Self-Locating Uncertainty and the Origin of Probability in Everettian Quantum Mechanics

TL;DR

This paper addresses the origin of the Born rule in Everettian quantum mechanics by analyzing self-locating uncertainty and demonstrating that the Born rule is the uniquely rational probability assignment, using principles from decoherence and envariance.

Contribution

It introduces a novel approach to deriving the Born rule in Everettian quantum mechanics based on self-locating uncertainty and environmental invariance principles.

Findings

The Born rule is uniquely derived as the rational probability assignment in Everettian quantum mechanics.

A new method for assigning probabilities in systems with classical and quantum self-locating uncertainty is proposed.

The approach provides solutions to quantum Sleeping Beauty problems and probabilities in quantum multiverses.

Abstract

A longstanding issue in attempts to understand the Everett (Many-Worlds) approach to quantum mechanics is the origin of the Born rule: why is the probability given by the square of the amplitude? Following Vaidman, we note that observers are in a position of self-locating uncertainty during the period between the branches of the wave function splitting via decoherence and the observer registering the outcome of the measurement. In this period it is tempting to regard each branch as equiprobable, but we argue that the temptation should be resisted. Applying lessons from this analysis, we demonstrate (using methods similar to those of Zurek's envariance-based derivation) that the Born rule is the uniquely rational way of apportioning credence in Everettian quantum mechanics. In doing so, we rely on a single key principle: changes purely to the environment do not affect the probabilities one ought to assign to measurement outcomes in a local subsystem. We arrive at a method for assigning probabilities in cases that involve both classical and quantum self-locating uncertainty. This method provides unique answers to quantum Sleeping Beauty problems, as well as a well-defined procedure for calculating probabilities in quantum cosmological multiverses with multiple similar observers.