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


Authors
Sean M. Carroll
California Institute of Technology
Charles Sebens
California Institute of Technology
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.
Keywords Interpretations of quantum mechanics  Philosophy of physics  Self-locating uncertainty
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Reprint years 2018
DOI 10.1093/bjps/axw004
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References found in this work BETA

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Citations of this work BETA

Everettian Quantum Mechanics and Physical Probability: Against the Principle of “State Supervenience”.Lina Jansson - 2016 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 53:45-53.
In Defence of the Self-Location Uncertainty Account of Probability in the Many-Worlds Interpretation.Kelvin J. McQueen & Lev Vaidman - forthcoming - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics.
Objective Probability and the Mind-Body Relation.Paul Tappenden - 2017 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 57:8-16.

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