite what one might be tempted to assume is absolutely forbidden, given that it would 141 not constitute a simple bifurcation point in unidirectional time, but would involve a causal discontinuity even from a bidirectional time viewpoint. One important aspect that needs to be emphasized here is that the situation of a universe which is submitted to a condition of closure of its configuration space trajectory is not the same as the situation of a universe which would evolve, as a result of Poincaré recurrence, to the exact same macroscopic state (characterized by the same observable conditions) in which it was at an earlier time, which could be satisfied even if the superspace trajectories associated with the retarded and advanced portions of history do not merge at any point along the shared coarse-grained trajectory that would take the universe to its earlier macroscopic state. In the present case it must be assumed that when the universal causal chain closes in the future it will be due to the fact that the retarded portion of history has by chance found itself in the exact same state as that in which the advanced portion of the process turned out to be, not just at an observable level, but even for what has to do with the unobservable states of those physical attributes which are the subject of quantum interference. The evolution along the closed causal chain, therefore, will not merely take the universe to a state that is similar to that in which it once was, but eventually to the exact same point it once occupied in configuration space, from which any further evolution would take the universe into the exact same history through which it once went, despite the random nature of this evolution. Yet, if an observer is present when the bifurcation point is reached, she would not be able to experience the same history she once experienced, but in reverse, because what would happen is indeed a reversal of the direction along which the causal chain is propagating with respect to unidirectional time, which means that the thermodynamic arrow of time would reverse and reality could only be experienced in the opposite direction along the closed trajectory (the same direction as that in which the observer experiences reality in the retarded portion of history). Under such conditions both an observer that is part of the retarded process and its counterpart that evolves as part of the advanced process would simply cease to experience reality at the bifurcation point, because consciousness is a thermodynamic process that necessarily takes place along the direction of time in which entropy is rising globally. But it must be understood that the closure of the universal causal chain does not take place in position space, but really in configuration space, or superspace and therefore it does not involve an annihilation of the particles present in the retarded portion of history by 142 those present in the advanced portion of history and it is not limited by the requirement of energy conservation that would otherwise need to apply with respect to unidirectional time, because in such a case continuity is only relevant from the bidirectional time viewpoint. Thus, the point in the future at which the retarded and advanced trajectories of the universal causal chain would merge from the unidirectional time viewpoint does not have to be of a very special nature and could be any instant of time. Again, though, it must be clear that the closure of the universal causal chain is a phenomenon that takes place in configuration space and therefore it may appear to violate the principle of local causality by occurring all at once in position space. Indeed, even if the bifurcation process may appear to take place at different times in distant regions of the universe from the viewpoint of certain observers, once it happened in one region of the universe it would have to rapidly occur in all the other regions, as the condition that is responsible for the continuous decrease of entropy in the past direction of time does not allow for oppositely directed thermodynamic arrows of time to be present simultaneously in the same universe. Also, if time can be extended to instants past the initial Big Bang singularity, then the moment in the past at which the universal causal chain would close would not necessarily need to be that at which the Big Bang itself occurs, but would likely be a time, arbitrarily distant in the past, prior to the Big Bang, when by chance alone the retarded and the advanced configuration space trajectories would meet. But it must be clear that the advanced portion of the known history is not the trajectory that unfolds prior to the Big Bang. Both the current history and that which may have taken place (with entropy growing in the opposite direction of time) before the Big Bang (as apparently allowed by certain quantum gravitation theories) have their own retarded and advanced portions of the same closed causal chain and could actually be very different histories involving different sets of observable events. If I believe that it is not a priori necessary to assume that the retarded and advanced configuration space trajectories meet at the Big Bang it is because, despite the uniformity of the matter distribution and the minimum gravitational entropy that characterized the initial maximum density state it remains that the retarded and advanced states could in principle be different in their unobservable quantum mechanically interfering details. This is especially true in the context where it must be assumed that the information contained in the microscopic state of the gravitational field grows with the density of matter, for reasons I have explained in section 3.7 of [1], so that 143 the probability of an exact correspondence of the retarded and advanced states is as small during the first instants of the Big Bang as it is at any other time (given that the universe has the same information content and the same number of microscopic degrees of freedom during the first instants of the Big Bang as it has at any other time). Thus, it would only need to be assumed that a meeting of the retarded and advanced configuration space trajectories occurs at the Big Bang if it turned out that it is impossible for bidirectional time to be extended past the initial maximum density state, as would be the case from a classical viewpoint in the presence of an initial spacetime singularity. In any case, if the hypothesis that the universal causal chain must be closed is justified then it becomes possible to confirm the validity of the conclusion stated at the end of section 8 to the effect that the sign of energy of the particles which can be observed to propagate forward in time in the retarded portion of history, must be opposite that of the same particles which are propagating backward in time in the advanced portion of history, which means that those energy signs remain unchanged relative to unidirectional time. Indeed, if the superspace trajectories associated with those two portions of history are smoothly joined at a remote point in the past, as well as in the future, then the particles which propagate forward in time in one portion of history must reverse their direction of propagation in time from the unidirectional viewpoint at both the past and the future bifurcation points, due precisely to the fact that they do not reverse their direction of propagation from the viewpoint of bidirectional time. But this means that the energy signs which necessarily remain unchanged relative to the direction of time in which those particles propagate (given that their action signs do not reverse) would appear to be reversed in comparison with those of the corresponding particles which propagate in the opposite direction of time in the current portion of history, in agreement with the conventional description of advanced wave phenomena. The only difference between the conventional description of advanced waves and that which emerges from the alternative definition of the time reversal operation I introduced in chapter 2 of [1] has to do with the fact that the signs of all the non-gravitational charges carried by the particles associated with those advanced waves would now appear to be reversed from the unidirectional time viewpoint, given that it is explicitly assumed that they remain unchanged from the viewpoint of bidirectional time when the trajectory of the universal causal chain bifurcates in the future and in the 144 past. This is without consequences, however, because the fields that provide the experimental conditions observed in the advanced portion of history all have their polarities reversed as well. The circular nature of history is also what allows to explain that quantum interferences do occur, even in the context where we are assuming that the retarded and advanced portions of a quantum process actually take place at two very distant epochs along the configuration space trajectory, which would appear to imply that they should have no effect at all on one another (locally). I believe that if there are quantum interferences between the many possible paths allowed for the retarded and advanced portions of history it is because the circular nature of history imposes a condition of continuity on the quantum phase equivalent to that I have identified in section 8 when discussing the significance of the negative probabilities which occur in the context of a time-symmetric formulation of quantum theory. Indeed, given that what one would need to estimate, ultimately, is the probability of observing a certain history of the universe that comprises a detailed description of all the individual subprocesses (decoherent or not) which occur in the course of that history, then one must recognize that the phase is actually a shared property of the unique configuration space trajectory that provides the most accurate account of the history of the universe. But, in the context where the whole history actually consists of a closed causal chain that feeds back on itself, there actually exists a constraint which imposes that all contributions by intermediary subprocesses to the evolution of the quantum phase of the complete cosmological process that takes place along the closed configuration space trajectory be such that they allow the phase to end up, after a complete turn, into the exact same state in which it was at the point of the trajectory that constitutes both its initial and its final boundary condition. Indeed, if the universe does, in effect, evolve back to the exact same state in which it once was, then this state cannot itself be different from what it actually is, even for what regards unobservable physical properties like the quantum phase, otherwise the concept would have no real significance. It had, in fact, already been realized [30] that there is a single phase associated with the whole cosmic process that is equivalent to one very rapidly moving clock hand. But in the context where time itself must be considered to constitute a periodic phenomenon it follows that this wave function must be similar to that which applies to quantum systems submitted to periodic boundary conditions (like an electron in orbit around a hydrogen nucleus, 145 whose wave function must necessarily involve an integer number of wavelengths). There may, thus, be something true to the previously discussed results from canonical quantum cosmology which appear to indicate that the wave function of the universe is of the stationary kind, even if in the present context this no longer means that time is irrelevant to quantum cosmology. In any case, this continuity condition is what allows me to explain why it is, in effect, appropriate to impose on the unobservable quantum phase that it does not end up in the course of an ordinary time-symmetric process in a state that would be incompatible with that in which it initially was, a requirement which I believe can be enforced in the context where certain time-symmetric histories (with which are associated negative probabilities) are allowed to diminish the probability of observing the very conditions necessary for their own occurrence. Indeed, it appears to be the requirement of continuity of the quantum phase that explains that individual time-symmetric processes have a larger probability to occur in ways that do not require a phase change that would increase the likelihood that this phase is not left invariant after a complete turn over the global configuration space trajectory (for the universe as a whole), because the phase associated with a local subprocess is reinitialized upon measurement (as a result of decoherence) which means that it is necessary to impose a constraint of continuity independently to those phase changes that take place in the course of individual time-symmetric processes, even if the real constraint applies to the universal causal chain on which is imposed the closure condition. Thus, it becomes possible to understand why it is that there are quantum interferences between multiple different histories for ordinary quantum processes, even in the context where we assume that only one history actually takes place. Those are very significant conclusions given that in the present context observation of quantum interferences is the only way by which the advanced portion of history can be deduced to exist from the viewpoint of an observer that is present in the retarded portion of history. Such an explanation of the origin of quantum interference effects would also appear to confirm that quantum non-locality is a consequence of the non-trivial topology of the configuration space trajectory. Indeed, according to Hans Reichenbach [31], when faced with unexpected non-local correlations one can either invoke 'preestablished harmony' in the form of instantaneous couplings of distant events that would violate the principle of local causality, or else recognize that one is dealing with a compact topological structure in which periodicity 146 naturally arises. What I have tried to explain is that the history of the universe is just such a structure and therefore its circular nature is what most naturally explains quantum non-locality as a phenomenon involving the entanglement of quantum phases. Now, as I mentioned in section 6, it has been argued by certain detractors of the more conventional time-symmetric interpretations of quantum theory that the problem with any such interpretation is that it is not possible to distinguish between situations where interferences among different histories must be assumed to exist and situations where they can actually be ignored. I have already explained that this erroneous conclusion arises merely when we fail to recognize that decoherence must occur, even from the viewpoint of a time-symmetric formulation of quantum theory, under the same conditions where it would be expected to happen according to a many-worlds interpretation, even if the phenomenon has a different meaning in the context of a time-symmetric interpretation. But, as I mentioned in section 10 there are two problems that one must face before one can conclude that decoherence does in effect provide the mechanism by which the quasiclassical character of macroscopic phenomena arises, even in the context of a time-symmetric formulation of quantum theory. The first of those problems has to do with the fact that it may never be possible to assume that decoherence itself constitutes a truly irreversible process. There is no reason, in effect, to reject the possibility that given enough time the processes giving rise to decoherence could eventually be reversed on an arbitrarily large scale, so that the many variables of the environment with which a quantum system has become correlated could be submitted to quantum interference, even without deliberate intervention and long after a measurement would normally be assumed to have occurred. Indeed, it appears that it is merely the improbability of such an evolution that explains that we do not feel compelled to recognize that measurements may not be definitive processes and could actually be overturned in the future, with consequences for the predictability of observable phenomena which are taking place right now. One may be tempted to argue that this is not a real problem, because the potential for entropy growth may be unlimited in the future and this may allow one to expect that, as the effects of a measurement spread irreversibly into an ever larger portion of the environment, the possibility that quantum interference involving all those correlated variables may be allowed to occur becomes ever more insignificant. Indeed, I have provided arguments in section 3.10 of [1] to the effect that the growth of gravitational 147 entropy may be unlimited in our universe, due to the presence of negative energy matter, which would appear to provide support for the conclusion that decoherence is truly irreversible, even in the context of a conventional interpretation of quantum theory. The problem, however, is that given an infinite amount of time, even such a continuously decreasing probability may not prevent fluctuations from eventually giving rise to quantum interference on a very large scale. Therefore, it would seem that one cannot avoid the conclusion that decoherence is not definitive, which should have significant consequences at the present epoch. Now, given that I have argued in section 3.7 of [1] that the expansion of the universe does not take place with a real growth in the amount of microscopic structure or information, due to the variation of information associated with the diminishing strength of local gravitational fields, it would appear that the probability that the universal causal chain closes at some point in the future is not diminishing with time. While this conclusion may perhaps appear to be irrelevant to the problem discussed here, that is not the case, because what it actually means is that unidirectional time will, by necessity, eventually end at some point in the future, however distant it might be. But, if history does not last forever, then the probability that decoherence may be reversed on a very large scale at some point in the future, in a universe with ever growing entropy, actually becomes null. In other words, what we are now allowed to expect is that the universal causal chain will eventually close in the future, before decoherence has the chance to be reversed on a large scale, which means that decoherence does not merely eliminate quantum interferences for all practical purpose, but gives rise to classical outcomes of measurement as a matter of principle and this conclusion remains valid even in the context were we do not postulate that irreversibility arises at a fundamental level. I believe that this constitute the decisive argument that allows one to make sense, at long last, of the observation that quantum measurements, once effected, produce definitive outcomes which are never overturned. The second problem one must confront is perhaps more significant. Indeed, I have explained in section 10 that certain relatively well-known developments [19] appear to indicate that the criterion of 'consistency' (in the sense of a consistent histories interpretation of quantum theory) would not be constraining enough to allow one to expect that the quasiclassical nature of reality would persist following a quantum measurement, conceived as an irreversible process during which decoherence is taking place (even when one 148 assumes that those measurements produce definitive outcomes). I can now explain why it is that the realist, time-symmetric interpretation of quantum theory I have developed is more appropriate for predicting the emergence of a quasiclassical world that remains classical once the consequence of one or another outcome of a quantum measurement irreversibly propagates into the environment. What holds the key to a complete and effective solution to this particular aspect of the quantum measurement problem and to an explanation of the quasiclassical nature of 'macroscopic' reality is the acknowledgment that the property of closure of the universal causal chain is not optional and must, according to the arguments provided above, be imposed as an absolutely essential consistency requirement. It is only when I recognized the unavoidable nature of this condition that I was able to understand that in the context where there must exist both a retarded and an advanced portion to every quantum process, additional constraints exist which only become apparent during processes which can be qualified as measurements. So, what is it indeed that characterizes a process that can be described as a quantum measurement? The essential ingredient of decoherence itself appears to be irreversibility (dissipation to be more specific), but as I mentioned above decoherence can only be part of the solution. So what happens as a consequence of irreversibility that does not take place under those conditions where quantum interferences exist? To answer that question it may help to consider what would be necessary for measurement not to occur and quantum interference to exist, even after a quantum system becomes entangled with its environment. It is obvious that what would be required is that the state of the quantum system along with that of the immediate environment to which it has become correlated do not become entangled with an even larger portion of the environment. In other words, there would need to be no traces in the larger portion of the environment that would allow one to tell through which history the system and its immediate environment actually went. The point at which irreversibility enters the picture, therefore, is through the making of a record of the events involved (conceived precisely as the kind of process during which the effects of one or another of several alternative outcomes of the evolution of a microscopic system is amplified to macroscopic proportions). Only when the state of each physical attribute whose determination would allow one to tell what the history of the system and its immediate environment was is submitted to quantum interference before this information has the time to spread into the environment, can 149 interferences actually be observed. It would therefore appear that if irreversibility is in effect necessary for the elimination of interferences it is because the making of a record can only occur when future evolution takes place irreversibly. What happens when a record is produced is that one unique cause in the past leaves multiple recognizable and mutually consistent traces of its occurrence in the future. A long lasting record is one whose mutually consistent traces themselves each produce multiple recognizable and mutually consistent traces in the future that can all be traced back to the same unique original cause in the past. What happens when a quantum measurement, conceived as a particular, but general instance of such a record making process, comes into effect, therefore, is that a unique, particular outcome of the evolution of a quantum system causally influences in a recognizable way a multitude of other events in the future, which would all have been affected in recognizably different ways had that original outcome been different or inexistent. What must then be responsible for the elimination of interferences that follows decoherence is the fact that a growing number of observable variables become correlated with one unique specific outcome of the evolution of a microscopic system, while all of those variables would have evolved differently if another outcome had been obtained for the same measurement in the past. Now, the important point in all of this is that the spreading of causal influences does not take place with respect to an arbitrarily chosen dynamic attribute, but always relative to position space. Indeed, as I have emphasized in section 7, at the most fundamental level reality appears to consists of elementary particles, which are objects that are localized in position space and which allow the propagation of causal influences through local contact, again in position space. There is, thus, something very particular with position space for what has to do with unidirectional causality and the irreversible propagation of effects and this is apparent in the fact that the spreading of wave fronts always occurs in position space and not in configuration space. The singular status of position space is made even clearer by the fact that the particular boundary condition which I have identified as being responsible for the asymmetry of the evolution in time of systems with a large number of independent, microscopic degrees of freedom is a condition that is imposed on the spatial distribution of matter in the first instants of the Big Bang. Indeed, it is the homogeneity of the spatial distribution of positive and negative energy matter particles in the maximum density state of the Big Bang that allows the universe to evolve irreversibly toward a state of 150 larger gravitational entropy characterized by a greater inhomogeneity of the two matter distributions, as space expands, in the future direction of time. But, as I explained in section 3.9 of [1] this condition is what allows one to assume that the cosmic horizon, which limits the scale of unidirectional causal influences, actually grows with time from the minimum value it had in the initial singularity. What is allowed to happen on a smaller scale as a result of this particular condition is for an irreversible spreading of effects into an ever larger volume of space to take place in the future direction of time, as elementary particles freely propagate in either the retarded or the advanced portion of history (this is particularly apparent in the case where dissipation is involved). In fact, as I explained above, the same constraint of global entanglement which gives rise to thermodynamic irreversibility is also responsible for allowing time to differentiate from the other three dimensions of space and therefore for giving rise to the causal structure of spacetime that is described by relativity theory and which is responsible for the fact that effects necessarily spread in space, either forward or backward in time. But what characterizes unidirectional causality is not only the fact that it operates relative to a unique dimension of space-time, but also the fact that it does indeed give rise to an irreversible spatial spreading of effects in the future direction of time, which is actually what causality is usually considered to be all about. Thus, as time goes, a growing number of independent, microscopic degrees of freedom can be causally influenced in recognizable ways by unique causes located in the past, while the reverse phenomenon is never observed to happen and this is really a property that is unique to the evolution of position states. We are now very near a solution to a very old problem. What I have just explained is that the making of a record is the essential condition for a quantum measurement to take place and that what it entices is the production of a multiplicity of correlated effects involving very many otherwise independent variables which could all have evolved differently in the future had the outcome of this measurement itself been different. A multitude of correlated effects as the outcome of one single quantum measurement. It is not very difficult to realize that, as time passes, the observable difference between the consequences of one single past measurement and what would have been the consequences of obtaining a different result for the same measurement becomes ever more significant. But in the context where one recognizes that the universal causal chain must, as a matter of principle, form a closed trajectory in superspace, then this remark becomes highly significant. 151 Indeed, in a world that would have been quasiclassical on a macroscopic scale until now, if a measurement performed on the retarded state of a quantum system was to give rise to an outcome that is different from that which was obtained as a result of a similar measurement performed on the advanced state of the same system by a measuring device whose irreversible evolution actually also takes place in the future direction of time, then as time goes (in the future) an exponentially growing number of independent variables from the environment of the system that evolves as part of the retarded portion of history, would be allowed to differ from those of the same system that evolves as part of the advanced portion of history. This means that the two trajectories in superspace, which until now had always been very similar to one another, would begin to diverge in a way that would actually make it increasingly less likely that they could ever merge with one another at some point in the future, because of this property of the record making process which is to produce an accumulation of recognizable changes in the states of an innumerable number of independently evolving degrees of freedom as a consequence of one little change in the past. It is the requirement of closure that applies to the universal causal chain that constrains the future evolution of the retarded and advanced portions of history to not be divergent in any observable way from the unidirectional time viewpoint, because if this condition was not obeyed the number of independent variables from both portions of history that would need to change together in the same recognizable way at some point in the future, so as to allow a merger of the two trajectories would become too large for the closure requirement to ever be fulfilled. As a result, the universal causal chain must be stretched into two similar trajectories evolving side by side along the unidirectional direction of time in superspace for the whole duration of history, as if two indistinguishable versions of history where taking place in parallel all the time without ever interacting with one another. But the constraint of non-divergence need not be any more restrictive than that, because what remains unobserved does not give rise to the formation of a record and has no irreversible consequences and therefore is not required to correspond for the two portions of history by the requirement of closure of the universal causal chain. Quantum interferences are not forbidden altogether, merely increasingly more probably as the entanglement of a quantum system with its environment becomes more significant and this is exactly what is required from an observational viewpoint. It must be clear, however, that despite the unique role played by posi152 tion in giving rise to the formation of records, the attribute of a quantum system that is known with perfect accuracy is not necessarily always its position. The privileged status of position space only means that even when the measured attribute is not position, it is nevertheless a spatial distribution of macroscopic constraints that allow such a measurement to be performed, because it is concerning those constraints that information is available in the form of records. This means that there is no freedom in deciding which dynamic attribute is classically well-defined in any particular situation where we have knowledge of a specific set of macroscopic conditions (while in fact such conditions are always present for one and only one dynamic attribute, as I mentioned in section 10). On the other hand, the attribute of a quantum system for which only a minimum amount of information is available in the form of irreversible records concerning the position states of various parts of a measuring device (the environment degrees of freedom), is the attribute that may go through any possible history in both the retarded and the advanced portions of history, thereby giving rise to interferences. What's important to understand is that given that it is for position space observables that the making of a record of past events can take place, then it follows that the constraint of non-divergence of the retarded and advanced configuration space trajectories is a constraint that applies only to the dynamic attribute of a system whose state is restricted to a subset of values as a result of being submitted to experimental conditions of such a nature. But such a constraint does not only give rise to non-interfering outcomes of measurement following decoherence, but really to a quasiclassical evolution that persists in time for the same family of consistent histories (the physically relevant set of histories). It had already been remarked, in effect, that decoherence, as it is traditionally conceived, allows to select position as the relevant collective observable (that which becomes correlated with the microscopic system under study), at least for mechanical systems in the presence of dissipation. It was conjectured that this is merely a consequence of the fact that the laws of physics (particularly in a quantum field theoretic context) are invariant under a change of reference system. In the present context, however, this could only be understood to mean that the selection of position as the relevant collective observable for decoherence is indeed a consequence of the fact that unidirectional causality (the irreversible spreading of effects) operates in position space, because what emerges as a result of relativistic invariance is the causal structure of spacetime, which under appropriate con153 ditions (when evolution is irreversible) gives rise to unidirectional causality and therefore to the existence of persistent records of past events. The fact that the phenomenon of dissipation merely consists in one particular instance of irreversible spreading that necessarily takes place in position space would therefore appear to confirm that it is the closure requirement (that must be applied to the universal causal chain) that allows quasiclassicality to emerge and to persist for those attributes of a quantum system whose states are restricted by macroscopic conditions of a spatial nature. There should be no doubt that the existence of such an objectively defined preferred basis is absolutely necessary from an observational viewpoint, as if none arose it would be impossible to determine what causes the persistence of the quasiclassical nature of reality (even under the assumption that the universal causal chain is closed), because if reality was classical with respect to one family of consistent, coarse-grained histories at a given time and then relative to another such family at a later time, as allowed in a more conventional context, then this reality would no longer appear classical from the first viewpoint after this transformation has occurred. But when quasiclassicality is the outcome of imposing a requirement of closure to the universal causal chain and irreversiblity is a feature of the spreading of effects in position space, it follows that a preferred basis (a preferred choice of dynamic attribute to represent quantum states) is naturally selected for the elimination of quantum interferences and it is from the viewpoint of the records which are available concerning the constraints (of a spatial nature) that select this dynamic physical attribute that the world necessarily appears to remain classical following a measurement. I believe that those conditions, therefore, allow to satisfy Dowker and Kent's requirement for an additional, purely quantum mechanical principle that would allow one to select a particular set of (consistent) histories as being of particular physical significance, without having to rely on solipsist arguments. So here we are, having actually explained why it is that in practice one never observes quantum superpositions involving macroscopic states of measuring apparatuses. If we never experience histories in which a cat is alive and dead all at once, it is because if the cat was not either alive or dead in both the retarded and the advanced portions of history this would change the future in ways which would render impossible an eventual meeting of the retarded and advanced trajectories in configuration space that is necessary for the universe to be self-determined from the viewpoint of causality. The identified constraint simply makes it extremely unlikely (as unlikely in fact as 154 the growth of entropy that took place while the retarded and advanced states became distinct is important) that such an evolution could ever be deduced to have occurred. The essential characteristic sought by Von Neumann and which would differentiate a measuring apparatus from the system it measures is simply the possibility that exists for the measuring device to generate a record of its particular evolution, which has decisive consequences in the context where reality is a causal chain that must close at some point in the future. From that viewpoint, of course, quantum interference of macroscopic states is not completely impossible, but even if such an unlikely phenomenon was to happen, then one would not see a cat that is both alive and dead at the same time, because one is always confined to directly perceive only the portion of history (either the retarded or the advanced) in which one happens to be located and in any such a history there is always a unique set of causally related facts. But this does not mean that a state of superposition involving a macroscopic portion of reality would have no apparent consequences, because if the advanced state was to become distinct from the retarded state on a large scale, then the estimation of transition probabilities for future processes would be affected in dramatic ways from the viewpoint of observers which are part of the process while it is under way, which means that their future would actually become unpredictable unless they assume that such a divergence from classicality has indeed occurred and this is how they would actually gain knowledge of this distinction between the current retarded and advanced states. But if the condition of closure of the universal causal chain has the expected consequences, then the observers which were part of such a process would not be allowed to remember through which history they went on either the retarded or the advanced portion of the process after quantum interference is over, as otherwise this knowledge could spread into the environment25. 25This observation cannot constitute the basis of an alternative explanation of thermodynamic time asymmetry, because if one does not assume that there exists a constraint for the retarded and advanced states not to diverge that is made necessary by the independent condition of low gravitational entropy at the Big Bang, which from my viewpoint is responsible for time irreversibility, then one has no reason to expect that the retarded and advanced portions of history should converge back to the same macroscopic state after having diverged on a large scale and this means that our memory of the particular history which actually took place would not need to vanish and therefore its persistence would not need to be correlated with a history where entropy grows in the future. 155 The point that is perhaps the most difficult to understand concerning what I believe would qualify as an appropriate account of experiments of the Schrödinger cat type in which there would be interferences of macroscopic states is that in the final state of such an experiment the cat would have to be neither in a live-with-no-poison-in-its-blood state, nor in a dead-withpoison-in-its-blood state, even though it is true that the animal may no longer exist in a recognizable form, because this is not the same as a cat that is dead due to having absorbed the poison released as a result of the measurement on the quantum particle having produced a negative result, even if it does mean that the cat may no longer be alive in the final state. What is required therefore is that it be impossible to tell from the information that is present in the final state whether the cat was killed by the poison or whether it might have been alive without any poison in its blood before the final measurement was performed that would have revealed the existence of quantum interferences, so that even if the cat no longer exists in the final state it would not be correct to say that it was killed as a result of the particular outcome of the particle disintegration process. In any case, given that no complex macroscopic system such as a cat was ever subjected to any reproducible experiment in which quantum interferences would have been observed, then it would appear that the requirement of closure which I suggest must be imposed on the universal causal chain is well motivated, because it does allow one to expect that macroscopic objects, which can never be completely isolated from their environment, should practically never be found in states of quantum superposition. An additional advantage of the approach proposed here, is that it allows one to understand how it is that global consistency would be enforced in the context where a classical time travel experience would occur and the course of history could potentially be altered so as to give rise to an alternate future. Indeed, when the effects of a future measurement can be propagated backward in time as a result of the existence of an advanced portion of history and there is a condition for the retarded and advanced portions of history to share the same observable macroscopic conditions in the future (so that the universal causal chain can close at some point), it follows that the present can only be influenced by the future to be such as to give rise (through forward in time causation) to classical outcomes of measurement rather than to a retarded state that would differ from the advanced state. In other words, the present cannot be influenced by the future in such a way that it would be likely to evolve toward a different future. Thus, even if the second law 156 of thermodynamics could be temporarily violated in a local region of space, perhaps as a result of a formidably improbable fluctuation, and information about the future would become available, no violation of the principle of global consistency could arise. The circularity of the causal process is what allows consistency to be preserved in a way that would be impossible in the absence of an advanced counterpart to every retarded propagation process. The conclusion that global consistency would always be preserved in a quantum mechanical context, therefore, need not depend on the hypothesis that all histories are followed all at once and that a 'splitting of branches' occurs whenever an alternate reality is produced, as is often assumed, because it can be derived much more naturally by recognizing that in order that the universe be causally self-determined, its history must consist in a closed causal chain. Yet it does seem appropriate to assume that it is quantum theory that would ultimately be responsible for the impossibility of even a classical time travel paradox, as I suggested in section 4, because the limitation discussed here is made unavoidable as a result of the time-symmetric nature of quantum reality, which through purely local causal influences enforces consistency on a global scale (as necessary for the existence of non-local correlations). Now, it must be clear that a condition of closure, similar to that which applies for the future, must also apply to the evolution that takes place in the past direction of time, because even if entropy does not increase in this direction of time, so that there is no constraint arising from the making of records (no record exists of the future), if we do not require the universal causal chain to close at a certain point in the past, then reality would not necessarily remain quasiclassical relative to the same family of consistent, coarse-grained histories in the past direction of time, which means that the existence of a unique past compatible with the ensemble of mutually consistent records of it would not be required. The fact that quasiclassicality persists in the past for those dynamic attributes which are submitted to the same kind of experimental conditions as applies on those that remain quasiclassical in the future, allows to confirm that past classicality is due to the same constraint of closure of the universal causal chain as applies on future evolution (now applying to the evolution that takes place before the Big Bang) and not merely to the fact that entropy diminishes in the past26. Just 26One should note that it is not possible to assume that the universal causal chain closes at the Big Bang and yet that there is a history taking place in reverse prior to the 157 as is the case for the future, it is not possible to say when it is exactly that such a meeting of the retarded and advanced configuration space trajectories would occur and the only condition is that it does not occur before the time at which the initial singularity is formed in the past, because otherwise global entanglement would not have had the time to occur and the universe would not have been allowed to exist as an entity formed of causally related elements. Thus, in the context where time would extend past the initial maximum density state of the Big Bang, there would actually exist a constraint that would apply to the evolution of the retarded and advanced states that takes place in this portion of history that would require them not to differ in their measured, observable properties, because entropy would then be growing in the past, for reasons I have discussed in section 3.9 of [1]. But this does not mean that the evolution that takes place in the past direction of time before the maximum density state is reached would not be similarly constrained by the closure requirement, because if this requirement is to be satisfied at some point in the distant past, on the other side in time of the initial singularity, then the past evolution that is taking place on our side in time of the Big Bang must already be such as to not allow a divergence that would involve a spatial position observable. Indeed, it is only when there is no such divergence as we approach the initial maximum density state in the past, before the thermodynamic arrow of time reverses, that the initial retarded and advanced states are allowed to be compatible with the closure requirement that applies to the evolution that takes place 'subsequently', in the past direction of time, prior to the Big Bang, and which is similar from the viewpoint of its thermodynamic properties to that which is taking place in the future, on our side in time of the initial singularity. Up to this point I have only discussed the emergence of quasiclassicality as it arises in a conventional quantum mechanical context where the metric properties of spacetime constitute a common, unique background over which both the retarded and advanced portions of a process unfold, either with or without interference, depending on whether or not the particular history of the particles propagating over this background space gives rise to the making of a record. But what right do we have to assume that the metric properties of Big Bang, otherwise the meeting of the retarded and advanced trajectories in superspace would no longer have any meaning even for the future, because when the closure condition would be met history could nevertheless continue as if nothing had actually happened. 158 spacetime themselves should always be shared by the retarded and advanced histories if all other physical quantities can under appropriate circumstances differ and interfere for the two trajectories of the universal causal chain? If the other macroscopic conditions which are shared by both portions of history are so determined merely as a result of the fact that they give rise to an irreversible spreading of effects, then why would the metric properties of spacetime which are shared by both portions of history be simply given once and for all in their classical form, instead of being subjected to the same rules that govern the other physical attributes of our universe? The truth, of course, is that the metric properties of space are not always classically well-defined and that they may differ and interfere for the two portions of history. It is already understood in fact that macroscopic changes to the gravitational field are a very potent way by which decoherence can be triggered, as confirmed by the fact that the motion of planets is one of the phenomena for which the absence of quantum interferences is the most conclusive and the most persistent, while it was shown that this is not unrelated to the magnitude of the gravitational fields involved. Now, I have already mentioned that in a quantum gravitational context what we would be dealing with are situations where the intrinsic curvature of space would be allowed to differ in the retarded and advanced portions of history. I may now add that this would occur whenever information in the form of records would only be available about the extrinsic curvature of space associated with its rate of change along the universal causal chain (for a rigorous definition of the distinction between intrinsic and extrinsic curvature see [32]). Indeed, the intrinsic and extrinsic curvatures of a spacelike hypersurface are the quantum gravitational equivalent of position and momentum and therefore they constitute conjugate physical attributes whose states cannot be determined together with arbitrarily high precision using one unique set of experimental constraints. But this does not mean that all histories involving distinct intrinsic curvatures are followed all at once when the extrinsic curvature is known with high precision, but merely that the intrinsic curvature may be different for the corresponding retarded and advanced portions of history under such conditions, because information in the form of records of the actual history is available only about the extrinsic curvature. The situation we normally experience (outside the quantum gravitational regime) is one where the curvature of space in general is classically welldefined (knowledge is available about both the intrinsic curvature and its 159 rate of change) and there are no quantum interferences arising from the curvature of space being potentially different for the retarded and advanced portions of a process, as is necessary for conventional quantum theory to provide a viable description of reality. But that need not always be the case and indeed under situations where we would try to determine the extrinsic curvature of space with a very high degree of precision, by measuring the rate of change of the gravitational field on a very small scale, then the intrinsic curvature of space would be subjected to quantum interference, as its state would no longer be constrained to be the same in the retarded and advanced portions of history, for reasons I already mentioned. Under such conditions it would no longer be possible to estimate transition probabilities while using one unique set of metric properties, that is to say, by assuming the existence of one single classical spacetime over which particles would propagate in both portions of a process and it would be necessary to take into account the possibility that the metric properties of space themselves could evolve differently in the two portions of history. It would then be quantum interferences between the many possible histories of space curvature which would determine what metric properties are likely to emerge upon observation. When interference would happen to be constructive, a given curvature would have more chances to be observed and when interference would be destructive, the very boundary conditions necessary for the observation of such a curvature would themselves be unlikely to have existed in the first place. From such considerations it transpires that time must still exist in a certain form, even in the quantum gravitational regime, despite the fact that causality may no longer operate in the same direction of spacetime uniformly over all space on the smallest scale. Indeed, the initial constraint of global entanglement that is responsible for selecting the particular signature of the metric of spacetime that gives rise to a universally valid distinction between time and the other three dimensions of space would no longer be effective on a very small scale, where quantum fluctuations can be expected to give rise to arbitrarily strong local gravitational fields. But it must be clear that time itself is not subject to quantum interferences or superpositions, as is sometimes suggested, and if it may be distinct for the two portions of history it is only in the sense that on a smaller scale time may flow faster, or slower, or in differing directions of spacetime locally for the two portions of a quantum gravitational process, due to the fact that the curvature of space may not be the same in both portions of history, which may therefore give rise to differing durations for otherwise similar propagation processes. 160 It is not that there is no definite space and time in the quantum gravitational regime, simply that even if there exists a unique curvature of space throughout history it can differ for the two corresponding portions of history along the universal causal chain, to the extent that there may in fact no longer be a simple correspondence between those two portions of history on a very small scale along the trajectory in superspace. Reality always remains a unique closed causal chain, even though on a very small scale the regularity and the linearity of its progression in superspace may be altered given that we need to take into account the fact that the metric properties of space and the gravitational field may themselves no longer remain unaffected by the inherent randomness of quantum mechanical evolution which is then, in effect, allowed to give rise to a divergence of the retarded and advanced trajectories in superspace, as long as no record is available regarding what those metric properties actually are. What is significant for a quantum mechanical description of gravitation and space curvature from the viewpoint of the developments introduced in the first part of this section is that there must be a level at which the curvature cannot remain superposed and must give rise to a quasiclassical evolution and this turning point would be determined by the availability of information concerning the metric properties of space. It is in effect precisely when the consequences on the propagation of elementary particles of a particular curvature of space irreversibly spreads into the environment and gives rise to the formation of mutually consistent records that the relevant metric properties must begin to evolve quasiclassically, because the requirement of closure of the universal causal chain can only be satisfied when such an evolution is observed, just as is the case in a more conventional context. Irreversibility would therefore be the essential condition for a classical spacetime structure to emerge and therefore it is when the state of the gravitational field becomes observable that it is no longer subjected to interference effects and that it is no longer allowed to affect the propagation of matter particles differently for the retarded and advanced portions of a process. What this means is that the existence of a decoherent spacetime is itself dependent on the existence of unidirectional time, which emphasizes just how important it is that there exists an independent constraint of the kind I have previously identified for the emergence of irreversibility, because in a quantum gravitational context, when the irreversible character of time itself does not emerge from the relevant theoretical description, decoherence cannot alone give rise to the classical spacetime structure. What will be 161 very important for the argument that will be developed in the concluding section of this report, is the observation that if random fluctuations of the metric properties of space exist that would have no observable effects of the kind that would require the gravitational field to actually have the exact same configuration in both the retarded and the advanced portions of history, then those fluctuations might be allowed to exert an unexpected influence on the propagation of elementary particles, even on a scale well above that at which gravitation becomes as strong as the other interactions. What I will now explain is how decisive this apparently inconsequential conclusion really is. 13 Objectification and the role of gravitation I must immediately warn the reader that the developments that will be the subject of this concluding section of my last report will probably be considered more speculative than other portions of my analysis and I would not myself consider such a judgment entirely inaccurate. Yet I believe that it is important to discuss what I have learned concerning the possible role played by gravitation in solving the problem of objectification, because the solution I will propose to this most insoluble problem of the interpretation of quantum theory is actually motivated by the same desire to uphold the validity of the principle of local causality that motivated the approach I followed in dealing with other problems in cosmology and quantum mechanics. Despite the fact that this discussion comes last, it is actually based on results I had obtained in the earliest portion of my research program, while I was still working on the problem of elaborating a generalized, classical theory of gravitation that would describe the interaction of positive and negative energy matter. It is one of those strange turns of fate that while I was searching for a paper in the immense science and engineering library at McGill University I came upon an article in a very old volume that discussed a failed theory that sought to explain the randomness of quantum measurement results as being caused by perturbations attributable to the interaction of a quantum system with a background of gravitons present in its environment. As I now understand, this was a particular instance of classical hidden variables theory which was inadequate mainly as a result of the fact that it was incompatible with the requirements imposed by quantum entanglement and non-locality. Yet, for some reason, I had the strong intuition that the idea that gravitation was involved in explaining certain aspects of the quantum mechanical 162 description of reality was generally valid and should be further explored. This imperative remained in the back of my mind as a guiding principle as I explored other problems in fundamental theoretical physics and even though I soon realized how such a proposal could be made viable it is only much later that I came to understand that there is actually something unavoidable with the hypothesis that gravitation must become an integral element of a truly consistent formulation of quantum theory. In the previous section I suggested that quantum theory, as it is currently interpreted, is incomplete given that it does not explicitly require the existence of a closed universal causal chain, while, as I have explained, such a concept is essential if we are to obtain a theory that allows for the emergence of a maximum quasiclassical domain. But at this point it was still possible to argue that the current formulation of quantum theory (under its most appropriate form) is compatible with this more complete version of the theory. However, given that the proposed interpretation is dependent on the assumption that there exists a unique reality, and in a certain sense a unique history, behind all quantum mechanical processes, even in the presence of quantum interferences, then it transpires that in order to obtain a complete solution to the quantum measurement problem one can no longer avoid having to address the issue associated with the existence of a unique datum as the outcome of every quantum measurement. Indeed, Omnès' argument (see for example [33]) to the effect that the problem of objectification simply does not exist, because there is no logical way to express it (how could it matter that the electron is found to exist in one particular state following measurement if one cannot even say that it went trough one or another slit in the double slit experiment) would only apply in the context of a more conventional interpretation of quantum theory according to which reality is not unique in any way when it is not observed27. I believe that this difficulty is merely a reflection of the inadequacy of the orthodox interpretation, which, as I have argued at length in the previous sections of the current report, suffers from logical inconsistencies of its own, due in part to its rejection of scientific realism. From the perspective of a more consistent interpretation of quantum theory which does not suffer 27There appears to be some confusion in Omnès' account concerning the true nature of the problem we are dealing with here, as he also argues that the problem of objectification arises merely when one assumes that decoherence is not a definitive process, while, as I have explained in sections 10 and 12 this is a distinct issue, which can be appropriately solved when one recognizes the necessity for a closure of the universal causal chain. 163 from such weaknesses it becomes not only easier to state the problem of objectification, but also easier to solve it. Anyhow, what should be clear is that while decoherence is constraining enough to predict classical outcomes of measurement (when a closure requirement is imposed on the universal causal chain), it does not select from the multiple possibilities so obtained a unique outcome, but rather leaves all potentialities on an equal footing, which is somewhat unsatisfactory, given that only one possibility is observed to be actualized following any measurement. As a result, here again one must face the possibility that quantum theory is incomplete, but now in a way that would appear to require that it be reformulated. Indeed, even in the context of the realist time-symmetric interpretation of quantum theory I have proposed, it would appear that the question of completeness can only be positively answered once one allows for a further extension of the formalism from the viewpoint of which the uniqueness of measurement results would no longer constitute an additional problem, but would rather provide a hint as to what goes on when a particle propagates in the space of its unobserved physical attributes. Those remarks are particularly significant given that the hypothesis that all the unobserved histories allowed by the quantum mechanical formalism are actually occurring all at once in the very same universe is not viable as a solution to the objectification problem, that is to say, for explaining the unique and random nature of measurement results, given that it would require assuming that despite all the evidence, history is not, in fact, unique. I have already explained, in effect, that it is inappropriate to argue that an attribute that is indefinite in the quantum mechanical sense of the word could be objectively indefinite, in the sense that it would not satisfy the requirements of scientific realism in any possible way. But if we are allowed to conceive of a reality of the kind I have proposed, where even in the absence of direct observation particles always follow unique, but possibly different paths in the retarded and advanced portions of history, then the question necessarily arises as to what determines which path is actually followed by a particle in between measurements? You may recall that I have argued in section 10 that the unpredictability of quantum measurement results is not a consequence of the measurement process itself. It is therefore necessary to assume that there is already randomness before a particle meets a detector, while it is still propagating in the two unobserved portions of history and what remains unexplained is the variable nature of this evolution, which applies even for physical systems 164 prepared in the exact same way. What is it indeed that determines the particular evolution of a certain physical attribute that takes place in between measurements and which causes one unique outcome of measurement to be actualized from among many apparently equivalent possibilities? What I have realized is that in order to answer this question it is necessary to recognize that the current theory is merely an idealization and that it must be reformulated to give rise to a more elaborate, but statistically equivalent model, in which the unique outcomes of measurement would be a natural consequence of the existence of fundamentally unobservable, random factors of influence, whose existence is inevitable and does not have to be postulated on purpose in order to solve the problem of objectification. A related question one may ask is whether the concept of objective chance which follows from the fundamental unpredictability of quantum measurement results itself constitutes an appropriate notion in the context of a realist interpretation of quantum theory? In other words, if objective indefiniteness is to be rejected, must one also reject the associated concept of objective chance? The conclusion to which I have arrived is that this depends on what we mean by objective chance. If we are asking whether the unpredictability of measurement results can be circumvented given a more precise assessment of the microscopic state of a quantum system, then the answer would definitely be no. But if what we understand by objective chance is the idea that the unique unobserved path of a quantum system might be 'determined' by nothing at all, instead of being the outcome of fundamentally unobservable causes, that is to say, if we are asking whether it is possible for a distinctive feature of an unobservable aspect of reality to have no identifiable cause, then the answer could only be provided in light of what we already know about reality at the level where it can be observed and by taking into account any possibility that there may be for such a distinctive feature to actually be causally determined (in the time-symmetric sense of the word). Only if we decide that an absence of causes is not physically unacceptable and if we can be confident that no influence exists that would provide such unobservable causes, can we argue that such a strong concept of objective chance is still applicable at the most fundamental level of description of physical phenomena. It is often remarked that the notion of objective chance conflicts with common sense, but that this merely reflects another failure of our intellect to grasp the essentially distinct and counterintuitive nature of quantum reality. Again, however, I would like to argue that this is not all there is and that 165 from the mere viewpoint of logical consistency there is actually something problematic with assuming that a reality can differ and yet that such a difference need not be the result of any known physical influence, even of a fundamentally unobservable nature. What is easy to overlook is that allowing for a difference that would have no 'cause' may conflict with the idea that the physical attributes of all the objects which are present in our universe need to be describable by referring only to aspects of reality which are an integral part of this universe. Indeed, if one assumes that it is acceptable for certain aspects of reality which would exist beyond the observable portion of physical phenomena to have no identifiable causes (even of a random nature) originating from within the universe in which those phenomena arise, then it may no longer be possible to avoid the conclusion that those particularities actually are the product of external intervention, which would simply mean that our universe is an incomplete instance of reality. I believe that a physical model that would offer a complete account of what happens inside any given universe must, therefore, avoid postulating an absence of causes for physically distinct aspects of our reality. This is probably the purest form of the principle of local causality. There is, thus, something rational in our aversion for a reality that would differ without any identifiable (even if potentially unobservable) causes, that is to say, there are good motives to doubt that a strong concept of objective chance is relevant to our description of physical reality. No distinctive feature of our universe should have as a cause 'nothing'. If events are in general related in statistically significant ways to other events of a similar nature through what we call causality, then we are justified to expect that there should be no event that would be related to something we call nothing. That does not mean, however, that we have to reject the notion that quantum measurements produce results which are absolutely unpredictable, as I already mentioned, because even a causally determined world would, in the context of the existence of closed causal chains and backward in time causation, involve an irreducible randomness, given that the cause of an event can be influenced backward in time by this very same event, despite the fact that no information is allowed to flow backward concerning that future event (so that it necessarily remains unpredictable), as I explained in section 4. What this means is that even if unobservable causes were to be found to exert an influence on unobserved portions of a quantum process, reality would remain fundamentally random and not just unpredictable, even if it is causally determined in every way. This is the exquisite beauty of time166 symmetric causality: it allows for causal determination without giving rise to complete determinism28. What allows the wave function to evolve deterministically, but only until a measurement occurs, even in the context where one must assume that the underlying evolution is of a random nature, is the fact that we are dealing with a unique reality for which what happens in the future contributes to determine what happens in the past. In such a context the outcome of a measurement on a quantum system at time t2 can change what happens to the system as far back as the time t1 when the system was prepared, which allows the evolution that took place immediately after t1 to agree with the outcome of a measurement that took place at time t2 despite the fact that this evolution is taking place randomly on a local level. Thus, the fact that the evolution of the system appears to have been deterministic until time t2 (at which decoherence took place and the state vector was reduced), is not incompatible with the hypothesis that the system evolved randomly before that measurement, because this random evolution was influenced all along by what happened at a later time, when the measurement was performed, given that from the viewpoint of time-symmetric causality the system is required to obey constraints which may be determined by what happens to the system following that measurement. But, once the potentialities are actualized at time t2 the observed outcome is only required to be compatible with what actually happened in the past and this is what explains that randomness becomes apparent. Quantum evolution is always random, but a real change is actually occurring when a measurement takes place which makes it seem like this is where randomness originates, because right until the measurement is actually performed multiple different outcomes are still possible and the system appears to evolve indifferently toward all those final states all at once and this is what makes this evolution appear deterministic, as it always happens in the same way from an observational viewpoint. In any case, as long as the unidentified causes which may explain the variation of the unobserved paths of quantum particles from one measurement to the other would themselves remain unobservable, reality would remain unpredictable from the viewpoint of all observers. I would therefore 28Such a conclusion would seem to confirm that a time reversal operation that would apply to the present state of the whole universe defined over a given space-like hypersurface would not necessarily give rise to the exact same history in reverse, but could potentially give rise to an entirely different and genuinely unpredictable evolution, as I suggested in section 3.6 of [1]. 167 object suggesting that the validity of a causal theory based on the realist conception of reality developed in the preceding sections of the present report would imply that the wave function provides an incomplete description of the state of a quantum system, because the wave function does provide the most complete account of how a system evolves as a result of the observable constraints exerted on it, only this still leaves us with a statistical description for the physical attributes which are left unconstrained by the macroscopic experimental conditions which apply to both the retarded and the advanced portions of a process. I believe that this provides an important clue as to the nature of those unobservable random factors of influence. What must be clear, first of all, is that the existence of such unobservable causes, obeying the principle of local causality, is not ruled out by the phenomenon of quantum entanglement in the context of the realist, timesymmetric interpretation of quantum theory I have proposed, because even if the trajectories of both elements of an entangled pair are separately influenced by those unobservable causes, when there is as much influence of the future on the past as there is of the past on the future it is possible for the two entangled systems to evolve so as to enforce the non-local requirements imposed by the existence of the shared quantum phase. This is why one must differentiate such an approach to the problem of objectification from the naive realist interpretations of quantum theory which were proposed in the past and which can be appropriately called classical hidden variables theories. Here it is the very concept of an objective reality that differs in essential ways, given that we are now dealing with a universal causal chain that feeds back on itself to give rise to two interfering, but otherwise independent versions of history for each and every process, to which must be independently applied the requirement of local causality. Thus, different unobservable causes can apply on the retarded and advanced portions of history along the trajectories followed by any of two entangled systems, but given that the two portions of both processes interfere with one another quantum mechanically as a result of being part of the same closed causal chain, it becomes possible for non-local correlations to exist between the outcomes of measurements performed on the two otherwise independently evolving systems. From my viewpoint, the reality that is causally determined is not unique in the classical sense and this is what allows even a causal theory to agree with the requirements imposed by the quantum entanglement of distant particles, without requiring complex and arbitrary non-local mechanisms of a 168 conspiratorial nature, in contrast with all classical hidden variables theories. The only difference between a causal theory involving unobservable causes of the kind I suggest may need to be considered and the orthodox interpretation of quantum theory would therefore be that, from my viewpoint, not only is it possible to assume that there can indeed exist a unique reality, even in between measurements of a certain physical attribute for which quantum interferences are observed, but it is also possible for this reality to be causally determined, as all observed phenomena. One of the advantages of this particular approach would therefore be that it naturally agrees with a much larger portion of observational evidence which clearly indicates that when there is an effect, there usually is a cause, even if its consequences may sometimes remain unpredictable. The approach I will now propose for solving the objectification problem is the exact opposite of an approach that would be based on the many-worlds interpretation of quantum theory, because instead of positing a deterministic evolution involving multiple simultaneously occurring histories, I'm assuming a random evolution involving one causally determined history (forming a closed causal chain). Thus, from my viewpoint, one no longer needs to assume that reality is deterministic theoretically, but random observationally, which all by itself certainly constitutes significant progress. In fact, it is well-known to specialists that the many-worlds interpretation of quantum theory suffers from an additional inconsistency which is associated precisely with the hypothesis that in general no unique outcome follows measurement. The problem is that when all potentialities are actualized together (in the same universe) it seems that outcome probabilities become meaningless, while quantum theory is all about probabilities and nothing else, which actually makes this usually favored approach completely useless. In any case, what should be clear already is that if the same measurements performed on identically prepared quantum systems may produce different outcomes, then those variations must originate from the fact that even when an optimal experimental characterization of the evolution of a physical system is available it necessarily leaves aside fundamentally unobservable, but causally significant aspects of the process. It is only the fact that traditionally it appeared impossible to assume the existence of such a more profound level of reality without explicitly violating the principle of local causality that explains that we came to believe that such an otherwise more consistent viewpoint was no longer viable, even though a time-symmetric interpreta169 tion of quantum theory of the kind I have proposed actually makes this more natural approach perfectly sensible. Indeed, once one recognizes that, as a matter of principle, no information could ever be obtained concerning the causes which may explain the randomly variable character of the paths of unobserved dynamic attributes, then one must conclude that no violation of the uncertainty principle could occur as a result of the existence of such causes. It is only under the incorrect assumption that additional information could be obtained about this unobserved layer of reality (that is not already accounted for by the quantum state of a system), that violations of the conservation of information and of the second law of thermodynamics would be allowed to arise. Now, even though it has long been my opinion that both the classical theory of gravitation and quantum field theory must be altered prior to being integrated into a quantum theory of the gravitational interaction, it is only after I realized that our understanding of classical gravitational fields leaves aside important aspects which are made unavoidable by the quantum nature of the gravitational interaction that I began to appreciate the fact that the quantization issue does not concern merely the general theory of relativity, but that it probably means that quantum theory itself needs to be reformulated so as to take into account those properties of the gravitational field which arise as a consequence of the very quantum mechanical nature of this interaction. To be more specific, while I do recognize that the classical theory of gravitation must be submitted to a quantization procedure on the appropriate quantum gravitational scale, I also believe that quantum theory must be made to obey the requirement of general covariance, but on a much larger scale, even under those conditions where we currently assume the existence of a flat and invariant spacetime. This requirement can be fulfilled once one acknowledges that the trajectory of the universal causal chain in superspace that describes the evolution of the intrinsic or extrinsic curvature of space for the whole universe can differ for the retarded and advanced portions of history, as a result of perturbations of this trajectory which are attributable to unobservable fluctuations of the classical gravitational field. What must be developed, therefore, is a theory where spacetime does not merely provide an additional set of macroscopic constraints, as a result of a particular state of the gravitational field being entangled with observable, irreversibly evolving environment degrees of freedom, but where the local inertial reference systems may be allowed to fluctuate in unobservable ways that may differ for the two time-reversed 170 portions of a process submitted to the same macroscopic conditions. In the preceding report of this series [1] I have developed a generalized framework for relativity theory which helped confirm the validity of the hypothesis that spacetime curvature really is a consequence of the existence of an interaction. Indeed, once one recognizes that local inertial reference systems are dependent on the energy sign of the particles experiencing them, then one must accept that there is no such thing as a metric structure of space independent from the nature of the interaction that determines its properties. Thus, the concept of negative energy matter which emerged from my analysis of the quantum mechanical notion of bidirectional time allowed me to develop a better classical theory of the gravitational field, which helped confirm the validity of the hypothesis that the metric properties of space and time really are the product of an interaction. What I would like to discuss now is the possibility that a better understanding of the microscopic properties of classical gravitational fields could provide the basis for a reformulation of quantum theory which may actually turn out to be necessary for producing a truly consistent quantum theory of the gravitational interaction. But, instead of arguing that it is the equivalence principle and the idea that gravitation is a manifestation of the curvature of space that is wrong, given that it appears to conflict with the current formulation of quantum theory, I would suggest that quantum theory itself must somehow come to incorporate the equivalence principle. It would be very surprising, indeed, that general covariance could turn out to be incorrect as a requirement to be imposed on our most fundamental theory of elementary particle interactions. If this requirement is found to be valid on the largest scale, as well as on the quantum gravitational scale, it should probably also be valid on the intermediary scale of ordinary quantum theory. Even from the viewpoint of the generalized gravitation theory I have proposed, it is still necessary to assume that the inertial and gravitational masses of a particle really constitute the same attribute, even though positive and negative masses would respond in the same way to an external force, which actually allows to reinforce the validity of the equivalence principle, as I have explained in section 1.5 of the preceding report. That does not mean that gravitation is not an interaction, but merely that the metric properties of space are a manifestation of the existence of such an interaction, which is indicative of the way quantum theory could be reformulated to integrate certain aspects of the gravitational interaction. Thus, I believe that gravitation must no longer be assumed to merely be involved in defining a deterministically evolving, locally uniform 171 spacetime background, but must be understood to provide a randomly variable influence participating in the determination of the unobserved paths of elementary particles under absolutely all circumstances. Thus, even if I do recognize that the classical theory of gravitation must be subjected to a quantization procedure on the scale at which this interaction becomes as strong as the other known interactions, I also believe that the quantized nature of gravitation would have consequences on a much larger scale at which this interaction can still be appropriately described by using the approximation of a continuous force field associated with the curvature of spacetime. The way this would be achieved is by reformulating quantum field theory so as to make it compatible with the requirement of general covariance even on the scale of ordinary quantum phenomena where we usually assume that there is no local variations of the metric properties of space. It must be clear, therefore, that the approach I will propose does not constitute a replacement for current quantum gravitation theories (such as loop quantum gravity), but merely provides a complementary contribution to the field, similar in scope to my derivation of the number of discrete degrees of freedom relevant to the state of matter under the influence of an elementary black hole (see sections 2.11 and 3.3 of [1]) or to my explanation of the emergence of a universal time variable in the initial Big Bang state (which was discussed in section 11 of the present report). What I'm suggesting, more specifically, is that one must recognize that due to a certain, usually overlooked property of classical gravitational fields associated with the quantized nature of the gravitational interaction it follows that a randomly variable influence is exerted on the trajectory of matter and radiation particles in the space of those dynamic physical attributes which are not the subject of direct observation. What is significant here is that even though such influences are indeed unobservable, they nevertheless have important consequences on the outcome of quantum measurements, given that they actually allow to explain what determines the unique, but randomly variable states which are singled out following decoherence. From that viewpoint, even the classical spacetime continuum over which the unobservable paths of quantum particles are assumed to unfold would no longer constitute a locally uniform, static background, but would fluctuate as much as the particle trajectories themselves. This proposal is merely an extension of the general relativistic idea that it is no longer possible to speak of a situation where there is an absence of gravitational field. Indeed, Einstein himself reflected on the irrelevance of such a notion by noting that even in those sit172 uations where the metric is Euclidean and no mass is present nearby, there is still a gravitational field, only it is a field that does not vary with position (while an absence of gravitational field would require that there exist no metric properties at all). Here the idea is that even when it would appear, from a superficial, macroscopic viewpoint, that the gravitational field does not vary with position, in fact it still exerts a decisive, randomly variable influence on the trajectories of elementary particles depicted in the sum-over-histories formulation of quantum theory. What makes such a viewpoint unavoidable, is the fact that even the conventional formulation of quantum theory implicitly takes into account the existence of gravitational interactions all along the unobservable trajectories of quantum particles, given that it assumes the relevance of a locally uniform spacetime background in which the matter particles propagate. But, as Lee Smolin once remarked, it is difficult to imagine how a dynamical theory of spacetime (such as a background independent quantum theory of gravitation) could actually be derived from a theory where the geometry of space is assumed to be fixed (such as conventional quantum field theory). What I'm suggesting is that once we recognize that gravitation exerts a decisive influence, even on the scale of ordinary quantum theory, then it is also necessary to recognize that the gravitational field is not constrained to have the properties of local uniformity and predictability that we usually attribute to it (in the context where large measures of action are involved and classical physics is a suitable approximation). The gravitational field definitely is omnipresent and does have an effect at every 'point' along the unobserved trajectories of elementary particles (including gravitons), but I believe that what the random, but unique character of the paths which are followed in the unobserved retarded and advanced portions of any process indicate is that this classical gravitational field cannot be required to be completely uniform and deterministically evolving locally, but must rather be allowed to fluctuate in ways that could differ for the retarded and advanced portions of the process, when the existence of those random fluctuations would have no immediate observational consequences. If there is no valid motive to reject the possibility that the gravitational field may so fluctuate in the absence of observations, then what one would have to recognize is that it is the local inertial reference systems which are allowed to vary unpredictably with position and time. In fact, I believe that this should have been expected, even independently from any consideration of a quantum mechanical nature, given that from a Machian viewpoint local 173 inertial reference systems arise as a result of the gravitational interaction with the ensemble of matter in the universe and such influences must necessarily involve unpredictable variations with both position and time, as the matter distribution itself is not perfectly unchanging and uniform over the entire universe and throughout history, even if, on the average, such fluctuations should necessarily cancel out due to the large number of individual interactions involved. What happens is that even in the presence of a statistically uniform distribution of forces, when the trajectory of a particle is the outcome of multiple, near simultaneous, quantized interactions, such as is the case with ordinary Brownian motion, then there necessarily arise fluctuations in the number of interactions taking place in one direction that are not necessarily matched by those taking place simultaneously in the opposite direction and this must give rise to small variations in the equilibrium of forces acting on the particle (which would here be the inertial forces that determine the local free-fall reference system). Those considerations are particularly significant in the context where, as I have explained in section 1.6 of [1], the absence of gravitational interactions with the matter that is missing in the direction of a void in an otherwise uniform matter distribution can actually have a considerable influence on the motion of matter particles, even if that is not always recognized. Thus, if the local inertial reference systems which determine the trajectory of a particle with a given sign of energy must ultimately be conceived as being the outcome of such an equilibrium in the sum of gravitational forces attributable to all the matter in the universe with the same sign of energy, as I explained in section 1.4 of the preceding report, then we certainly have enough reasons to believe that the unobservable trajectories entering the sum-over-histories formulation of quantum theory should be randomly influenced by the presence of fluctuations in the equilibrium of inertial forces, given that gravitational forces are themselves conveyed by elementary particles and must, therefore, fluctuate. The crucial point is that this would be true even in the context where the approximation of a classical spacetime continuum would still be valid (and the metric would remain Euclidean locally), given that we are not concerned here with individual quantum interactions, but with fluctuations in a very large number of such interactions taking place nearly simultaneously. It is possible to understand why such unobservable fluctuations in the equilibrium of inertial gravitational forces should have decisive consequences on the evolution of quantum systems, even outside the quantum gravitational 174 regime, by recognizing that even though the gravitational interaction is very weak, inertia, as a gravitational phenomenon, exerts a very significant influence on the trajectories of elementary particles, given that it is an outcome of the interactions which are taking place with all the other matter particles present in the universe, whose number largely compensates the very small probability that a given particle emits a graviton in the course of an ordinary quantum process29. In such a context it would appear that it is merely the existence of statistical regularities in the random fluctuations of the classical gravitational field that allows the metric properties of spacetime to be described as deterministically evolving on the scale at which ordinary quantum theory itself becomes irrelevant. If those considerations are valid it would then mean that what one needs to formulate is a time-symmetric version of stochastic gravitational field theory (based on the generalized gravitational field equations introduced in section 1.15 of my preceding report) that would apply to individual portions of the universal causal chain, independently. For this purpose, it is necessary to recognize that the locally uniform and deterministically evolving, classical gravitational field merely constitutes an approximation that must emerge from a more accurate description where randomness is explicitly involved. The classical description can therefore be expected to break down on the action scale associated with ordinary quantum phenomena, where random fluctuations of the metric properties of space are unavoidable. What explains that such fluctuations can usually be ignored is the fact that it is precisely on such a scale that they can be expected to remain unobservable, while they must cancel out for the most part when larger measures of action are involved. It may then be that it is only because we fail to take into account the existence of such local fluctuations in the metric properties of spacetime that we obtain a description of quantum processes that violates the requirement of general covariance and in which the mass of particles appears to constitute a relevant parameter, which puts quantum theory at odds with general relativity (this is apparent in the context of experiments which show that quantum interference effects can exist which are dependent on the mass of a particle, even when gravitation is the only macroscopic constraint involved, as is the case with the classical neutron interferometer experiment 29One can appreciate the strength of inertial forces by observing that even in the absence of local masses, the equivalent gravitational field which balances the external force on a particle as it deviates from its free-fall state of motion is easily as large as that which would be attributable to an entire planet located in its immediate vicinity. 175 in a gravitational field). A more adequate formulation of quantum field theory that would integrate this semi-classical description of gravitational fields would allow to eliminate this incompatibility. Such a theory, which would be similar in form to that of near-equilibrium thermodynamics (given that it would allow for random fluctuations in a medium that is nevertheless classically well-defined on a local level), would only break down on the quantum gravitational scale where the approximation of a classical spacetime continuum would no longer be valid. This means that there are actually three levels of applicability to a theory of the gravitational field, because the intermediary, semi-classical level, where gravitation is usually assumed to be irrelevant actually also involves this interaction in a decisive way. On such a scale gravitation may already be considered to merge with quantum theory, but merely in the sense that fluctuations of a quantum mechanical origin must now apply to the classical gravitational field, while quantum evolution becomes causally determined as a consequence of the very gravitational nature of the inertial forces to which it is submitted, even in the absence of observable, local perturbations of the curvature of spacetime. What makes this hypothesis significant is the universal nature of the gravitational interaction and the fact that it is allowed to affect not only the propagation of all matter particles, but also that of the particles associated with all interaction fields, including its own, without having to refer to a preexisting background structure, given that this is the interaction that determines the very metric properties of the spacetime over which the other fields fluctuate. Now, if local fluctuations of the metric properties of spacetime actually occur which remain unobservable, then they would have effects which would be indistinguishable from temporary violations of the conservation of momentum and energy, given that energy would be exchanged with the gravitational field that would not be accounted for classically. I believe that this is what explains that virtual processes, like ordinary particle interaction processes, involve such violations of energy and momentum conservation, which are allowed to occur merely as long as they remain within the limits of quantum uncertainty, that is to say, as long as they remain unobservable. Indeed, even from a semi-classical viewpoint the reality of a particle's existence may depend on the presence of a local gravitational field or acceleration (think about the Unruh effect for instance) and in such a case all that matters is that once the presence of a particle is actually measured by a detector, even when this is made possible as a result of an exchange of energy with the gravitational 176 field, then this event must become an established fact that is not dependent on the position or the state of acceleration of an observer, as is possible when the reality of particle detection is enforced by quantum interference. What's different from the viewpoint of the approach advocated here, is that the undetected virtual particles present in the vacuum can now be considered to be as real as other matter particles, because what differentiates them is merely the fact that they do not exist permanently, with invariant energies, but merely as a result of energy exchanges with the randomly fluctuating classical gravitational field30. Anyhow, if the unmeasurable violations of energy and momentum which are allowed by quantum indeterminacy are taking place as a result of undetectable exchanges of energy with the fluctuating gravitational field, this would explain why it is that only the conservation of energy, momentum and angular momentum is allowed to be violated in such a way, while the electric and other non-gravitational charges of elementary particles (the static attributes) are always rigorously conserved despite quantum uncertainty. In this context the fact that the quantum indefiniteness associated with the position of a particle diminishes with the magnitude of its momentum would also appear all the more natural, given that a particle with a larger energy can be expected to interact with more gravitons all at once and therefore to be less affected by individual interactions, as if it was experiencing a reduced level of fluctuation in the equilibrium between the sum of all such interactions (which may actually explain why the variation of the quantum phase associated with the propagation of elementary particles is dependent not only on the energy of the particles involved, but also on their mass, even though this parameter would drop out of the equations if one considered the appropriate locally fluctuating, inertial reference system). Similarly, the fact that quantum indefiniteness in momentum rises as we consider increasingly smaller regions of space can be seen to be a reflection of the fact that the level of random fluctuations in the classical gravitational field rises as we consider smaller space intervals for which the quantized nature of the gravitational field is more pronounced, until we reach the Planck 30It is interesting to observe that the description of black hole radiation as being an outcome of the quantum tunneling of particles past the gravitational potential energy barrier would in this context imply that it is actually a local variation of the gravitational potential energy of the black hole itself that allows the decay to occur, because quantum tunneling would then be the outcome of a local, but unobservable variation of gravitational energy. 177 scale where (as I explained in section 2.11 of my preceding report) every matter particle is submitted to the gravitational field of an elementary black hole and momentum is totally undetermined (given that it can be either positive or negative, but with maximum magnitude in both the retarded and the advanced portions of a process). To avoid confusion, however, it is necessary to understand that despite the fact that the degree of randomness to which are submitted elementary particles as a result of the existence of unobservable fluctuations in the gravitational field may depend on the magnitude of their energy (given that the frequency associated with the propagation of a particle is determined by the magnitude of its energy), interference effects cannot be considered to be an aspect of the gravitational field itself, because fluctuations in the metric properties of space merely explain why it is that one particular trajectory is followed in the retarded and advanced portions of history, while it is still the constructive or destructive nature of the interferences associated with a complete time-symmetric process which determines whether those trajectories are likely to be followed, when one takes into account the existence of the quantum phase and the closed nature of the universal causal chain. An interesting outcome of such an approach is that it allows one to more easily understand why it is that photons and other massless particles are allowed to have unmeasurable (but theoretically mandatory) velocities larger or smaller than the normal speed of light in a vacuum and to travel along curved trajectories on a small scale (as Feynman diagrams for radiative corrections so appropriately illustrate), because when one takes into account the existence of unobservable, local fluctuations of the metric properties of space, it is still possible to assume that massless particles in a given energy eigenstate always travel along straight lines at their normal c velocity, as long as one recognizes that this propagation takes place along the geodesics of a locally curved spacetime. This is made possible in the context of a generalized gravitation theory of the kind I proposed in [1], where matter configurations may exist that give rise not to gravitational attraction and an apparent diminution of the speed of light, but to gravitational repulsion and an apparent increase of the limiting velocity experienced by massless positive energy particles (as a result of space dilation). From such a perspective the multiple possible trajectories of unobserved, dynamic quantum attributes would simply be the causally determined geodesics of a randomly evolving dynamical spacetime, rather than the random paths of particles evolving over a locally invariant and deterministically evolving spacetime. 178 It must be emphasized that what I'm proposing is not that there arise stochastic perturbations of the Schrödinger equation itself when a measurement takes place, as is sometimes proposed in order to try to explain the random nature of quantum measurement results. Once again, it should be clear that the irreducible randomness of quantum processes cannot be assumed to be a consequence of what goes on during measurement and the desired generally covariant formulation, that would allow to reproduce the statistical predictions of the current theory, would differ merely in that it would allow to explain what determines the particular unobservable trajectories followed by elementary particles in between measurements, while the absence of interferences that follows quantum measurement would still be a mere consequence of decoherence enforced by the requirement of closure of the universal causal chain. From my viewpoint it would also be decoherence and the closure requirement that would trigger the process of state vector reduction that would arise when a quantum superposition of randomly fluctuating space curvatures would develop that would have observable consequences. As long as the randomly fluctuating curvature of space that may exist in a certain retarded portion of history and that which may exist in the related, advanced portion of history remain without immediate observable consequences, they are allowed to differ as any other attribute of the systems which are taking part in a quantum process. Such differences in the curvature of space may trigger decoherence, just like other observable distinctions between the retarded and the advanced states, but it is precisely the fact that that they are not required to do so under all circumstances that explains the randomly variable nature of quantum measurement results. To sum up, I believe that instead of simply rejecting the foundations of the current classical theory of gravitation to accommodate the quantum mechanical nature of reality, we should first redefine the foundations of quantum theory to take into account a certain overlooked but unavoidable aspect of a consistent semi-classical theory of gravitation that would allow to explain how the unique, but random outcomes of quantum measurement are determined from the perspective of time-symmetric causality. It is important to mention, however, that the idea that the unique retarded and advanced portions of history which take part in every quantum process are influenced by local fluctuations in the classical gravitational field is not absolutely necessary for the validity of the solutions I have provided to other aspects of the problem of the interpretation of quantum theory. In fact, one may even consider that what solves the problem of objectification in the context of the 179 realist interpretation of quantum theory I have proposed is the very fact that such an interpretation allows for reality to be unique in a certain way. It is clear, indeed, that even when the unique reality behind interfering quantum mechanical histories is not causally determined in every way, it nevertheless remains unique from a time-symmetric viewpoint, which already goes a long way toward easing the tension between the theory and the observed outcomes of measurement. But while we may never be able to directly confirm that the unobserved quantum paths, despite their absolutely unpredictable nature, are nevertheless causally determined in every way, the fact that it is already possible to envisage the exact form of a theory that would satisfy those consistency requirements should encourage us to recognize that the only reasonable conclusion is that reality is not fundamentally without causes. 14 Conclusion When I began doing research in fundamental theoretical physics some 30 years ago, I did not suspect that some of the early ideas and insights I was trying to develop would eventually become essential for producing a consistent interpretation of quantum theory. But, the hypothesis that the gravitational interaction is symmetric under exchange of positive and negative energy matter turned out to be indispensable to the formulation of an interpretation of quantum mechanics in which no implicit or explicit assumptions contradict one another or some observable aspects of reality, because this idea is what allows one to understand how it is possible for thermodynamic time asymmetry to emerge despite the time-symmetric nature of causality. Indeed, outside the context of the generalized gravitation theory introduced in chapter 1 of [1] there would be no meaning to consider that there must be a constraint on the emergence of a maximum quasiclassical domain imposed by a requirement of closure of the universal causal chain. Actually it wouldn't even be possible to assume that there exists a universal time variable along which the causal chain unfolds. As a matter of fact, if we were to ignore the theoretical developments I previously introduced it wouldn't be possible to assume that there is a reality at all in the absence of measurement, unless we are willing to reject some equally unavoidable theoretical requirements derived from observation, like the principle of local causality. Now, the most significant aspect of a quantum mechanical description of 180 reality is certainly the use of interfering probability amplitudes in place of conventional probabilities (or equivalently the appearance of negative probabilities for time-symmetric histories). But in the context of an interpretation of quantum theory that satisfies the requirement of scientific realism the existence of interference effects can be understood to be a consequence of the circular nature of causality that is associated with the closed nature of the universal causal chain and this again serves to demonstrate the dependence of a consistent interpretation of quantum theory on purely cosmological aspects of reality, where a generalized theory of gravitation constitutes an essential element of the appropriate model. This dependence is further emphasized by the fact that gravitation may ultimately be involved in giving rise to a completely satisfactory solution to the objectification problem in the context where a more accurate understanding of the phenomenon of inertia implies that one must reconsider the validity of the conventional formulation of quantum field theory and contemplate the possibility that it be replaced by a statistically equivalent theory no longer dependent on the concept of a locally uniform, deterministic spacetime background. It is also the notion that causes cannot be restricted to propagate only in the future direction of time, as the classical principle of causality would appear to require, that made unavoidable a picture of quantum reality involving two corresponding, time-reversed, but noninteracting histories for each process. The understanding that this is made necessary when all causes are required to belong within our universe then made possible the elaboration of the first complete solution to the quantum measurement problem. Indeed, I have explained that the requirement of a relational description of reality imposes a condition of continuity to the universal causal chain which can be most naturally satisfied when causality is appropriately conceived of as a circular phenomenon in which time plays a role similar to that which would be played by space in a closed universe, while such a closure is what allows to explain the persistence of quasiclassicality following decoherence. In such a context it becomes clear that there is no real difficulty associated with the assumption that there does exist a unique reality at all times, as long as one recognizes that this reality does not consist of one single classical history propagating in one single direction of time at all times, which would require some extraneous 'pilot wave' to perhaps explain the existence of quantum interferences involving multiple distinct trajectories. Once this is understood one no longer needs to retreat into complicated and confused philosophy in order to try to explain the simplest and most elementary phenomena taking 181 place right in front of us all the time. The problem that there was traditionally is that we regarded quantum non-locality as a mere curiosity of a quantum mechanical description of reality and we were convinced that it did not constitute a challenge to our conventional understanding of causality, simply because we could not see how the difficulty could be resolved if it is, in effect, real. The fact that the theory nevertheless allowed to produce accurate predictions, while the kind of non-locality involved did not allow information to be transmitted instantaneously appeared to legitimate this position and this is what explains that people stopped searching for a solution to the problem of the apparent incompatibility between quantum entanglement and the constraint imposed by relativity theory on the propagation of causal influences. All along we continued searching, with more and more sophisticated experiments, for possible loopholes that could explain quantum non-locality as being an outcome of conventional unidirectional causality, just like people kept searching for manifestations of our motion relative to absolute space over a century ago. This happened because we were not willing to accept the conclusion that reality is non-local, a fact which can only be made acceptable once it is recognized that quantum phenomena still satisfy a certain time-symmetric notion of local causality. While I was progressing toward a better understanding of quantum mechanics I realized that my position concerning the many-worlds interpretation of quantum theory is somewhat similar to my position regarding the weak anthropic principle. Indeed, while I do believe that both anthropic selection and the existence of a multiplicity of causally independent universes are necessary concepts, I have also shown that the many-worlds interpretation, which is often considered to be a multiverse theory, is not viable as a realist interpretation of quantum theory, from both a logical and an observational viewpoint. But, I have also explained why the quantum measurement problem is not to be considered as a mere illusion in a world where the emergence of quasiclassicality would be a subjective notion associated with the biased nature of the perception of reality that would be characteristic of our conscious experience. But such an approach could only be made legitimate on the basis of the validity of the weak anthropic principle, whose relevance is therefore diminished by the developments I have introduced in this report. It is somewhat ironical, therefore, that the weak anthropic principle was once considered to be bad science on the basis of the fact that it would require the existence of multiple universes, whose existence could not be confirmed 182 by any other means, because, as I previously mentioned, this stubbornness is actually a form of solipsism which in the above described context would be supported by the weak anthropic principle, which would therefore require the existence of a multiplicity of universes. Concerning the realist conception of quantum reality developed in this report, it is perhaps appropriate to note that while it can be expected that the most virulent objections to such an interpretation of quantum theory would probably have to do with the 'hypothesis' of a unique reality behind interfering quantum mechanical histories, I think that this resistance is not merely an undesirable byproduct of the long tradition of instrumentalism that emerged from the Copenhagen interpretation, but also constitutes an unfortunate consequence of the more profound inadequacy of a philosophical position that originates from Descartes' desire to free himself from the 'superfluous' hypothesis that his mind may not be all that there is in the world. I must emphasize once again that it is my strong belief that the most significant challenge currently facing fundamental theoretical physics and the development of a consistent philosophy of the natural world is that of overcoming the psychological barrier associated with the reluctance to accept as real what one cannot perceive directly and to realize the sterility and the inadequacy of the opposite viewpoint, when what one wants to assess is the nature of reality itself. Here it may not be consistency alone which is at stake, but the very meaningfulness of the whole exercise, that which embodies the quest for the ultimate representation of reality. 15 Summary To conclude this report, I would like to provide a summary of all the results which were obtained concerning both the issue of time-symmetric causality and the problem of the interpretation of quantum theory in the context of the revised understanding of the concepts of time reversal and thermodynamic irreversibility which was developed in the preceding report of this series. The decisive results are the following. 1. The causal relationships that may exist between various events are always established by the propagation of elementary particles across spatial distances either forward or backward in time. 2. One must distinguish between a classical, unidirectional concept of 183 causality according to which causes always exert their effects in the same unique future direction of time and a more fundamental, bidirectional concept of causality where causes are allowed to produce effects which are located in their own past. 3. The unique, invariable direction of time relative to which entropy grows and information flows (as a result of the formation of records) is independent from the direction of propagation in time of elementary particles which determines the true direction in which causality operates and effects propagate. 4. It is possible to assume that a unique future is causally related to the experienced present just like a unique past is causally related to the same present, because what makes it seem like the future is not unique is merely the fact that information is only available about the past, while unconstrained evolution is only possible in the future direction of time as a result of the limit imposed by the constraint of global entanglement on entropy growth in the past. In such a context, imposing final conditions cannot be less appropriate than imposing initial conditions. 5. It is not possible for backward in time propagated effects to change past history, because if an event in the future changes the outcome of an observation in the past, this change is already effected at the moment in the past at which the observation first occurred. 6. Even though backward in time causation is not forbidden, the causal ordering postulate is still valid, because special-relativistic transformations are merely required to preserve the direction in which a causal chain propagates in time and this requirement can be satisfied even when the direction involved is not the future. 7. The time-symmetric nature of causality implies that a certain event can both influence another event and be influenced by that very same event, which means that the cause of a certain event can also be an effect of the same event. 8. As a consistency requirement, it must be imposed on histories that they are not self-contradictory. But despite the fact that backward causation may appear to allow this condition to be violated, given that 184 it may give rise to closed causal chains, it is in fact ultimately the timesymmetric nature of causality that is responsible for circumventing the development of factual inconsistencies. 9. In the context where it is impossible for the future to be causally determined by the past alone, because the future itself can be involved in determining the past that determines this very future, reality remains fundamentally random, even when causally determined. 10. Once it is recognized that a universe actually consists of a unique ensemble of events causally related to one another and to nothing else, then it follows that if an event in the past is influenced by an event in the future, this past event cannot be altered in such a way that it would become causally related to a different future, as may occur in the course of a hypothetical time-travel experience according to a certain version of the many-worlds interpretation of quantum theory. 11. What would differentiate a time travel experience from the kind of backward in time propagation that routinely takes place in the course of certain elementary particle processes is the fact that with time travel a macroscopic system would need to evolve with its thermodynamic arrow of time reversed and pointing toward the past instead of the future, which is not fundamentally impossible, but which is formidably unlikely given that it would require a violation of the second principle of thermodynamics and a growth of entropy in the past direction of time, which is forbidden by the constraint of global entanglement that imposes a low entropy Big Bang. 12. Given that for a knowledge paradox to occur, a sustained increase of entropy would need to take place in the past direction of time while the information is being transferred from the future toward the past, then it follows what what makes such a phenomenon unlikely to observe is not the requirement of global consistency, but simply the constraint that is responsible for thermodynamic time asymmetry. 13. What is forbidden is not backward in time propagation, but the decrease of entropy that would be required for traveling back in time as a thermodynamic phenomenon. 185 14. What makes time travel paradoxes fundamentally impossible is not the requirement of entropy growth in the past and the necessary violation of the second law of thermodynamics which explains the unlikeliness of time travel, but the very same constraints that forbid a contradiction to occur at a fundamental level, as when elementary particles are propagating backward in time without being involved in anti-thermodynamic evolution. 15. It is the fact that we are used to experience the future as unknowable in advance that explains that it appears doubtful that we would not be able to alter the course of reality at will if we were able to travel back in time, even though it is necessary to assume that a unique future is causally related to our present state and that events would necessarily happen that would prevent a time traveler from influencing the past in a way that would change its own future. 16. The absence of advanced waves cannot be attributed merely to the unlikeliness of such a phenomenon as it would be observed from the unidirectional time viewpoint, because the very same convergence of wave fronts is actually taking place in the past direction of time and this is not the outcome of the unlikeliness of present conditions. In the absence of a specific constraint what one would expect to observe is a spreading of wave fronts in both the future and the past directions of time. 17. What the difficulties encountered by early time-symmetric approaches to a solution to the problem of advanced waves illustrates is that it is not possible to explain the absence of advanced waves as being a mere consequence of constructive and destructive interference effects. 18. Given that in a quantum mechanical context the presence of advanced waves would require an increase of entropy to take place in the past direction of time, then it is necessary to recognize that such a phenomenon and more generally the propagation of information from the future toward the past, is forbidden by the condition of ever decreasing entropy imposed on past evolution by the global entanglement constraint, which does not mean that elementary particles cannot propagate backward in time, but merely that the number of 'final' states 186 toward which they can evolve in the past practically never grows with time. 19. The processes we experience in this portion of history are all mirrored by processes which obey the same macroscopic observable macroscopic conditions, but which take place in the opposite chronological order in a portion of history that must be assumed independent of that we experience from the viewpoint of local causality. 20. It is the fact that early time-symmetric interpretations of quantum theory required assuming that the retarded and advanced waves are propagating in the same portion of history that is problematic, because in such a context the particle submitted to the constraint of those classical waves in the classical double slit experiment must go through only one slit, corresponding to this unique history, which in turn requires a certain fundamental temporal asymmetry to be introduced in the theory, in violation of the time-symmetric nature of its equations. 21. The fact that two causally independent histories unfolding in opposite directions of time are involved in every quantum process is reflected in the fact that one must multiply the wave function by its complex conjugate to obtain the appropriate probability for a process to occur. 22. Our reluctance to recognize the reality of post selection, or the possibility for a state vector to be determined by what 'happened' in the future instead of what happened in the past, is merely a consequence of the prejudice toward a unidirectional conception of causality which we inherited from our thermodynamically constrained experience of reality and does not rest on any rationally formulated argument. 23. Once it is recognized that among the two portions of history associated with every quantum process there necessarily exists at least one portion of history that unfolds from the past toward the future, then it becomes possible to explain the thermodynamic arrow of time as being the consequence of the initial condition of low gravitational entropy imposed on the initial Big Bang state by the global entanglement constraint, because the evolution of at least one of the two state vectors associated with those two portions of history is then determined by past conditions. 187 24. It is imperative to avoid altering the conventional rules of logic in order to understand facts and this can only be achieved by generalizing our concepts about the physical world in such a way that no implicit or explicit contradiction is allowed to persist. 25. It is still possible and desirable to provide a realist description of physical processes based on the concept of particle trajectory even in the context where quantum interference involving multiple position states must be assumed to constitute an essential aspect of reality. 26. Once it is recognized that the elementary particle concept is essential to a consistent interpretation of quantum theory, we have no choice but to recognize that the current interpretation of the theory is incomplete, because it does not provide a clear and unambiguous description of what happens when a particle's position is not under direct observation. 27. What must be considered undeniable about reality is precisely that it is real and rejecting this hypothesis in order to avoid certain conceptual difficulties would constitute a logical contradiction. But it would not make sense to attribute reality only to something that exists as a fact rather than as a possibility and to avoid describing the actual ways by which certain physical processes can occur when it is not possible to directly observe what happens in the course of any one particular process. 28. If the only alternative to assuming the existence of classical hidden variables in a realist interpretation of quantum theory was to consider the wave function as reality itself, then explicit non-locality would be unavoidable, because the wave function, like classical hidden variables themselves, is a non-local entity. 29. A consistent interpretation of quantum theory must satisfy two apparently incompatible requirements which are the uniqueness of history and the necessity to allow quantum interferences to occur between the many distinct possibilities that may exist for the unobservable aspects of this unique history. 30. If the values taken by conjugate physical attributes cannot be determined at the same time with an arbitrarily high degree of precision it is simply because the macroscopic experimental constraints necessary 188 to determine the exact state of those physical attributes cannot be realized all at the same time, while it is those macroscopic constraints (associated with the existence of records) that determine which physical observable is not subject to quantum interferences. 31. If a purely phenomenological model of reality such as that which constitutes the core of the orthodox interpretation of quantum theory may appear to be more appropriate than a realist model for explaining certain observations, this is merely because the constraint of scientific realism cannot be applied to quantum phenomena as they are traditionally described, but only becomes appropriate in the context of a time-symmetric description of those phenomena. 32. Even if the wave function provides the most complete description of the state of a quantum system, it is necessary to assume that two systems prepared in the same quantum state may evolve differently at the level of the dynamic physical attributes whose states are not determined by the macroscopic conditions of an experiment, given that a subsequent measurement of those originally undetermined attributes may produce outcomes that differ from one experiment to the other. 33. To solve the quantum reality problem one must explain how it is possible for a particle to follow a path along which all of its conjugate dynamic attributes have unique values at all times, despite the fact that the many trajectories which can be followed by the attribute that is not directly observed interfere with one another, as if no single, definite trajectory was ever followed. 34. There exists no valid argument in support of the hypothesis that all histories are followed together in the same universe as different coexisting and interfering 'branches' and all experimental evidence indicates that there exists a unique history of some kind. 35. When it is assumed that decoherence merely allows to eliminate the interferences between many coexisting 'branches' of history, then quantum entanglement becomes problematic, because it requires the existence of explicitly non-local influences to enforce the selection of one branch over another following measurement. 189 36. Backward in time causation, even when it obeys the principle of local causality, may give rise to non-local correlations, but if the existence of such correlations cannot be assumed to allow faster-than-light communication it is because the backward propagated influences are submitted to the constraint of diminishing entropy that is imposed on past evolution by the constraint of global entanglement, which means that such backward causation cannot allow information to flow from the future toward the past. 37. Our conventional, unidirectional experience of reality is not necessarily incompatible with backward causation, as long as the effects which are propagated backward in time do not give rise to the kind of backward in time communication that would be allowed in the absence of a constraint on the growth of entropy in the past direction of time. 38. In the context of a time-symmetric formulation of quantum theory it is no longer necessary to assume that there exists an absolute distinction between a cause and its effect and this allows one to avoid the contradiction that emerges from a conventional viewpoint when we are dealing with measurements performed at space-like separated locations on entangled systems and chronological order is an observer dependent aspect. 39. If the two histories which constitute the retarded and advanced portions of every quantum process were to be identical, even in terms of their unobserved physical attributes, they would still differ in that the direction of propagation in time of all the particles involved would be opposite for those two histories. 40. The path followed by a quantum system in the space of its unobserved dynamic attributes must be allowed to differ for the retarded and the advanced portions of a process and this is what explains that all paths must be taken into account in the determination of transition probabilities for any given process, even though the system only ever goes through one particular path in the retarded portion of history and then again through one particular (but possibly different) path in the advanced portion of history. 41. It is no longer necessary to assume that when the path followed by a particle is not observed the object actually behaves as if it was a differ190 ent entity (a classical wave), because in the context of a realist, timesymmetric interpretation of quantum theory one can explain the interferences which are made conspicuous in the statistical distribution of measurement results without having to adopt such a self-contradictory viewpoint. 42. Once it is understood that two causally independent histories are involved in any single quantum process then it becomes clear that what the existence of interferences involving multiple different paths means is not that the unobserved attribute of a quantum system is in no state at all, or that it is at once in all possible states, but merely that while many possibilities are allowed for its state in the retarded portion of history, many possibilities are also allowed for its state in the advanced portion of history which need not be the same as its state in the retarded portion of history. 43. Even if the retarded portion of history can be distinct from its timereversed portion at the level of their intricate, unobservable details, it must be required of those two portions of history that they nevertheless remain identical from the viewpoint of their observable macroscopic features. 44. What explains that it is possible for the probability of occurrence of one single event to be null, or for the event to be absolutely certain, despite the fact that not all the paths contributing to a determination of those probabilities are followed at once in one single history, is the fact that the presence of quantum interferences allows a complete time-symmetric history (composed of a retarded and an advanced portion) to contribute negatively to the final probability of a process and this actually allows all the different alternatives to contribute to the probability of one single process. 45. The profound significance of the apparently inconsistent probabilities, which are obtained for certain processes and which are usually considered (from the viewpoint of the consistent histories interpretation of quantum theory) to imply that nothing can be said of reality under such conditions only emerges when they are considered in the context of a realist, time-symmetric conception of reality. 191 46. The fact that conventional logic still applies on the classical scale, even from the viewpoint of a conventional interpretation of quantum theory, can be understood to result not from the fact that reality is only consistent on such a scale, but from the fact that the two portions of history which are unfolding in opposite time directions always appear to be the same on such a scale. 47. Once one acknowledges the existence of the unobservable quantum phase, one must conclude that whenever the probability for a timesymmetric process involving unobserved attributes to occur in one specific way is negative, if the process was to occur in this specific way it would diminish the chances that the initial conditions which would have actually given rise to it existed in the first place, thereby making the sum of probabilities for all the possible ways the process could occur smaller than it would otherwise be. Likewise, when the probability of an individual time-symmetric history involving unobserved attributes is larger than one, then its occurrence would decrease the chances that alternative initial conditions existed, which is another way to say that it would actually increase the chances that the actual initial conditions that gave rise to this history did indeed occur. 48. It is merely the fact that negative probabilities can only arise when quantum interferences are actually present, while in general interferences are only apparent when the actual path followed by a quantum system is not subjected to direct observation, that explains that we appear to be justified to assume that negative probabilities cannot arise and must be physically insignificant, even though this concept is essential to a proper understanding of quantum reality and can be assigned a clear meaning. 49. What enforces the non-local character of the consequences of a choice of measurement that is to be performed on one of two entangled particles is the existence of an advanced portion of history which allows the effect of a measurement performed in the future on this particle to propagate backward in time to the initial entangled state and then forward in time in the retarded portion of the other particle's history to affect the measurement result performed on this other particle, even when this measurement is separated from the measurement performed on the first particle by a space-like interval. 192 50. In the presence of an advanced portion to each quantum process, the interference effects which are observed to characterize the measurements performed on one of two entangled particles depend on the experimental conditions which apply on its entangled counterpart, simply because the phase changes which arise in the course of such processes are occurring as a result of the boundary conditions applying on the complete time-symmetric process and therefore over the entire experimental setup and not just as a result of the conditions imposed on the propagation of one or the other particle. 51. If it seems impossible from a conventional viewpoint to assume that each of two entangled particles follow a unique and causally independent trajectory prior to a measurement on one or the other particle, it is because this measurement may determine whether interferences will be observed or not for both particles and when interferences are present the trajectories of both particles are no longer well-defined from a classical viewpoint. Thus, unless it is the state of the correlated attribute that is actually measured for one of two entangled particles it is not possible, as a matter of principle, to tell what the two corresponding trajectories really are in any particular case and as a result interferences do arise. 52. The manner by which the past state of one of two entangled particles is causally influenced by the choice of measurement performed on the other particle in the future is not different from the usual manner by which causal influences are propagated forward in time, except that no information can be carried by the effects so produced, given that entropy cannot rise as the causal influences propagate in the past direction of time when a condition of global entanglement must apply on the initial Big Bang state. 53. The fact that the wave function sometimes appear to be a subjective property, dependent on whether information concerning the conditions of a future measurement to be performed on a system is available or not, is a mere consequence of the fact that we cannot know in advance what the backward in time evolving state of a complete time-symmetric process is before we obtain information about that future measurement, even though this measurement already affects the present state of the system. 193 54. The idea that the concept of a localized elementary particle may no longer be valid in the presence of quantum entanglement and that it should be replaced by a holistic (explicitly non-local) concept of reality at a fundamental level is not justified. 55. Even though there must exist a time-reverse analog to ordinary quantum entanglement that must give rise to non-local correlations arising from post selection, the existence of such correlations cannot allow faster than light communication, because the constraint of global entanglement requires entropy to decrease in the past for all processes which are occurring in the same universe and this means that no causal signal can propagate toward the future and then backward in time to a distant location as a result of post selection, even if causality does operate both forward and backward in time at a fundamental level. 56. The decoherent branches hypothesis would not allow one to avoid having to postulate the existence of distinct dynamical laws that would apply only during processes that can be qualified as measurements, because in such a context instead of having to explain what is the cause of the unique outcome of measurement that is observed following decoherence, one would have to explain what are the multiple causes of the many different outcomes which would be actualized all at once, which means that the uniqueness of measurement results is not less, but rather more problematic when one assumes that all trajectories are followed all at once when an attribute is not subject to measurement. 57. While it may not be possible to reject the hypothesis that an infinity of causally independent universes exist in parallel, it must be clear that the idea that many interfering branches of history exist in the same universe is a distinct hypothesis which is certainly not as unavoidable. 58. It is not necessary to assume the existence of many branches of history in order to avoid the conclusion that a unique classically well-defined state existed before decoherence took place, that would merely have been revealed by the measurement, because the unique reality that would characterize a quantum process in the absence of measurement on a certain dynamic attribute does not involve a unique classical path, but rather involves both a unique retarded state and a unique and possibly different advanced state, which allows all possible intermediary 194 states to contribute to the final probability amplitude, as required from an experimental viewpoint. 59. If reality was not of the unique time-symmetric type and the decoherent branches hypothesis was assumed to alone provide a solution to the quantum measurement problem, then an alternative explanation of quantum non-locality would have to be found, as it cannot be provided by this interpretation. 60. The fact that no quantum interference is ever observed for irreversibly evolving systems indicates that the classical definiteness of measurement results is related to the irreversible character of the measurement process. 61. It would not be appropriate to assume that the changes which are taking place in the course of a measurement are merely subjective, because following measurement the observed attribute is no longer unique merely in a time-symmetric quantum way, but acquires the same unique value in both the retarded and the advanced portions of history. 62. The complexity and the large number of independent degrees of freedom of a macroscopic system with which an observed quantum system may become entangled, do not alone provide the conditions necessary for giving rise to a quantum measurement. 63. The global entanglement constraint is what allows decoherence to occur and to always take place in the same future direction of time, which is necessary but not entirely sufficient to explain the persistence of the quasiclassical nature of history that follows quantum measurements. 64. Despite the fact that the wave function always evolves deterministically, except during measurements, it is not appropriate in the context of a realist interpretation of quantum theory to assume that it is the evolution that takes place in the course of a measurement which is alone responsible for giving rise to the unpredictability of quantum phenomena and it is incorrect to assume that different physical laws apply when quantum potentialities are actualized that do not apply during the 'unitary' evolution that takes place in between measurements. 195 65. In face of the experimental evidence from which quantum theory emerged, the desire to restrict the application of the criterion of logical consistency to aspects of reality which behave in conformity with classical expectations is just as irrational as the desire to uphold determinism. 66. The problem with the suggestion that if we perceive a quasiclassical world it is merely because, as observers, we have evolved to take advantage of only those 'consistent' formulations of history according to which the world does in effect remain quasiclassical, is that it would require one to assume that all evidence of past quasiclassicality and all expectations of future quasiclassicality are mere illusions for which no rational explanation would exist. 67. If we want to explain observations, then we must identify the constraint that allows to select the physically relevant set of histories in which quasiclassicality is experienced by all observers. 68. To obtain a satisfactory extension of the current formalism of consistent histories that would allow to solve the quantum measurement problem, a criterion must be provided for the selection of a set of histories that is not a priori 'consistent' (in the classical sense), but that would nevertheless allow both the quasiclassical character of reality and the consistency of its historical description to naturally emerge on the appropriate scale. 69. For the current explanation of the observed absence of quantum interferences following decoherence to be valid, it must be shown that it is appropriate to assume that the practical limitations that may prevent the observation of interferences between macroscopic states will never be overturned at any time in the future, because even if there is only an infinitesimal chance that such an observation is performed, given an infinite amount of time it should eventually happen and in such a case the consequences would be felt immediately. 70. The absence of change on the scale of the universe as a whole, which one may expect to be a consequence of the fact that the universe has a fixed value of energy, does not mean that time is not a meaningful concept for relating the changes taking place in one part of the universe with those occurring in another part, because it is not required of local subsystems that they have invariant energies. 196 71. Time would be irrelevant to our description of reality on the cosmological scale only if it could not differentiate itself from the other three dimensions of spacetime in the context where all four dimensions are kept on an equal footing and are required to be equivalent from a fundamental viewpoint by the general theory of relativity. 72. It is possible to understand how a metric of spacetime can emerge that uniformly selects one particular direction of four-dimensional spacetime as being that which is associated with the dimension of time across an entire space-like hypersurface in the context where it is recognized that the smoothness of the initial matter distribution at the Big Bang arises as a consequence of imposing a constraint of global entanglement that applies uniformly, down to the quantum gravitational scale, over that entire slice of spacetime, because this constraint is actually a condition for the existence of relationships of local causality between all elements of the universe which are present in the initial state, while on the quantum gravitational scale the principle of local causality is enforced by an embryonic element of time directionality associated with the causal structure of spin foams. 73. What is required by the global entanglement constraint is that at least one space-like hypersurface exists over which the embryonic, quantum gravitational element of time directionality is oriented in the same direction of spacetime in all locations, thereby consistently imparting on spacetime a unique signature with which is associated a uniform direction for the flow of time that is shared throughout the universe and that is allowed to persist due precisely to the condition of smoothness which is imposed by this constraint on the initial matter distribution. 74. It is no longer necessary to appeal to the weak anthropic principle to explain either thermodynamic time asymmetry or the very existence of a universal time variable. 75. The conclusion that there must emerge a unique dimension of time in four-dimensional spacetime legitimizes a formulation of quantum cosmology as having to do with the dynamics of extended three-dimensional space-like hypersurfaces whose histories constitute unique trajectories in superspace. 197 76. The entire history of three-dimensional space-like hypersurfaces cannot be predicted from knowledge of one particular slice of spacetime and at each local measurement the state of the universe needs to be actualized, which illustrates the relevance of time and more specifically of causality in establishing the actual relationships between the multiple extended three-dimensional spaces forming a history. 77. What would invalidate a truly timeless quantum theory of gravitation is the fact that such a theory would be incompatible with the existence of a fundamental time direction degree of freedom, such as revealed by violations of T symmetry, because any relationship of time directionality must necessarily involve a sequence of events related to one another following a definite and unique order and such a relationship is essential to a consistent description of physical reality in a semi-classical context. 78. Even though time, like space itself, is not present in its classical form on the quantum gravitational scale, if time, or more specifically local causality, did not exist under any form at a fundamental level, then we should not experience a dimension of time distinct from the other dimensions of space. 79. The present state of the universe as a whole, including that of its gravitational field or spacetime curvature, can be defined over one space-like hypersurface which can be represented as a point in superspace, while time must be conceived as the global variable to which are related the multiple local measures of change that take place as the state of the universe evolves along one particular trajectory in this configuration space and which determines how those extended states are ordered along this trajectory. 80. When the thermodynamic arrow of time is a consequence of the constraint of global entanglement, the conclusion that closed time-like curves cannot naturally arise becomes unavoidable, which means that the history of any universe satisfying this constraint (which would be any universe whose elements must be causally related to one another) can always be represented as a path in the configuration space of threedimensional space-like hypersurfaces. 81. From the viewpoint of a realist, time-symmetric interpretation of quantum theory the purpose of quantum cosmology is to estimate the prob198 ability of observing a global state of the universe, defined as a point in superspace, when another such global state has been observed, by summing-up the probabilities associated with all the different ways by which those two points can be joined together as a result of evolving once forward and once backward in time along two possibly distinct trajectories in superspace for which even the curvature of space could differ locally, as long as this difference remains unobservable. 82. If the history of the universe was described by one universal causal chain freely evolving in superspace along the dimension corresponding to unidirectional time, there would need to be external causes that would determine how the universe began to get going along the particular trajectory in which it is found to be, but this cannot be allowed given that the existence of an external cause is forbidden by the constraint of relational definition of the physical attributes of the universe which constitutes a basic consistency requirement. 83. If there is to be no first cause not determined from within the universe itself, then the history of the universe must consist of a closed causal chain that is stretched along the direction relative to which unidirectional time unfolds in superspace, which is the only way the universe can provide the cause of its own present condition as being nothing but a remote effect of this very same present condition. 84. When the history of the universe consists of a closed trajectory in superspace it is necessary, in order to obtain the right correlation probabilities, to take into account the existence of two otherwise independent histories evolving in opposite directions of time, even though from a cosmological viewpoint there is only one history which goes through observationally indistinguishable trajectories once forward and then once backward along the particular direction of superspace that corresponds to unidirectional time. 85. It is no longer necessary to assume without reason that the particles taking part in different possible versions of history do not interact with one another in order to avoid the contradiction that emerges in the context of a conventional interpretation of quantum theory when it is assumed that those interfering realities actually coexist in the same portion of the universe's history, because the retarded and advanced 199 portions of history do not really happen at the same epoch despite the fact that they share the same macroscopic conditions. 86. From the viewpoint of unidirectional time the universal causal chain would eventually need to close and when it would the time we experience would come to an end, but despite the unobservable nature of such an event the validity of the theoretical requirement of closure can actually be confirmed by the observation that reality is of a quasiclassical nature. 87. For the universal causal chain to close at some point in the future it is required that the retarded portion of history by chance finds itself in the exact same, partly unobservable state as that in which the advanced portion of the process turns out to be. 88. If time extends to instants past the initial Big Bang singularity, then the moment in the past at which the causal chain would close would not necessarily be that at which the Big Bang itself occurs, but could be any arbitrarily distant moment in the past, prior to the Big Bang, because even under the conditions of uniform matter distribution and minimum gravitational entropy that prevailed in the initial maximum density state, the retarded and advanced states could be very different in their unobservable quantum mechanically interfering details, given that the information contained in the microscopic state of the gravitational field grows with the density of positive and negative energy matter. 89. Due to the condition of continuity which must apply to the past and future bifurcation points of the universal causal chain, the energy of the particles which can be observed to propagate forward in time in the retarded portion of history, must be opposite that of the same particles which are propagating backward in time in the advanced portion of history, which means that they remain unchanged relative to unidirectional time. The signs of all the non-gravitational charges carried by the particles which are propagating backward in time in the advanced portion of history would for their part appear to be reversed from the unidirectional time viewpoint, but this is without consequences, because the fields that provide the experimental conditions present in the advanced portion of history all have their polarities reversed as well. 200 90. The circular nature of history allows to explain that quantum interferences do occur, even in the context where we are assuming that only one history actually takes place and it is recognized that the retarded and advanced portions of a quantum process actually take place at two very distant epochs along the configuration space trajectory, because this circularity imposes a condition of continuity on the quantum phase, which can only be satisfied when all contributions by intermediary subprocesses to the evolution of the quantum phase of the complete cosmological process that takes place along the closed configuration space trajectory are such that they allow this quantum phase to end up, after a complete turn along this trajectory, into the exact same state in which it was at the point of the trajectory that constitutes both its initial and its final boundary condition. 91. Given that the amount of microscopic structure or information does not grow when the universe expands, due to the variation of information associated with the diminishing strength of local gravitational fields, it follows that the probability that the universal causal chain closes at some point in the future is not diminishing with time and therefore it can be expected that unidirectional time will eventually end at some point in the future which is not infinitely distant and in such a case the probability that decoherence may eventually be reversed on a very large scale in the remote future, in a universe with ever growing entropy, actually becomes null. 92. The fact that the making of a record is necessary for the elimination of quantum interferences means that it is the irreversible growth in the number of observable variables from the environment of a quantum system which become correlated in observationally distinguishable ways with one unique specific outcome of a measurement performed on this system that must be responsible for the absence of interferences that follow measurement of an originally superposed physical attribute. 93. The irreversible spreading of effects that characterizes the making of a record does not take place with respect to an arbitrarily chosen dynamic attribute, but always relative to position space, because what is growing irreversibly as time passes is the number of available position states which can be influenced in a recognizable way by unique causes located in the past. 201 94. When it is recognized that the property of closure of the universal causal chain is not optional and must be imposed as an absolutely essential consistency requirement, one is allowed to explain the quasiclassical nature of the evolution that follows a quantum measurement, that is to say, the fact that the retarded and advanced states of that part of the environment that becomes entangled with a quantum system are very unlikely to become different in any observable way in the future (as unlikely as the growth of entropy that would have taken place while they would have become distinct is important), because in a world that would have been quasiclassical on a macroscopic scale until now, if a measurement performed on the retarded state of a quantum system was to give rise to an outcome that is different from that which was obtained as a result of a similar measurement performed on the advanced state of the same system, then as time passes an exponentially growing number of independent variables from the environment of the system that evolves as part of the retarded portion of history, would be allowed to differ from those of the same system that evolves as part of the advanced portion of history and this means that it would become increasingly less likely that the retarded and advanced trajectories in superspace could ever merge with one another at some point in the future. 95. As a result of the closure requirement, the universal causal chain must be stretched into two similar trajectories evolving side by side along the unidirectional direction of time in superspace for the whole duration of history, as if two observationally indistinguishable versions of history where taking place in parallel all the time without ever interacting with one another, even though what cannot be observed and is without irreversible consequences is not required to correspond for the related portions of those two histories, which allows for the histories of unobserved attributes to interfere quantum mechanically. 96. The privileged status of position space in triggering decoherence only means that even when the measured attribute is not position, it is nevertheless a spatial distribution of macroscopic constraints that allows such a measurement to be performed, because it is concerning those constraints that information is available in the form of records. But, this means that there is no freedom in deciding which dynamic at202 tribute is classically well-defined in any particular situation where we have knowledge of a specific set of macroscopic conditions and therefore it is relative to the dynamic attribute of a system whose state is restricted to a subset of values as a result of being submitted to experimental conditions of such a nature that a constraint of non-divergence of the retarded and advanced superspace trajectories exists which does not only give rise to non-superposed measurement results following decoherence, but really to a quasiclassical evolution that persists in time for the same family of consistent histories (the physically relevant set of histories). 97. In the context where a condition of closure must be imposed on the universal causal chain it becomes possible to understand how global consistency would be enforced even in the context where information about the future would become available, because if the universal causal chain is to be allowed to close at some point, the retarded and advanced portions of history must share the same observable macroscopic conditions in the future which means that the present can only be influenced by the future (through backward causation) to be such as to give rise (through forward causation) to a retarded state that is identical to the advanced state and not to a different future. 98. Even if entropy does not increase in the past direction of time, so that there is no constraint arising from the making of records of the future, reality must remain quasiclassical relative to the same family of consistent coarse-grained histories in this direction of time as well, because the same constraint of closure of the universal causal chain as applies on future evolution also applies to the evolution which may be assumed to take place before the Big Bang and this evolution involves an irreversible increase of entropy in the past, which means that if this requirement is to be satisfied at some point in the distant past, on the other side in time of the initial singularity, then the past evolution that is taking place on our side in time of the Big Bang must already be such as to not allow a divergence of the retarded and advanced trajectories that would involve a spatial position observable given that if this condition is not fulfilled this would prevent the closure requirement from being satisfied at a prior time (in the more remote past). 99. In a quantum gravitational context we would be dealing with situations 203 where the intrinsic curvature of space would be allowed to differ in the retarded and advanced portions of history, which could occur whenever information in the form of records would only be available about the extrinsic curvature of space associated with its rate of change along the universal causal chain. Under such conditions it would no longer be possible to estimate transition probabilities in ordinary quantum mechanics while assuming the existence of one single spacetime over which particles would propagate in both portions of a process. 100. Given that the constraint of global entanglement that is responsible for selecting the particular signature of the metric of spacetime that gives rise to a universally valid distinction between time and the other three dimensions of space would no longer be effective on the quantum gravitational scale, where fluctuations can be expected to give rise to arbitrarily strong local gravitational fields, it follows that causality may no longer operate in the same direction of spacetime uniformly over all space on that scale, so that there may in fact no longer be a simple correspondence between the retarded and the advanced portions of the trajectory in superspace. 101. The metric properties of space can only be classically well-defined when the consequences on the propagation of elementary particles of a particular curvature of space irreversibly spreads into the environment and gives rise to the formation of mutually consistent records and this means that the existence of a decoherent spacetime is itself dependent on the existence of a unidirectional time variable. 102. The hypothesis that all the interfering histories allowed by the observable conditions of an experiment are actually occurring all at once in the very same universe is not viable as a solution to the objectification problem, that is to say, for explaining the unique and random nature of measurement results, given that it would require assuming that despite all the evidence, history is not, in fact, unique. 103. Given that it is necessary to assume that there is already randomness before a measurement is performed on a particle, while the object is still propagating in the two unobserved portions of history, then a solution to the objectification problem must allow to explain what determines the particular evolution of a certain physical attribute that takes place 204 in between measurements and which later causes one unique outcome of measurement to be actualized from among many apparently equivalent possibilities. 104. Quantum theory is an idealization and it must be reformulated to give rise to a more elaborate, but statistically equivalent model, from the viewpoint of which the unique outcomes of measurement would be a natural consequence of the existence of fundamentally unobservable, random factors of influence operating all along the unobserved trajectories of elementary particles. 105. If what we understand by objective chance is the idea that the unique unobserved paths of quantum systems may have no identifiable cause at all, instead of being the unpredictable outcome of fundamentally unobservable causes, then it would appear that the concept of objective chance is problematic, because it may violate the requirement that all the distinct physical attributes of our universe be describable by referring only to aspects of reality which are an integral part of this universe. 106. In the context where backward in time causation is allowed, even a causally determined world would involve an irreducible randomness, given that the cause of an event can then be influenced backward in time by this very same event, despite the fact that no information is allowed to flow backward concerning that future event. 107. The fact that a quantum system only appears to evolve randomly after a measurement is performed on a previously superposed physical attribute of that system is not incompatible with the hypothesis that the system evolved randomly before that measurement, because in the context of a time-symmetric interpretation of quantum theory one must assume that this random evolution was influenced all along by what happened at a later time, when the measurement was performed. 108. The existence of unobservable causes obeying the principle of local causality is not ruled out by the phenomenon of quantum entanglement in the context of a realist, time-symmetric interpretation of quantum theory, because even if the trajectories of both elements of an entangled pair are independently influenced by those unobservable causes, when 205 there is as much influence of the future on the past as there is of the past on the future it is possible for the two entangled systems to evolve so as to enforce the non-locality imposed by the existence of the shared quantum phase. 109. When, as a matter of principle, no information can be obtained concerning the causes which may explain the randomly variable character of the paths of the unobserved dynamic attributes of a quantum system, then no violations of the uncertainty principle are allowed to occur as a result of the existence of such causes. 110. It is possible for the trajectory of the universal causal chain in superspace that describes the evolution of the intrinsic or extrinsic curvature of space for the whole universe to differ for the retarded and advanced portions of history as a result of the existence of local perturbations which would be attributable to unobservable, random fluctuations of the classical gravitational field arising from the quantized nature of inertial gravitational forces (which determine the local inertial reference systems) and this may provide the basis for a reformulation of quantum theory that would provide a satisfactory solution to the objectification problem. 111. Gravitation may not merely be involved in defining a deterministically evolving, locally uniform spacetime background over which quantum processes unfold, but must be understood to provide a randomly variable influence participating in the determination of the unobserved paths of elementary particles under absolutely all circumstances. 112. When the trajectory of a particle is the outcome of multiple, near simultaneous, quantized interactions, such as is the case with ordinary Brownian motion, then there necessarily arise fluctuations in the statistical equilibrium of forces acting on the particle and one can expect that this would be the case with the inertial forces that determine the local inertial reference systems, even in the context where the approximation of a classical spacetime continuum would still be valid locally. 113. It may be that it is because we fail to take into account the existence of unobservable, local fluctuations in the metric properties of spacetime that we obtain a description of quantum processes that is not generally 206 covariant and in which the mass of particles appears to constitute a relevant parameter. 114. If unobservable, local fluctuations of the metric properties of spacetime actually occur, they would have effects which would be indistinguishable from those violations of the conservation of momentum and energy which are allowed by the uncertainty principle, given that under such conditions energy would be exchanged with the gravitational field that would not be accounted for classically. 115. The fact that quantum indefiniteness in momentum rises as we consider increasingly smaller regions of space may be a reflection of the fact that the magnitude of random fluctuations in the classical gravitational field rises as we consider smaller space intervals for which the consequences of the quantized nature of the gravitational field become more significant. 116. When one takes into account the existence of unobservable, local fluctuations in the metric properties of space, it is possible to assume that massless particles in a given energy eigenstate always travel along straight lines at their normal c velocity locally, as long as one recognizes that this propagation takes place along the geodesics of a locally curved spacetime and in such a context the multiple possible trajectories of unobserved, dynamic quantum attributes really are the causally determined geodesics of a randomly evolving dynamical spacetime, rather than the random paths of particles evolving over a locally invariant and deterministically evolving spacetime. 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Princeton University Press, 1999. 210 Index absolute space, 71, 182 action at a distance, 44, 67, 76, 88, 95, 98, 146 advanced waves, see advanced solutions, wave equations advanced waves problem, 31, 33–36, 85n Aharonov, Yakir, 39, 87 alternative counterfactual, 17 artificial superintelligence, 42 ATP interferometer experiment, 87 backward in time signaling, 67, 69, 71, 92, 97, 190, 194 Barbour, Julian, 128, 129 Bell's inequality, 66, 68, 88, 90 Bell, John, 115 Bergmann, Peter, 39 Big Bang boundary conditions, 150, 155n initial conditions, 3, 14, 16, 18, 25, 27, 41, 69, 105, 108, 121, 122, 129, 130, 133, 137, 143, 172, 185, 187, 193, 197 maximum energy densities, 97, 143, 150, 158, 200 past singularity, 143, 150, 157, 200, 203 radiation reflector, 31 time before the Big Bang, 143, 157, 200, 203 black hole entropy, 4 event horizon, 8 information, 4 matter degrees of freedom, 172 thermal radiation, 47, 176n Bohr, Neils, 51, 56, 98 Boltzmann, Ludwig, 99 Boolean logic, 45, 52, 58, 76, 81, 116, 187, 191 causal chain closed, 11, 20, 24, 26, 79, 82, 124, 134, 138, 157, 166, 169, 180, 184, 199, 205 invariant direction in time, 18, 184 particle-antiparticle loop, 21 time-reversed, 16, 17 traditional concept, 133 unidirectional, 15, 18 universal, see universal causal chain causality absolute time order, 21, 71 backward causation, 12, 13, 15, 20–22, 26–28, 33, 39, 41, 66, 69, 71, 76, 79, 83, 87, 89, 92, 96, 104, 116, 135, 156, 166, 168, 183, 184, 187, 189, 192, 193, 203, 205 bidirectional, see time-symmetric, causality causal circularity, see closed, causal chain causal discontinuity, 141 causal influences, 14, 17, 28, 68, 69, 95, 150, 182, 193, 201 causal ordering postulate, 18, 184 causal process continuity, 134n, 141, 142, 181, 200 211 causal relationships, 12, 29, 166, 183 causal signals, 137 causal structure of spacetime, 14, 33, 66, 137, 151, 153 causal theory, 167, 168 causally independent branches, 65 causes and effects, 3, 13, 14, 15n, 16, 17, 20, 23, 33, 69, 71, 107, 135, 150, 168, 183, 184, 190, 199 classical, see unidirectional, causality definite time order, 19 direct contact, 12 external cause, 134, 135, 165, 199 faster-than-light communication, 66, 70, 97, 182, 189, 194 faster-than-light propagation, 67 final causes, 19, 21, 69, 72 final conditions, 17, 35, 184 first cause, 136, 199 global consistency requirement, 17, 20, 23, 26, 28, 41, 65, 79, 82, 104, 135, 156, 184, 185, 203 local, 14, 39, 88, 95, 122, 124, 157, 182, 198 local contact, 150 most essential aspect of time, 125 non-local, 58 past and future light cones, 14, 33, 68, 122 principle of local causality, 3, 11, 35, 48, 52, 53, 60, 62, 66, 69, 70, 85, 86, 96, 121, 143, 146, 162, 165, 168, 169, 180, 187, 189, 197, 205 psychological expectation, 19, 39, 187 relative time order, 21, 71 relativistic speed limit, 18, 33, 65, 68, 69, 88, 182 relevance to cosmology, 137 spreading of effects, 151, 153, 158, 161, 201, 204 teleological character, 16 time-symmetric, 3, 13, 14, 15n, 16, 17, 19–21, 29, 59, 63, 66, 69, 79, 86, 97–99, 134, 135, 165, 166, 168, 179, 180, 182– 184, 194, 205 time-symmetric causality violation, 135 two essential conditions for the universe, 137 unidirectional, 3, 13, 14, 17, 18, 21, 22, 26, 27, 33, 39, 69, 71, 92, 123, 150, 153, 181, 183, 187 unique direction in spacetime, 122, 123, 125, 129–131, 160, 204 classical curvature of space, 159 classical gravitational field, 170 microscopic properties, 171 classical history, 36, 40, 41, 51, 181 classical measuring device, 112 classical neutron interferometer experiment, 175 classical particle, 36, 43, 56 classical path, 104, 194 classical physics, 43, 44, 173 classical probability, 63, 75, 77, 80, 84, 180 classical reality, 57, 60, 63, 77, 86, 112, 137, 195 classical scale, 174, 191 212 classical space and time, 129, 131 classical spacetime, 122, 126, 127, 131, 140, 158, 159, 161, 172, 203 classical state, 66, 76, 94, 110 classical trajectory, 36, 47, 87, 91, 94, 95n, 140 classical wave, 36, 40, 43, 57, 75, 77, 85, 187, 190 classically meaningful probability, 80, 100, 110, 112–114 classically unique reality, 104, 194, 195 closed circuit analogy, 10 pairs of polarized wires, 11, 136 compact topological structure, 146 complex number, 84 complex-number weighting coefficients, 60 constraint of relational definition absence of external cause, 181 absolute direction, 119n direction of propagation in time, 10, 16, 19, 41, 72 metaphysical elements of reality, 119n physical attributes, 7, 23, 119, 165, 205 physical attributes of the universe, 134, 199 sign of charge, 10 time, 121, 133, 196 conventional rules of logic, see Boolean logic converging wave front, 30, 33, 186 correlated phases, 30 correlation probability, 13, 14, 17, 21, 28, 50, 80, 125, 134, 138, 198, 199 cosmic horizon, 150 cosmology, 3, 4, 9 global measure of change, 124 local variations of the flow of time, 131n problem of time asymmetry, 99, 127n time as a local measure of change, 198 time as a measure of relative changes, 121, 133, 196 uniform direction for the flow of time, 129, 197 uniform time flow, 123, 131 universal time variable, 119, 122, 124–126, 131, 133, 172, 180, 197 Costa de Beauregard, Olivier, 32 Cramer, John, 36, 37, 39 d'Espagnat, Bernard, 115 delayed choice experiment, 39, 62 Descartes, René, 183 determinism, 112, 166, 195 deterministic evolution, 53, 109, 124, 167, 169, 195 deterministic theory, 21, 169 Deutsch, David, 22, 24 discrete symmetry operations, 4 field polarities, 144, 200 microscopic state, 4 sign of charge, 144, 200 time reversal T , 3, 4, 126, 144, 166n, 198 double slit experiment, 36, 39, 57, 60, 73, 75, 80, 83, 163, 187 Dowker, Fay, 105, 113, 114, 154 Einstein, Albert, 53, 59, 65, 98 213 electromagnetic waves, 30, 32, 34 elementary particle conjugate attributes, 64 indistinguishable, 54 interactions, 48, 171 localized nature, 46, 57, 95, 150, 193 quantum reality, 44, 46, 55, 58, 59, 63, 72, 188 reality through interaction, 117 relevance of time, 127 static attribute, 54, 177 wavelength, 46 energy out of nothing problem work and useful energy, 33 equivalence of inertial and gravitational masses, 171 equivalent gravitational field, 174n Everett III, Hugh, 100 Feynman diagrams, 55, 56 Feynman, Richard, 12, 31, 44, 48n, 54, 56n, 82 free-will, 17, 22, 28, 79, 186 fundamental principles, 7 Gell-Mann, Murray, 95, 110, 114 general relativistic theory, 4, 170 absence of gravitational field, 172 classical approximation, 175 closed time-like curve, 130, 198 curvature of space, 171, 198 deterministic and locally uniform gravitational field, 173, 175 deterministically evolving metric properties, 174, 206 differentiation of time from space, 121, 123, 129–131, 136, 151, 160, 196–198, 204 dynamical theory, 119, 123, 129, 173, 197 Euclidean metric, 172 extrinsic curvature of space, 159, 170, 203, 206 fluctuating metric properties of space and time, 175–177, 206, 207 foundations, 179 generalized gravitation theory, 3, 4, 124, 129, 162, 171, 178, 180 generalized gravitational field equations, 171, 175 gravitational field equations, 119, 130 intrinsic curvature of space, 132, 159, 170, 203, 206 local variations of light cone structure, 122, 123 locally Euclidean metric, 174 metric properties of space and time, 133, 158, 159, 161, 171, 176, 204 omnipresent gravitational field, 173, 176 proper time interval, 123 Riemannian spacetime, 45 semi-classical theory, 179 simultaneity hyperplanes, 129 slicing of spacetime, 119, 121, 129, 131, 133 solution of gravitational field equations, 122 space dilation, 178 space-like hypersurface, 119, 121, 129, 132, 133, 136, 159, 166n, 197, 198 spacetime curvature as the outcome of an interaction, 171 214 spacetime foliation, 119 time-symmetric stochastic gravitational field theory, 175 unique metric signature, 119, 121, 130, 137, 160, 197, 204 global entanglement constraint, 12, 14, 17, 18, 25, 27, 32–34, 40, 66, 69, 97, 108, 121, 125, 137, 151, 157, 160, 161, 184–187, 189, 193–195, 197, 198, 204 global inertial reference system, 121n gravitational forces from voids in a matter distribution, 174 gravitational physics, 3, 9 gravitational repulsion, 10, 178 Griffiths, Robert, 110, 114 Hartle, James, 110, 114 Heisenberg, Werner, 51, 57 Hilbert space linearity, 61 idealism, 50 inconsistent probabilities, 80, 82, 191 inertial gravitational force, 206 information conservation, 26, 104, 169 cosmic expansion, 148 creation out of nothing, 26 gravitational field, 148 invariant measure, 143, 148, 201 microscopic state of gravitational field, 143, 200, 201 initial matter energy distribution homogeneity, 16, 121, 122, 129, 143, 150, 197, 200 primordial inhomogeneities, 123 instrumentalism, 8, 183 interaction boson, 48 interference pattern, 78, 86 interferometer experiment, 39, 89, 93 intuitive leap, 59, 72 invariance of the sign of action, 144 Kent, Adrian, 105, 113, 114, 154 large scale structure fluctuations in matter distribution, 173 larger than one probability, 82, 84 least action principle, 44 Lebowitz, Joel, 39 Liouville's equation, see Liouville's theorem Liouville's theorem, 104 local gravitational fields, 122, 160 local inertial reference system energy sign dependence, 171 equilibrium of inertial forces, 174 interaction with all the particles in the universe, 174 Machian viewpoint, 173 unobservable fluctuations, 170, 173, 177, 206 Lorentz transformation, 71 Maxwell equations, 30, 31 Maxwell, James Clerk, 30 memory state, 128 multiverse, 7, 24 causally independent universes, 23, 102, 103, 137, 182, 194 ensemble of possible universal causal chains, 138 mutually consistent records, 113, 128, 150, 157, 161, 204 215 long-term records, 128, 150 short-term memories, 128 negative energy advanced waves, 30 concept, 3 in quantum field theory, 4 negative action, 10, 30n, 88 negative energy matter, 3, 16, 25, 69, 97, 108, 123–125, 147, 150, 162, 171 inhomogeneities, 131 requirement of exchange symmetry, 180 voids in positive vacuum energy, 47 negative mass negative inertial mass, 171 negative probability, 82, 83, 90, 114, 134, 145, 180, 192 Newton, Isaac, 43 Newtonian physics, 123 Omnès, Roland, 108, 110, 116, 163 pairs of linearly polarized photons, 95n angles of polarization, 95n Penrose, Roger, 115 perception of the passage of time, 128, 129 philosophy, 5, 183 photon's angle of impact, 89, 91, 93, 98 Poincaré recurrence, 142 polarity, 10 Popescu, Sandu, 87 principle of equivalence, 45, 171 probability distribution, 60 probability of occurrence, 36, 38, 40, 50, 78, 79, 84, 90, 187, 191, 192 negative contribution, 78, 82, 83, 191, 192 whole universe history, 145 quantization of electromagnetic radiation, 32 quantum cosmology, 105, 111, 119, 123, 124, 129, 131, 134, 136, 197 ADM formalism, 133 boundary conditions over superspace, 134 canonical, 120, 130, 145 circular history, 140, 145, 146, 200 closed trajectory in superspace, 140, 199, 200 configuration space, 130, 134, 136, 138 diverging superspace trajectories, 151, 160 dynamic elements, 125 equivalent superspace trajectories, 133 global state, 129, 131, 134, 138, 198 histories of space curvature, 159 identity of initial and final boundary conditions, 145, 200 irrelevance of space, 121n irrelevance of time, 119, 121, 126, 128, 131, 133, 145, 196 meeting of superspace trajectories, 141, 151, 154, 157, 201 monotonic foliation of space-like hypersurfaces, 130 216 network of local relationships, 133 pair of indistinguishable trajectories in superspace, 138, 199 periodicity, 146 periodicity of time, 145 point in superspace, 134, 139, 142, 198 predetermined relationships, 124, 197 rapidly moving clock hand analogy, 145 relevance of time, 124, 132, 197 shared coarse-grained superspace trajectory, 142 superspace, 130, 132, 139, 150, 198 timeless, 127n topology of superspace trajectory, 146 trajectory in superspace, 123, 130, 133–136, 139, 141, 145, 146, 151, 160, 170, 197, 198, 200, 204, 206 uniqueness of history, 128, 129, 133, 138, 146, 199 Wheeler-DeWitt equation, 120 quantum field theory, 24, 31, 32, 36, 46, 49, 54, 107, 124, 126, 170 conventional formulation, 180 Dirac's equation, 34 fermion loops, 107 Feynman diagrams for radiative corrections, 178 fixed geometry of space, 173 general relativistic theory, 4 position dependent interaction probability, 48n radiative correction terms, 107 reformulation, 172, 176 relativistic invariance, 42, 153 renormalization procedure, 107 quantum formalism complex conjugation as time reversal, 38, 187 consistent histories, 38, 81, 110, 113, 114, 153, 154, 157, 196, 202, 203 extension of formalism, 164, 196 generally covariant formulation, 178 Heisenberg's matrix mechanics, 54n incomplete description, 167 linear equations, 100 linearly positive histories, 114 most adequate, 63 relation to gravitation, 162 Schrödinger equation, 40, 43 squaring of the wave function, 38, 79, 187 stationary Schrödinger equation, 120 sum-over-histories formulation, 42, 50, 54, 56, 63, 72, 172, 174 time-reversal invariant, 114 time-symmetric formulation, 71, 88, 109, 119, 145, 147, 190 traditional formulation, 54, 173 two-state vector formalism, 39, 42, 70, 72, 97, 187 unitarity, 56n unitary evolution, 39, 70, 108, 109, 195 quantum gravitation, 3, 143, 159, 161, 170–172, 174, 177, 203, 206, 207 background independent theory, 119, 173, 176 217 canonical, 125, 129 causal sets, 121 causal structure of spin foams, 121, 122, 197 causality, 129 discontinuous time flow, 129 discrete elements of structure, 125 elementary black hole, 172, 177 embryonic concept of time, 119 embryonic element of time directionality, 121, 124, 197 embryonic notion of space, 125 emergence of continuous time, 131 emergence of space, 125 emergence of time, 119, 123, 131, 172 fluctuating gravitational field, 160, 161, 204 fluctuating metric properties of space, 160, 161 four-dimensional boundary conditions, 125 fundamental element of causality, 124 fundamental scale, see Planck scale, quantum gravitation irrelevance of time, 120, 126 loop quantum gravity, 172 non-unique spacetime metric signature, 129, 160 opposite energy solutions, 124, 129 Planck scale, 4, 119, 122, 126, 129, 137, 160, 161, 170, 171, 176, 177, 197, 198, 204 Planck time, 25 probability to emit a graviton, 174 quantization procedure, 170, 172 relevance of time, 125, 160, 198 semi-classical description, 46, 126, 176 spin foams, 124 spin network, 122, 125, 136 superposed space curvatures, 161 timeless theory, 126, 129, 198 unsolved issues, 123 quantum gravitational scale, see Planck scale, quantum gravitation quantum handshake process, 36, 37, 85 confirmation wave, 36 offer wave, 36 quantum measurement absence of interference, 75, 178 absence of quasiclassicality, 117 actualization of potentialities, 60, 78, 93, 95, 99–101, 104, 105, 107, 109, 124, 164, 167, 169, 194, 195, 197, 204 amplification process, 107 classical outcome, 148, 156, 164, 195 coarse-grained history, 84, 110, 112, 114, 116 coarse-graining, 80, 81, 113 consciousness, 118 conspiracy theory, 103 correlated attribute, 94, 95n, 193, 201 correlated effects, 151 decoherence, 6, 57, 65, 81, 93, 98, 99, 101–103, 105, 106, 108, 110, 113, 115, 118, 131, 145– 147, 153, 159, 161, 163n, 164, 167, 172, 178, 181, 189, 194– 196, 201, 202 decoherent branches, see splitting 218 branches, quantum measurement decoherent space and time, 127, 131, 161, 204 delocalized phase relations, 106 diagonalization of reduced density operator, 101 discontinuous, 48, 60 distinct dynamical laws, 101, 106, 194 emergence of quasiclassicality, see persistence of quasiclassicality, quantum measurement ensemble entropy, 104 entangled particles, 79, 89, 91, 93, 98, 192, 193 environment degrees of freedom, 6, 93, 99, 105–107, 110, 115, 137, 147, 148, 151, 155, 161, 170, 201, 204 EPR-type experiment, 86, 88, 94, 98 essential condition, 151, 154 evidence of past quasiclassicality, 114, 117, 196 expectation of future quasiclassicality, 114, 117, 196 factual definiteness of reality, 116 family of coarse-grained histories, 81, 112, 154, 157, 203 gravitational field, 159 graviton perturbations, 162 identically prepared systems, 34, 64, 164, 169, 189 interaction-free, 37, 111 irrelevance of complexity, 107, 195 irreversibility, 6, 106, 107n, 115, 147, 150, 163n, 195, 196, 201 likeliness of alternative conditions, 82, 192 likeliness of initial conditions, 82, 90, 145, 192 likeliness of macroscopic conditions, 82, 90 logical consistency of history, 108, 114, 196 macroscopic experimental constraints, see observable macroscopic conditions, quantum measurement maximum quasiclassical domain, 3, 65, 107, 112, 114, 119, 141, 148, 151, 154, 163, 180, 196, 200, 201 meaningless probabilities, 84, 169 measuring device, 105, 117, 151 metric properties, 159 mixed quantum state, 110 mutually exclusive macroscopic constraints, 64 non-local, 48, 51, 65, 96, 104, 189, 192 non-subjective, 107 non-superposed outcomes, 106, 202 observable macroscopic conditions, 35–37, 39n, 40, 47, 54, 56, 60, 62, 64, 72, 73, 78, 80, 82, 85, 88, 90, 92, 106, 109, 111, 131, 137, 138, 142–144, 152, 156, 157, 167, 170, 187–189, 191, 192, 200, 202, 204 observable outcome, 10 observed history, 84 observed physical attribute, 53, 57, 61, 62, 65, 92, 101, 106, 110, 131, 153, 195 observer, 118 219 observer awareness, 37 observer dependent knowledge, 93 origin of randomness, 62, 167 overturning, 147, 201 persistence of quasiclassicality, 3, 11, 49, 99, 102, 105, 108, 109, 112, 113, 115, 118, 119, 123, 131, 140, 147, 148, 153, 157, 158, 161, 181, 182, 195, 196, 201–203 physically relevant set, 112, 113, 153, 154, 196, 202 position measurement, 96 post selection, 39, 41, 62, 70, 87, 97, 104, 187, 194 predictable outcome, 50, 78, 191 preexisting correlation, 95 preferred basis, 154 probability of future outcome, 83 probability sum rules, 114 quasiclassical gravitational field, 131 quasiclassical reality, 6, 11 quasiclassical world, see maximum quasiclassical domain, quantum measurement quasiclassicality as an evolutionary advantage, 114, 196 random outcome, 67, 162, 164, 167, 172, 178, 204 relative time order, 71, 95, 98n, 190 relevant collective observable, 153 Schrödinger cat experiment, 154, 155 splitting branches, 22, 23, 28, 65, 78, 95, 100, 103, 104, 157, 194, 195 spreading of effects, 147 state vector reduction, 71, 96, 98, 104, 108, 115, 118, 167, 178 statistical distribution, 57, 75–77, 86, 116n, 190 stochastic perturbations of the Schrödinger equation, 178 subjectivity, 93, 195 subjectivity of quasiclassicality, 182 summed-over aspects, 110, 113, 116 superposition of macroscopic observables, 100, 102, 112, 115, 116n, 154, 196, 199 time symmetry, 107 unique datum, 163 unique outcome, 164, 169, 172, 194, 201, 204 unique preexisting state, 104, 194 uniqueness of experimental facts, see uniqueness of measurement results, quantum measurement uniqueness of measurement results, 44, 52, 58, 60, 64, 68, 78, 101, 103, 104, 107, 118, 179, 194 universe as a whole, 105 unnatural coincidences, 95 unpredictability, 109, 164, 166, 195, 205 variable outcomes, 62, 64, 172, 189 quantum reality, 35, 179 absence of causes, 165, 205 advanced portion of history, 35, 40, 73, 76, 78, 82, 85–89, 91, 96, 104, 107, 115, 131, 134, 138, 146, 148, 151, 154, 156, 158, 164, 167, 170, 173, 177, 178, 187, 190–192, 195, 198– 220 201, 203, 206 advanced state, 92, 104, 143, 151, 154, 156, 158, 178, 193, 194, 200, 201, 203 alternative conception, 47 backward evolving process, 41 backward evolving state, 39 causal determination, 164–166, 168, 176, 178, 185, 205 classical aspects, 81, 81n classical hidden variables, 86, 104, 188 conjugate physical attributes, 53, 56, 59, 61, 63, 64, 104, 110, 139, 159, 188, 189 contradictory nature, 45, 58, 61, 63, 65, 68, 76, 98n, 100, 103, 190, 199 correlations, 87 created by observation, 62, 180 criterion of consistency, 49, 81, 98n, 112, 114, 140, 148, 196 decoherent branches of history, 64 dependence on experimental conditions, 53 determined by measurement, 49 dynamic attribute, 50, 59, 66, 100, 113, 137, 150, 154, 201, 202 electron spin state, 76 energy eigenstate, 178, 207 energy state, 48 entangled pair, 66, 71, 79, 88, 90, 92, 93, 168, 190, 192, 205 entangled state, 89, 92, 192 entangled systems, 67, 79, 86, 89, 96 entanglement, 3, 46, 65, 69, 70, 86, 95, 97, 146, 162, 168, 182, 189, 193, 205 expanding spherical wave function, 96 fine-grained history, 110, 114 forward evolving state, 40 fundamental hypothesis, 35 fundamental randomness, 21, 185 future entanglement, 97 generalized consistency conditions, 114 history, 44, 109 holistic, 95, 193 inadequate representations, 35 initial phase, 82, 83, 90 interferences, 5, 34, 36, 37, 39, 43, 47, 51–53, 57, 59, 66, 68, 69, 75, 78, 82, 84, 89, 90, 93, 95n, 100, 102, 106, 110, 112, 115, 116, 118, 142, 143, 145–147, 149, 152, 154, 155, 159, 161, 163, 168, 175–177, 180, 188, 190–192, 195, 196, 200, 201 interfering histories, 19, 22, 39, 42, 48, 50, 52, 54, 57, 63, 65, 68, 73, 77, 78, 81, 89, 91, 93, 96, 101, 102, 114, 120, 145– 147, 158, 179, 183, 189–191, 194, 199, 202, 204 interfering states, 50, 62, 99, 188 intermediate virtual processes, 54n irreconcilable requirements, 54 irreducible randomness, 166, 178, 205 large scale interferences, 148 locality assumption, 68 logical consistency, 81, 84, 112, 115, 136, 137, 165, 191, 195 meaningful aspects, 81 221 minimally coarse-grained histories, 38, 80, 82, 83 momentum eigenstate, 48, 50, 57 momentum state, 47, 56, 60 multiple branches hypothesis, 60, 63, 65, 68, 73, 75, 76, 78, 95, 100, 109, 116, 134, 138, 157, 159, 164, 169, 189, 191, 194, 199, 204 multiple coexisting trajectories, see multiple branches hypothesis, quantum reality mutually exclusive representations, 56 naive conception, 59, 66, 86 non-classical nature, 8 non-classical uniqueness, 168 non-interfering histories, 115 non-local correlations, 66, 70, 76, 85, 88, 90, 97, 99, 146, 157, 168, 189, 194 non-local hidden variables, 51, 62, 70 non-local influences, 62, 65, 67, 69, 70, 76, 86, 90, 189 non-locality, 5, 11, 46, 51, 65, 67, 69, 71, 76, 86, 88, 95, 98, 99, 104, 134, 146, 162, 182, 188, 193, 195, 205 non-objective, 68 objective chance, 53, 165, 205 objective indefiniteness, 53, 164, 165 objective reality, 8, 76, 168 observer dependent facts, 68 pair of causally independent histories, 40, 42, 72, 76, 78, 85, 96, 138, 140, 145, 152, 154, 168, 181, 187, 191, 199, 202 pair of histories unfolding in opposite time directions, 38, 40, 41, 72, 73, 77, 80, 81, 83, 93, 96, 134, 137, 138, 181, 187, 190, 191, 199 pair of interfering histories, 60, 110, 134, 140, 168 pair of simultaneous states, 59 particle trajectory, 19, 44, 47, 48, 51, 73, 75, 172, 174, 188, 193 periodic evolution, 48 phenomenological model, 59, 189 position state, 47, 48, 60, 68 predetermination, 86 preestablished harmony, 146 probability amplitude, 5, 36, 38, 48, 48n, 63, 68, 75, 77–79, 84, 104, 107, 110, 180, 194 quantum field, 48 quantum indefiniteness, 57 quantum indeterminacy, 53, 61, 139, 188 quantum phase, 63, 82, 83, 89, 106, 177, 192 quantum phase continuity, 145, 200 quantum state, 21, 38, 39, 76, 96, 169 quantum strangeness, 56, 58, 60, 76, 81, 104 quantum superposition of random space curvatures, 178 quantum tunneling, 176n quantum uncertainty, 46, 56, 61, 176 randomness, 39n, 62, 109, 124, 142, 164, 167, 169, 173, 204–206 realist conception, 8, 47, 49, 50, 222 54, 56, 59, 63, 66, 69, 70, 72, 76, 84, 86, 88, 124, 167, 183, 188, 189, 191 realist description, see realist conception, quantum reality relational description, 118 relative notion, 68 retarded portion of history, 40, 41, 73, 76, 78, 82, 85–89, 91–93, 96, 104, 107, 115, 131, 134, 138, 145, 146, 148, 151, 154, 156, 158, 164, 167, 170, 173, 177, 178, 187, 190–192, 195, 198–201, 203, 206 retarded state, 92, 104, 143, 151, 154, 156, 158, 178, 194, 200, 201, 203 shared quantum phase, 92, 145, 168, 205 state indefiniteness, 57 state superposition, 60, 69, 76, 86, 92, 100, 101, 103, 110, 116, 138 state vector, 39n, 41, 60, 77, 100, 109, 187 statistical description, 167 subjective wave function, 93, 193 superposed physical attribute, 201, 205 time symmetry, 78, 102, 104, 106, 109, 116, 157, 195 time-symmetric conception, 80, 131, 191 time-symmetric history, 84, 180, 191, 192 time-symmetric process, 78, 80, 82–84, 87, 90, 145, 177, 192, 193 understandable, 44 undetermined state, 76, 110, 191 unique history, 49, 50, 52–54, 56, 59, 61, 63, 66, 72, 73, 81, 85, 109, 138, 163, 164, 179, 187– 189, 191, 204 unique trajectory, 47, 50, 56–58, 60, 63, 72, 73, 91, 93, 96, 112, 164, 165, 189, 190, 193 uniqueness, 51, 53, 64, 76, 78, 86, 99, 102, 103, 107, 109, 118, 139, 163, 167, 168, 173, 179, 181, 183, 189, 195 uniqueness of historical facts, see uniqueness of measurement results, quantum measurement unobservable aspects, 7, 19, 42, 49, 53, 59, 60, 62, 63, 81, 83, 86, 115, 118, 134, 138, 139, 143, 165, 169, 175, 176, 178, 188, 191, 198, 200, 202, 206 unobservable causes, 165, 167, 169, 205 unobservable hidden variables, 53 unobservable history, 64, 188 unobservable random factors of influence, 164, 165, 167, 171, 172, 205, 206 unobservable state, 76, 142, 200 unobservable trajectory, 47, 50, 57, 73, 79, 93, 112, 173, 174, 178 unobserved path, 50, 73, 75, 80, 84, 87, 96, 109, 165, 167, 171, 172, 179, 190, 192, 205, 206 unobserved physical attribute, 49, 50, 52, 55, 57, 59, 60, 63, 64, 68, 73, 75, 76, 83, 86, 95, 99, 102, 103, 139, 142, 164, 167– 223 169, 172, 178, 188–192, 194, 202, 204, 206, 207 unobserved portion of history, 84, 86, 164, 166, 173, 204 unpredictability, 21, 53, 109, 166– 168, 179, 195 vacuum fluctuations, 46, 47 visualization, 56, 57, 61, 75 wave function, 34, 39n, 41, 44n, 48, 50, 51, 60, 62, 66, 70, 82, 93, 96, 98, 109, 167, 187–189, 195 wave packet, 47 wave-particle duality, 48 wavelike nature, 48 quantum theory, 4, 32 absolute determinism, 86, 95 alternative interpretations, 35, 36, 38, 40, 53, 60, 65, 68, 77, 85, 86, 187 basic principles, 4 central problem of interpretation, 117 classical hidden variables theory, 36, 51, 53, 54, 58, 62, 69, 70, 85, 95, 162, 168 complementarity principle, 56, 81 consistent histories interpretation, 49, 64, 80, 81n, 98n, 105, 110, 112, 119, 140, 148, 191 consistent interpretation, 44, 48, 49, 51, 59, 62, 63, 65, 70, 72, 76, 77, 91, 99, 114, 119, 132, 138, 163, 169, 180, 188 conventional interpretation, see orthodox interpretation, quantum theory conventional quantum mechanics, 54, 159, 203 Copenhagen interpretation, 52, 54, 56, 112, 183 cosmological theory, 131 counterintuitive aspect, 42–44, 136, 165 current formulation, 171 currently favored interpretation, 60, 117 domain of validity, 34 epistemological viewpoint, 44 existing interpretations, 6, 43, 45, 78 flat invariant spacetime, 170 foundations, 179 fundamental time asymmetry, 36, 41 hidden variables theory, 21 idealist position, 98 incomplete interpretations, 49, 98, 117, 188 incompleteness, 119, 163, 164 inconsistent interpretations, 43, 45, 61, 65, 68, 163, 169 instrumentalist interpretation, 62, 63, 65 interpretation problem, 3, 5, 6, 8, 9, 43, 45, 54, 58, 59, 72, 85n, 88, 106, 131, 162, 179 known interpretations, 118 lack of intelligibility, 43, 57 many-worlds interpretation, 22, 23, 28, 60, 78, 102, 104, 109, 112, 116, 147, 169, 182, 185 mathematical framework, 5, 6, 38, 42, 45, 49, 53, 64, 79, 106, 109, 118, 119, 140 mathematical structure, 35, 68, 70 224 measurement problem, 3, 6, 10, 24, 37, 49, 60, 88, 99, 103, 104, 111, 112, 115, 116, 119, 140, 148, 163, 181, 182, 195, 196 naive realist interpretations, 168 non-realist interpretation, see instrumentalist interpretation, quantum theory objectification problem, 3, 162– 164, 168, 169, 179, 180, 204, 206 ontological viewpoint, 44 orthodox interpretation, 3, 37, 42, 49, 51, 53, 54, 59, 61, 62, 65, 67, 68, 81, 88, 91, 98, 100, 104, 118, 147, 163, 168, 189, 191, 199 probabilistic inferences, 112 probabilistic nature, 43, 50, 169 QBism, 93 quantum logic, 45 quantum reality problem, 5, 189 quantum scale of action, 175 realist interpretation, 3, 8, 11, 39, 42, 49, 53, 54, 59, 60, 62, 65, 68, 72, 76, 84, 88, 95, 98–100, 109, 112, 165, 179, 182, 188, 195 realist time-symmetric interpretation, 67, 78, 79, 83, 84, 85n, 87, 90, 96, 97, 112, 115, 138, 148, 164, 168, 189, 190, 198, 205 reformulation, 164, 170, 171, 205, 206 relational interpretation, 68, 117 revised interpretation, 35, 43, 44 satisfactory interpretation, 111, 131 selection principle, 154 standard theory, 37, 39, 70, 73 state-of-the-art interpretation, 114 statistical predictions, 34, 36, 42, 44n time-symmetric, 20, 35, 37, 38, 59, 63, 70, 77, 85, 86, 187 time-symmetric interpretation, 138, 147, 169, 205 traditional interpretation, see orthodox interpretation, quantum theory transactional interpretation, 37, 39, 85 uncertainty principle, 43, 48, 59, 64, 169, 206, 207 unsettling viewpoint, 75 real probability, 84 reformulated quantum theory causally determined geodesics of a random spacetime, 178, 207 classical gravitational field fluctuations, 170, 172, 174, 176, 177, 179, 206, 207 classical spacetime continuum approximation, 174, 176, 206 dependence of uncertainty on energy magnitude, 177 dependence of uncertainty on spatial scale, 207 energy exchanges with the fluctuating gravitational field, 176, 207 fluctuating equilibrium of inertial forces, 173, 177, 206 locally uniform spacetime back225 ground, 171, 172, 180, 206 massless particles with curved trajectories, 178, 207 massless particles with non-c velocities, 178 random particle paths in a fixed spacetime, 178, 207 randomly variable local space curvature, 172 relevance of particle masses, 175, 177, 206 requirement of general covariance, 170, 171 statistically equivalent theory, 164, 178, 180, 205 straight trajectories in a locally curved spacetime, 178, 207 temporary violations of energy conservation, 176, 207 violation of general covariance, 175, 206 Reichenbach, Hans, 20, 133, 146 relativity of particle existence, 176 Schrödinger, Erwin, 43 scientific realism, 8, 50, 67–69, 76, 98, 114, 163, 164, 180, 189 scientific research, 180 second law of thermodynamics, 10, 130 anti-thermodynamic evolution, 28, 185 branch systems, 25 entropy, 15, 17, 18, 25, 26, 28, 33, 41, 66, 69, 92, 97, 105, 106, 108, 128, 130, 135, 139, 142, 148, 154, 157, 184–186, 189, 193, 194, 201, 203 entropy decreasing fluctuation, 26, 27, 135, 156 gravitational entropy, 25, 32, 41, 47, 108, 124, 130, 137, 141, 143, 147, 150, 155n, 187, 200 microscopic degrees of freedom, 143, 150 subjective entropy growth, 127n thermal equilibrium, 27 unlimited entropy growth, 147 violation, 25, 26, 135, 156, 169, 185, 186 sign of energy, 88, 144, 200 Smolin, Lee, 173 solipsism, 8, 50, 114, 126, 154, 182 space-like separated events, 71, 89, 190, 192 relative time order, 16 special relativity, 16 causal time, 18 time-like interval, 18 spreading wave front, 150, 186 statistical mechanics, 53, 63, 99 Brownian motion, 173, 206 multiple near simultaneous interactions, 173, 206 near-equilibrium thermodynamics, 176 Planck's definition of entropy, 32 quantum field theory, 5 statistically uniform distribution of forces, 173 thermal equilibrium, 107 teleological problem of time, 19 thermal time, 127 thermodynamics, 9, 127 thought experiment, 87 226 time as a reference system, 126 time direction degree of freedom, 126, 198 antiparticles, 13, 14, 16, 19, 25, 34, 70, 79, 88, 135 backward propagating particle, 4, 12, 13, 16, 19, 21, 24, 27, 28, 32, 33, 70, 79, 135, 144, 183, 185, 186, 200 bidirectional time, 3, 32, 141–143, 171 condition of continuity of the flow of time, 134n direction of propagation in time, 4, 13, 14, 16, 19, 20, 72, 88, 144, 183, 184, 200 Feynman's interpretation, 12, 16 pair creation and annihilation, 142 particle world-line, 21 time-symmetric viewpoint, see bidirectional time, time direction degree of freedom uniquely ordered sequence of events, 126, 198 time directionality, 3, 13, 14, 66, 126, 132, 184, 198 local topological order, 21 time irreversibility, 10, 12–14, 15n, 17, 40, 99, 105, 106, 108, 111, 115, 116, 118, 123, 124, 126, 150, 151, 153, 155n, 158, 161, 170, 180, 185, 195, 197 astronomical processes, 15n boundary conditions, 14, 34 conditions on current state, 30, 186 cosmic evolution, 33 dissipation, 15n, 106, 127, 149, 151, 153 electromagnetic arrow of time, 33 formation of a record, 15, 25, 27, 54, 57, 73, 75, 107, 107n, 149, 151, 157, 158, 160, 184, 188, 201–204 fundamental irreversibility, 16, 18, 27, 34, 106, 133, 148, 187 information flow, 13, 14, 18, 25, 26, 28, 33, 39, 66, 92, 166, 184–186, 189, 193, 205 interaction with radiation, 31 origin, 6, 25, 41 singular status of position space, 150, 152, 201, 202 temporal parallelism, 15n, 25 thermodynamic arrow of time, 13, 15, 19, 21, 25, 27, 41, 67, 99, 122, 130, 142, 158, 185, 187, 198 thermodynamic time, 33 unidirectional time, 3, 11, 14, 18, 21, 25, 27, 30, 33, 34, 69, 79, 127, 130, 134, 136, 138, 141, 142, 144, 148, 152, 161, 186, 190, 195, 199–202, 204 wave retardation, 32 wavefront propagation, 30, 32, 33 wavelike processes, 31 time travel, 26, 29, 33, 79, 130, 134, 185, 186 causality violation, 22, 25, 27 continuous information flow, 135 contradictory accounts, 23, 28 knowledge paradox, 26, 135, 185 paradox, 22, 27, 156, 185 reversal of information flow, 203 Tollaksen, Jeff, 87 227 transition probability, 48, 56n, 60, 73, 80, 82–84, 108, 116, 155, 159, 190, 203 universal causal chain, 11, 129, 134, 136, 158, 160, 170, 175, 181, 199, 203, 206 bifurcation point, 141, 142, 144, 200 closed causal chain, 136, 138, 140, 142, 144–146, 148, 154, 157, 160, 163, 168, 177, 180, 200, 201, 203 closure requirement, 11, 141, 144, 146, 148, 151–153, 157, 161, 163n, 178, 180, 181, 200, 201, 203 constraint of non-divergence of superspace trajectories, 152, 153, 202, 203 end of time, 141, 142, 148, 200, 201 interrupted trajectory, 141 irrelevance to quantum cosmology, 128 local topological ordering properties of spacetime, 133 non-decreasing probability of closure, 148, 201 parallel stretching of superspace trajectories, 152, 199, 202 relativity of direction of propagation in time, 141 relativity of past and future, 141 relevance to quantum cosmology, 128, 131 sequential order of events, 125, 132, 198 universe causal horizon, 121 causal relationships, 3, 7, 23, 25, 33, 52, 61, 65, 108, 121–124, 130, 137, 157, 185, 197, 198 causal structure, 134 causally self-determined, 138, 154, 157 conservation of energy, 142 four-dimensional, 121, 123 history, 65, 136, 137, 140, 145, 197–199 incomplete instance of reality, 165 invariant total energy, 119, 121, 133, 196 isolated system, 119 low-gravitational-entropy Big Crunch, 97 unique future, 16, 19, 28, 124, 184, 186 unique past, 16, 17, 29, 69, 124, 184 wave function, 120, 124, 134, 145 zero angular momentum condition, 119n zero energy condition, 119n, 121n, 124 zero momentum condition, 119n, 121n Unruh effect, 176 vacuum energy accelerating observer, 47 maximum density, 47 persistent microscopic structure, 107n uniform distribution, 47 virtual particles, 46, 47, 176 228 voids in negative vacuum energy positive energy matter, 47 Von Neumann equation, 104 Von Neumann, John, 37, 63, 118, 154 wave equations absorber theory, 31, 34, 35, 37 advanced solutions, 30, 35, 36, 40, 85, 144, 186, 187 boundary conditions, 37, 39 constructive interference, 31, 75, 159, 177, 186 destructive interference, 31, 37, 75, 82, 83, 90, 159, 177, 186 periodic boundary conditions, 145 pilot wave, 181 probability wave, 58 propagating in opposite directions of time, 42 relativistically invariant, 31 retarded solutions, 30, 31, 37, 40, 85, 187 stationary wave, 145 weak anthropic principle, 103, 123, 127n, 128, 182, 197 Wheeler, John, 31 Zeh, Heinz Dieter, 104