Probability in many-worlds theories

TL;DR

This paper explores how to define probability distributions in deterministic many-worlds theories, aiming to explain quantum theory's empirical success and derive the Born rule through axioms.

Contribution

It introduces three axioms that lead to the Born rule in quantum mechanics and applies them to other deterministic many-worlds scenarios.

Findings

Axioms lead to the Born rule in quantum theory

Results extend to classical stochastic dynamics

Provides a framework for understanding probabilities in many-worlds theories

Abstract

We consider how to define a natural probability distribution over worlds within a simple class of deterministic many-worlds theories. This can help us understand the typical properties of worlds within such states, and hence explain the empirical success of quantum theory within a many-worlds framework. We give three reasonable axioms which lead to the Born rule in the case of quantum theory, and also yield natural results in other cases, including a many-worlds variant of classical stochastic dynamics.