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Studies in History and Philosophy of Science Part A

Stapp's theorem without counterfactual commitments: Why it fails nonetheless

Michael Dickson

Published Dec 1, 1993• 9 citations
Publisher

Abstract

Stapp's attempt to derive Bell's Inequality from a weak locality condition (Parameter Independence only) while retaining indeterminism, requires careful scrutiny to ensure unambiguous definitions and valid reasoning. Such scrutiny reveals that the argument is fallacious. This result is obtained without commitment to any particular formal analysis of truth conditions for counterfactuals nor to conditions for world similarity.

DOI
10.1016/0039-3681(93)90064-q

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Stapp's attempt to derive Bell's Inequality from a weak locality condition (Parameter Independence only) while retaining indeterminism, requires careful scrutiny to ensure unambiguous definitions and valid reasoning. Such scrutiny reveals that the argument is fallacious. This result is obtained without commitment to any particular formal analysis of truth conditions for counterfactuals nor to conditions for world similarity.
Blaylock argues that the derivation of Bell’s inequality requires a hidden assumption, counterfactual definiteness, of which Bell was unaware. A careful analysis of Bell’s argument shows that Bell presupposes only locality and the predictions of standard quantum mechanics. Counterfactual definiteness, insofar as it is required, is derived in the course of the argument rather than presumed. Bell’s theorem has no direct bearing on the many worlds interpretation not because that interpretation denies counterfactual definiteness but because it does not recover the predictions of standard quantum mechanics.
Bell's theorem is 50 years old. Still there is a controversy about its implications. Much of it has its roots in confusion regarding the premises from which the theorem can be derived. Some claim that a derivation of Bell's inequalities requires just locality assumption, and nothing more. Violations of the inequalities are then interpreted as ``nonlocality'' or ``quantum nonlocality''. We show that such claims are unfounded and that every derivation of Bell's inequalities requires a premise -- in addition to locality and freedom of choice -- which is either assumed tacitly, or unconsciously, or is embedded in a single compound condition (like Bell's ``local causality''). The premise is equivalent to the assumption of existence of additional variables which do not appear in the quantum formalism (in form of determinism, or joint probability for outcomes of all conceivable measurements, or ``additional causes`'', or ``hidden variables'', ``complete description of the state'' or counterfactual definiteness, etc.). A certain irony is that perhaps the main message of violation of Bell's inequalities is that our notion of locality should be based on an operationally well-defined no-signalling condition, rather than on local causality.
We formally prove the existence of an enduring incongruence pervading a widespread interpretation of the Bell inequality and explain how to rationally avoid it with a natural assumption justified by explicit reference to a mathematical property of Bell’s probabilistic model. Although the amendment does not alter the relevance of the theorem regarding local realism, it brings back Bell theorem from the realm of philosophical discussions about counterfactual conditionals to the concrete experimental arena.
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.
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.