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Quantum nonlocality or nonergodicity? A critical study of Bell's arguments

Andrei Yu. Khrennikov

Published Jan 1, 2008• 4 citations
OpenAlex

Abstract

We pay attention that through Bell’s arguments one can not distinguish quantum nonlocality and nonergodicity. Therefore experimental violations of Bell’s inequality can be as well interpreted as supporting the hypothesis that stochastic processes induced by quantum measurements could be nonergodic. 1

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The aim of this note is to attract attention of the quantum foundational community to the fact that in Bell’s arguments, one cannot distinguish two hypotheses: (a) quantum mechanics is nonlocal, (b) quantum mechanics is nonergodic. Therefore, experimental violations of Bell’s inequality can be as well interpreted as supporting the hypothesis that stochastic processes induced by quantum measurements are nonergodic. The latter hypothesis was discussed actively by Buonomano since 1980. However, in contrast to Bell’s hypothesis on nonlocality, it did not attract so much attention. The only experiment testing the hypothesis on nonergodicity was performed in neutron interferometry (by Summhammer, in 1989). This experiment can be considered as rejecting this hypothesis. However, it cannot be considered as a decisive experiment. New experiments are badly needed. We point out that a nonergodic model can be realistic, i.e. the distribution of hidden (local!) variables is well-defined. We also discuss coupling of violation of the Bell inequality with violation of the condition of weak mixing for ergodic dynamical systems.
Despite their Nobel prize-winning empirical confirmation, the interpretation of the Bell inequality remains controversial. By carefully analyzing Bell's work on nonlocality, we show how the correct appreciation of Bell's rationale calls for reformulating a widespread argument on quantum nonlocality, yielding a more consistent formulation of the problem. We delve into a formal proof of quantum mechanics' violation of local causality strikingly overlooked in favor of less appropriate arguments. For completeness, we also mention a few alternatives that may rationally justify considering quantum mechanics as a local theory.
Despite their Nobel prize-winning empirical verification, the interpretation of the Bell inequality remains controversial. The alleged nonlocal character of quantum mechanics is inextricably related to the formulation of the Bell theorem. However, as is usually presented, the relation disagrees with Bell's approach and is inappropriately posed. The departure from the clear line of reasoning that Bell tried to convey has contributed to a polarization of part of the scientific community. We review part of Bell's work and show how the correct appreciation of Bell's rationale calls for reformulating a widespread argument on quantum nonlocality, yielding a more balanced perspective of the problem. We highlight a more formal proof of quantum mechanics' violation of local causality. For completeness, we mention a few alternatives that may justify considering quantum mechanics as a local theory.
Despite their Nobel prize-winning empirical falsification, the interpretation of the Bell inequality remains controversial. An objective analysis of Bell's work on nonlocality shows that Bell's rationale calls for reconsidering a widespread argument on quantum nonlocality yielding a clearer formulation free from the usual obscurities that lead to misleading controversies. By dismissing unnecessary metaphysical tenets, it is possible to probe the core of the problem and determine under what rational assumptions locality or nonlocality become feasible alternatives. The approach renders a more balanced perspective on a long-standing polarized interpretative debate.
Despite their Nobel Prize-winning empirical implementation, the Bell inequality interpretation remains controversial. An objective analysis of Bell's work on nonlocality shows that Bell's rationale calls for reconsidering a widespread argument on quantum nonlocality, yielding a precise formulation free from the usual obscurities that lead to misleading controversies. By dismissing unnecessary metaphysical tenets, it is possible to probe the core of the problem and determine under what rational assumptions locality or nonlocality become feasible alternatives clarifying their relation to the Bell inequality. The approach renders a more balanced perspective over a long-standing polarized interpretative debate.