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Supermeasured: Violating Bell-Statistical Independence without violating physical statistical independence

Lookup NU author(s): Dr Jonte HanceORCiD

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This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).


Abstract

Bell’s theorem is often said to imply that quantum mechanics violates local causality, and that local causality cannot be restored with a hidden-variables theory. This however is only correct if the hidden-variables theory fulfils an assumption called Statistical Independence. Violations of Statistical Independence are commonly interpreted as correlations between the measurement settings and the hidden variables (which determine the measurement outcomes). Such correlations have been discarded as “fine-tuning” or a “conspiracy”. We here point out that the common interpretation is at best physically ambiguous and at worst incorrect. The problem with the common interpretation is that Statistical Independence might be violated because of a non-trivial measure in state space, a possibility we propose to call “supermeasured”. We use Invariant Set Theory as an example of a supermeasured theory that violates the Statistical Independence assumption in Bell’s theorem without requiring correlations between hidden variables and measurement settings (physical statistical independence).


Publication metadata

Author(s): Hance JR, Hossenfelder S, Palmer TN

Publication type: Article

Publication status: Published

Journal: Foundations of Physics

Year: 2022

Volume: 52

Print publication date: 19/07/2022

Online publication date: 19/07/2022

Acceptance date: 04/07/2022

Date deposited: 08/04/2024

ISSN (print): 0015-9018

ISSN (electronic): 1572-9516

Publisher: Springer New York LLC

URL: https://doi.org/10.1007/s10701-022-00602-9

DOI: 10.1007/s10701-022-00602-9


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Funding

Funder referenceFunder name
Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)
EP/M013472/1
EP/R513386/1
EP/T001011/1
EPSRC
Royal Society Research Professorship

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