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arXiv:quant-ph/9812024

TSQT `Elements of Possibility'?

Ruth E. Kastner

Published Dec 12, 1998• 5 citations
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Abstract

I defend my arguments in quant-ph/9806002, which have recently been criticized by L. Vaidman (quant-ph/9811092). I emphasize that the correct usage of the ABL rule applies not to a genuine counterfactual statement but rather to a conjunction of material conditionals. I argue that the only kind of valid counterfactual statement one can make using the ABL rule is a ``might'' counterfactual, which is not adequate for the attribution of `elements of reality' to a quantum system.

DOI
10.48550/arxiv.quant-ph/9812024

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I defend my arguments in quant-ph/9806002, which have recently been criticized by L. Vaidman (quant-ph/9811092). I emphasize that the correct usage of the ABL rule applies not to a genuine counterfactual statement but rather to a conjunction of material conditionals. I argue that the only kind of valid counterfactual statement one can make using the ABL rule is a ``might'' counterfactual, which is not adequate for the attribution of `elements of reality' to a quantum system.
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 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.
David Mermin suggests that my recent proof pertaining to quantum nonlocality is undermined by an essential ambiguity pertaining to the meaning of counterfactual statements in quantum physics. The ambiguity he cites arises from his imposition of a certain criterion for the meaningfulness of such counterfactual statements. That criterion conflates the meaning of a counterfactual statement with the details of a proof of its validity in such a way as to make the meaning of such a statement dependent upon the context in which it occurs. That dependence violates the normal demand in logic that the meaning of a statement be defined by the words in the statement itself, not by the context in which the statement occurs. My proof conforms to that normal requirement. I describe the context-independent meaning within my proof of the counterfactual statements in question.
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.