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arXiv:1111.5121

A logical analysis of Stapp's non-locality theorem

Giusepp Nisticò

Published Nov 22, 2011• 0 citations
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Abstract

According to an argument proposed by Stapp, Quantum Mechanics violates the Locality Principle if the two hypotheses of {\sl Free Choices} and {\sl No backward-in-time influence} are assumed to hold, without the need of introducing hidden variables or criteria of reality. We develop an approach that endows the new hypotheses with a logico-mathematical formulation which allow us to perform an analysis of Stapp's argument, based on ordinary, not counterfactual, logic. According to our results, the analyzed argument is not able to conclude that Quantum Mechanics violates the Locality Principle.

DOI
10.48550/arxiv.1111.5121

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According to an argument proposed by Stapp, Quantum Mechanics violates the Locality Principle if the two hypotheses of {\sl Free Choices} and {\sl No backward-in-time influence} are assumed to hold, without the need of introducing hidden variables or criteria of reality. We develop an approach that endows the new hypotheses with a logico-mathematical formulation which allow us to perform an analysis of Stapp's argument, based on ordinary, not counterfactual, logic. According to our results, the analyzed argument is not able to conclude that Quantum Mechanics violates the Locality Principle.
In this tribute to Henry P. Stapp, I outline the historical development of the problem of non-locality in quantum mechanics starting from the EPR argument through Bell’s theorem up to Stapp’s own contributions. My focus is on Stapp’s 1997 proof of quantum non-locality that uses the logic of counterfactuals. On the basis of my own version of the proof presented in 2010, I give its informal analysis, emphasizing the role of Einstein’s criterion of reality in the derivation. I conclude that the proof achieves its objective, and I briefly point at its significance for the philosophical mind-body problem.
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.
A 1997 paper by Henry Stapp attempts to achieve a definitive argument for his long-sustained thesis that quantum mechanics implies a nonlocality inconsistent with the locality of relativity theory. His argument assumes both the validity of counterfactual reasoning under certain circumstances and the free choice of performance of experiments, and it specifically refrains from any assumptions about “elements of physical reality” as understood by Einstein, Podolsky, and Rosen. In Sec. I we drastically condense his argument but retain his central principle of inference, called “LOC2,” which he claims is a consequence of relativistic locality. By careful attention to counterfactual reasoning we then throw doubt upon this claim and hence upon his argument as a whole. In Sec. II we answer Stapp’s reply to our critique of the 1997 paper. Section III is a postscript, commenting briefly on Stapp’s answer to Sec. II.
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.
Stapp ([1971], [1977], [1985a], henceforth Stapp 1) claims to give a proof of the existence of nonlocal influences acting on correlated spin-1/2 particles in the singlet state which does not require any particular interpretation of quantum mechanics (QM). (Except Stapp holds that the proof fails under a many-worlds interpretation of QM—a claim we analyse in 1.2.) Recently, in responding to Redhead's ([1987], pp. 90-6) criticism that the Stapp 1 proof fails under an indeterministic interpretation of QM, Stapp [1989] (henceforth Stapp 2), has revised the logical structure of his proof including its crucial locality assumption. Our main aim is to show that this revision is a step in the wrong direction because it faces two difficulties which undermine the resulting proof's significance (3.1) and validity (3. 2). We also clarify and extend the Stapp 1 proof (1. 1) with the aid of Lewis' analysis of counterfactuals (1. 2) and causal dependence (2. 2 and 2. 3). In so doing, we are able to identify two new defects in the Stapp 1 proof (1. 3 and 2. 1) in addition to corroborating Redhead's criticism (2. 2). Also, the additional assumptions which save the Stapp 1 proof's validity are detailed (2. 3) and some new difficulties for the determinist are pointed out by exploiting a slightly extended version of the proof (2. 4). In providing this full analysis of the Stapp 1 proof, we also construct the necessary framework within which to provide a critique of Stapp 2's proof (3).