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

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 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 Introduction 2 Preliminaries: Many-Worlds, Self-locating Uncertainty, and Branch-counting 2.1 The many-worlds interpretation 2.2 Self-locating uncertainty and the Everettian multiverse 2.3 Indifference and the quantitative probability problem 2.4 Against branch-counting 3 The Epistemic Irrelevance of the Environment 3.1 The epistemic separability principle 3.2 Deriving the Born rule 4 Varieties of Uncertainty 4.1 Epistemic separability principle and indifference 4.2 Mixed uncertainties

Realism about the wave function

“…There has been significant progress in addressing the probability challenge with the tools of typicality, decision theory, and self-locating probabilities. For some recent examples, see Barrett (2017), Wallace (2012), Sebens and Carroll (2016), and the references therein. 15 It has been developed and defended by Loewer (1996), Ney, (2012, and North (2013), although North is primarily concerned with the first part of the thesis, i.e., the fundamental space is a high-dimensional space.…”

“…There has been significant progress in addressing the probability challenge with the tools of typicality, decision theory, and self‐locating probabilities. For some recent examples, see Barrett (), Wallace (), Sebens and Carroll (), and the references therein.…”

Reformulating Bell's theorem: The search for a truly local quantum theory

“…In branching models, many approaches deny that Alice is uncertain about the future, but argue that Alice is uncertain about her location in the multiverse often enough to solve the incoherence problem. This approach is taken by McQueen and Vaidman (2019) in the context of semi-local branching and by Sebens and Carroll (2018) in the context of global branching.…”

Typical worlds

“…Such effective priors may evolve to be unbiased over the evolved descriptions on this sort of model if agents are, for some reason, rewarded for using maximally informative signals. 24 It is presumably for this reason that both Graham (1973, 251-2) and Sebens and Carroll (2016) require the number of Everett worlds be finite.…”