Physical Probability and Locality in No-Collapse Quantum Theory

TL;DR

This paper proposes a local interpretation of no-collapse quantum mechanics by introducing a physical probability postulate with a locality condition, deriving the Born rule without hidden variables, and clarifying the nature of Bell inequality violations.

Contribution

It introduces a novel locality condition for physical probability in no-collapse quantum theory, leading to a local derivation of the Born rule without hidden variables.

Findings

Probabilities in no-collapse quantum mechanics can be local.

Bell inequality violations are due to entanglement, not nonlocality.

The Born rule emerges from equiprobable microstates in equiamplitude expansions.

Abstract

Probability is distinguished into two kinds: physical and epistemic, also, but less accurately, called objective and subjective. Simple postulates are given for physical probability, the only novel one being a locality condition. Translated into no-collapse quantum mechanics, without hidden variables, the postulates imply that the elements in any equiamplitude expansion of the quantum state are equiprobable. Such expansions therefore provide ensembles of microstates that can be used to define probabilities in the manner of frequentism, in von Mises sense (where the probability of P is the frequency of occurrence of P in a suitable ensemble). The result is the Born rule. Since satisfying our postulates, and in particular the locality condition (meaning no action-at-a-distance), these probabilities for no-collapse quantum mechanics are perfectly local, even though they violate Bell inequalities. The latter can be traced to a violation of outcome independence, used to derive the inequalities. But in no-collapse theory that is not a locality condition; it is a criterion for entanglement, not locality.