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American Journal of Physics

Meaning of counterfactual statements in quantum physics

Henry Pierce Stapp

Published Oct 1, 1998• 74 citations
Publisher

Abstract

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.

DOI
10.1119/1.18989

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David Mermin's recent paper with the same title as this one makes it clear that his claim to have found a gap in my reasoning rests on his claim that my argument violates a criterion for meaningfulness of counterfactual statements that I myself had set down. I set down no such requirement. But I am willing to accept it as a conservative sufficient condition. This already entails, within my proof, that nature must have a deep structure that extends beyond what actually occurs. It imposes, without appeal to the notion of determinism or hidden variables, constraints connecting, at the macroscopic level, what did occur to what would have occurred if certain quantum choices had gone differently. All the statements in the proof have natural meanings within the context of an examination of that deep structure.

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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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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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In a recent article under the above title (but without the question mark) Henry Stapp has presented arguments which lead him to conclude that under suitable conditions “the truth of a statement that refers only to phenomena confined to an earlier time” must “depend on which measurement an experimenter freely chooses to perform at a later time.” I suggest that this conclusion contains an essential ambiguity as regards the meaning of the expression “statement referring only to phenomena confined to an earlier time,” when such a statement talks about the outcome of an experiment that was not actually performed. As a result Stapp’s argumentation does not imply that future choices can affect present facts. But it does provide a wonderful and instructively different opportunity to reexamine a central point of Bohr’s famous reply to Einstein, Podolsky, and Rosen.

arXiv:quant-ph/9711052•American Journal of Physics•Oct 1, 1998•99 citations
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.
David Mermin's recent paper with the same title as this one makes it clear that his claim to have found a gap in my reasoning rests on his claim that my argument violates a criterion for meaningfulness of counterfactual statements that I myself had set down. I set down no such requirement. But I am willing to accept it as a conservative sufficient condition. This already entails, within my proof, that nature must have a deep structure that extends beyond what actually occurs. It imposes, without appeal to the notion of determinism or hidden variables, constraints connecting, at the macroscopic level, what did occur to what would have occurred if certain quantum choices had gone differently. All the statements in the proof have natural meanings within the context of an examination of that deep structure.
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.
In a recent article under the above title (but without the question mark) Henry Stapp has presented arguments which lead him to conclude that under suitable conditions “the truth of a statement that refers only to phenomena confined to an earlier time” must “depend on which measurement an experimenter freely chooses to perform at a later time.” I suggest that this conclusion contains an essential ambiguity as regards the meaning of the expression “statement referring only to phenomena confined to an earlier time,” when such a statement talks about the outcome of an experiment that was not actually performed. As a result Stapp’s argumentation does not imply that future choices can affect present facts. But it does provide a wonderful and instructively different opportunity to reexamine a central point of Bohr’s famous reply to Einstein, Podolsky, and Rosen.