Physical Probability in the Everett Interpretation and Bell Inequalities

TL;DR

This paper introduces a local causality principle modeled after Bell's, explores its loopholes, and presents a theory of physical probability compatible with the Everett interpretation, providing evidence for many worlds without action at a distance.

Contribution

It proposes a new local causality principle with loopholes, and develops a physical probability theory consistent with Everett's many-worlds interpretation.

Findings

Bell inequalities are derived with two loopholes: retrocausation and nonuniqueness of remote outcomes.

A theory of physical probability in Everett's interpretation aligns with the Born rule and violates Bell inequalities.

Violations of Bell inequalities support the many-worlds interpretation without requiring action at a distance.

Abstract

I define a notion of local causality LOC closely modelled on the Bell principle, construed as the condition that single case probabilities cannot be modified by actions at spacelike separation. The new principle, like that of Bell, forces Bell inequalities, but with two loopholes: one is retrocausation, known to Bell, but the other is nonuniqueness of remote outcomes, a loophole only for LOC, not for the Bell 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 violations of Bell inequalities is powerful evidence for many worlds.