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Buonomano against Bell: Nonergodicity or nonlocality?
Linnaeus University, Faculty of Technology, Department of Mathematics. Natl Res Univ Informat Technol Mech & Opt ITMO, Russia. (Int Ctr Math Modeling)ORCID iD: 0000-0002-9857-0938
2017 (English)In: International Journal of Quantum Information, ISSN 0219-7499, E-ISSN 1793-6918, Vol. 15, no 8, article id 1740010Article in journal (Refereed) Published
Abstract [en]

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 (locall) 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.

Place, publisher, year, edition, pages
World Scientific, 2017. Vol. 15, no 8, article id 1740010
Keywords [en]
Hypothesis of ergodicity, Bell inequality, time and ensemble averages, locality, realism, ontic and epistemic descriptions, ergodic theorems, weak mixing
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-70940DOI: 10.1142/S021974991740010XISI: 000423492600011OAI: oai:DiVA.org:lnu-70940DiVA, id: diva2:1183078
Conference
8th Workshop on From Foundations of Quantum Mechanics to Quantum Information and Quantum Metrology and Sensing (Quantum), MAY 07-13, 2017, Turin, ITALY
Available from: 2018-02-15 Created: 2018-02-15 Last updated: 2018-02-15Bibliographically approved

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Khrennikov, Andrei

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