Self-Locating Uncertainty and the Origin of Probability in Everettian Quantum
Mechanics
Charles T. Sebens <http://arxiv.org/find/quant-ph/1/au:+Sebens_C/0/1/0/all/0/1>,Sean M.
Carroll <http://arxiv.org/find/quant-ph/1/au:+Carroll_S/0/1/0/all/0/1>
(Submitted on 29 May 2014)
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 give new reasons why that would be inadvisable. Applying lessons from this
analysis, we demonstrate (using arguments similar to those in Zurek's
envariance-based
derivation) that the Born rule is the uniquely rational way of apportioning
credence
in Everettian quantum mechanics. In particular, 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.
http://arxiv.org/pdf/1405.7577v1.pdf
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