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Everettian Mechanics with Hyperfinitely Many Worlds

Barrett, Jeffrey A. and Goldbring, Isaac (2021) Everettian Mechanics with Hyperfinitely Many Worlds. [Preprint]

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Abstract

The present paper shows how one might model Everettian quantum mechanics using hyperfinitely many worlds. A hyperfinite model allows one to consider idealized measurements of observables with continuous-valued spectra where different outcomes are associated with possibly infinitesimal probabilities. One can also prove hyperfinite formulations of Everett's limiting relative-frequency and randomness properties, theorems he considered central to his formulation of quantum mechanics. Finally, this model provides an intuitive framework in which to consider no-collapse formulations of quantum mechanics more generally.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Barrett, Jeffrey A.j.barrett@uci.edu
Goldbring, Isaacisaac@math.uci.edu
Keywords: Everettian quantum mechanics, many worlds, nonstandard analysis, hyperfinite quantum mechanics, quantum probability
Subjects: Specific Sciences > Mathematics > Applicability
General Issues > Models and Idealization
Specific Sciences > Probability/Statistics
Specific Sciences > Physics > Quantum Mechanics
General Issues > Structure of Theories
Depositing User: Jeffrey Barrett
Date Deposited: 07 Aug 2021 23:53
Last Modified: 07 Aug 2021 23:53
Item ID: 19419
Subjects: Specific Sciences > Mathematics > Applicability
General Issues > Models and Idealization
Specific Sciences > Probability/Statistics
Specific Sciences > Physics > Quantum Mechanics
General Issues > Structure of Theories
Date: 2021
URI: https://philsci-archive.pitt.edu/id/eprint/19419

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