Branch-counting in the Everett Interpretation of quantum mechanics

TL;DR

This paper defends a new branch-counting rule in the Everett interpretation of quantum mechanics that aligns with the Born rule and offers an objective probability measure based on decoherence theory.

Contribution

It introduces a continuous, state-dependent branch-counting rule using decoherent histories, improving upon the traditional, flawed branch-counting approach in many-worlds interpretation.

Findings

The new rule agrees with the Born rule.

It provides an objective probability similar to frequentism.

The approach connects with thermodynamic and quantum statistical methods.

Abstract

A defence is offered of a version of the branch-counting rule for probability in the Everett interpretation (otherwise known as many-worlds interpretation) of quantum mechanics that both depends on the state and is continuous in the norm topology on Hilbert space. The well-known branch-counting rule, for realistic models of measurements, in which branches are defined by decoherence theory, fails this test. The new rule hinges on the use of decoherence theory in defining branching structure, and specifically decoherent histories theory. On this basis ratios of branch numbers are defined, free of any convention. They agree with the Born rule, and deliver a notion of objective probability similar to na\"ive frequentism, save that the frequencies of outcomes are not confined to a single world at different times, but spread over worlds at a single time. Nor is it ad hoc: it is recognizably akin to the combinatorial approach to thermodynamic probability, as introduced by Boltzmann in 1879. It is identical to the procedure followed by Planck, Bose, Einstein and Dirac in defining the equilibrium distribution of the Bose-Einstein gas. It also connects in a simple way with the decision-theory approach to quantum probability.