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 time reversal invariance that distorts the subsequent discussion. The present article not only has the remedial goal of setting the record straight about the meaning of time reversal 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)

David Albert has recently argued that classical electromagnetic theory (EM) is not time reversal invariant (non-TRI), while David Malament rejects this argument and maintains the orthodox result, that EM is TRI. Both Albert's and Malament's arguments are analysed, and both are found wanting in certain respects. It is argued here that the result really depends on the choice of theoretical ontology choosen to interpret EM theory, and there is more than one plausible choice. Albert and Malament have choosen (...) different plausible ontologies; but neither shows that their choice of interpretation is definitive. Deeper principles about this choice are examined. The extension to EM theory with magnetic monopoles is also examined. It is concluded that, despite certain flaws in his account, Albert's analysis does reveal serious problems in the orthodox account, which Malament's response does not adequately address. (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 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)

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)

It is commonly thought that there is some tension between the second law of thermodynam- ics and the time reversal invariance of the microdynamics. Recently, however, Jos Uffink has argued that the origin of time reversal non-invariance in thermodynamics is not in the second law. Uffink argues that the relationship between the second law and time reversal 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 time reversal invariant. In this paper, I attempt to spell out the traditional argument for incompatibility between the second law and time reversal 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 time reversal 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 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.

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 time-reversal invariance of a physical theory in causal terms, such that whatever can happen forwards in time can also happen backwards in time. This has led many to hold that time-reversal symmetry is incompatible with the asymmetry of cause and effect. This article critiques the causal reading (...) of time reversal. 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 time-reversal 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 time reversal, whereby time reversal leaves causal relations invariant. On the non-causal reading, time-reversal symmetry poses no significant conceptual nor epistemological problems for causation. _1_ Introduction _1.1_ The directionality argument _1.2_ Time reversal _2_ What Does Time Reversal Reverse? _2.1_ The B- and C-theory of time _2.2_ Time reversal on the C-theory _2.3_ Answers _3_ Does Time Reversal Reverse Causal Relations? _3.1_ Causation, billiards, and snooker _3.2_ The epistemology of causal direction _3.3_ Answers _4_ Is Time-Reversal Symmetry Compatible with Causation? _4.1_ Incompatibilism _4.2_ Compatibilism _4.3_ Answers _5_ Outlook. (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. (shrink)

What grounds the standard claim that classical mechanics is time-reversal invariant? Hutchison (1993, 1995) challenges the conventional reasoning underlying the belief that classical mechanics is time reversal invariant and argues that it is not in any well-defined sense. I find a defensible criterion that will exclude his cases, thereby rescuing a sense in which we can say that classical mechanics is time reversal invariant.

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)

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.

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 concluding section applies the results of the previous part to some important thermodynamical systems. Even if time reversibility is allowed, it is shown that the flow vectors used to derive Onsager reciprocity from time translational invariance is of questionable validity. The fundamental fluctuation dissipation theorem of Callen, Welton, Green and Kubo which underpin descriptions of irreversibility, insofar as they are derived from time translational invariance, is also questioned; from Part I, they cannot be derived (...) properly from time reversal symmetry. The common view of entropy as some type of caloric fluid flow is critiqued as not conforming to the Kelvin Clausius Planck definition. An example of developing reciprocal relations to any order in the coupling indices based on the peculiar physical and defining characteristics of conductive heat is given for the steady state whenever a temperature gradient is present, free from time reversible and translation assumptions. A major challenge in the theory is to extend it to isothermal states. It is concluded that other more deterministic views mediated by authentic work anamnesis may be needed for long term coherence. (shrink)

This book is an attempt to get to the bottom of an acute and perennial tension between our best scientific pictures of the fundamental physical structure of the world and our everyday empirical experience of it. The trouble is about the direction of time. The situation (very briefly) is that it is a consequence of almost every one of those fundamental scientific pictures--and that it is at the same time radically at odds with our common sense--that whatever can (...) happen can just as naturally happen backwards. Albert provides an unprecedentedly clear, lively, and systematic new account--in the context of a Newtonian-Mechanical picture of the world--of the ultimate origins of the statistical regularities we see around us, of the temporal irreversibility of the Second Law of Thermodynamics, of the asymmetries in our epistemic access to the past and the future, and of our conviction that by acting now we can affect the future but not the past. Then, in the final section of the book, he generalizes the Newtonian picture to the quantum-mechanical case and (most interestingly) suggests a very deep potential connection between the problem of the direction of time and the quantum-mechanical measurement problem. The book aims to be both an original contribution to the present scientific and philosophical understanding of these matters at the most advanced level, and something in the nature of an elementary textbook on the subject accessible to interested high-school students. Table of Contents: Preface 1. Time-Reversal Invariance 2. Thermodynamics 3. Statistical Mechanics 4. The Reversibility Objections and the Past-Hypothesis 5. The Scope of Thermodynamics 6. The Asymmetries of Knowledge and Intervention 7. Quantum Mechanics Appendix: Gedankenexperiments with Heat Engines Index Reviews of this book: The foundations of statistical mechanisms are often presented in physics textbooks in a rather obscure and confused way. By challenging common ways of thinking about this subject, Time and Chance can do quite a lot to improve this situation. --Jean Bricmont, Science Albert is perfecting a style of foundational analysis that is uniquely his own...It has a surgical precision...and it is ruthless with pretensions. The foundations of thermodynamics is a topic that has accumulated a good deal of dead wood; this is a fire that will burn and burn. --Simon W. Saunders, Oxford University As usual with Albert's work, the exposition is brisk and to the point, and exceptionally clear...The book will be an extremely valuable contribution to the literature on the subject of philosophical issues in thermodynamics and statistical mechanics, a literature which has been thin on the ground but is now growing as it deserves to. --Lawrence Sklar, University of Michigan. (shrink)

Physicists routinely claim that the fundamental laws of physics are 'time symmetric' or 'time reversal invariant' or 'reversible'. In particular, it is claimed that the theory of quantum mechanics is time symmetric. But it is shown in this paper that the orthodox analysis suffers from a fatal conceptual error, because the logical criterion for judging the time symmetry of probabilistic theories has been incorrectly formulated. The correct criterion requires symmetry between future-directed laws and past-directed laws. (...) This criterion is formulated and proved in detail. The orthodox claim that quantum mechanics is reversible is re-evaluated. The property demonstrated in the orthodox analysis is shown to be quite distinct from time reversal invariance. The view of Satosi Watanabe that quantum mechanics is time asymmetric is verified, as well as his view that this feature does not merely show a de facto or 'contingent' asymmetry, as commonly supposed, but implies a genuine failure of time reversal invariance of the laws of quantum mechanics. The laws of quantum mechanics would be incompatible with a time-reversed version of our universe. (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)

Testable predictions of quantum mechanics are invariant under time reversal. 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.

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)

The aim of this paper is to analyze time-asymmetric quantum mechanics with respect to the problems of irreversibility and of time's arrow. We begin with arguing that both problems are conceptually different. Then, we show that, contrary to a common opinion, the theory's ability to describe irreversible quantum processes is not a consequence of the semigroup evolution laws expressing the non-time-reversal invariance of the theory. Finally, we argue that time-asymmetric quantum mechanics, either in Prigogine's (...) version or in Bohm's version, does not solve the problem of the arrow of time because it does not supply a substantial and theoretically founded criterion for distinguishing between the two directions of time. (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)

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.

It has been recently argued that by Leifer and Pusey, and Price, that time-symmetric quantum mechanics must entail retrocausality. Adlam responds that such theories might also entail ‘spooky action at a distance’. This paper proposes a third alternative: time-symmetric quantum mechanics might entail temporal global correlations. Unlike the traditional analysis of time symmetries in quantum mechanics, which consider linear and unitary interpretations, this paper considers the time-symmetric collapse models advanced by Bedingham and Maroney. These models are (...) specially interesting since it has been widely believed that collapse theories cannot be time-reversal invariant. (shrink)

An increasing number of experiments at the Belle, BNL, CERN, DAΦNE and SLAC accelerators are confirming the violation of time reversal 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)

It is argued that time's arrow is present in all equations of motion. But it is absent in the point particle approximations commonly made. In particular, the Lorentz-Abraham-Dirac equation is time-reversal invariant only because it approximates the charged particle by a point. But since classical electrodynamics is valid only for finite size particles, the equations of motion for particles of finite size must be considered. Those equations are indeed found to lack time-reversal invariance, thus (...) ensuring an arrow of time. Similarly, more careful considerations of the equations of motion for gravitational interactions also show an arrow of time. The existence of arrows of time in quantum dynamics is also emphasized. (shrink)

This paper is a sequel to various papers by the author devoted to the EPR correlation. The leading idea remains that the EPR correlation (either in its well-known form of nonseparability of future measurements, or in its less well-known time-reversed form of nonseparability of past preparations) displays the intrinsic time symmetry existing in almost all physical theories at the elementary level. But, as explicit Lorentz invariance has been an essential requirement in both the formalization and the conceptualization (...) of my papers, the noninvariant concept ofT symmetry has to yield in favor of the invariant concept ofPT symmetry, or even (asC symmetry is not universally valid) to that ofCPT invariance. A distinction is then drawn between “macro” special relativity, defined by invariance under the orthochronous Lorentz group and submission to the retarded causality concept, and “micro” special relativity, defined by invariance under the full Lorentz group and includingCPT symmetry. TheCPT theorem clearly implies that “micro special relativity”is relativity theory at the quantal level. It is thus of fundamental significance not only in the search of interaction Lagrangians, etc., but also in the basic interpretation of quantum mechanics, including the understanding of the EPR correlation. While the experimental existence of the EPR correlations is manifestly incompatible with macro relativity, it is fully consistent with micro relativity. Going from a retarded concept of causality to one that isCPT invariant has very radical consequences, which are briefly discussed. (shrink)

The problem of time’s arrow is (roughly) to understand why macroscopic physical processes typically evolve in a specific direction (the one we call “the future”) even though the underlying laws of physics describing the individual microscopic systems are time-reversal invariant. The standard answer to this problem is given by Boltzmann’s explanation of the II law of thermodynamics: a classical system starting in a non-equilibrium state spontaneously (i.e. with a high level of probability) tends towards equilibrium, thus implementing (...) an irreversible process. However, this explanation has two drawbacks: 1. it needs a further assumption on the entropy of the initial state of the universe (past hypothesis); 2. microscopic systems (e.g. molecules in a box) should be represented as quantum states and not classical states. In this talk, I want to propose a different hypothesis to explain the origin of time’s arrow, based on quantum mechanics, specifically on decoherence theory. Differently from isolated systems, open quantum systems described by decoherence theory show irreversible behavior, as they evolve towards decoherence and von Neumann entropy increase. Is this behavior a sign of genuine irreversibility? And, if so, can this be linked to thermodynamic irreversibility? (shrink)

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)

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)

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 time reversal. 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)

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 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)

Since the nineteenth century, the problem of the arrow of time has been traditionally analyzed in terms of entropy by relating the direction past-to-future to the gradient of the entropy function of the universe. In this paper, we reject this traditional perspective and argue for a global and non-entropic approach to the problem, according to which the arrow of time can be defined in terms of the geometrical properties of spacetime. In particular, we show how the global non-entropic (...) arrow can be transferred to the local level, where it takes the form of a non-spacelike local energy flow that provides the criterion for breaking the symmetry resulting from time-reversal invariant local laws. (shrink)

This paper states and proves a precise sense in which, if all the measurable properties of an ordinary quantum mechanical system are ultimately derivable from position, then time in quantum mechanics can have no preferred direction. In particular, I show that when the position observable forms a complete set of commuting observables, Galilei invariant quantum mechanics is guaranteed to be time reversal invariant.

Two views on the direction of time can be distinguished—primitivism and non-primitivism. According to the former, time’s direction is an in-built, fundamental property of the physical world. According to the latter, time’s direction is a derivative property of a fundamentally directionless reality. In the literature, non-primitivism has been widely supported since most our fundamental dynamical laws are time-reversal invariant. In this paper, I offer a way out to the primitivist. I argue that we do have (...) good grounds to support a primitive direction of time in the quantum realm. The rationale depends on exploiting the metaphysical and dynamical underdetermination of quantum theories to make a case in favor of primitivism. In particular, primitivism can be grounded in spontaneous collapse theories. The specific sense in which these theories capture a primitive direction of time is that, when the ontology of the theory is seriously taken into account, it does not remain invariant under time reversal. In taking GRW with a matter-density field, I will argue that primitivism about the direction of time can be defended in the quantum case. (shrink)

An early, very preliminary edition of this book was circulated in 1962 under the title Set-theoretical Structures in Science. There are many reasons for maintaining that such structures play a role in the philosophy of science. Perhaps the best is that they provide the right setting for investigating problems of representation and invariance in any systematic part of science, past or present. Examples are easy to cite. Sophisticated analysis of the nature of representation in perception is to be found (...) already in Plato and Aristotle. One of the great intellectual triumphs of the nineteenth century was the mechanical explanation of such familiar concepts as temperature and pressure by their representation in terms of the motion of particles. A more disturbing change of viewpoint was the realization at the beginning of the twentieth century that the separate invariant properties of space and time must be replaced by the space-time invariants of Einstein's special relativity. Another example, the focus of the longest chapter in this book, is controversy extending over several centuries on the proper representation of probability. The six major positions on this question are critically examined. Topics covered in other chapters include an unusually detailed treatment of theoretical and experimental work on visual space, the two senses of invariance represented by weak and strong reversibility of causal processes, and the representation of hidden variables in quantum mechanics. The final chapter concentrates on different kinds of representations of language, concluding with some empirical results on brain-wave representations of words and sentences. (shrink)

In Minkowski flat space-time, it is perceived that time inversion is unitary rather than antiunitary, with energy being a time vector changing sign under time inversion. The Dirac equation, in the case of electromagnetic interaction, is not invariant under unitary time inversion, giving rise to a “Klein paradox.” To render unitary time inversion invariance, a nonlinear wave equation is constructed, in which the “Klein paradox” disappears. In the case of Coulomb interaction, the revised (...) nonlinear equation can be linearized to give energy solutions for Hydrogen-like ions without singularity when nuclear number Z>137, showing a reversed energy order pending for experimental tests such as Zeeman effects. In non-relativistic limit, this nonlinear equation reduces to nonlinear Schrödinger equation with soliton-like solutions. Moreover, particle conjugation and electron-proton scattering with a nonsingular current-potential interaction are discussed. Finally the explicit form of gauge function is found, the uniqueness of Lorentz gauge is proven and the Lagrangian density of quantum electrodynamics (QED) is revised as well. The implementation of unitary time inversion leads to the ultimate derivation of nonlinear QED. (shrink)

Wigner gave a well-known proof of Kramers degeneracy, for time reversal 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.

Many philosophers of physics take the failure of the laws of physics to be invariant under the time reversal transformation to give us good reason to think that spacetime is temporally anisotropic, yet the details of this inference are rarely made explicit. I discuss two reasonable ways of filling in the details of this inference, the first of which utilizes a symmetry principle proposed by John Earman and the second of which utilizes Harvey Brown’s account of spacetime. I (...) contend that neither of the resulting arguments is sound. (shrink)

This paper claims that, to the extent that temporal direction figures in physics at all, it is found there as part of the extra-scientific language science employs. The asymmetry between “before” and “after” is not captured by the mathematics of any theory, nor can it be derived from the laws of any theory. This, I argue, is true even of theories whose laws are not time reversal invariant. Recognizing that physics does not yield temporal direction but receives it (...) from the background in which physics develops and operates does not, however, expose any hitherto unknown limitations or deficiencies of physics. The claim is not about physics, but about metaphysical stances regarding physics, specifically, physicalism, which requires from physics to deliver more than it does, or should. Once the place of temporal direction in physics is understood, infamous difficulties can be addressed in a novel way. Issues emerging from the 2nd law of thermodynamics, such as the minimum problem, and the worry that the law generates outlandish predictions, are removed. A side benefit is the recognition that the past hypothesis is superfluous. A final conclusion of the paper is that the relationship between physics and everyday language, far from being a source of difficulties, is healthy and beneficial to both. (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 time reversal. I dispute this claim, on several grounds.

While the fundamental laws of physics are time-reversal invariant, most macroscopic processes are irreversible. Given that the fundamental laws are taken to underpin all other processes, how can the fundamental time-symmetry be reconciled with the asymmetry manifest elsewhere? In statistical mechanics, progress can be made with this question. What I dub the ‘Zwanzig–Zeh–Wallace framework’ can be used to construct the irreversible equations of SM from the underlying microdynamics. Yet this framework uses coarse-graining, a procedure that has faced (...) much criticism. I focus on two objections in the literature: claims that coarse-graining makes time-asymmetry ‘illusory’ and ‘anthropocentric’. I argue that these objections arise from an unsatisfactory justification of coarse-graining prevalent in the literature, rather than from coarse-graining itself. This justification relies on the idea of measurement imprecision. By considering the role that abstraction and autonomy play, I provide an alternative justification and offer replies to the illusory and anthropocentric objections. Finally, I consider the broader consequences of this alternative justification: the connection to debates about inter-theoretic reduction and the implication that the time-asymmetry in SM is weakly emergent. 1Introduction 1.1Prospectus2The Zwanzig–Zeh–Wallace Framework3Why Does This Method Work? 3.1The special conditions account3.2When is a density forwards-compatible?4Anthropocentrism and Illusion: Two Objections 4.1The two objections in more detail4.2Against the justification by measurement imprecision5An Alternative Justification 5.1Abstraction and autonomy5.2An illustration: the Game of Life6Reply to Illusory7Reply to Anthropocentric8The Wider Landscape: Concluding Remarks 8.1Inter-theoretic relations8.2The nature of irreversibility. (shrink)

It is claimed that the `problem of the arrow of time in classical dynamics' has been solved. Since all classical particles have a self-field (gravitational and in some cases also electromagnetic), their dynamics must include self-interaction. This fact and the observation that the domain of validity of classical physics is restricted to distances not less than of the order of a Compton wavelength (thus excluding point particles), leads to the conclusion that the fundamental classical equations of motion are not (...) invariant under time reversal: retarded self-interactions lead to different equations than advanced ones. Since causality (the time order of cause and effect) requires retarded rather than advanced self-interaction, it is causality which is ultimately responsible for the arrow of time. Classical motions described by equations with advanced self-interactions differ from retarded ones and do not occur in nature. (shrink)

I will argue, pace a great many of my contemporaries, that there's something right about Boltzmann's attempt to ground the second law of thermodynamics in a suitably amended deterministic time-reversal invariant classical dynamics, and that in order to appreciate what's right about (what was at least at one time) Boltzmann's explanatory project, one has to fully apprehend the nature of microphysical causal structure, time-reversal invariance, and the relationship between Boltzmann entropy and the work of (...) Rudolf Clausius. (shrink)

We present a Gedankenexperiment that leads to a violation of detailed balance if quantum mechanical transition probabilities are treated in the usual way by applying Fermi’s “golden rule”. This Gedankenexperiment introduces a collection of two-level systems that absorb and emit radiation randomly through non-reciprocal coupling to a waveguide, as realized in specific chiral quantum optical systems. The non-reciprocal coupling is modeled by a hermitean Hamiltonian and is compatible with the time-reversal invariance of unitary quantum dynamics. Surprisingly, the (...) combination of non-reciprocity with probabilistic radiation processes entails negative entropy production. Although the considered system appears to fulfill all conditions for Markovian stochastic dynamics, such a dynamics violates the Clausius inequality, a formulation of the second law of thermodynamics. Several implications concerning the interpretation of the quantum mechanical formalism are discussed. (shrink)

In this chapter, I urge a fresh look at the problem of explaining equilibration. The process of equilibration, I argue, is best seen not as part of the subject matter of thermodynamics, but as a presupposition of thermodynamics. Further, the relevant tension between the macroscopic phenomena of equilibration and the underlying microdynamics lies not in a tension between time-reversal invariance of the microdynamics and the temporal asymmetry of equilibration, but in a tension between preservation of distinguishability of (...) states at the level of microphysics and the continual effacing of the past at the macroscopic level. This suggests an open systems approach, where the puzzling question is not the erasure of the past, but the question of how reliable prediction, given only macroscopic data, is ever possible at all. I suggest that the answer lies in an approach that has not been afforded sufficient attention in the philosophical literature, namely, one based on the temporal asymmetry of causal explanation. (shrink)

In Newcomb’s paradox you can choose to receive either the contents of a particular closed box, or the contents of both that closed box and another one. Before you choose though, an antagonist uses a prediction algorithm to accurately deduce your choice, and uses that deduction to fill the two boxes. The way they do this guarantees that you made the wrong choice. Newcomb’s paradox is that game theory’s expected utility and dominance principles appear to provide conflicting recommendations for what (...) you should choose. Here we show that the conflicting recommendations assume different probabilistic structures relating your choice and the algorithm’s prediction. This resolves the paradox: the reason there appears to be two conflicting recommendations is that the probabilistic structure relating the problem’s random variables is open to two, conflicting interpretations. We then show that the accuracy of the prediction algorithm in Newcomb’s paradox, the focus of much previous work, is irrelevant. We end by showing that Newcomb’s paradox is time-reversal invariant; both the paradox and its resolution are unchanged if the algorithm makes its ‘prediction’ after you make your choice rather than before. (shrink)

This article discusses some philosophical theories of causation and their application to several areas of science. Topics addressed include regularity, counterfactual, and causal process theories of causation; the causal interpretation of structural equation models and directed graphs; independence assumptions in causal reasoning; and the role of causal concepts in physics. In connection with this last topic, this article focuses on the relationship between causal asymmetries, the time-reversal invariance of most fundamental physical laws, and the significance of differences (...) among varieties of differential equations in causal interpretation. It concludes with some remarks about “grounding” special science causal generalizations in physics. (shrink)