Physical Probability in the Everett Interpretation, and Bell Inequalities

Abstract The chapter defines a notion of local causality (LOC), closely modeled 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, entails Bell inequalities, but with two loopholes: one is retrocausation, already noted by Bell, while the other is the non-uniqueness of remote outcomes—a loophole that applies to LOC but not to Bell’s original principle. The author also develops a theory of physical probability, applicable to the Everett interpretation, that aligns with the Born rule and therefore violates Bell inequalities. It is then shown that this theory is consistent with LOC. Notably, both loopholes are exploited. The author concludes not only that probability in the Everett interpretation involves no action at a distance, but also that the observed violations of Bell inequalities provide strong evidence for the many-worlds interpretation.