• DOI:10.1093/bjps/axw004
• Corpus ID: 53648469

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

@article{Sebens2014SelflocatingUA,
  title={Self-locating Uncertainty and the Origin of Probability in Everettian Quantum Mechanics},
  author={Charles T. Sebens and S. Carroll},
  journal={The British Journal for the Philosophy of Science},
  year={2014},
  volume={69},
  pages={25 - 74}
}

• C. Sebens, S. Carroll
• Published 29 May 2014
• Philosophy
• The British Journal for the Philosophy of Science

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 to the environment alone 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. 1. Introduction2. Preliminaries: Many-Worlds, Self-locating Uncertainty, and Branch-counting 2.1. The many-worlds interpretation2.2. Self-locating uncertainty and the Everettian multiverse2.3. Indifference and the quantitative probability problem2.4. Against branch-counting3. The Epistemic Irrelevance of the Environment 3.1. The epistemic separability principle3.2. Deriving the Born rule4. Varieties of Uncertainty 4.1. Epistemic separability principle and indifference4.2. Mixed uncertainties4.3. Large universe cosmology and the quantum multiverse5. Probability in Practice 5.1. Betting and branching5.2. Theory confirmation6. Comparison to Other Approaches 6.1. Zurek’s envariance-based derivation of the Born rule6.2. The decision-theoretic programme7. Conclusion Appendix Introduction Preliminaries: Many-Worlds, Self-locating Uncertainty, and Branch-counting 2.1. The many-worlds interpretation2.2. Self-locating uncertainty and the Everettian multiverse2.3. Indifference and the quantitative probability problem2.4. Against branch-counting The many-worlds interpretation Self-locating uncertainty and the Everettian multiverse Indifference and the quantitative probability problem Against branch-counting The Epistemic Irrelevance of the Environment 3.1. The epistemic separability principle3.2. Deriving the Born rule The epistemic separability principle Deriving the Born rule Varieties of Uncertainty 4.1. Epistemic separability principle and indifference4.2. Mixed uncertainties4.3. Large universe cosmology and the quantum multiverse Epistemic separability principle and indifference Mixed uncertainties Large universe cosmology and the quantum multiverse Probability in Practice 5.1. Betting and branching5.2. Theory confirmation Betting and branching Theory confirmation Comparison to Other Approaches 6.1. Zurek’s envariance-based derivation of the Born rule6.2. The decision-theoretic programme Zurek’s envariance-based derivation of the Born rule The decision-theoretic programme Conclusion Appendix