The CPT theorem of quantum field theory states that any relativistic (Lorentz-invariant) quantum field theory must also be invariant under CPT, the composition of charge conjugation, parity reversal and time reversal. This paper sketches a puzzle that seems to arise when one puts the existence of this sort of theorem alongside a standard way of thinking about symmetries, according to which spacetime symmetries (at any rate) are associated with features of the spacetime structure. The puzzle is, roughly, that the existence (...) of a CPT theorem seems to show that it is not possible for a well-formulated theory that does not make use of a preferred frame or foliation to make use of a temporal orientation. Since a manifold with only a Lorentzian metric can be temporally orientable—capable of admitting a temporal orientation—this seems to be an odd sort of necessary connection between distinct existences. The paper then suggests a solution to the puzzle: it is suggested that the CPT theorem arises because temporal orientation is unlike other pieces of spacetime structure, in that one cannot represent it by a tensor field. To avoid irrelevant technical details, the discussion is carried out in the setting of classical field theory, using a little-known classical analog of the CPT theorem. (shrink)

Time is generally thought to be one of the more mysterious ingredients of the universe. In this intriguing book, Paul Horwich makes precise and explicit the interrelationships between time and a large number of philosophically important notions.Ideas of temporal order and priority interact in subtle and convoluted ways with the deepest elements in our network of basic concepts. Confronting this conceptual jigsaw puzzle, Horwich notes that there are glaring differences in how we regard the past and future directions of time. (...) For example, we can influence the future but not the past, and can easily gain knowledge of the past but not of the future. Moreover we see a profusion of decay processes but little spontaneous generation of order; time appears to "flow" in one privileged direction, not the other; and we tend to explain phenomena in terms of antecedent circumstances, rather than subsequent ones. Horwich explains such time asymmetries and examines their bearing on the nature of time itself.Asymmetries in Time covers many notoriously difficult problems in the philosophy of science: causation, knowledge, entropy, explanation, time travel, rational choice, laws of nature, and counterfactual implication -- and gives a unified treatment of these matters. The book covers an unusually broad range of topics in a lucid and nontechnical way and includes alternative points of view in the philosophical literature. (shrink)

Or better: time asymmetry in thermodynamics. Better still: time asymmetry in thermodynamic phenomena. “Time in thermodynamics” misleadingly suggests that thermodynamics will tell us about the fundamental nature of time. But we don’t think that thermodynamics is a fundamental theory. It is a theory of macroscopic behavior, often called a “phenomenological science.” And to the extent that physics can tell us about the fundamental features of the world, including such things as the nature of time, we generally think that only fundamental (...) physics can. On its own, a science like thermodynamics won’t be able to tell us about time per se. But the theory will have much to say about everyday processes that occur in time; and in particular, the apparent asymmetry of those processes. The pressing question of time in the context of thermodynamics is about the asymmetry of things in time, not the asymmetry of time, to paraphrase Price ( , ). I use the title anyway, to underscore what is, to my mind, the centrality of thermodynamics to any discussion of the nature of time and our experience in it. The two issues—the temporal features of processes in time, and the intrinsic structure of time itself—are related. Indeed, it is in part this relation that makes the question of time asymmetry in thermodynamics so interesting. This, plus the fact that thermodynamics describes a surprisingly wide range of our ordinary experience. We’ll return to this. First, we need to get the question of time asymmetry in thermodynamics out on the table. (shrink)

This paper presents a critical examination of claims advanced by several philosophers to the effect that 'time travel' represents a physical possibility and that the interpretation of certain actually observed phenomena in terms of 'time travel' is both legitimate and advantageous. It is argued that (a) no convincing motivation for the introduction of the time travel hypothesis has been presented; (b) no coherent and interesting sense of 'going backward in time' has been supplied which makes 'time travel' compatible with Special (...) Relativity; (c) even the conceptual possibility of 'time travel' is an unsettled and somewhat nebulous question. (shrink)

This dissertation is about the sense in which the laws of quantum theory distinguish between the past and the future. I begin with an account of what it means for quantum theory to make such a distinction, by providing a novel derivation of the meaning of "time reversal." I then show that if Galilei invariant quantum theory does distinguish a preferred direction in time, then this has consequences for the ontology of the theory. In particular, it requires matter to admit (...) "internal" degrees of freedom, in that the position observable generates a maximal abelian algebra. I proceed to show that this is not a purely quantum phenomenon, but can be expressed in classical mechanics as well. I then illustrate three routes for generating quantum systems that distinguish a preferred temporal direction in this way. (shrink)

Focusing on spacetime singularities, Earman engages with a host of foundational issues at the intersection of science and philosophy, ranging from the big bang to the possibility of time travel.

In the literature on the compatibility between the time of our experience and the time of physics, the special theory of relativity has enjoyed central stage. By bringing into the discussion the general theory of relativity, I suggest a new analysis of the misunderstood notion of becoming, developed from hints in Gödel's published and unpublished arguments for the ideality of time. I claim that recent endorsements of such arguments, based on Gödel's own ‘rotating’ solution to Einstein's field equation, fail: once (...) understood in the right way, becoming can be shown to be both mind-independent and compatible with spacetime physics. Being a neededtertium quidbetween views of time traditionally regarded as in conflict, such a new approach to becoming should also help to dissolve a crucial aspect of the century-old debate between the so-called A and B theories of time. (shrink)

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)

This paper considers the possibility that nonrelativistic quantum mechanics tells us that Nature cares about time reversal. In a classical world we have a fundamentally reversible world that appears irreversible at higher levels, e.g., the thermodynamic level. But in a quantum world we see, if I am correct, a fundamentally irreversible world that appears reversible at higher levels, e.g., the level of classical mechanics. I consider two related symmetries, time reversal invariance and what I call ‘Wigner reversal invariance.’ Violation of (...) the first is interesting, for not only would it fly in the face of the usual story about temporal symmetry, but it also appears to imply (as I’ll explain) that time is ‘handed’, or as some have misleadingly said in the literature, ‘anisotropic’. Violation of the second is, as I hope to show, even more interesting. The paper also contains a discussion of two mostly neglected topics: what it means to say time is handed and what warrants such an attribution to time. (shrink)

In a classical mechanical world, the fundamental laws of nature are reversible. The laws of nature treat the past and future as mirror images of each other. Temporally asymmetric phenomena are ultimately said to arise from initial conditions. But are the laws of nature also reversible in a quantum world? This paper argues that they are not, that time in a quantum world prefers a particular 'hand' or ordering. I argue, first, that the probabilistic algorithm used in the theory picks (...) out a preferred direction of time for almost all interpretations of the theory, and second, that contrary to the received wisdom the Schr?dinger evolution is also irreversible. The status of Wigner reversal invariance is then discussed. I conclude that the quantum world is fundamentally irreversible, but manages to appear (thanks to Wigner reversal invariance) reversible at the classical level. (shrink)

Is there more that one "Curie's principle"? How far are different formulations legitimate? What are the aspects that make it so scientifically fruitful, independently of how it is formulated? The paper is devoted to exploring these questions. We start with illustrating Curie's original 1894 article and his focus. Then, we consider the way that the discussion of the principle took shape from early commentators to its modern form. We say why we think that the modern focus on the inter-state version (...) of the principle loses sight of some of the most interesting significant applications of the principle. Finally, we address criticism of the principle put forward by Norton and purported counterexamples due to Roberts. (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)

This thesis is an attempt to accurately formulate and solve one of the problems associated with the direction of time. Processes in nature appear to be 'irreversible', for instance, heat flows from hot to cold but never from cold to hot. The problem of the direction of time, roughly put, is the difficulty of squaring this irreversible behavior with the apparent fact that the fundamental laws of physics are completely reversible. ;In the first three chapters I critically review the foundations (...) of statistical mechanics. After arguing that entropy is an objective property of the thermodynamic world, I contrast the 'Boltzmannian' single-system approach to statistical mechanics with the 'Gibbsian' many-system approach. Based in part on its ability to handle irreversibility, I judge the Boltzmann approach to be superior from a philosophical perspective. I argue, however, that the statistical mechanical probabilities cannot be interpreted in such a way as to allow the theory to give the sort of explanation originally desired. ;The next four chapters are devoted to the direction of time. Chapters four and five attempt to provide the problem with the philosophically mature geography that has so far eluded it. Chapter six discusses the problem in the context of quantum mechanics, and chapter seven criticizes the problem's standard formulation. I show that the problem is really a much more general one than has previously been appreciated; indeed, I try to show that it is a problem afflicting all the special sciences. ;Finally, the remaining three chapters investigate three separate issues. Chapter eight discusses the tensed theory of time. I claim the best argument for the tensed theory relies on various temporal asymmetries, e.g., the asymmetry of causation. I provide reasons for not being persuaded by this argument. The tensed theory, I conclude, is not incoherent, as many have claimed, instead it is simply an implausible explanation of our experience. Chapter nine examines the possibility that quantum mechanics implies our world is temporally anisotropic, and chapter ten looks at some conceptual difficulties associated with our conception of time reversal invariance. (shrink)

Many have suggested that the transformation standardly referred to as `time reversal' 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.

The paper analyzes the philosophical consequences of the recent discovery of direct violations of the time–reversal symmetry of weak interactions. It shows that although we have here an important case of the time asymmetry of one of the fundamental physical forces which could have had a great impact on the form of our world with an excess of matter over antimatter, this asymmetry cannot be treated as the asymmetry of time itself but rather as an asymmetry of some specific physical (...) process in time. The paper also analyzes the consequences of the new discovery for the general problem of the possible connections between direction of time and time-asymmetric laws of nature. These problems are analyzed in the context of Horwich’s Asymmetries in time: problems in the philosophy of science argumentation, trying to show that existence of a time–asymmetric law of nature is a sufficient condition for time to be anisotropic. Instead of Horwich’s sufficient condition for anisotropy of time, it is stressed that for a theory of asymmetry of time to be acceptable it should explain all fundamental time asymmetries: the asymmetry of traces, the asymmetry of causation, and the asymmetry between the fixed past and open future. It is so because the problem of the direction of time has originated from our attempts to understand these asymmetries and every plausible theory of the direction of time should explain them. (shrink)

Gödel's remarks concerning the ideality of time are examined. In the literature, some of these remarks have been somewhat neglected while others have been heavily criticized. In this note, we propose a clear and defensible sense in which Gödel's work bears on the question of whether there is an objective lapse of time in our world.

I point out that some common folk wisdom about time reversal invariance in classical mechanics is strictly incorrect, by showing some explicit examples in which classical time reversal invariance fails, even among conservative systems. I then show that there is nevertheless a broad class of familiar classical systems that are time reversal invariant.

In a recent paper, Malament (2004) employs a time reversal transformation that differs from the standard one, without explicitly arguing for it. This is a new and important understanding of time reversal 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 time reversal 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 protected]. (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 time reversal operator T. David Albert and Paul Horwich have suggested that (...) one should not allow such time reversal operations T on states. I will argue that time reversal operations on fundamental states should be allowed. I will furthermore argue that the form that time reversal 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)

Pierre Curie claimed that a symmetry of a cause must be found in the produced effects. This paper shows why this principle works in Curie’s example of the electrostatics of central fields, but fails in many others. The failure of Curie’s claim is then shown to be of special empirical interest, in that this failure underpins the experimental discovery of parity violation and of CP violation in the twentieth century.

In this paper I draw the distinction between intuitive and theory-relative accounts of the time reversal 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 time reversal 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 time reversal has the interesting feature that it makes the nature of the time reversal symmetry an empirical feature of the world without requiring us to assume that any particular physical theory is time reversal invariant from the start. Finally, I provide an analysis of several toy cases that reveals differences between my new account of time reversal and its competitors. (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: time reversal 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 time reversal in classical electromagnetism. (shrink)

Schulman (Entropy 7(4):221–233, 2005) has argued that Boltzmann’s intuition, that the psychological arrow of time is necessarily aligned with the thermodynamic arrow, is correct. Schulman gives an explicit physical mechanism for this connection, based on the brain being representable as a computer, together with certain thermodynamic properties of computational processes. Hawking (Physical Origins of Time Asymmetry, Cambridge University Press, Cambridge, 1994) presents similar, if briefer, arguments. The purpose of this paper is to critically examine the support for the link between (...) thermodynamics and an arrow of time for computers. The principal arguments put forward by Schulman and Hawking will be shown to fail. It will be shown that any computational process that can take place in an entropy increasing universe, can equally take place in an entropy decreasing universe. This conclusion does not automatically imply a psychological arrow can run counter to the thermodynamic arrow. Some alternative possible explanations for the alignment of the two arrows will be briefly discussed. (shrink)

David Albert claims that classical electromagnetic theory is not time reversal 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 time reversal 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 time reversal 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 a classical mechanical world, the fundamental laws of nature are reversible. The laws of nature treat the past and future as mirror images of each other. Temporally asymmetric phenomena are ultimately said to arise from initial conditions. But are the laws of nature also reversible in a quantum world? This paper argues that they are not, that time in a quantum world prefers a particular 'hand' or ordering. I argue, first, that the probabilistic algorithm used in the theory picks (...) out a preferred direction of time for almost all interpretations of the theory, and second, that contrary to the received wisdom the Schr?dinger evolution is also irreversible. The status of Wigner reversal invariance is then discussed. I conclude that the quantum world is fundamentally irreversible, but manages to appear reversible at the classical level. (shrink)