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AGPhil: Arbeitsgruppe Philosophie der Physik

AGPhil 5: Quantum Foundations 2

AGPhil 5.1: Hauptvortrag

Mittwoch, 22. März 2023, 14:00–14:45, JAN/0027

Physical probability is relative frequency — •Simon Saunders — Oxford University

Frequentism as a philosophy of probability is a perennial favourite among scientists, but for reasons I shall explain, has long been abandoned by philosophers of probability (physical probability, probability as something in nature). However, this consensus rests on the presupposition that there is only a single world. That assumption is challenged by the Everett interpretation of quantum mechanics, which is independently motivated. Understanding Everett's branches in terms of decoherence theory, there is a ready candidate for an ensemble even in the case of a single experiment: the equi-amplitude branches produced on any given trial. Relative frequencies for ensembles like these agree with the Born rule. As I shall show, for ensembles of this kind, the usual difficulties that render frequentism untenable no longer arise. Arguably, all physical probabilities are quantum probabilities, so the account is quite general.

The argument is strengthened by a recent result due to Tony Short, where given the possibility of swapping branch amplitudes, a probability measure over an ensemble of branches invariant under swapping must agree with the relative frequency rule, for it must treat equi-amplitude branches as equi-probable. It must therefore agree with the Born rule as well. I conclude with a critical evaluation of the invariance condition, and a limited defence. This work extends my https://arxiv.org/abs/2201.06087; The paper by Short is at https://arxiv.org/abs/2106.16145.