Saunders, Simon (2026) Physical Probability in the Everett interpretation and Bell inequalities. [Preprint]
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Abstract
I define a notion of local causality LOC, closely modelled on Bell’s principle, 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 retrocausation, 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 agreement with the Born rule, and therefore violating Bell inequalities. I show it is consistent with LOC. Surprisingly, both loopholes are exploited. I conclude not only that probability in the Everett interpretation involves no action-at-a-distance, but that the observed violation of Bell inequalities is powerful evidence for many worlds.
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