Many Worlds, the Born Rule, and Self-Locating Uncertainty

TL;DR

This paper derives the Born Rule within the Everett interpretation of quantum mechanics by using the concept of self-locating uncertainty, showing a rational way to assign probabilities that aligns with standard quantum predictions.

Contribution

It provides a novel derivation of the Born Rule based on self-locating uncertainty, applicable to both quantum and cosmological multiverse scenarios.

Findings

Derivation of the Born Rule from rational credence in self-locating uncertainty

Generalization to classical-quantum combined uncertainty cases

Supports Everett interpretation with a rational probability framework

Abstract

We provide a derivation of the Born Rule in the context of the Everett (Many-Worlds) approach to quantum mechanics. Our argument is based on the idea of self-locating uncertainty: in the period between the wave function branching via decoherence and an observer registering the outcome of the measurement, that observer can know the state of the universe precisely without knowing which branch they are on. We show that there is a uniquely rational way to apportion credence in such cases, which leads directly to the Born Rule. Our analysis generalizes straightforwardly to cases of combined classical and quantum self-locating uncertainty, as in the cosmological multiverse.