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Philosophy of Science

The Rise and Fall of Time-Symmetrized Quantum Mechanics

W. David Sharp, Niall Shanks

Published Sep 1, 1993• 41 citations
Publisher

Abstract

In the context of a discussion of time symmetry in the quantum mechanical measurement process, Aharonov et al. (1964) derived an expression concerning probabilities for the outcomes of measurements conducted on systems which have been pre- and postselected on the basis of both preceding and succeeding measurements. Recent literature has claimed that a resulting “time-symmetrized” interpretation of quantum mechanics has significant implications for some basic issues, such as contextuality and determinateness, in elementary, nonrelativistic quantum mechanics. Bub and Brown (1986) have shown that under the standard interpretation of the aforementioned expression, these claims employ ensembles which are not well defined. It is argued here that under a counterfactual interpretation of the expression, these claims may be understood as employing well-defined ensembles; it is shown, however, that such an interpretation cannot be reconciled with the standard interpretation of quantum mechanics.

DOI
10.1086/289749

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In the context of a discussion of time symmetry in the quantum mechanical measurement process, Aharonov et al. (1964) derived an expression concerning probabilities for the outcomes of measurements conducted on systems which have been pre- and postselected on the basis of both preceding and succeeding measurements. Recent literature has claimed that a resulting “time-symmetrized” interpretation of quantum mechanics has significant implications for some basic issues, such as contextuality and determinateness, in elementary, nonrelativistic quantum mechanics. Bub and Brown (1986) have shown that under the standard interpretation of the aforementioned expression, these claims employ ensembles which are not well defined. It is argued here that under a counterfactual interpretation of the expression, these claims may be understood as employing well-defined ensembles; it is shown, however, that such an interpretation cannot be reconciled with the standard interpretation of quantum mechanics.
A currently discussed interpretation of quantum theory, Time-Symmetrized Quantum Theory, makes certain claims about the properties of systems between pre- and post- selection measurements. These claims are based on a counterfactual usage of the Aharonov-Bergmann-Lebowitz (ABL) rule for calculating the probabilities of measurement outcomes between such measurements. It has been argued by several authors that the counterfactual usage of the ABL rule is, in general, incorrect. This paper examines what might appear to be a loophole in those arguments and shows that this apparent loophole cannot be used to support a counterfactual interpretation of the ABL rule. It is noted that the invalidity of the counterfactual usage of the ABL rule implies that the characterization of those outcomes receiving probability 1 in a counterfactual application of the rule as `elements of reality' is, in general, unfounded.
Recently, several authors have criticized time-symmetrized quantum theory originated by the work of Aharonov et al. (1964). The core of this criticism was the proof, which appeared in various forms, showing that counterfactual interpretation of time-symmetrized quantum theory cannot be reconciled with the standard quantum theory. I argue here that the apparent contradiction appears due to inappropriate usage of traditional time asymmetric approach to counterfactuals, and that the contradiction disappears when the problem is analyzed in terms of time-symmetric counterfactuals. I analyze various aspects of time-symmetry of quantum theory and defend the time-symmetrized formalism.
Recently, several authors have criticized the time-symmetrized quantum theory originated by the work of Aharonov et al. (1964). The core of this criticism was a proof, appearing in various forms, which showed that the counterfactual interpretation of time-symmetrized quantum theory cannot be reconciled with standard quantum theory. I argue here that the apparent contradiction is due to a logical error. I analyze the concept of counterfactuals in quantum theory and introduce time-symmetrized counterfactuals. These counterfactuals do not lead to any contradiction with the predictions of quantum theory. I discuss applications of time-symmetrized counterfactuals to several surprising examples and show the usefulness of the time-symmetrized quantum formalism.
We examine the assertion that the "reduction of the wave packet," implicit in the quantum theory of measurement introduces into the foundations of quantum physics a time-asymmetric element, which in turn leads to irreversibility. We argue that this time assymmetry is actually related to the manner in which statistical ensembles are constructed. If we construct an ensemble time symmetrically by using both initial and final states of the system to delimit the sample, then the resulting probability distribution turns out to be time symmetric as well. The conventional expressions for prediction as well as those for "retrodiction" may be recovered from the time-symmetric expressions formally by separating the final (or the initial) selection procedure from the measurements under consideration by sequences of "coherence destroying" manipulations. We can proceed from this situation, which resembles prediction, to true prediction (which does not involve any postselection) by adding to the time-symmetric theory a postulate which asserts that ensembles with unambiguous probability distributions may be constructed on the basis of preselection only. If, as we believe, the validity of this postulate and the falsity of its time reverse result from the macroscopic irreversibility of our universe as a whole, then the basic laws of quantum physics, including those referring to measurements, are as completely time symmetric as the laws of classical physics. As a by-product of our analysis, we also find that during the time interval between two noncommuting observations, we may assign to a system the quantum state corresponding to the observation that follows with as much justification as we assign, ordinarily, the state corresponding to the preceding measurement.
Recently, several authors have criticized the time-symmetrized quantum theory originated by the work of Aharonov et al. (1964). The core of this criticism was a proof, appearing in various forms, which showed that the counterfactual interpretation of time-symmetrized quantum theory cannot be reconciled with standard quantum theory. I, (Vaidman, 1996a, 1997) have argued that the apparent contradiction is due to a logical error and introduced consistent time-symmetrized quantum counterfactuals. Here I repeat my arguments defending the time-symmetrized quantum theory and reply to the criticism of these arguments by Kastner (1999).
We examine some surprising results that have been obtained for pre- and postselected quantum systems. We show that these results depend on a counterfactual interpretation of the rule of Aharonov, Bergmann, and Lebowitz [Phys. Rev. 134, B1410 (1964)] (the ABL rule) and that this interpretation is not valid in general. We then argue, with the help of the consistent histories interpretation of quantum mechanics, that there is a special class of situations where application of the counterfactual interpretation of the ABL rule can be justified. We then reexamine the aforementioned surprising results.