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Cambridge University Press eBooks

Averaging

Chris Godsil, Hanmeng Zhan

Published Dec 23, 2022• 0 citations
Publisher

Abstract

The axioms of quantum physics imply that in general it makes no sense to speak of the long-term behaviour of a quantum walk. In this chapter we introduce a process that allows us to develop a meaningful substitute for a simple average.
DOI
10.1017/9781009261692.005

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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.
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