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Time, symmetry and structure: a study in the foundations of quantum theory

Bryan Wilson Roberts

Published Oct 2, 2012• 9 citations
OpenAlex

Abstract

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.

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Does quantum time have a preferred direction

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Abstract. This paper states and proves a precise sense in which, if all the mea-surable properties of an ordinary quantum mechanical system are ultimately deriv-able from position, then time in quantum mechanics can have no preferred direc-tion. 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. 1.

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Symmetries have a crucial role in today's physics. In this thesis, we are mostly concerned with time reversal invariance (T-symmetry). A physical system is time reversal invariant if its underlying laws are not sensitive to the direction of time. There are various accounts of time reversal transformation resulting in different views on whether or not a given theory in physics is time reversal invariant. With a focus on quantum mechanics, I describe the standard account of time reversal and compare it with my alternative account, arguing why it deserves serious attention. Then, I review three known ways to T-violation in quantum mechanics, and explain two unique experiments made to detect it in the neutral K and B mesons.

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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.

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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.

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Hidden Determinism, Probability, and Time's Arrow

Hans Primas

In present-day physics the fundamental dynamical laws are taken as a time-translation-invariant and time-reversal-invariant one-parameter groups of automorphisms of the underlying mathematical structure. In this context-independent and empirically inaccessible description there is no past, present or future, hence no distinction between cause and effect. To get the familiar description in terms of causes and effects, the time-reversal symmetry of the fundamental dynamics has to be broken. Thereby one gets two representations, one satisfying the generally accepted rules of retarded causality (no effect can precede its cause). The other one describes the strange rules of advanced causality. For entangled (but not necessarily interacting) quantum systems the arrow of time must have the same direction for all subsystems. But for classical systems, or for classical subsystems of quantum systems, this argument does not hold. As a cosequence, classical systems allow the conceptual possibility of advanced causality in addition to retarded causality. Every mathematically formulated dynamics of statistically reproducible events can be extended to a description in terms of a one-parameter group of automorphisms of an enlarged mathematical structure which describes a fictitious hidden determinism. Consequently, randomness in the sense of mathematical probability theory is only a weak generalization of determinism. The popular ideas that in quantum theory there are gaps in the causal chain which allow the accommodation of the freedom of human action are fantasies which have no basis in present-day quantum mechanics. Quantum events are governed by strict statistical laws. Freedom of action is a constitutive necessity of all experimental science which requires a violation of the statistical predictions of physics. We conclude that the presently adopted first principles of theoretical physics can neither explain the autonomy of the psyche nor account for the freedom of action necessary for experimental science.

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In this chapter, I discuss time in nonrelativistic quantum theories. Within an instrumentalist theory like von Neumann's axiomatic quantum mechanics, I focus on the meaning of time as an observable quantity, on the idea of time quantization, and whether the wavefunction collapse suggests that there is a preferred temporal direction. I explore this last issue within realist quantum theories as well, focusing on time reversal symmetry, and I analyze whether some theories are more hospitable for time travel than others.

Routledge eBooks•Sep 2, 2025•0 citations
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.
Symmetries have a crucial role in today's physics. In this thesis, we are mostly concerned with time reversal invariance (T-symmetry). A physical system is time reversal invariant if its underlying laws are not sensitive to the direction of time. There are various accounts of time reversal transformation resulting in different views on whether or not a given theory in physics is time reversal invariant. With a focus on quantum mechanics, I describe the standard account of time reversal and compare it with my alternative account, arguing why it deserves serious attention. Then, I review three known ways to T-violation in quantum mechanics, and explain two unique experiments made to detect it in the neutral K and B mesons.
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.
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.
In present-day physics the fundamental dynamical laws are taken as a time-translation-invariant and time-reversal-invariant one-parameter groups of automorphisms of the underlying mathematical structure. In this context-independent and empirically inaccessible description there is no past, present or future, hence no distinction between cause and effect. To get the familiar description in terms of causes and effects, the time-reversal symmetry of the fundamental dynamics has to be broken. Thereby one gets two representations, one satisfying the generally accepted rules of retarded causality (no effect can precede its cause). The other one describes the strange rules of advanced causality. For entangled (but not necessarily interacting) quantum systems the arrow of time must have the same direction for all subsystems. But for classical systems, or for classical subsystems of quantum systems, this argument does not hold. As a cosequence, classical systems allow the conceptual possibility of advanced causality in addition to retarded causality. Every mathematically formulated dynamics of statistically reproducible events can be extended to a description in terms of a one-parameter group of automorphisms of an enlarged mathematical structure which describes a fictitious hidden determinism. Consequently, randomness in the sense of mathematical probability theory is only a weak generalization of determinism. The popular ideas that in quantum theory there are gaps in the causal chain which allow the accommodation of the freedom of human action are fantasies which have no basis in present-day quantum mechanics. Quantum events are governed by strict statistical laws. Freedom of action is a constitutive necessity of all experimental science which requires a violation of the statistical predictions of physics. We conclude that the presently adopted first principles of theoretical physics can neither explain the autonomy of the psyche nor account for the freedom of action necessary for experimental science.
In this chapter, I discuss time in nonrelativistic quantum theories. Within an instrumentalist theory like von Neumann's axiomatic quantum mechanics, I focus on the meaning of time as an observable quantity, on the idea of time quantization, and whether the wavefunction collapse suggests that there is a preferred temporal direction. I explore this last issue within realist quantum theories as well, focusing on time reversal symmetry, and I analyze whether some theories are more hospitable for time travel than others.