What would it be for a process to happen backwards in time? Would such a process involve different causal relations? It is common to understand the timereversal invariance of a physical theory in causal terms, such that whatever can happen forwards in time (according to the theory) can also happen backwards in time. This has led many to hold that timereversal symmetry is incompatible with the asymmetry of cause and effect. This (...) paper critiques the causal reading of timereversal. First, I argue that the causal reading requires time-reversal-related models to be understood as representing distinct possible worlds, and on such a reading causal relations are compatible with timereversal symmetry. Second, I argue that the former approach does however raise serious sceptical problems regarding the causal relations of paradigm causal processes, and as a consequence there are overwhelming reasons to prefer a non-causal reading of timereversal whereby timereversal leaves causal relations invariant. On the non-causal reading, timereversal symmetry poses no significant conceptual nor epistemological problems for causation. -/- . (shrink)
Many have suggested that the transformation standardly referred to as `timereversal' in quantum theory is not deserving of the name. I argue on the contrary that the standard definition is perfectly appropriate, and is indeed forced by basic considerations about the nature of time in the quantum formalism.
It was repeatedly underlined in literature that quantum mechanics cannot be considered a closed theory if the Born Rule is postulated rather than derived from the first principles. In this work the Born Rule is derived from the time-reversal symmetry of quantum equations of motion. The derivation is based on a simple functional equation that takes into account properties of probability, as well as the linearity and time-reversal symmetry of quantum equations of motion. The derivation presented (...) in this work also allows to determine certain limits to applicability of the Born Rule. (shrink)
The aim of this paper is to analyze time-asymmetric quantum mechanics with respect of its validity as a non time-reversal invariant, time-asymmetric theory as well as of its ability to determine an arrow of time.
David Albert's Time and Chance (2000) provides a fresh and interesting perspective on the problem of the direction of time. Unfortunately, the book opens with a highly non-standard exposition of timereversal invariance that distorts the subsequent discussion. The present article not only has the remedial goal of setting the record straight about the meaning of timereversal invariance, but it also aims to show how the niceties of this symmetry concept matter to the (...) problem of the direction of time and to related foundation issues in physics. (shrink)
Richard Feynman has claimed that anti-particles are nothing but particles `propagating backwards in time'; that time reversing a particle state always turns it into the corresponding anti-particle state. According to standard quantum field theory textbooks this is not so: timereversal does not turn particles into anti-particles. Feynman's view is interesting because, in particular, it suggests a nonstandard, and possibly illuminating, interpretation of the CPT theorem. In this paper, we explore a classical analog of Feynman's view, (...) in the context of the recent debate between David Albert and David Malament over timereversal in classical electromagnetism. (shrink)
David Albert claims that classical electromagnetic theory is not timereversal invariant. He acknowledges that all physics books say that it is, but claims they are ``simply wrong" because they rely on an incorrect account of how the timereversal operator acts on magnetic fields. On that account, electric fields are left intact by the operator, but magnetic fields are inverted. Albert sees no reason for the asymmetric treatment, and insists that neither field should be inverted. (...) I argue, to the contrary, that the inversion of magnetic fields makes good sense and is, in fact, forced by elementary geometric considerations. I also suggest a way of thinking about the timereversal invariance of classical electromagnetic theory -- one that makes use of the invariant (four-dimensional) formulation of the theory -- that makes no reference to magnetic fields at all. It is my hope that it will be of interest in its own right, Albert aside. It has the advantage that it allows for arbitrary curvature in the background spacetime structure, and is therefore suitable for the framework of general relativity. (The only assumption one needs is temporal orientability.). (shrink)
In this paper, I argue that the recent discussion on the time - reversal invariance of classical electrodynamics (see (Albert 2000: ch.1), (Arntzenius 2004), (Earman 2002), (Malament 2004),(Horwich 1987: ch.3)) can be best understood assuming that the disagreement among the various authors is actually a disagreement about the metaphysics of classical electrodynamics. If so, the controversy will not be resolved until we have established which alternative is the most natural. It turns out that we have a paradox, namely (...) that the following three claims are incompatible: the electromagnetic fields are real, classical electrodynamics is time-reversal invariant, and the content of the state of affairs of the world does not depend on whether it belongs to a forward or a backward sequence of states of the world. (shrink)
In a recent paper, Malament (2004) employs a timereversal transformation that differs from the standard one, without explicitly arguing for it. This is a new and important understanding of timereversal that deserves arguing for in its own right. I argue that it improves upon the standard one. Recent discussion has focused on whether velocities should undergo a timereversal operation. I address a prior question: What is the proper notion of time (...)reversal? This is important, for it will affect our conclusion as to whether our best theories are time-reversal symmetric, and hence whether our spacetime is temporally oriented. *Received February 2007; revised March 2008. †To contact the author, please write to: Department of Philosophy, Yale University, P.O. Box 208306, New Haven, CT 06520-8306; e-mail: email@example.com. (shrink)
A theory is usually said to be time reversible if whenever a sequence of states S 1 , S 2 , S 3 is possible according to that theory, then the reverse sequence of time reversed states S 3 T , S 2 T , S 1 T is also possible according to that theory; i.e., one normally not only inverts the sequence of states, but also operates on the states with a timereversal operator T (...) . David Albert and Paul Horwich have suggested that one should not allow such timereversal operations T on states. I will argue that timereversal operations on fundamental states should be allowed. I will furthermore argue that the form that timereversal operations take is determined by the type of fundamental geometric quantities that occur in nature and that we have good reason to believe that the fundamental geometric quantities that occur in nature correspond to irreducible representations of the Lorentz transformations. Finally, I will argue that we have good reason to believe that space-time has a temporal orientation. (shrink)
Wigner timereversal implemented by antiunitary transformations on the wavefunctions is to be refined if we are to deal with systems with internal symmetry. The necessary refinements are formulated. Application to a number of physical problems is made with some unexpected revelations about some popular models.
Dynamical collapse models embody the idea of a physical collapse of the wave function in a mathematically well-defined way. They involve modifications to the standard rules of quantum theory in order to describe collapse as a physical process. This appears to introduce a timereversal asymmetry into the dynamics since the state at any given time depends on collapses in the past but not in the future. Here we challenge this conclusion by demonstrating that, subject to specified (...) model constraints, collapse models can be given a structurally time symmetric formulation in which the collapse events are the primitive objects of the theory. Three different examples of time asymmetries associated with collapse models are then examined and in each case it is shown that the same dynamical rule determining the collapse events works in both the forward and backward in time directions. Any physically observed time asymmetries that arise in such models are due to the asymmetric imposition of initial or final time boundary conditions, rather than from an inherent asymmetry in the dynamical law. This is the standard explanation of time asymmetric behaviour resulting from time symmetric laws. (shrink)
In this paper I draw the distinction between intuitive and theory-relative accounts of the timereversal symmetry and identify problems with each. I then propose an alternative to these two types of accounts that steers a middle course between them and minimizes each account’s problems. This new account of timereversal requires that, when dealing with sets of physical theories that satisfy certain constraints, we determine all of the discrete symmetries of the physical laws we are (...) interested in and look for involutions that leave spatial coordinates unaffected and that act consistently across our physical laws. This new account of timereversal has the interesting feature that it makes the nature of the timereversal symmetry an empirical feature of the world without requiring us to assume that any particular physical theory is timereversal invariant from the start. Finally, I provide an analysis of several toy cases that reveals differences between my new account of timereversal and its competitors. (shrink)
A theory is usually said to be time reversible if whenever a sequence of states S 1, S 2, S 3 is possible according to that theory, then the reverse sequence of time reversed states S 3 T, S 2 T, S 1 T is also possible according to that theory; i.e., one normally not only inverts the sequence of states, but also operates on the states with a timereversal operator T. David Albert and Paul (...) Horwich have suggested that one should not allow such timereversal operations T on states. I will argue that timereversal operations on fundamental states should be allowed. I will furthermore argue that the form that timereversal operations take is determined by the type of fundamental geometric quantities that occur in nature and that we have good reason to believe that the fundamental geometric quantities that occur in nature correspond to irreducible representations of the Lorentz transformations. Finally, I will argue that we have good reason to believe that space-time has a temporal orientation. (shrink)
It is commonly thought that there is some tension between the second law of thermodynam- ics and the timereversal invariance of the microdynamics. Recently, however, Jos Uffink has argued that the origin of timereversal non-invariance in thermodynamics is not in the second law. Uffink argues that the relationship between the second law and timereversal invariance depends on the formulation of the second law. He claims that a recent version of the second (...) law due to Lieb and Yngvason allows irreversible processes, yet is timereversal invariant. In this paper, I attempt to spell out the traditional argument for incompatibility between the second law and timereversal invariant dynamics, making the assumptions on which it depends explicit. I argue that this argument does not vary with different versions of the second law and can be formulated for Lieb and Yngvason's version as for other versions. Uffink's argument regarding timereversal invariance in Lieb and Yngvason is based on a certain symmetry of some of their axioms. However, these axioms do not constitute the full expression of the second law in their system. (shrink)
The aim of this paper is to analyze the concepts of time-reversal invariance and irreversibility in the so-called 'time-asymmetric quantum mechanics'. We begin with pointing out the difference between these two concepts. On this basis, we show that irreversibility is not as tightly linked to the semigroup evolution laws of the theory -which lead to its non time-reversal invariance- as usually suggested. In turn, we argue that the irreversible evolutions described by the theory are coarse-grained (...) processes. (shrink)
Active timereversal in the sense of “object reversal” and passive timereversal in the sense of a frame reversal of time are discussed separately and then together so as to bring out their dual nature. An understanding of that duality makes it unavoidable to contrast symmetry properties of matter with symmetry properties to be assigned to antimatter. Only frame reversal of time can “see” all conceivable active time reversals relevant (...) to physical objects. Only frame reversal of time can be used for a meaningful extension of the Neumann principle to the time domain. (shrink)
We show that it is possible to consider parity and timereversal, as basic geometric symmetry operations, as being absolutely conserved. The observations of symmetry-violating pseudoscalar quantities can be attributed to the fact that some particles, due to their internal structure, are not eigenstates of parity or CP, and there is no reason that they should be. In terms of a model it is shown how, in spite of this, pseudoscalar terms are small in strong interactions. The neutrino (...) plays an essential role in these considerations. (shrink)
A new interpretation of the time-reversal invariance principle is given. As a result, it is shown that microscopic dynamic reversibility has no basis in physics. The existing contradiction between one-way time and two-way time is reconciled. It is also pointed out that the common notion that clocks run backwards when time is reversed is wrong.
Two approaches toward the arrow of time for scattering processes have been proposed in rigged Hilbert space quantum mechanics. One, due to Arno Bohm, involves preparations and registrations in laboratory operations and results in two semigroups oriented in the forward direction of time. The other, employed by the Brussels-Austin group, is more general, involving excitations and de-excitations of systems, and apparently results in two semigroups oriented in opposite directions of time. It turns out that these two (...) class='Hi'>time arrows can be related to each other via Wigner's extensions of the spacetime symmetry group. Furthermore, their are subtle differences in causality as well as the possibilities for the existence and creation of time-reversed states depending on which time arrow is chosen. (shrink)
The reversal in the relation of time and movement which Deleuze describes in his Cinema books does not only concern a change in the filmic arts. Deleuze associates it with a wider Copernican turn in science, philosophy, art and indeed modern experience as a whole. Experience no longer consists of an idea plus the time it takes to realize it. Instead, time is implicated in the determination, literally the creation of the terminus of any movement of (...) experience. Deleuze describes this open movement structure as determinable virtuality. Because it is determinable, experience as a whole is neither actual nor actualisable. The whole is virtual. I use the phrase determinable virtuality as a kind of organizational device with which to organise a study of the reversal of time and movement in Deleuze's work. I study the concept of determinability as it appears in Deleuze's reading of the relation of time and movement in Kant's description of the whole of possible experience, or the Transcendental Ideas. In a following section I take up the idea of virtuality which I trace back to Duns Scotus who uses the idea of the virtual to distinguish between univocal and equivocal movements, forms of movement which, I argue, anticipate the kinostructures and chronogeneses, or movement and time-images which Deleuze places at the center of his work on cinema. (shrink)
Agendanken experiment is proposed for distinguishing between two models accounting for the macroscopic arrow of time. The experiment involves the veloeity revesal of components of an isolated system, and the two models give contrasting predictions as to its behavior.
Bertrand Russell famously argued that causation is not part of the fundamental physical description of the world, describing the notion of cause as “a relic of a bygone age”. This paper assesses one of Russell’s arguments for this conclusion: the ‘Directionality Argument’, which holds that the time symmetry of fundamental physics is inconsistent with the time asymmetry of causation. We claim that the coherence and success of the Directionality Argument crucially depends on the proper interpretation of the ‘ (...)time symmetry’ of fundamental physics as it appears in the argument, and offer two alternative interpretations. We argue that: if ‘ time symmetry’ is understood as the time -reversal invariance of physical theories, then the crucial premise of the Directionality Argument should be rejected; and if ‘ time symmetry’ is understood as the temporally bidirectional nomic dependence relations of physical laws, then the crucial premise of the Directionality Argument is far more plausible. We defend the second reading as continuous with Russell’s writings, and consider the consequences of the bidirectionality of nomic dependence relations in physics for the metaphysics of causation. (shrink)
A time-symmetric formulation of nonrelativistic quantum mechanics is developed by applying two consecutive boundary conditions onto solutions of a time- symmetrized wave equation. From known probabilities in ordinary quantum mechanics, a time-symmetric parameter P0 is then derived that properly weights the likelihood of any complete sequence of measurement outcomes on a quantum system. The results appear to match standard quantum mechanics, but do so without requiring a time-asymmetric collapse of the wavefunction upon measurement, thereby realigning quantum (...) mechanics with an important fundamental symmetry. (shrink)
It has been a longstanding problem to show how the irreversible behaviour of macroscopic systems can be reconciled with the time-reversal invariance of these same systems when considered from a microscopic point of view. A result by Lanford shows that, under certain conditions, the famous Boltzmann equation, describing the irreversible behaviour of a dilute gas, can be obtained from the time-reversal invariant Hamiltonian equations of motion for the hard spheres model. Here, we examine how and in (...) what sense Lanford’s theorem succeeds in deriving this remarkable result. Many authors have expressed different views on the question which of the ingredients in Lanford’s theorem is responsible for the emergence of irreversibility. We claim that these interpretations miss the target. In fact, we argue that there is no time-asymmetric ingredient at all. (shrink)
Wigner gave a well-known proof of Kramers degeneracy, for timereversal invariant systems containing an odd number of half-integer spin particles. But Wigner's proof relies on the assumption that the Hamiltonian has an eigenvector, and thus does not apply to many quantum systems of physical interest. This note illustrates an algebraic way to talk about Kramers degeneracy that does not appeal to eigenvectors, and provides a derivation of Kramers degeneracy in this more general context.
Testable predictions of quantum mechanics are invariant under timereversal. But the evolution of the quantum state in time is not so, neither in the collapse nor in the no-collapse interpretations of the theory. This is a fact that challenges any realistic interpretation of the quantum state. On the other hand, this fact raises no difficulty if we interpret the quantum state as a mere calculation device, bookkeeping past real quantum events.
It is a remarkable fact that all processes occurring in the observable universe are irre- versible, whereas the equations through which the fundamental laws of physics are formu- lated are invariant under timereversal. The emergence of irreversibility from the funda- mental laws has been a topic of consideration by physicists, astronomers and philosophers since Boltzmann's formulation of his famous \H" theorem. In this paper we shall discuss some aspects of this problem and its connection with the dynamics (...) of space-time, within the framework of modern cosmology. We conclude that the existence of cosmological horizons allows a coupling of the global state of the universe with the local events deter- mined through electromagnetic processes. (shrink)
Rohrlich claims that “the problem of the arrow of time in classical dynamics has been solved”. The solution he proposes is based on the equations governing the motion of extended particles. Rohrlich claims that these equations, which must take self-interaction into account, are not invariant under timereversal. I dispute this claim, on several grounds.
An increasing number of experiments at the Belle, BNL, CERN, DAΦNE and SLAC accelerators are confirming the violation of timereversal invariance (T). The violation signifies a fundamental asymmetry between the past and future and calls for a major shift in the way we think about time. Here we show that processes which violate T symmetry induce destructive interference between different paths that the universe can take through time. The interference eliminates all paths except for two (...) that represent continuously forwards and continuously backwards time evolution. Evidence from the accelerator experiments indicates which path the universe is effectively following. This work may provide fresh insight into the long-standing problem of modeling the dynamics of T violation processes. It suggests that T violation has previously unknown, large-scale physical effects and that these effects underlie the origin of the unidirectionality of time. It may have implications for the Wheeler-DeWitt equation of canonical quantum gravity. Finally it provides a view of the quantum nature of time itself. (shrink)
The problem of the direction of time is reconsidered in the light of a generalized version of the theory of abstract deterministic dynamical systems, thanks to which the mathematical model of time can be provided with an internal dynamics, solely depending on its algebraic structure. This result calls for a reinterpretation of the directional properties of physical time, which have been typically understood in a strictly topological sense, as well as for a reexamination of the theoretical meaning (...) of the widespread time-reversal invariance of classical physical processes. (shrink)