Bayesian Probabilities and the Histories Algebra

TL;DR

This paper generalizes the consistent histories approach in quantum mechanics by applying Cox's axioms to define a universal probability notion, extending Bayesian methods to quantum gravity and cosmology.

Contribution

It introduces a Cox-axiom-based probability framework for histories, generalizes Bayes' theorem for quantum contexts, and discusses implications for quantum gravity and cosmology.

Findings

Probability notion obeys Cox's axioms for all history propositions

Generalized Bayes' theorem applicable to quantum histories

Potential applications in quantum gravity and cosmology

Abstract

We attempt a justification of a generalisation of the consistent histories programme using a notion of probability that is valid for all complete sets of history propositions. This consists of introducing Cox's axioms of probability theory and showing that our candidate notion of probability obeys them. We also give a generalisation of Bayes' theorem and comment upon how Bayesianism should be useful for the quantum gravity/cosmology programmes.