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

Sebens, Charles T. and Carroll, Sean M. (2018) Self-Locating Uncertainty and the Origin of Probability in Everettian Quantum Mechanics. British Journal for the Philosophy of Science, 69 (1). pp. 25-74. ISSN 0007-0882. doi:10.1093/bjps/axw004.

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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.

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Carroll, Sean M.0000-0002-4226-5758
Additional Information:© 2016 The Author. Published by Oxford University Press on behalf of British Society for the Philosophy of Science. Revision Received: 28 May 2015; Accepted: 05 June 2015; Received: 30 January 2016; Published: 02 July 2016. Charles Sebens would like to thank John-Mark Allen, David Baker, Gordon Belot, Adrian Kent (see Kent [2014]), David Manley, Daniel Peterson, Barry Loewer, and Laura Ruetsche for very useful comments on drafts of this article. He would also like to thank Simon Saunders and David Wallace for a wonderful introduction to the Everett interpretation. Sean Carroll would like to thank Scott Aaronson, David Albert, Andreas Albrecht, Hirosi Ooguri, Simon Saunders, and David Wallace for helpful conversations. Funding: National Science Foundation (DGE 0718128 to Charles Sebens); Department of Energy (DE-FG02-92ER40701 to S.C.); Gordon and Betty Moore Foundation through Caltech Moore Center for Theoretical Cosmology and Physics (776 to Sean Carroll and Charles Sebens).
Group:Moore Center for Theoretical Cosmology and Physics, Walter Burke Institute for Theoretical Physics
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NSF Graduate Research FellowshipDGE-0718128
Department of Energy (DOE)DE-FG02-92ER40701
Gordon and Betty Moore Foundation776
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Issue or Number:1
Record Number:CaltechAUTHORS:20141216-201958532
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Official Citation:Charles T Sebens, Sean M Carroll; Self-locating Uncertainty and the Origin of Probability in Everettian Quantum Mechanics, The British Journal for the Philosophy of Science, Volume 69, Issue 1, 1 March 2018, Pages 25–74,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:52922
Deposited By: Joy Painter
Deposited On:17 Dec 2014 17:19
Last Modified:10 Nov 2021 19:45

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