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Philosophies

The EPR-Bell Experiments: The Role of Counterfactuality and Probability in the Context of Actually Conducted Experiments

Anthony J. Leggett

Published Aug 27, 2024• 1 citation
Publisher

Abstract

Some aspects of the concepts of counterfactuality and probability are explored as they apply to the specific example of the famous “EPR-Bell” experiments realized by physicists over the last half-century. In particular the question is raised: what hypotheses about actually conducted experiments do the results exclude? It is argued that the answer depends on both whether these hypotheses are deterministic or stochastic, and on the “cardinality” of the experiment relative to the theory.

DOI
10.3390/philosophies9050133

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Some aspects of the concepts of counterfactuality and probability are explored as they apply to the specific example of the famous “EPR-Bell” experiments realized by physicists over the last half-century. In particular the question is raised: what hypotheses about actually conducted experiments do the results exclude? It is argued that the answer depends on both whether these hypotheses are deterministic or stochastic, and on the “cardinality” of the experiment relative to the theory.
Most physicists agree that the Einstein–Podolsky–Rosen–Bell paradox exemplifies much of the strange behavior of quantum mechanics, but argument persists about what assumptions underlie the paradox. To clarify what the debate is about, we employ a simple and well-known thought experiment involving two correlated photons to help us focus on the logical assumptions needed to construct the EPR and Bell arguments. The view presented in this paper is that the minimal assumptions behind Bell’s inequality are locality and counterfactual definiteness but not scientific realism, determinism, or hidden variables as are often suggested. We further examine the resulting constraints on physical theory with an illustration from the many-worlds interpretation of quantum mechanics—an interpretation that we argue is deterministic, local, and realist but that nonetheless violates the Bell inequality.
Re-evaluation of the evidence (some of it unpublished) shows that experimenters conducting Einstein-Podolsky-Bohm (EPR) experiments may have been deceived by various pre-conceptions and artifacts. False or unproven assumptions were made regarding, in some cases, fair sampling, in others timing, accidental coincidences and enhancement. Realist possibilities, assuming a purely wave model of light, are presented heuristically, and suggestions given for fruitful lines of research. Quantum Mechanics can be proved false, but Bell tests have turned out to be unsuitable for the task.
Skyrms's formulation of the argument against stochastic hidden variables in quantum mechanics using conditionals with chance consequences suffers from an ambiguity in its “conservation“ assumption. The strong version, which Skyrms needs, packs in a “no-rapport” assumption in addition to the weaker statement of the “experimental facts.“ On the positive side, I argue that Skyrms's proof has two unnoted virtues (not shared by previous proofs): (1) it shows that certain difficulties that arise for deterministic hidden variable theories that exploit a non-classical probability theory extend to the stochastic case; (2) the use of counterfactual conditionals relates the Bell puzzle to Dummett's (1976) discussion of realism in quantum mechanics.
Review and preview In chapters 6 and 7, I described some links between locality and the treatment of probabilities in models of the EPR–Bohm experiment. From chapter 6, the main lesson was that, given the strict correlations of quantum mechanics, factorizability of the two-time probabilities is equivalent to two-time determinism. I also noted there that an adequate factorizable theory – one that avoids Bell's theorem – is possible only if λ-independence fails. In chapter 7, I argued that weak symmetry, local determination, and independent evolution together entail deterministic results and weak deterministic transitions. In chapter 8, I discussed the relationships among the locality conditions of chapter 6 and 7, Lorentz-invariance, and ‘metaphysical’ locality, especially local causality. I have by no means tried to give general answers to the questions raised there. Indeed, part of my thesis is that there is no general answer to be had. Nonetheless, one can use the results of chapters 6 and 7 to investigate the status of various interpretations. Most obviously, they can be used to evaluate whether a given theory is local: if a theory can be shown to violate one or more of the types of determinism entailed by the locality conditions of chapters 6 and 7, then that theory must be non-local in some sense.