Finite frequentism explains quantum probability

TL;DR

This paper extends classical frequentist probability to quantum mechanics by proposing a finite frequentism framework based on decoherent quantum histories, replacing infinite ensembles with finite superpositions of microstates.

Contribution

It introduces a finite frequentism approach that applies to quantum systems, aligning with the Everett interpretation and decoherence theory.

Findings

Finite frequentism models quantum probability using finite microstates.

Quantum states are represented as superpositions of decohering microstates.

The approach aligns with the Everett interpretation of quantum mechanics.

Abstract

I show that frequentism, as an explanation of probability in classical statistical mechanics, can be extended in a natural way to a decoherent quantum history space, the analogue of a classical phase space. The result is a form of finite frequentism, in which the Gibbs concept of an infinite ensemble of gases is replaced by the quantum state expressed as a superposition of a finite number of decohering microstates. It is a form of finite and actual (as opposed to hypothetical) frequentism insofar as all the microstates exist, even though they may differ macroscopically, in keeping with the decoherence-based Everett interpretation of quantum mechanics.