In the transition to Einstein’s theory of Special Relativity (SR), certain concepts that had previously been thought to be univocal or absolute properties of systems turn out not to be. For instance, mass bifurcates into (i) the relativistically invariant proper mass m0, and (ii) the mass relative to an inertial frame in which it is moving at a speed v = βc, its relative mass m, whose quantity is a factor γ = (1 – β2) -1/2 times the proper mass, (...) m = γm0. (shrink)

In this paper I try to sort out a tangle of issues regarding time, inertia, proper time and the so-called “clock hypothesis” raised by Harvey Brown's discussion of them in his recent book, Physical Relativity. I attempt to clarify the connection between time and inertia, as well as the deficiencies in Newton's “derivation” of Corollary 5, by giving a group theoretic treatment original with J.-P. Provost. This shows how both the Galilei and Lorentz transformations may be derived from the relativity (...) principle on the basis of certain elementary assumptions regarding time. I then reflect on the implications of this derivation for understanding proper time and the clock hypothesis. (shrink)

This paper relates both to the metaphysics of probability and to the physics of time asymmetry. Using the formalism of decoherent histories, it investigates whether intuitions about intrinsic time directedness that are often associated with probability can be justified in the context of no-collapse approaches to quantum mechanics. The standard (two-vector) approach to time symmetry in the decoherent histories literature is criticised, and an alternative approach is proposed, based on two decoherence conditions ('forwards' and 'backwards') within the one-vector formalism. In (...) turn, considerations of forwards and backwards decoherence and of decoherence and recoherence suggest that a time-directed interpretation of probabilities, if adopted, should be both contingent and perspectival. (shrink)

Arguments about temporal becoming often get nowhere. One reason for the impasse lies in the fact that the issue has been formulated as a choice between science on the one hand and common sense (or ordinary language) on the other as the primary source of ontological commitment.' Often' proponents of attributing temporal becoming to the physical universe look to everyday temporal concepts, find them infested with notions involving temporal becoming and conclude that becoming is a basic feature of the physical (...) world. Their opponents may look to physical science, find no reference to temporal becoming and conclude that becoming is not part of the extramental universe.2 Thus construed, the issue of temporal becoming is not directly amenable to argument. This stalemate will be broken, however, if I accomplish my aim: to (re)formulate the question of temporal becoming so that it is subject to adjudication; to show how objections to the thesis of the mind-dependence of becoming can fruitfully be seen (and in a sense unified) as attacks on a single argument for the thesis, an argument from physics; and to defend the con'elusion of the argument from physics from heretofore unanswered objections. The question of the status of temporal becoming is the question of the status of past, present and future.' Events which are at one time in the future, are said to become present and subsequently to recede into the past. Since past and future can be defined as 'earlier than now' and 'later than.. (shrink)

I examine the issue of persistence over time in the context of the special theory of relativity (SR). The four-dimensional ontology of perduring objects is clearly favored by SR. But it is a different question if and to what extent this ontology is required, and the rival endurantist ontology ruled out, by this theory. In addressing this question, I take the essential idea of endurantism, that objects are wholly present at single moments of time, and argue that it commits one (...) to unacceptable conclusions regarding coexistence, in the context of SR. I then propose and discuss a plausible account of coexistence for perduring objects, which is free of these defects. This leaves the endurantist room for some maneuvers. I consider them and show that they do not really help the endurantist out. She can accommodate the notion of coexistence in the relativistic framework only at the cost of renouncing central endurantist intuitions. (shrink)

In a revolutionary new book, a theoretical physicist attacks the foundations of modern scientific theory, including the notion of time, as he shares evidence of ...

This paper addresses the extent to which both Julian Barbour‘s Machian formulation of general relativity and his interpretation of canonical quantum gravity can be called timeless. We differentiate two types of timelessness in Barbour‘s (1994a, 1994b and 1999c). We argue that Barbour‘s metaphysical contention that ours is a timeless world is crucially lacking an account of the essential features of time—an account of what features our world would need to have if it were to count as being one in which (...) there is time. We attempt to provide such an account through considerations of both the representation of time in physical theory and in orthodox metaphysical analyses. We subsequently argue that Barbour‘s claim of timelessness is dubious with respect to his Machian formulation of general relativity but warranted with respect to his interpretation of canonical quantum gravity. We conclude by discussing the extent to which we should be concerned by the implications of Barbour‘s view. (shrink)

In 1949 the great logician Kurt Gödel constructed the first mathematical models of the universe in which travel into the past is, in theory at least, possible. Within the framework of Einstein’s general theory of relativity Gödel produced cosmological solutions to Einstein’s field equations which contain closed time-like curves, that is, curves in spacetime which, despite being closed, still represent possible paths of bodies. An object moving along such a path would travel back into its own past, to the very (...) moment at which it “began” the journey. More generally, Gödel showed that, in his “universe”, for any two points P and Q on a body’s track through spacetime (its world line), such that P temporally precedes Q, there is a timelike curve linking P and Q on which Q temporally precedes P. This means that, in principle at least, one could board a “time machine” and travel to any point of the past. Gödel inferred, in consonance (as he observes) with the views of Parmenides, Kant and the modern idealists, that under these circumstances there could be no such thing as an objective lapse of time, that time or, more generally, change, is an illusion arising from our special mode of perception. For consider an observer initially at point P (with time coordinate t seconds as indicated by his own clock). At point Q (with time coordinate t′) he boards a time machine and travels back to point P, taking time t′′ to do so. In that case, according to his own clock, t′ – t + t′′ > 0 seconds have elapsed, and yet an identical clock left at P would show that 0 seconds have elapsed. In short, there has been no “objective” lapse of time at all. Gödel remarks that in his universe this situation is typical: for every possible definition of an “objective” time one could travel into regions which are past according to that definition. He continues. (shrink)

Logik, Begriffe, Prinzipien des Handelns (Logic, Concepts, Principles of Action). Thomas Müller/ Albert Newen (eds.), mentis Verlag GmbII, 2007, pp. 13–31.

Branching space-time is a simple blend of relativity and indeterminism. Postulates and definitions rigorously describe the causal order relation between possible point events. The key postulate is a version of everything has a causal origin; key defined terms include history and choice point. Some elementary but helpful facts are proved. Application is made to the status of causal contemporaries of indeterministic events, to how splitting of histories happens, to indeterminism without choice, and to Einstein-Podolsky-Rosen distant correlations.

This chapter is concerned with the representation of time and change in classical (i.e., non-quantum) physical theories. One of the main goals of the chapter is to attempt to clarify the nature and scope of the so-called problem of time: a knot of technical and interpretative problems that appear to stand in the way of attempts to quantize general relativity, and which have their roots in the general covariance of that theory. The most natural approach to these questions is via (...) a consideration of more clear cases. So much of the chapter is given over to a discussion of the representation of time and change in other, better understood theories, starting with the most straightforward cases and proceeding through a consideration of cases that lead up to the features of general relativity that are responsible for the problem of time. (shrink)

Some have thought that the process of the expansion of the universe can be used to define an absolute ‘cosmic time’ which then serves as the absolute time required by tensed theories of time. Indeed, this is the very reason why many tense theorists are happy to concede that special relativity is incompatible with the tense thesis, because they think that general relativity, which trumps special relativity, and on which modern cosmology rests, supplies the means of defining temporal becoming using (...) cosmic time. I argue that cosmic time is not up to the task, and that these tense theorists should rethink their strategy in dealing with the theories of relativity. Introduction The Mellor-Rees argument against tense theories Can expansion combat such wrinkles? Event and creation horizons Bursting the balloon. (shrink)

This paper forms part of a wider campaign: to deny pointillisme. That is the doctrine that a physical theory's fundamental quantities are defined at points of space or of spacetime, and represent intrinsic properties of such points or point-sized objects located there; so that properties of spatial or spatiotemporal regions and their material contents are determined by the point-by-point facts. Elsewhere, I argued against pointillisme about chrono-geometry, and about velocity in classical mechanics. In both cases, attention focussed on temporal extrinsicality: (...) i.e. on what an ascription of a property implies about other times. Therefore, I also discussed the metaphysical debate whether persistence should be understood as endurance or perdurance. In this paper, I focus instead on spatial extrinsicality: i.e. on what an ascription of a property implies about other places. The main idea will be that the classical mechanics of continuous media (solids or fluids) involves a good deal of spatial extrinsicality---which seems not to have been noticed by philosophers, even those who have no inclination to pointillisme. I begin by describing my wider campaign. Then I present some elementary aspects of stress, strain and elasticity---emphasising the kinds of spatial extrinsicality they each involve. I conduct the discussion entirely in the context of `Newtonian' ideas about space and time. But my arguments carry over to relativistic physics. (shrink)

These nine essays address fundamental questions about time in philosophy, physics, linguistics, and psychology. Are there facts about the future? Could we affect the past? In physics, general relativity and quantum theory give contradictory treatments of time. So in the current search for a theory of quantum gravity, which should give way: general relativity or quantum theory? In linguistics and psychology, how does our language represent time, and how do our minds keep track of it?

What is the difference between time and space? This question, once a central one in metaphysics, has not been treated kindly by recent history. By joining together space and time into spacetime Minkowski sapped some of the spirit out of this project. That is unfortunate, however, for even in relativistic theories there remain sharp and important metrical and topological distinctions between the timelike and spacelike directions of spacetime. Questions about what these differences are, why they exist and how they are (...) related are fascinating. Why, for instance, is time one-dimensional in virtually all physical theories? What does the “minus sign” in the relativistic metric have to do with time? Is there a connection between the two? At a time when researchers in quantum gravity regularly propose speculative theories with no time at all, a better understanding of time in physics is all the more important—even if only to see what is lost by its absence. (shrink)

No one conception of time emerges from a study of physics. As science changes—over time or through varying interpretations at a time—our conception of physical time changes. Each of these changes and resulting theories of time has been the subject of philosophical scrutiny, so there are many philosophical controversies internal to particular physical theories. For instance, the move to special relativity radically transformed our understanding of time, but it also gave rise to debates about the nature of simultaneity within the (...) theory itself. Nevertheless, there are some philosophical puzzles that appear at every stage of the development of physics. Perhaps most generally, there is the perennial question, Is there a ‘gap’ between the conception of time as found in physics and the conception of time as found in philosophy? (shrink)

The manifest image is teeming with activity. Objects are booming and buzzing by, changing their locations and properties, vivid perceptions are replaced, and we seem to be inexorably slipping into the future. Time—or at least our experience in time— seems a very turbulent sort of thing. By contrast, time in the scientist image seems very still. The fundamental laws of physics don’t differentiate between past and future, nor do they pick out a present moment that flows. Except for a minus (...) sign in the relativistic metric, there are few differences between the temporal and spatial coordinates in natural science. We seem to have, to echo another debate, an “explanatory gap” between time as we find it in experience and as we find it in science. Reconciling these two images of the world is the principal goal of philosophy of time. (shrink)

The Past Hypothesis is the claim that the Boltzmann entropy of the universe was extremely low when the universe began. Can we make sense of this claim when *classical* gravitation is included in the system? I first show that the standard rationale for not worrying about gravity is too quick. If the paper does nothing else, my hope is that it gets the problems induced by gravity the attention they deserve in the foundations of physics. I then try to make (...) plausible a very weak claim: that there is a well-defined Boltzmann entropy that *can* increase in *some* interesting self-gravitating systems. More work is needed before we can say whether this claim answers the threat to the standard explanation of entropy increase. (shrink)

A realist causal model of quantum cosmology (QC) is developed. By applying the de Broglie-Bohm interpretation of quantum mechanics to QC, we resolve the notorious 'problem of time' in QC, and derive exact equations of motion for cosmological dynamical variables. Due to this success, it is argued that if the situation in QC is used as a yardstick by which other interpretations are measured, the de Broglie-Bohm theory seems uniquely fit as an interpretation of quantum mechanics.

The cyclical theory f time, which is better known under the name of the 'theory of eternal recurrence,' is usually associated with certain ancient thinkers--in particular, Pythagoreans and Stoics. The most famous among those who have tried to revive the theory in the modern era is unquestionably Friedrich Nietzsche. It is less well known that the theory was defended also by C.S. Peirce and, as late as 1927, by the French historian of science, Abel Rey. The contemporary discussion of the (...) problem of the direction of time has a direct bearing on the problem of eternal recurrence. The primary purpose of this paper is to evaluate critically the theory itself and then to show how this critical analysis can be applied to Peirce's own version of this theory. (shrink)

We formulate Suppes predicates for various kinds of space-time: classical Euclidean, Minkowski's, and that of General Relativity. Starting with topological properties, these continua are mathematically constructed with the help of a basic algebra of events; this algebra constitutes a kind of mereology, in the sense of Lesniewski. There are several alternative, possible constructions, depending, for instance, on the use of the common field of reals or of a non-Archimedian field (with infinitesimals). Our approach was inspired by the work of (...) class='Hi'>Whitehead (1919), though our philosophical stance is completely different from his. The structures obtained are idealized constructs underlying extant, physical space-time. (shrink)

The physics behind the limerick is that within Einstein’s special theory of relativity there is a subtle connection between faster-than-light and backwards-in-time travel. If you could do one, then in principle you could also do the other. But relativity is carefully contrived to prevent superluminal and back-in-time travel and communication.

This column is a followup to a previous Alternate View column [Analog, June-'89] about "wormholes", faster-than-light travel, and time machines, which was based on a spectacular theoretical breakthrough in general relativity. It described how a sufficiently advanced civilization might construct a stable wormhole (a curved-space shortcut between one region of space and another) and use it both for faster-than-light travel and for time travel, with no laws of physics violated in the process except causality (the principle that a cause must (...) precede its effects). (shrink)

Science fiction writers, to avoid undue delays in the story's plot line, need a way of beating the speed of light speed limit of the universe. Most readers of this magazine are familiar with the gimmicks that have been used for faster than light travel: warp drives, detours through hyperspace, matter to tachyon conversion, trans spatial jumps, and dives past the singularity of a rotating black hole. But perhaps the faster than light mechanism which has the best credentials in orthodox (...) physics is the wormhole, also known as a Schwartzschild wormhole or an Einstein Rosen bridge. (shrink)

We formulate Suppes predicates for various kinds of space-time: classical Euclidean, Minkowski's, and that of General Relativity. Starting with topological properties, these continua are mathematically constructed with the help of a basic algebra of events; this algebra constitutes a kind of mereology, in the sense of Lesniewski. There are several alternative, possible constructions, depending, for instance, on the use of the common field of reals or of a non-Archimedian field (with infinitesimals). Our approach was inspired by the work of Whitehead (...) (1919), though our philosophical stance is completely different from his. The structures obtained are idealized constructs underlying extant, physical space-time. (shrink)

The physics of time asymmetry has never been a single well-defined subject, but more a collection of consistency problems which arise in almost all branches ...

It is a central aspect of our ordinary concept of time that history unfolds and events come into being. It is only natural to take this seriously. However, it is notoriously difficult to explain further what this `becoming' consists in, or even to show that the notion is consistent at all. In this article I first argue that the idea of a global temporal ordering, involving a succession of cosmic nows, is not indispensable for our concept of time. Our experience (...) does not support the existence of global simultaneity and arguments from modern physics further support the conclusion that time should not be seen as a succession of cosmic nows. Accordingly, I propose that if we want to make sense of becoming we should attempt to interpret it as something purely local. Second, I address the question of what this local becoming consists in. I maintain that processes of becoming are nothing but the successive happening of events, and that this happening of events consists entirely in the occurring of these events at their own spacetime locations. This leads to a consistent view of becoming, which is applicable even to rather pathological spacetimes. (shrink)

In recent times, there have been notable attempts to introduce an objective present in Minkowski spacetime, a structure that, however, should also be capable to explain some aspects of our experience of time. I claim that the “interactive present” introduced by Arthur and Savitt for such purposes is inadequate, since it turns out to be neither a physically relevant property nor a good explanans of our temporal experience. In its conclusive part, and after having proposed a more adequate model for (...) the time of our experience, I draw some general morals about the relationship between physical time and experiential time. (shrink)

My first and main claim is that physics cannot provide empirical evidence for the objectivity (mind-independence) of absolute becoming, for the simple reason that it must presuppose it, at least to the extent that classical (i.e., non-quantum) spacetime theories presuppose an ontology of events. However, the fact that a theory of absolute becoming must be situated in the a priori realm of metaphysics does not make becoming completely irrelevant for physics, since my second claim will consist in showing that relational (...) becoming, once appropriately defined and understood, properly belongs to the tangled set of issues usually referred to with the label “the arrow of time”. In this respect it is argued that the arrow of becoming is more fundamental both than the causal arrow and of other well-known physical processes that are temporally asymmetric. (shrink)

Indeed, this is the first serious book-length study of the subject by a philosopher of science.

Nearly all accounts of the genesis of special relativity unhesitatingly assume that the theory was worked out in a roughly five week period following the discovery of the relativity of simultaneity. Not only is there no direct evidence for this common presupposition, there are numerous considerations which militate against it. The evidence suggests it is far more reasonable that Einstein was already in possession of the Lorentz and field transformations, that he had applied these to the dynamics of the electron, (...) and that portions of the 1905 paper had actually been drafted well before the epistemological analysis of time. (shrink)

Spacetime substantivalism leads to a radical form of indeterminism within a very broad class of spacetime theories which include our best spacetime theory, general relativity. Extending an argument from Einstein, we show that spacetime substantivalists are committed to very many more distinct physical states than these theories' equations can determine, even with the most extensive boundary conditions.

The standard theory of computation excludes computations whose completion requires an infinite number of steps. Malament-Hogarth spacetimes admit observers whose pasts contain entire future-directed, timelike half-curves of infinite proper length. We investigate the physical properties of these spacetimes and ask whether they and other spacetimes allow the observer to know the outcome of a computation with infinitely many steps.

Now available in an updated addition: ""Integrating concepts of time derived from the physical sciences and world religions, "The Becoming of Time" examines ...

A research professor of nuclear physics explores the mysterious essence of time in its two aspects---one of accurate measurement, the other of human sensation-- ...

This paper assesses branching spacetime theories in light of metaphysical considerations concerning time. I present the A, B, and C series in terms of the temporal structure they impose on sets of events, and raise problems for two elements of extant branching spacetime theories—McCall’s ‘branch attrition’, and the ‘no backward branching’ feature of Belnap’s ‘branching space-time’—in terms of their respective A- and B-theoretic nature. I argue that McCall’s presentation of branch attrition can only be coherently formulated on a model with (...) at least two temporal dimensions, and that this results in severing the link between branch attrition and the flow of time. I argue that ‘no backward branching’ prohibits Belnap’s theory from capturing the modal content of indeterministic physical theories, and results in it ascribing to the world a time-asymmetric modal structure that lacks physical justification. (shrink)

Inertia is enshrined in Newton’s first law of motion, a body at rest or in uniform motion remains in that state unless a force is applied to it. Now, consider (1). (1) Pat stopped the car before it hit the tree. Can we conclude from (1) that the car struck the tree? Not without further information such as that supplied in (2). (2) But the bus behind kept going. A post-condition for Pat stopping the car is that the car be (...) at rest. To satisfy a pre-condition for the car hitting the tree (namely, that the car not be at rest), inertia requires that some intervening force act on the car (as hinted, for example, by (2)). In the absence of such a force, (1) would appear to suggest that Pat prevented a collision between car and tree. Exactly what bit of physics are we importing into natural language interpretation here? Oversimplified, Newton’s first law of motion says: no change without force. Identifying force with cause, we come to the slogan no temporality without cause, capturing in a phrase the proposal from Steedman 2000 that.. (shrink)

This paper is concerned with the debate between substantival and relational theories of space-time, and discusses two difficulties that beset the relationalist: a difficulty posed by field theories, and another difficulty (discussed at greater length) called the problem of quantities. A main purpose of the paper is to argue that possibility can not always be used as a surrogate of ontology, and that in particular that there is no hope of using possibility to solve the problem of quantities.

This paper considers traditional debates and position regarding time and the future in relation to Einstein's physics of space-time.

This work represents a guided tour to the interdisciplinary, integrated study of time.

Looks at the history of the idea of time, the origins of the universe, relativity, life, the brain's perception of time, aging, death, memory, and time keeping ...

One of the recurrent problems in the foundations of physics is to explain why we rarely observe certain phenomena that are allowed by our theories and laws. In thermodynamics, for example, the spontaneous approach towards equilibrium is ubiquitous yet the time-reversal-invariant laws that presumably govern thermal behaviour in the microscopic level equally allow spontaneous departure from equilibrium to occur. Why are the former processes frequently observed while the latter are almost never reported? Another example comes from quantum mechanics where the (...) formalism, if considered complete and universally applicable, predicts the existence of macroscopic superpositions—monstrous Schr¨odinger cats—and these are never observed: while electrons and atoms enjoy the cloudiness of waves, macroscopic objects are always localized to definite positions. (shrink)

Metaphysical theories of change incorporate substantive commitments to theories of persistence. The two most prominent classes of such theories are endurantism and perdurantism. Defenders of endurance-style accounts of change such as Klein, Hinchliff, and Oderberg, do so through appeal to a priori intuitions about change. We argue that this methodology is understandable but mistaken-- an adequate metaphysics of change must accommodate all experiences of change, not merely intuitions about a limited variety of cases. Once we examine additional experiences of change, (...) particularly those in (special) relativistic circumstances, it becomes clear that only a perdurance account of change is adequate. (shrink)

This paper argues that the Einstein-Minkowski space-time of special relativity provides an adequate model for classical tense logic, including rigorous definitions of tensed becoming and of the logical priority of proper time. In addition, the extension of classical tense logic with an operator for predicate-term negation provides us with a framework for interpreting and defending the significance of future contingency in special relativity. The framework for future contingents developed here involves the dual falsehood of non-logical contraries, only one of which (...) becomes true. This has several methodological, metaphysical and physical advantages over the alternative traditional frameworks for handling future contingents. (shrink)

The conceptual and technical difficulties involved in creating a quantum theory of gravity have led some physicists to question, and even in some cases to deny, the reality of time. More surprisingly, this denial has found a sympathetic audience among certain philosophers of physics. What should we make of these wild ideas? Does it even make sense to deny the reality of time? In fact physical science has been chipping away at common sense aspects of time ever since its inception. (...) Section 1 offers a brief survey of the demolition process. Section 2 distinguishes a tempered from an extremely radical form that a denial of time might take, and argues that extreme radicalism is empirically self-refuting. Section 3 begins an investigation of the prospects for tempered radicalism in a timeless theory of quantum gravity. (shrink)

Einstein's special and general theory of relativity abolished the Newtonian concept of absolute time. Moreover, Einsteinian physics revealed the mutual interdependence of space, time, and matter. Applying general relativity to cosmology leads again to the existence of a preferred time coordinate among the homogeneous and isotropic cosmological models. Einstein referred to this time coordinate as ,,almost absolute time." What is the exact relation between absolute time in relativistic cosmology and absolute time in Newtonian physics? To answer this question firstly we (...) investigate which features are characteristic of Newtonian absolute time. Secondly we show how the preferred time in relativistic cosmology is related to the cosmological principle. After that we compare the two concepts of time. Finally, we consider the concept of time in particular cosmological models like the static Einstein universe, the relation between cosmic time and the evolution of the universe and different possibilities to introduce the time coordinate in oscillating cosmological models. German Die Spezielle und Allgemeine Relativitätstheorie Einsteins räumten mit dem Konzept einer absoluten Zeit, wie es von Newton für seine Physik vorausgesetzt worden war, auf und zeigten die wechselseitige Abhängigkeit von Raum, Zeit und Materie. In Anwendung der Allgemeinen Relativitätstheorie auf das kosmologische Problem ergibt sich jedoch für die üblicherweise herangezogene Klasse der homogenen und isotropen Weltmodelle die Möglichkeit, eine ausgezeichnete Zeitkoordinate einzuführen, die Einstein als ,,quasi-absolute Zeit bezeichnete. Wie verhält sich die absolute Zeit der relativistischen Kosmologie zur absoluten Zeit Newtons? Diese Frage wird beantwortet, indem die wichtigsten Momente der absoluten Zeit Newtons herausgestellt werden, die auf dem Kosmologischen Prinzip basierende Möglichkeit der Einführung einer ausgezeichneten Zeit in der Kosmologie erörtert wird und anschließend beide Zeitkonzepte konfrontiert werden. Abschließend wird der Begriff der Zeit im Rahmen bestimmter kosmologischer Modelle weiter untersucht, vor allem seine Bedeutung im statischen Einstein-Universum, seine Verknüpfung mit der Evolution des Universums und die verschiedenen Möglichkeiten, die Zeit in oszillierenden bzw. zyklischen Modellen zu definieren. (shrink)

A recent proposal by Norton (2003) to show that a simple Newtonian system can exhibit stochastic acausal behavior by giving rise to spontaneous movements of a mass on the dome of a certain shape is examined. We discuss the physical significance of an often overlooked and yet important Lipschitz condition the violation of which leads to the existence of anomalous nontrivial solutions in this and similar cases. We show that the Lipschitz condition is closely linked with the time reversibility of (...) certain solutions in Newtonian mechanics and the failure to incorporate this condition within Newtonian mechanics may unsurprisingly lead to physically impossible solutions that have no serious metaphysical implications. ‡I thank Steven Savitt of the Philosophy Department at the University of British Columbia for drawing my attention to the Lipschitz condition, and Alexei Cheviakov of the Mathematics Department at the University of British Columbia for useful discussions. †To contact the author, please write to: Department of Philosophy, University of British Columbia, Vancouver, BC, V6T 1Z1, Canada; e-mail: korolev@interchange.ubc.ca. (shrink)

Thinking about time travel is an entertaining way to explore how to understand time and its location in the broad conceptual landscape that includes causation, fate, action, possibility, experience, and reality. It is uncontroversial that time travel towards the future exists, and time travel to the past is generally recognized as permitted by Einstein’s general theory of relativity, though no one knows yet whether nature truly allows it. Coherent time travel stories have added flair to traditional debates over the metaphysical (...) status of the past, the reality of temporal passage, and the existence of free will. Moreover, plausible models of time travel and time machines can be used to investigate the subtle relation between space-time structure and causality. -/- It surveys some philosophical issues concerning time travel and should serves as a quick introduction. It includes a new and improved way to define a time machine. (shrink)

Extending on an earlier paper [Found. Phys. Ltt., 16(4) 343–355, (2003)], it is argued that instants of time and the instantaneous (including instantaneous relative position) do not actually exist. This conclusion, one which is also argued to represent the correct solution to Zeno’s motion paradoxes, has several implications for modern physics and for our philosophical view of time, including that time and space cannot be quantized; that contrary to common interpretation, motion and change are compatible with the “block” universe and (...) relativity; and that time, space, and space-time too, cannot exist. Instead, motion and change become the major players. (shrink)

The paper first tries to explain how the possibility of "time travel" arises in the Godel universe. It then goes on to discuss a technical problem conerning minimal acceleration requirements for time travel. A theorem is stated and a conjecture posed. If the latter is correct, time travel can be ruled out as a practical possibility in the Godel universe.

The standard mathematical account of the sub-metrical geometry of a space employs topology, whose foundational concept is the open set. This proves to be an unhappy choice for discrete spaces, and offers no insight into the physical origin of geometrical structure. I outline an alternative, the Theory of Linear Structures, whose foundational concept is the line. Application to Relativistic space-time reveals that the whole geometry of space-time derives from temporal structure. In this sense, instead of spatializing time, Relativity temporalizes space.

This second edition also includes a new author's preface and an additional appendix.

This paper sketches a taxonomy of forms of substantivalism and relationism concerning space and time, and of the traditional arguments for these positions. Several natural sorts of relationism are able to account for Newton's bucket experiment. Conversely, appropriately constructed substantivalism can survive Leibniz's critique, a fact which has been obscured by the conflation of two of Leibniz's arguments. The form of relationism appropriate to the Special Theory of Relativity is also able to evade the problems raised by Field. I survey (...) the effect of the General Theory of Relativity and of plenism on these considerations. (shrink)

This paper demonstrates that John Wheeler and Richard Feynman's strategy for avoiding causal paradoxes threatened by backward causation and time-travel can be defeated by designing self-interacting mechanisms with a non-simple topological structure. Time-travel therefore requires constraints on the allowable data on space-like hypersurfaces. The nature and significance of these constraints is discussed.

I argue that Norton & Earman's hole argument, despite its historical association with General Relativity, turns upon very general features of any linguistic system that can represent substances by names. After exploring various means by which mathematical objects can be interpreted as representing physical possibilities, I suggest that a form of essentialism can solve the hole dilemma without abandoning either determinism or substantivalism. Finally, I identify the basic tenets of such an essentialism in Newton's writings and consider how they can (...) be updated to apply to the case provided by General Relativity. (shrink)

In this paper I expound an argument which seems to establish that probabilism and special relativity are incompatible. I examine the argument critically, and consider its implications for interpretative problems of quantum theory, and for theoretical physics as a whole.

This paper delves into McTaggart’s metaphysical account of reality without time, and compares and contrasts McTaggart’s account with the account of reality given by modern physics. This comparison is of interest, because there are suggestions from contemporary physics that there is no time at the fundamental level. Physicists and philosophers of physics recognize that we do not have a good understanding of how the world could be such that time is unreal. I argue that, from the perspective of one who (...) is trying to understand modern physics, McTaggart’s metaphysical views do provide some insight into how reality can be timeless at the fundamental level, but the insight that they provide is limited. (shrink)

Earman and Norton argue that manifold realism leads to inequivalence of Leibniz-shifted space-time models, with undesirable consequences such as indeterminism. I respond that intrinsic axiomatization of space-time geometry shows the variant models to be isomorphic with respect to the physically meaningful geometric predicates, and therefore certainly physically equivalent because no theory can characterize its models more closely than this. The contrary philosophical arguments involve confusions about identity and representation of space-time points, fostered by extrinsic coordinate formulations and irrelevant modal metaphysics. (...) I conclude that neither the revived Einstein hole argument nor the original Leibniz indiscernibility argument have any force against manifold realism. (shrink)

Book Information Time and the Metaphysics of Relativity. By William Lane Craig. Kluwer Academic Publishers. Dordrecht. 2001. Pp. xi + 279. Hardback, £62.