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.
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.
This is Part 1 of a four part paper, intended to redress some of the most fundamental confusions in the subject of physical time directionality, and represent the concepts accurately. There are widespread fallacies in the subject that need to be corrected in introductory courses for physics students and philosophers. Parts 1 and 2 are about quantum mechanics, Part 3 is about fundamental concepts, and Part 4 is about cosmology. We start in Part 1 by analysing the time reversal symmetry of quantum probability laws. Time reversal symmetry is defined as the property of invariance under the time reversal transformation, T: t -> -t. It is shown that quantum mechanics (classical or relativistic) is strongly time asymmetric in its probability laws. This contradicts the orthodox analysis, found throughout the conventional literature on physical time, which claims that quantum mechanics is time symmetric or reversible. This is widely claimed as settled scientific fact, and large philosophical and scientific conclusions are drawn from it. But it is an error. The fact is that while quantum mechanics is widely claimed to be reversible on the basis of two formal mathematical properties (that it does have), these properties do not represent invariance under the time reversal transformation. A recent experiment (Batalhao at alia, 2015) showing irreversibility of quantum thermodynamics is discussed as an illustration of this result. Most physicists remain unaware of the errors, decades after they were first demonstrated. Orthodox specialists in the philosophy of time who are aware of the error continue to refer to the ‘time symmetry’ or ‘reversibility’ of quantum mechanics anyway – and exploit the ambiguity to claim false implications about physical time reversal symmetry in nature. The excuse for perpetrating the confusion is that, since it is has now become customary to refer to the formal properties of quantum mechanics as ‘reversibility’ or ‘time reversal symmetry’, we should just keep referring to them by this name, even though they are not time reversal symmetry. This causes endless confusion, in attempts to explain the physical irreversibility of our universe, and in philosophical discussions of implications of physics for the nature of time. The failure of time reversal symmetry in quantum mechanics changes the interpretation of modern physics in a deep way. It changes the problem of explaining the real irreversibility found throughout nature.
In this paper I shall shed some doubts on a widely-held claim: standard quantum mechanics is time-reversal invariant, and thereby, blind to the direction of time. Building bridges between physics and philosophy, I shall argue that such a claim features some puzzling assumptions that are frequently overlooked in the literature. In particular, I shall first argue that the claim involves some methodological and metaphysical commitments that should be evaluated more prudently from philosophy and from physics. Second, I shall point out that the common inference that goes from symmetry to metaphysical conclusions needs some correction and refinement to be acceptable for time symmetry and the debate around the arrow of time
In a classical mechanical world, the fundamental laws of nature are reversible. The laws of nature treat the past and future as mirror images of each other. Temporally asymmetric phenomena are ultimately said to arise from initial conditions. But are the laws of nature also reversible in a quantum world? This paper argues that they are not, that time in a quantum world prefers a particular ‘hand’ or ordering. I argue, first, that the probabilistic algorithm used in the theory picks out a preferred direction of time for almost all interpretations of the theory, and second, that contrary to the received wisdom the Schrödinger evolution is also irreversible. The status of Wigner reversal invariance is then discussed. I conclude that the quantum world is fundamentally irreversible, but manages to appear (thanks to Wigner reversal invariance) reversible at the classical level.
A fundamental problem in understanding the nature of time is to explain its 'directionality'. The commonplace view is that this directionality is provided by the 'flow of time'. Unfortunately this concept of 'time flow', which seems to make perfect sense to us in our everyday lives, has resisted philosophical and scientific analysis so well that today it is widely regarded as having no place in the scientific account of the world. Instead, various alternative physical concepts of the directionality of time have been developed, principally the notions of the time reversibility of physical laws or theories, and of the time asymmetry of physical processes. It is frequently argued by philosophers of physics that the scientific account of the directionality of time must be framed entirely in terms of these physical notions. The thesis of the present work is that this conclusion has been reached far too hastily. It is argued that the concept of time flow is a legitimate physical concept, and furthermore, that time flow plays a real part in quantum theory. A number of conceptual investigations are necessary to support this argument. Firstly, it is necessary to give an analysis of what a physical theory of time flow might be like, and how it might be empirically established. This is given in Chapter One, which at the same time is an overview of the results of later chapters. It is found in Chapter One that the concept of physical time flow has an important connection with the concept of time reversibility, which makes it necessary to give an analysis of this notion. A detailed discussion of reversibility and time symmetry is given in Chapters Two to Five. Here it is demonstrated that the orthodox analysis of the reversibility of probabilistic theories is flawed. This conclusion allows it to be shown, in Chapter Six, that, contrary to current scientific belief, quantum theory is profoundly irreversible. This result, together with the argument of Chapter One, allows a strong prima facie case for an interpretation of quantum probabilities as involving time flow to be given. However, because of the traditional problems with the notion of time flow, for this interpretation to become respectable it needs to be demonstrated that it is possible to construct a formal model of a physical ontology in which time flow can be represented. This is undertaken in Chapter Seven. In Chapter Eight, various points about the role of probabilities in quantum theory are discussed. Finally, in Chapter Nine, the implications of relativity theory for the proposed theory of time flow are considered. It is found that relativity theory poses a serious problem for a physical theory of time flow, but the implications of relativity theory for the proposed interpretation of quantum probabilities is not clear because of deeper foundational problems with quantum theory.
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.
Dynamical collapse models embody the idea of a physical collapse of the wave function in a mathematically well-defined way. They involve modifications to the standard rules of quantum theory in order to describe collapse as a physical process. This appears to introduce a time reversal asymmetry into the dynamics since the state at any given time depends on collapses in the past but not in the future. Here we challenge this conclusion by demonstrating that, subject to specified model constraints, collapse models can be given a structurally time symmetric formulation in which the collapse events are the primitive objects of the theory. Three different examples of time asymmetries associated with collapse models are then examined and in each case it is shown that the same dynamical rule determining the collapse events works in both the forward and backward in time directions. Any physically observed time asymmetries that arise in such models are due to the asymmetric imposition of initial or final time boundary conditions, rather than from an inherent asymmetry in the dynamical law. This is the standard explanation of time asymmetric behaviour resulting from time symmetric laws.