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

Brown, Harvey R.; Porath, Gal Ben

doi:10.1007/978-3-030-34316-3_7

Cited by 6 publications

(5 citation statements)

References 44 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The status of the Principal Principle in decision-theoretic approaches to probability in Everett quantum mechanics is discussed in[67], and a derivation thereof in the context of non-Everett quantum mechanics is given in[68] 14. The idea that preclusion explains evolution which then explains subjective probability was presented in my previous paper[53], though not the supporting model of Secs.…”

mentioning

confidence: 99%

Probability, Preclusion and Biological Evolution in Heisenberg-Picture Everett Quantum Mechanics

Rubin

2020

Preprint

View full text Add to dashboard Cite

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-picturebased 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.

show abstract

mentioning

confidence: 99%

Probability, Preclusion and Biological Evolution in Heisenberg-Picture Everett Quantum Mechanics

Rubin

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…We have just dealt with the objection, for example in Albert (2016), that betting behaviour cannot be explanatory of the observed statistics. There is also the radical proposal, proposed by Deutsch (2016) and Brown and Porath (2020), that physical probability simply has no meaning in the Everett interpretation, and there are only agent-specific personal probabilities. But ratios in branch numbers are physical, and in view of the similarities with naïve frequentism, to deny that they have anything to do with probability seems capricious.…”

Section: Discussionmentioning

confidence: 99%

Branch-counting in the Everett interpretation of quantum mechanics

Saunders

2021

Proc. R. Soc. A.

View full text Add to dashboard Cite

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.

show abstract

“…For those who doubt the existence of chances, the import of the DW theorem will be slightly different; rather than providing a basis for reifying the branch weights as chances, the theorem will simply be taken to show that, within EQM, it is possible both to make sense of probabilistic claims and to derive the Born rule, providing the probabilities therein are understood as (rationally constrained) credences. See for example Deutsch (1999, 3136); Brown and Porath (2020) provide an extensive defence of this view.…”

Section: The Gm Approachmentioning

confidence: 99%

“…

I defend the Deutsch-Wallace (DW) theorem against a dilemma presented by Dawid and Thébault (2014), and endorsed in part by Read (2018), andBrown andPorath (2020), according to which the theorem is either redundant or in conflict with general frequency-tochance inferences. I argue that neither horn of the dilemma is wellposed.

…”

mentioning

confidence: 99%