Abstract: Recent work by Dawid and Tibault (2014) claims that the Deutsch--Wallace theorem (DW) is, in the words of March (2024), `redundant' in high-weight branches of the wavefunction: we get everything we need to know from standard statistical inference. March (2024) challenges this claim by arguing that the Deutsch--Wallace theorem really gives us rational betting behaviour as a /prediction/ of Everettian quantum mechanics (EQM), which can be confirmed or falisified by experiment.
I will go further than this: I will argue that regarding DW as redundant is circular. Wallace (2012) has already pointed out that the problem in Everettian quantum mechanics (EQM) also exists in general for stochastic theories. Indeed, the conclusion of DW is similar to the statistical postulate (SP), which states that large regions of phase space are more probable than small regions, in other words, that one should take it that the correct probability distribution over phase space is uniform. One can argue for SP in a similar fashion to how one derives DW, based on symmetry arguments. In statistical mechanics, a proof of SP is certainly not redundant: it prevents us from trying to make a circular argument like `high-entropy states are more likely because they take up more volume in phase space'.
To expand on this, I will look at what the above kind of claim tells us in both EQM and hidden-variables theories. Specifically, I will sketch a model of so-called `superdeterminism' and examine what inhabitants of a superdeterministic world would need to believe in order to reject SP. I will compare this to what inhabitants of high-weight branches would need to believe in order to reject DW. I will also show what inhabitants of low-weight branches would need to believe in order to accept DW. I will argue that in all of these cases the necessary beliefs would be incompatible with normal scientific reasoning: DW, then, far from being redundant, is in fact a necessary component of EQM.
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Philosophy of Physics Graduate Lunch Seminar Convenors: Paolo Faglia, Gregor Gajic and Rachel Pederson
