Physical probability in the Everett interpretation and Bell inequalities

Abstract:I define a notion of locality LOC, closely modelled on Bell's principle of local causality, construed as the condition that single-case probabilities cannot be modified by actions at spacelike separation. The new principle, like Bell's, forces Bell inequalities, but with two loopholes: one is violation of measurement independence, known to Bell, but the other is non-uniqueness of remote outcomes, a loophole only for LOC, not for Bell's principle. I also set out a theory of physical probability, applicable to the Everett interpretation, in which the Born rule is derived, and which therefore violates Bell inequalities. I show it is consistent with LOC. Surprisingly, both loopholes are exploited. I conclude not only that physical probability in the Everett interpretation involves no action at a distance, in the sense of LOC, but that the observed violation of Bell inequalities is powerful evidence for many worlds.

To appear in Local Quantum Mechanics: Everett, many worlds, and reality, A. Ney (ed.), Oxford University Press. This is a revised version of arXiv: 2601.12159, the latter a revision of arXiv:2512.00575. It is identical to the published version

Quantum Physics (quant-ph); History and Philosophy of Physics (physics.hist-ph)

arXiv:2601.12159 [quant-ph]

(or arXiv:2601.12159v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2601.12159 Focus to learn more arXiv-issued DOI via DataCite

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