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Probability in the Everett Picture

David H. Albert

Published Jun 24, 2010• 77 citations
Publisher

Abstract

Abstract This chapter reviews and criticizes various strategies for making sense of quantum-mechanical probability-talk in the context of Everett Picture, with particular attention to recent such strategies involving decision theory.
DOI
10.1093/acprof:oso/9780199560561.003.0013

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Abstract Those who criticize the Everett interpretation on the grounds that it makes no sense of probability apply a double-standard, for no other physical theory of probability does any better in explaining probability or in deriving its link with decision theory. In fact, others do worse, for in any one world theory it is a mystery as to why, given that only a single outcome of a chance process occurs, we should nevertheless act so as to maximize expected utilities, which involves all possible outcomes of a chance process. This difficulty does not apply to the Everett interpretation, in which all outcomes happen.
This chapter extends chapter 5's formal proof into a general discussion of how we should assess evidence — and, in particular, how we should test scientific theories — given the possibility that Everettian quantum mechanics is correct. The chapter proves — initially with informal arguments, but in due course with full mathematical rigor — that rational scientists should treat the branch weights assigned by quantum theory to quantum-mechanical branches exactly as if they were probabilities; as such, the chapter argues, probability is actually on firmer conceptual footing in quantum theory than in classical physics. After a brief digression to consider probability in approaches to quantum theory other than the Everett interpretation, the chapter concludes by placing the work in the broader context of recent work on Everett probability.
This chapter begins my discussion of probability — generally held to be the most severe difficulty for the Everett interpretation. The chapter argues that since mathematically speaking probability has a natural place in the Everett interpretation, any ‘probability problem’ is philosophical in nature. Accordingly, the chapter's strategy is to review various different approaches to understanding probability — in particular, those based on long-run frequencies, on betting preferences, and on symmetries — and to argue that there are no problems with any of these approaches that are specific to Everettian quantum theory. The chapter concludes by arguing that, if probability is to be understood in terms of symmetry, it actually makes more sense in quantum than in classical physics. The chapter concludes with a sketch proof of the quantum probability rule on the basis of symmetry.
The Everett interpretation of quantum mechanics is an increasingly popular alternative to the traditional Copenhagen interpretation, but there are a few major issues that prevent the widespread adoption. One of these issues is the origin of probabilities in the Everett interpretation, which this thesis will attempt to survey. The most successful resolution of the probability problem thus far is the decision-theoretic program, which attempts to frame probabilities as outcomes of rational decision making. This marks a departure from orthodox interpretations of probabilities in the physical sciences, where probabilities are thought to be objective, stemming from symmetry considerations. This thesis will attempt to offer evaluations on the decision-theoretic program.