Branch-counting in the Everett interpretation of quantum mechanics

A defence is offered of a version of the branch-counting rule in the Everett interpretation (otherwise known as many worlds interpretation) of quantum mechanics that both depends on the state and is continuous in the norm topology on Hilbert space. The well-known branch-counting 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 naive 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 Bose–Einstein gas. It also connects in a simple way with the decision-theory approach to quantum probability.

Probability, preclusion and biological evolution in Heisenberg-picture Everett quantum mechanics

The fact that certain “extraordinary” probabilistic phenomena — in particular, macroscopic violations of the second law of thermodynamics — have never been observed to occur can be accounted for by taking hard preclusion as a basic physical law, i.e. precluding from existence events corresponding to very small but nonzero values of quantum-mechanical weight. This approach is not consistent with the usual ontology of the Everett interpretation, in which outcomes correspond to branches of the state vector, but can be successfully implemented using a Heisenberg-picture-based ontology in which outcomes are encoded in transformations of operators. Hard preclusion can provide an explanation for biological evolution, which can in turn explain our subjective experiences of, and reactions to, “ordinary” probabilistic phenomena, and the compatibility of those experiences and reactions with what we conventionally take to be objective probabilities arising from physical laws.

On the Plurality of Quantum Theories: Quantum Theory as a Framework, and its Implications for the Quantum Measurement Problem

‘Quantum theory’ is not a single physical theory but a framework in which many different concrete theories fit. As such, a solution to the quantum measurement problem ought to provide a recipe to interpret each such concrete theory, in a mutually consistent way. But with the exception of the Everett interpretation, the main extant solutions either try to make sense of the abstract framework as if it were concrete, or else interpret one particular quantum theory under the fiction that it is fundamental and exact. In either case, these approaches are unable to help themselves to the very theory-laden, level-relative ways in which quantum theory makes contact with experiment in mainstream physics, and so are committed to major revisionary projects which have not been carried out even in outline. As such, only the Everett interpretation is currently suited to make sense of quantum physics as it is found.