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The British Journal for the Philosophy of Science

Epistemic Separability and Everettian Branches: A Critique of Sebens and Carroll

Richard Dawid, Simon Friederich

Published Jan 28, 2020• 4 citations
Publisher

Abstract

We discuss the proposal by Sebens and Carroll to derive the Born rule in Everettian quantum mechanics from a principle they call ‘ESP-QM’. We argue that the proposal fails: ESP-QM is not, as Sebens and Carroll argue, a ‘less general version’ of an independently plausible principle, ESP, and can only be motivated by the empirical success of quantum mechanics, including use of the Born rule. Therefore, ESP-QM cannot have the status of a meta-theoretical principle of reasoning and provides no viable basis for deriving the Born rule.

DOI
10.1093/bjps/axaa002

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We discuss the proposal by Sebens and Carroll to derive the Born rule in Everettian quantum mechanics from a principle they call ‘ESP-QM’. We argue that the proposal fails: ESP-QM is not, as Sebens and Carroll argue, a ‘less general version’ of an independently plausible principle, ESP, and can only be motivated by the empirical success of quantum mechanics, including use of the Born rule. Therefore, ESP-QM cannot have the status of a meta-theoretical principle of reasoning and provides no viable basis for deriving the Born rule.
The measurement problem remains one of the most profound puzzles in the foundation of quantum mechanics. It contains two distinct aspects: the collapse of the wavefunction and the origin of probabilities. While Everettian Quantum Mechanics (EQM) and the Many Worlds Interpretation (MWI) work around the collapse aspect, by positing that the universe branches through pure unitary evolution, it leaves unresolved the question of why measurement outcomes occur with frequencies given by the Born Rule. This paper explores a recent derivation of the Born Rule by Carroll and Sebens based on principles of Self-Locating Uncertainty (SLU) and the Epistemic Separability Principle (ESP). By examining this framework in detail, beginning with an equal amplitude case and extending to an unequal amplitude case, we show how these principles account for the probabilities given by the Born Rule, hence showing that SLU and the ESP, within the scope of EQM, offer a solution to the measurement problem. We further show the significance and implications of deriving the Born Rule and highlight the relevance of the measurement problem to more recent developments like quantum gravity.
Objective probability in quantum mechanics is often thought to involve a stochastic process whereby an actual future is selected from a range of possibilities. Everett's seminal idea is that all possible definite futures on the pointer basis exist as components of a macroscopic linear superposition. I demonstrate that these two conceptions of what is involved in quantum processes are linked by two alternative interpretation of the mind-body relation. This leads to a fission, rather than divergence, interpretation of Everettian theory and to a novel explanation of why a principle of indifference does not apply to self-location uncertainty for a post-measurement, pre-observation subject, just as Sebens and Carroll claim. Their Epistemic Separability Principle is shown to arise out of this explanation and the derivation of the Born rule for Everettian theory is thereby put on a firmer footing.
Abstract In Everettian quantum mechanics, justifications for the Born rule appeal to self-locating uncertainty or decision theory. Such justifications have focused exclusively on a pure-state Everettian multiverse, represented by a wavefunction. Recent works in quantum foundations suggest that it is viable to consider a mixed-state Everettian multiverse, represented by a (mixed-state) density matrix. Here, we discuss the conceptual foundations for decoherence and branching in a mixed-state multiverse, and extend arguments for the Born rule to this setting. This extended framework provides a unification of ‘classical’ and ‘quantum’ probabilities, and additional theoretical benefits, for the Everettian picture.
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. ConclusionAppendix
Any viable interpretation of quantum theory needs to account for the Born rule, from which the theory gets its probabilistic empirical predictions. In this paper, we give an overview of possible approaches to this problem in the context of the Many Worlds interpretation. We argue that, for structural reasons, none of them can possibly succeed. More precisely, we argue that the Many Worlds interpretation must obtain the Born rule by proceeding either axiomatically, deductively, or inductively, and that all three of these approaches run into general, fundamental obstructions.
A longstanding issue in the Everettian (Many-Worlds) interpretation is to justify and make sense of the Born rule that underlies the statistical predictions of standard quantum mechanics. The paper offers a reappraisal of Everett’s original account in light of the recent literature on the concept of typicality. It argues that Everett’s derivation of the Born rule is sound and, in a certain sense, even an optimal result, and defends it against the charge of circularity. The conclusion is that Everett’s typicality argument can successfully ground post-factum explanations of Born statistics, while questions remain about the predictive power of the Many-Worlds interpretation.