Counterfactual Logic and the Hardy Paradox: Remarks on Shimony and Stein's Criticism of Stapp's Proof

Tomasz Bigaj

Published May 1, 2004• 2 citations

Abstract

This is an extended critique of comments made by Abner Shimony and Howard Stein on Henry Stapp’s proof of the non-locality of quantum mechanics. Although I claim that ultimately Stapp’s proof does not establish its purported conclusion, yet Shimony and Stein’s criticism contains a number of weak points, which need to be clarified.

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Reply to “Comment on ‘Nonlocality counterfactuals, and quantum mechanics’ ”

William George Unruh

Stapp [preceding Comment, Phys. Rev. A 60, 2595 (1999)] has argued that my criticism of his nonlocality proof is wrong. I point out that counterfactual arguments are fraught with dangers, and that any such claim should use them in a conservative manner. A reanalysis of his claims continues to lead me to the conclusion that the nonlocality of quantum mechanics remains unproven.

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Recent discussions by Mermin [1] and Stapp [2] in this journal on non-locality and counterfactuality are shown to contain linguistic problems that require verification. As such they can at most provide us with two subjective choices for the meaning of 'counterfactual statements' in quantum mechanics. We shall show that the word 'counterfactual' is in fact inappropriate here and should be replaced by the word 'hypothetical'. Mermin's choice imposes a strictly contextual meaning based upon an interpretation of counterfactuality which he used to refute, without proof as we shall see, Stapp's logical proof [3] of non-locality in quantum theory. In linguistic theory both authors' choices of meaning: counterfactual versus hypothetical are equally acceptable and therefore some of the issues they discussed lie outside the domain of physics. The issues they discussed are further confused by the fact that in his reply Stapp [2] seems to have adopted Mermin's counterfactual interpretation against his own original [3] hypothetical interpretation. In the rest of this paper we shall adopt the hypothetical sense of Stapp's original statements but we modify his crucial statement LOC2 appropriately, then following his argumentations, we shall show that there is no conflict between relativity and quantum mechanics. We suggest that this should be the natural (pragmatic) choice of meaning in defining the predictions of events in the Hardy experiment.

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Comment on “Nonlocal character of quantum theory,” by Henry P. Stapp [Am. J. Phys. 65 (4), 300–304 (1997)]

Abner Shimony, Howard Stein

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Nonlocality, counterfactuals, and quantum mechanics

William George Unruh

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Comment on “Nonlocality, counterfactuals, and quantum mechanics”

Henry Pierce Stapp

A recent proof [H. P. Stapp, Am. J. Phys. 65, 300 (1997)], formulated in the symbolic language of modal logic, claims to show that contemporary quantum theory, viewed as a set of rules that allow us to calculate statistical predictions among certain kinds of observations, cannot be imbedded in any rational framework that conforms to the principles that (1) the experimenters' choices of which experiments they will perform can be considered to be free choices, (2) outcomes of measurements are unique, and (3) the free choices just mentioned have no backward-in-time effects of any kind. This claim is similar to Bell's theorem, but much stronger, because no reality assumption alien to quantum philosophy is used. The paper being commented on [W. Unruh, Phys. Rev. A 59, 126 (1999)] argues that some such reality assumption has been ``smuggled'' in. That argument is examined here and shown, I believe, to be defective.

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