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.

We present a precise form of structural realism, called group structural realism , which identifies ‘structure’ in quantum theory with symmetry groups. However, working out the details of this view actually illuminates a major problem for structural realism; namely, a structure can itself have structure. This article argues that, once a precise characterization of structure is given, the ‘metaphysical hierarchy’ on which group structural realism rests is overly extravagant and ultimately unmotivated.

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.

A supertask is a task that consists in infinitely many component steps, but which in some sense is completed in a finite amount of time. Supertasks were studied by the pre-Socratics and continue to be objects of interest to modern philosophers, logicians and physicists. The term “super-task” itself was coined by J.F. Thomson (1954). Here we begin with an overview of the analysis of supertasks and their mechanics. We then discuss the possibility of supertasks from the perspective of general relativity.

'The arrow of time' refers to the curious asymmetry that distinguishes the future from the past. Reversing the Arrow of Time argues that there is an intimate link between the symmetries of 'time itself' and time reversal symmetry in physical theories, which has wide-ranging implications for both physics and its philosophy. This link helps to clarify how we can learn about the symmetries of our world, how to understand the relationship between symmetries and what is real, and how to overcome (...) pervasive illusions about the direction of time. Roberts explains the significance of time reversal in a way that intertwines physics and philosophy, to establish what the arrow of time means and how we can come to know it. This book is both mathematically and philosophically rigorous yet remains accessible to advanced undergraduates in physics and the philosophy of physics. This title is also available as Open Access on Cambridge Core. (shrink)

Leibniz Equivalence is a principle of applied mathematics that is widely assumed in both general relativity textbooks and in the philosophical literature on Einstein’s hole argument. In this article, I clarify an ambiguity in the statement of this Leibniz Equivalence, and argue that the relevant expression of it for the hole argument is strictly false. I then show that the hole argument still succeeds as a refutation of manifold substantivalism; however, recent proposals that the hole argument is undermined by principles (...) of representational equivalence do not fare so well. (shrink)

Why is gauge symmetry so important in modern physics, given that one must eliminate it when interpreting what the theory represents? In this paper we discuss the sense in which gauge symmetry can be fruitfully applied to constrain the space of possible dynamical models in such a way that forces and charges are appropriately coupled. We review the most well-known application of this kind, known as the 'gauge argument' or 'gauge principle', discuss its difficulties, and then reconstruct the gauge argument (...) as a valid theorem in quantum theory. We then present what we take to be a better and more general gauge argument, based on Noether's second theorem in classical Lagrangian field theory, and argue that this provides a more appropriate framework for understanding how gauge symmetry helps to constrain the dynamics of physical theories. (shrink)

This paper is a tour of how the laws of nature can distinguish between the past and the future, or be T-violating. I argue that, in terms of the basic argumentative structure, there are basically just three approaches currently being explored. The first is an application of Curie's Principle, together with the CPT theorem. The second route makes use of a principle due to Pasha Kabir which allows for a direct detection. The third route makes use of a Non-degeneracy Principle, (...) and is related to the energy spectrum of elementary particles. I show how each provides a general template for detecting T-violation, illustrate each with an example, and discuss their prospects in extensions of particle physics beyond the standard model. (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.

I point out a simple sense in which the standard formulation of Curie’s principle is false when the symmetry transformation it describes is time reversal.

How should we characterise the observable aspects of quantum theory? This paper argues that philosophers and physicists should jettison a standard dogma: that observables must be represented by self-adjoint or Hermitian operators. Four classes of non-standard observables are identified: normal operators, symmetric operators, real-spectrum operators, and none of these. The philosophical and physical implications of each are explored.

I propose a general geometric framework in which to discuss the existence of time observables. This framework allows one to describe a local sense in which time observables always exist, and a global sense in which they can sometimes exist subject to a restriction on the vector fields that they generate. Pauli׳s prohibition on quantum time observables is derived as a corollary to this result. I will then discuss how time observables can be regained in modest extensions of quantum theory (...) beyond its standard formulation. (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.

Jim Weatherall has suggested that Einstein's hole argument, as presented by Earman and Norton, is based on a misleading use of mathematics. I argue on the contrary that Weatherall demands an implausible restriction on how mathematics is used. The hole argument, on the other hand, is in no new danger at all.

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.

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)

Ashtekar has illustrated that two of the available roads to testing for time asymmetry can be generalized beyond the structure of quantum theory, to much more general formulations of mechanics. The purpose of this note is to show that a third road to T-violation, which I have called "Wigner's Principle," can be generalized in this way as well.

This special issue of Foundations of Physics collects together articles representing some recent new perspectives on the hole argument in the history and philosophy of physics. Our task here is to introduce those new perspectives.

This paper introduces a little-known episode in the history of physics, in which a mathematical proof by Pierre Fermat vindicated Galileo’s characterization of freefall. The first part of the paper reviews the historical context leading up to Fermat’s proof. The second part illustrates how a physical and a mathematical insight enabled Fermat’s result, and that a simple modification would satisfy any of Fermat’s critics. The result is an illustration of how a purely theoretical argument can settle an apparently empirical debate.

In this contribution in honour of Paul Busch, we criticise the claims of many expositions that the time-energy uncertainty principle allows both a violation of energy conservation and particle creation, provided that this happens for a sufficiently short time. But we agree that there are grains of truth in these claims: which we make precise and justify using perturbation theory.

This note argues that quantum observables can include not just self-adjoint operators, but any member of the class of normal operators, including those with non-real eigenvalues. Concrete experiments, statistics, and symmetries are all expressed in this more general context. However, this more general class of observables also introduces a new restriction on which sets of operators can be interpreted as observables at once. These sets are referred to here as 'sharp sets.

A free eBook introduction to the philosophy of science, based on a course taught by Dr Bryan W. Roberts, Assistant Professor of Philosophy, Logic & Scientific Method at the London School of Economics.

Galileo's refutation of the speed-distance law of fall in his Two New Sciences is routinely dismissed as a moment of confused argumentation. We urge that Galileo's argument correctly identified why the speed-distance law is untenable, failing only in its very last step. Using an ingenious combination of scaling and self-similarity arguments, Galileo found correctly that bodies, falling from rest according to this law, fall all distances in equal times. What he failed to recognize in the last step is that this (...) time is infinite, the result of an exponential dependence of distance on time. Instead, Galileo conflated it with the other motion that satisfies this ‘equal time’ property, instantaneous motion. (shrink)

In this reply, we respond to the comments of Palmerino and Laird on our article, "Galileo's Refutation of the Speed Distance Law of Fall Rehabilitated," published in the same issue of Centaurus.

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.

Rovelli argues that the there is disharmony with respect to the arrow of time from the perspective of testable predictions, as compared to the perspective of Schroedinger evolution, and uses this claim as evidence against realist interpretations of the wave function. I argue on the contrary that this disharmony arises only out of a non-standard definition of time reversal that ignores the 'big-T', and that harmony is restored when the standard definition is adopted.

It’s often been thought that Curie’s principle says something that’s just obviously true about the world. However, Bryan Roberts has discovered a simple way in which Curie’s principle fails.

In this contribution in honour of Paul Busch, we criticise the claims of many expositions that the time-energy uncertainty principle allows both a violation of energy conservation, and particle creation, provided that this happens for a sufficiently short time. But we agree that there are grains of truth in these claims: which we make precise and justify using perturbation theory.