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Fortschritte der Physik

Time-Symmetrized Quantum Theory and Counterfactuals

Ruth E. Kastner

Published Nov 1, 1998• 1 citation
Publisher

Abstract

Recent authors have raised objections to the counterfactual interpretation of the Aharonov-Bergmann-Lebowitz (ABL) rule of time symmetrized quantum theory (TSQT). L. Vaidman has responded to those objections by proposing a new kind of time-symmetrized counterfactual, which he has defined in two different ways. It is argued that both definitions are problematic, and that the ABL rule cannot in general be used counterfactually. In particular, it is shown that Vaidman's counterargument to the Sharp and Shanks inconsistency proof fails. However, it is possible to retain a meaningful counterfactual reading of the ABL rule in a limited special case. This special case, which falls under a class identified by Cohen and Hiley, is discussed from a time-symmetry standpoint.

DOI
10.1002/(sici)1521-3978(199811)46:6/8<881::aid-prop881>3.0.co;2-u

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Recent authors have raised objections to the counterfactual interpretation of the Aharonov-Bergmann-Lebowitz (ABL) rule of time symmetrized quantum theory (TSQT). L. Vaidman has responded to those objections by proposing a new kind of time-symmetrized counterfactual, which he has defined in two different ways. It is argued that both definitions are problematic, and that the ABL rule cannot in general be used counterfactually. In particular, it is shown that Vaidman's counterargument to the Sharp and Shanks inconsistency proof fails. However, it is possible to retain a meaningful counterfactual reading of the ABL rule in a limited special case. This special case, which falls under a class identified by Cohen and Hiley, is discussed from a time-symmetry standpoint.
Recent authors have raised objections to the counterfactual interpretation of the Aharonov-Bergmann-Lebowitz (ABL) rule of time symmetrized quantum theory (TSQT). I distinguish between two different readings of the ABL rule, counterfactual and non-counterfactual, and confirm that TSQT advocate L. Vaidman is employing the counterfactual reading to which these authors object. Vaidman has responded to the objections by proposing a new kind of time-symmetrized counterfactual, which he has defined in two different ways. It is argued that neither definition succeeds in overcoming the objections, except in a special case previously noted by Cohen and Hiley. In addition, a connection is made between TSQT and Price's concept of `advanced action', which further supports the special case discussed.
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.
It is proposed that the recent controversy over “time-symmetric quantum counterfactuals” (TSQCs), based on the Aharonov-Bergmann-Lebowitz Rule for measurements of pre- and post-selected systems, can be clarified by taking TSQCs to be counterfactuals with a specific type of compound antecedent. In that case, inconsistency proofs such as that of Sharp and Shanks (1993) are not applicable, and the main issue becomes not whether such statements are true, but whether they are nontrivial. The latter question is addressed and answered in the negative. Thus it is concluded that TSQCs, understood as counterfactuals with a compound antecedent, are true but only trivially so, and provide no new contingent information about specific quantum systems (except in special cases already identified in literature).
It is argued that the proofs [W. D. Sharp and N. Shanks, Philos. Sci. 60, 488 (1993); O. Cohen, Phys. Rev. A 51, 4373 (1995); D. J. Miller, Phys. Lett. A 222, 31 (1996)] of the general nonvalidity of the counterfactual interpretation of the Aharonov-Bergmann-Lebowitz rule [Y. Aharonov, P. G. Bergmann, and J. L. Lebowitz, Phys. Rev. 134, B1410 (1964)] are perfectly valid, and that Vaidman's rejection of these proofs [L. Vaidman, Phys. Rev. A (Comment for which this paper is the Reply)] is unsustainable. It is demonstrated that Vaidman's proposed formulation of ``counterfactual probability,'' on which his rejection of these proofs depends, is problematic and inconsistent in several respects.