This is Part 2 of a four part paper, intended as an introduction to the key concepts and issues of time directionality for physicists and philosophers. It redresses some fundamental confusions in the subject. These need to be corrected in introductory courses for physics and philosophy of physics students. Here we analyze the quantum mechanical time reversal operator and the reversal of the deterministic Schrodinger equation. It is argued that quantum mechanics is anti-symmetric w.r.t. time reversal in its deterministic laws. (...) This contradicts the orthodox analysis, found throughout the conventional literature on physical time, which claims that quantum mechanics is time symmetric (reversible), and that we must adopt the anti-unitary operator (T*) instead of the unitary time reversal operator (T) for time reversal in quantum mechanics. This is widely claimed as settled scientific fact, and large metaphysical conclusions about the symmetry of time are drawn from it. But it is an error. (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)

“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)

Much has been written on the role of causal notions and causal reasoning in the so-called 'special sciences' and in common sense. But does causal reasoning also play a role in physics? Mathias Frisch argues that, contrary to what influential philosophical arguments purport to show, the answer is yes. Time-asymmetric causal structures are as integral a part of the representational toolkit of physics as a theory's dynamical equations. Frisch develops his argument partly through a critique of anti-causal arguments and partly (...) through a detailed examination of actual examples of causal notions in physics, including causal principles invoked in linear response theory and in representations of radiation phenomena. Offering a new perspective on the nature of scientific theories and causal reasoning, this book will be of interest to professional philosophers, graduate students, and anyone interested in the role of causal thinking in science. (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.

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)

The analysis of the reversibility of quantum mechanics depends upon the choice of the time reversal operator for quantum mechanical states. The orthodox choice for the time reversal operator on QM states is known as the Wigner operator, T*, where * performs complex conjugation. The peculiarity is that this is not simply the unitary time reversal operation, but an anti-unitary operator, involving complex conjugation in addition to ordinary time reversal. The alternative choice is the Racah operator, which is simply ordinary (...) time reversal, T. Orthodox treatments hold that it is either logically or empirically necessary to adopt the Wigner operator, and the Racah operator has received little attention. The basis for this choice is analysed in detail, and it is concluded that all the conventional arguments for rejecting the Racah operator and adopting the Wigner operator are mistaken. The additional problem of whether the deterministic part of quantum mechanics should be judged to be reversible or not is also considered. The adoption of the Racah operator for time reversal appears prima facie to entail that quantum mechanics is irreversible. However, it is concluded that the real answer to question depends upon the choice of interpretation of the theory. In any case, the conventional reasons for claiming that quantum mechanics is reversible are incorrect. (shrink)

ABSTRACT The debate between proponents and opponents of causal foundationalism has recently surfaced as a disparity between causal structuralism and causal anti-foundationalism in the structural realist camp. The paper outlines and dissolves the problem of disparity for structural realism. I follow John Collier to specify causation in terms of the transmission of information. Unlike them, I built upon the reverse quantum data-processing inequality to show how this approach models causation as a symmetric process at the level of fundamental physics. I (...) show how this suggestion reduces the disparity about causation to a problem of application to diverse contexts. (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)

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.

We often use symmetries to infer outcomes’ probabilities, as when we infer that each side of a fair coin is equally likely to come up on a given toss. Why are these inferences successful? I argue against answering this with an a priori indifference principle. Reasons to reject that principle are familiar, yet instructive. They point to a new, empirical explanation for the success of our probabilistic predictions. This has implications for indifference reasoning in general. I argue that a priori (...) symmetries need never constrain our probability attributions, even when it comes to our initial credences. (shrink)

Curie’s Principle says that any symmetry property of a cause must be found in its effect. In this article, I consider Curie’s Principle from the point of view of graphical causal models, and demonstrate that, under one definition of a symmetry transformation, the causal modeling framework does not require anything like Curie’s Principle to be true. On another definition of a symmetry transformation, the graphical causal modeling formalism does imply a version of Curie’s Principle. These results yield a better understanding (...) of the logical landscape with respect to the relationship between Curie’s Principle and graphical causal modeling. (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.

This paper outlines a new interpretation of an argument of Kant's for the existence of absolute space. The Kant argument, found in a 1768 essay on topology, argues for the existence of Newtonian-Euclidean absolute space on the basis of the existence of incongruous counterparts (such as a left and a right hand, or any asymmetrical object and its mirror-image). The clear, intrinsic difference between a left hand and a right hand, Kant claimed, cannot be understood on a relational view of (...) space - for in terms of the spatial relations of their parts, there is no difference to be found. Kant's argument has been interpreted by, among others, Graham Nerlich (in 1973, Hands, Knees and Absolute Space, The Journal of Philosophy). I briefly discuss Nerlich, and then offer a different reconstruction of the argument, one that appears to be closer to Kant's text. The reconstruction, however, essentially involves ascription of primitive identity to parts of space. Comparing the Kantian absolutist account of incongruous counterparts using primitive identity to the correct relationist account, I conclude that the absolutist account pays a heavy metaphysical price, without buying any genuine explanatory advantage over the relationist. I go on to examine recent suggestions that parity-non-conservation phenomena in quantum physics allow a stronger version of Kant's challenge to relationism. On closer examination, it turns out that here too the absolutist or substantivalist must be appealing to space parts with primitive identity in order to claim an advantage over relationists; and here too, I argue the substantivalist story really has no advantage over the correct relationist account. (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)

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)

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.

It is often claimed that one cannot locate a notion of causation in fundamental physical theories. The reason most commonly given is that the dynamics of those theories do not support any distinction between the past and the future, and this vitiates any attempt to locate a notion of causal asymmetry—and thus of causation—in fundamental physical theories. I argue that this is incorrect: the ubiquitous generation of entanglement between quantum systems grounds a relevant asymmetry in the dynamical evolution of quantum (...) systems. I show that by exploiting a connection between the amount of entanglement in a quantum state and the algorithmic complexity of that state, one can use recently developed tools for causal inference to identify a causal asymmetry—and a notion of causation—in the dynamical evolution of quantum systems. (shrink)

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)