Saunders, Simon
(2021)
Branchcounting in the Everett interpretation of quantum mechanics.
Proceedings of the Royal Society A, 477.
Abstract
A defence is offered of a version of the branchcounting rule for probability in the Everett interpretation (otherwise known as manyworlds interpretation) of quantum mechanics that both depends on the state and is continuous in the norm topology on Hilbert space. The wellknown branchcounting rule, for realistic models of measurements, in which branches are defined by decoherence theory, fails this test. The new rule hinges on the use of decoherence theory in defining branching structure, and specifically decoherent histories theory. On this basis ratios of branch numbers are defined, free of any convention. They agree with the Born rule, and deliver a notion of objective probability similar to naïve frequentism, save that the frequencies of outcomes are not confined to a single world at different times, but spread over worlds at a single time. Nor is it ad hoc: it is recognizably akin to the combinatorial approach to thermodynamic probability, as introduced by Boltzmann in 1879. It is identical to the procedure followed by Planck, Bose, Einstein and Dirac in defining the equilibrium distribution of the BoseEinstein gas. It also connects in a simple way with the decisiontheory approach to quantum probability.
Monthly Views for the past 3 years
Monthly Downloads for the past 3 years
Plum Analytics
Altmetric.com
Actions (login required)

View Item 