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Jerusalem studies in philosophy and history of science

Everettian Probabilities, The Deutsch-Wallace Theorem and the Principal Principle

Harvey R. Brown, Gal Ben Porath

Published Jan 1, 2020• 10 citations
Publisher
DOI
10.1007/978-3-030-34316-3_7

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I defend the Deutsch-Wallace (DW) theorem against a dilemma presented by Dawid and Thébault (2014), and endorsed in part by Read (2018), and Brown and Porath (2020), according to which the theorem is either redundant or in conflict with general frequency-to-chance inferences. I argue that neither horn of the dilemma is well-posed. On the one hand, the DW theorem is not in conflict with general frequency-to-chance inferences on the most natural way of stating the theorem. On the other hand, the DW theorem is crucial for establishing the Born rule as a prediction of Everettian quantum mechanics (EQM), and so cannot be redundant within the theory.
The 2022 Tel Aviv conference on the many-worlds interpretation of quantum mechanics highlighted many differences between theorists. A very significant dichotomy is between Everettian fission (splitting) and Saunders–Wallace–Wilson divergence. For fission, an observer may have multiple futures, whereas for divergence they always have a single future. Divergence was explicitly introduced to resolve the problem of pre-measurement uncertainty for Everettian theory, which is universally believed to be absent for fission. Here I maintain that there is indeed pre-measurement uncertainty prior to fission, so long as objective probability is a property of Everettian branches. This is made possible if the universe is a set and branches are subsets with a probability measure. A universe that is a set of universes that are macroscopically isomorphic and span all possible configurations of local beäbles fulfills that role. If objective probability is a property of branches, then a successful Deutsch–Wallace decision-theoretic argument would justify the Principal Principle and be part of probability theory rather than specific to many-worlds theory. Any macroscopic object in our environment becomes a set of isomorphs with different microscopic configurations, each in an elemental universe (elemental in the set-theoretic sense). This is similar to the many-interacting-worlds theory, but the observer inhabits the set of worlds, not an individual world. An observer has many elemental bodies.