This paper distinguishes between 3 meanings of reversal, all of which are mathematically equivalent in classical mechanics: velocity reversal, retrodiction, and time reversal. It then concludes that in order to have well defined velocities a primitive arrow of time must be included in every time slice. The paper briefly mentions that this arrow cannot come from the Second Law of thermodynamics, but this point is developed in more details elsewhere.

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)

Substantivalists believe that spacetime and its parts are fundamental constituents of reality. Relationalists deny this, claiming that spacetime enjoys only a derivative existence. I begin by describing how the Galilean symmetries of Newtonian physics tell against both Newton's brand of substantivalism and the most obvious relationalist alternative. I then review the obvious substantivalist response to the problem, which is to ditch substantival space for substantival spacetime. The resulting position has many affinities with what are arguably the most natural interpretations of (...) special and general relativity. I move on to consider and reject two recent antisubstantivalist lines of thought. The interim conclusion is that the best argument for relationalism is an appeal to Ockham's razor. However, for this to be successful there must be genuine relationalist theories that share the theoretical virtues of their substantivalist rivals but without the additional ontological commitment. The bulk of the paper is therefore an investigation of various concrete relationalist proposals. I distinguish three options for the relationalist in the face of the success of Galilean invariant physics and trace how these generalise to relativistic physics. One of the options is particularly promising but, since its basic objects end up being spacetime points, this does not help the prospects of relationalism as traditionally conceived. I end with some reflections on the fate of substantivalism in the aftermath of the Hole Argument, concluding that we have as yet to be given good reasons to abandon the natural, substantivalist interpretation of current physics. (shrink)

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)

Relativistic quantum theories are equipped with a background Minkowski spacetime and non-relativistic quantum theories with a Galilean space-time. Traditional investigations have distinguished their distinct space-time structures and have examined ways in which relativistic theories become sufficiently like Galilean theories in a low velocity approximation or limit. A different way to look at their relationship is to see that both kinds of theories are special cases of a certain five-dimensional generalization involving no limiting procedures or approximations. When one compares them, striking (...) features emerge that bear on philosophical questions, including the ontological status of the wave function and time reversal invariance. (shrink)

This is an extensive review of recent work on the foundations of statistical mechanics.

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)

Many agree that the pilot-wave theory is to be understood as a first-order theory, in which the law constrains the velocity of the particles. However, while Dürr, Goldstein and Zanghì maintain that the pilot-wave theory is Galilei invariant, Valentini argues that such a symmetry is mathematical but it has no physical significance. Moreover, some wavefunction realists insist that the pilot-wave theory is not Galilei invariant in any sense. It has been maintained by some that this disagreement originates in the disagreement (...) about ontology, as Valentini, contrary to Dürr, Goldstein and Zanghì, has been taken to endorse wavefunction realism. In this paper I argue that Valentini’s argument is independent of the choice of the ontology of matter: it is based of the notion of natural kinematics for a theory, and the idea that the kinematics should match the dynamics. If so, I also argue that there are several reasons to dispute Valentini’s claim that the kinematical symmetries should constrain dynamical ones. (shrink)

“The universe is expanding, not contracting.” Many statements of this form appear unambiguously true; after all, the discovery of the universe’s expansion is one of the great triumphs of empirical science. However, the statement is time-directed: the universe expands towards what we call the future; it contracts towards the past. If we deny that time has a direction, should we also deny that the universe is really expanding? This article draws together and discusses what I call ‘C-theories’ of time — (...) in short, philosophical positions that hold time lacks a direction — from different areas of the literature. I set out the various motivations, aims, and problems for C-theories, and outline different versions of antirealism about the direction of time. (shrink)

Against what is commonly accepted in many contexts, it has been recently suggested that both deterministic and indeterministic quantum theories are not time‐reversal invariant, and thus time is handed in a quantum world. In this paper, I analyze these arguments and evaluate possible reactions to them. In the context of deterministic theories, first I show that this conclusion depends on the controversial assumption that the wave‐function is a physically real scalar field in configuration space. Then I argue that answers which (...) restore invariance by assuming the wave‐function is a ray in Hilbert space fall short. Instead, I propose that one should deny that the wave‐function represents physical systems, along the lines proposed by the so‐called primitive ontology approach. Moreover, in the context of indeterministic theories, I argue that time‐reversal invariance can be restored suitably redefining its meaning. (shrink)

This article deals with the question of what time reversal means. It begins with a presentation of the standard account of time reversal, with plenty of examples, followed by a popular non-standard account. I argue that, in spite of recent commentary to the contrary, the standard approach to the meaning of time reversal is the only one that is philosophically and physically viable. The article concludes with a few open research problems about time reversal.

In this paper I investigate, within the framework of realistic interpretations of the wave function in nonrelativistic quantum mechanics, the mathematical and physical nature of the wave function. I argue against the view that mathematically the wave function is a two-component scalar field on configuration space. First, I review how this view makes quantum mechanics non- Galilei invariant and yields the wrong classical limit. Moreover, I argue that interpreting the wave function as a ray, in agreement many physicists, Galilei invariance (...) is preserved. In addition, I discuss how the wave function behaves more similarly to a gauge potential than to a field. Finally I show how this favors a nomological rather than an ontological view of the wave function. (shrink)

We argue that the asymmetry between diverging and converging electromagnetic waves is just one of many asymmetries in observed phenomena that can be explained by a past hypothesis and statistical postulate (together assigning probabilities to different states of matter and field in the early universe). The arrow of electromagnetic radiation is thus absorbed into a broader account of temporal asymmetries in nature. We give an accessible introduction to the problem of explaining the arrow of radiation and compare our preferred strategy (...) for explaining the arrow to three alternatives: (i) modifying the laws of electromagnetism by adding a radiation condition requiring that electromagnetic fields always be attributable to past sources, (ii) removing electromagnetic fields and having particles interact directly with one another through retarded action-at-a-distance, (iii) adopting the Wheeler-Feynman approach and having particles interact directly through half-retarded half-advanced action-at-a-distance. In addition to the asymmetry between diverging and converging waves, we also consider the related asymmetry of radiation reaction. (shrink)

It has become something of a dogma in the philosophy of science that modern cosmology has completed Boltzmann's program for explaining the statistical validity of the Second Law of thermodynamics by providing the low entropy initial state needed to ground the asymmetry in entropic behavior that underwrites our inference about the past. This dogma is challenged on several grounds. In particular, it is argued that it is likely that the Boltzmann entropy of the initial state of the universe is an (...) ill-defined or severely hobbled concept. It is also argued that even if the entropy of the initial state of the universe had a well-defined, low value, this would not suffice to explain why thermodynamics works as well as it does for the kinds of systems we care about. Because the role of Boltzmann entropy in our inferences to the past has been vastly overrated, the failure of the Boltzmann program does not pose a serious problem for our knowledge of the past. But it does call a different explanation of why thermodynamics works as well as it does. A suggestion is offered for a different approach. (shrink)

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)

Every process studied in any science other than physics defines an arrow of time – to say nothing for the directedness of the processes of causation, inference, memory, control, and counterfactual dependence that occur in everyday life. The discussion in this chapter is confined to the arrow of time as it occurs in physics. The chapter briefly discusses those features of microscopic physics, which seem to conflict with time asymmetry. It explains just how this conflict plays out in the important (...) context of thermodynamics and statistical mechanics. The chapter then reviews the main strategies available for resolving the conflict between reversible microdynamics and irreversible macrodynamics, working within the context of the quantitative, time‐irreversible evolution laws that seem to apply to large‐scale phenomena. Finally, it offers a broad the discussion covering other arrows of time within physics. (shrink)

This paper forms part of a wider campaign: to deny pointillisme, 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. More specifically, this paper argues against pointillisme about the concept of velocity in classical mechanics; especially against proposals by Tooley, Robinson and Lewis. (...) A companion paper argues against pointillisme about -geometry, as proposed by Bricker. To avoid technicalities, I conduct the argument almost entirely in the context of "Newtonian" ideas about space and time, and the classical mechanics of point-particles, i.e. extensionless particles moving in a void. But both the debate and my arguments carry over to relativistic physics. Introduction The wider campaign 2.1 Connecting physics and metaphysics 2.1.1 Avoiding controversy about the intrinsic–extrinsic distinction 2.1.2 Distinction from three mathematical distinctions 2.2 Classical mechanics is not pointilliste, and can be perdurantist 2.2.1 Two versions of pointillisme 2.2.2 Two common claims 2.2.3 My contrary claims 2.3 In more detail... 2.3.1 Four violations of pointillisme 2.3.2 For perdurantism Velocity as intrinsic? 3.1 Can properties represented by vectors be intrinsic to a point? 3.2 Orthodox velocity is extrinsic but local 3.2.1 A question and a debate 3.2.2 The verdict 3.3 Against intrinsic velocity 3.3.1 A common view—and a common problem 3.3.2 Tooley's proposal and his arguments 3.3.3 Tooley's further discussion "Shadow velocities": Lewis and Robinson 4.1 The proposal 4.2 Criticism: the vector field remains unspecified 4.3 Avoiding the presupposition of persistence, using Hilbert's symbol 4.4 Comparison with Robinson and Lewis. (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.

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)

Why does time reversal involve two operations, a temporal reflection and the operation of complex conjugation? Why is it that time reversal preserves position and reverses momentum and spin? This puzzle of time reversal in quantum mechanics has been with us since Wigner’s first presentation. In this paper, I propose a new solution to this puzzle. First, it is shown that the standard account of time reversal can be derived based on the assumption that the probability current is reversed by (...) the time reversal transformation. Next, this assumption is justified and the meaning of time reversal is clarified by analyzing the relationship between the rates of change and the instantaneous quantities which determine them. Finally, I explain how the new analysis help solve the puzzle of time reversal in quantum mechanics. (shrink)

How may we characterize the intrinsic structure of physical quantities such as mass, length, or electric charge? This article shows that group-theoretic methods—specifically, the notion of a free and transitive group action—provide an elegant way of characterizing the structure of scalar quantities, and uses this to give an intrinsic treatment of vector quantities. It also gives a general account of how different scalar or vector quantities may be algebraically combined with one another. Finally, it uses this apparatus to give a (...) simple intrinsic treatment of Newtonian gravitation. (shrink)

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)

In this paper I argue that the concept of time-reversal invariance in physics suffers from metaphysical underdetermination, that is, that the concept may be understood differently depending on one’s metaphysics about time, laws, and a theory’s basic properties. This metaphysical under-determinacy also affects subsidiary debates in philosophy of physics that rely on the concept of time-reversal invariance, paradigmatically the problem of the arrow of time. I bring up three cases that, I believe, fairly illustrate my point. I conclude, on the (...) one hand, that any formal representation of time reversal should be explicit about the metaphysical assumptions of the concept that it intends to represent; on the other, that philosophical arguments that rely on time reversal to argue against a direction of time require additional premises. (shrink)

What happens to the causal structure of a world when time is reversed? At first glance it seems there are two possible answers: the causal relations are reversed, or they are not. I argue that neither of these answers is correct: we should either deny that time-reversed worlds have causal relations at all, or deny that causal concepts developed in the actual world are reliable guides to the causal structure of time-reversed worlds. The first option is motivated by the instability (...) of time-reversed dynamical evolutions under interventions. The second option is motivated by a recognition of how contingent structural features of the actual world shape our causal concepts and reasoning strategies. (shrink)

The notion of time reversal has caused some recent controversy in philosophy of physics. The debate has mainly put the focus on how the concept of time reversal should be formally implemented across different physical theories and models, as if time reversal were a single, unified concept that physical theories should capture. In this paper, I shift the focus of the debate and defend that the concept of time reversal involves at least three facets, where each of them gives rise (...) to opposing views. In particular, I submit that any account of time reversal presupposes (explicitly or implicitly) modal, metaphysical, and heuristic facets. The comprehension of this multi-faceted nature of time reversal, I conclude, shows that time reversal can be coherently said in many ways, suggesting a disunified concept. (shrink)

I review the role of probability in contemporary physics and the origin of probabilistic time asymmetry, beginning with the pre-quantum case but concentrating on quantum theory. I argue that quantum mechanics radically changes the pre-quantum situation and that the philosophical nature of objective probability in physics, and of probabilistic asymmetry in time, is dependent on the correct resolution of the quantum measurement problem.

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)

This dissertation explores several issues related to the CPT theorem. Chapter 2 explores the meaning of spacetime symmetries in general and time reversal in particular. It is proposed that a third conception of time reversal, 'geometric time reversal', is more appropriate for certain theoretical purposes than the existing 'active' and 'passive' conceptions. It is argued that, in the case of classical electromagnetism, a particular nonstandard time reversal operation is at least as defensible as the standard view. This unorthodox time reversal (...) operation is of interest because it is the classical counterpart of a view according to which the so-called 'CPT theorem' of quantum field theory is better called 'PT theorem'; on this view, a puzzle about how an operation as apparently non-spatio-temporal as charge conjugation can be linked to spacetime symmetries in as intimate a way as a CPT theorem would seem to suggest dissolves. In chapter 3, we turn to the question of whether the CPT theorem is an essentially quantum-theoretic result. We state and prove a classical analogue of the CPT theorem for systems of tensor fields. This classical analogue, however, appears not to extend to systems of spinor fields. The intriguing answer to our question thus appears to be that the CPT theorem for spinors is essentially quantum-theoretic, but that the CPT theorem for tensor fields applies equally to the classical and quantum cases. Chapter4 explores a puzzle that arises when one puts the CPT theorem alongside a standard way of understanding spacetime symmetries, according to which spacetime symmetries are to be understood in terms of background spacetime structure. The puzzle is that a 'PT theorem' amounts to a statement that the theory may not make essential use of a preferred direction of time, and this seems odd. We propose a solution to that puzzle for the case of tensor field theories. (shrink)

David Malament has recently responded to David Albert's argument that classical electrodynamics is not time-reversal invariant by introducing a novel conception of time reversal, which supports the conventional view that under time reversal the magnetic field changes sign but the electric field remains unchanged. I will argue here that Malament's transformation has both passive and active versions. I will claim that the passive version is not relevant to Albert's argument, and the active version does not lead to the conventional transformation.