Everettian mechanics with hyperfinitely many worlds

TL;DR

This paper introduces a hyperfinite model of Everettian quantum mechanics with infinitely many worlds, enabling analysis of continuous spectra, infinitesimal probabilities, and foundational properties like relative frequency and randomness.

Contribution

It presents a novel hyperfinite framework for Everettian quantum mechanics, extending the analysis to continuous spectra and infinitesimal probabilities, and formalizing key theorems.

Findings

Hyperfinite models accommodate continuous spectra and infinitesimal probabilities.

Hyperfinite formulations of Everett's relative-frequency and randomness theorems are established.

Provides a general framework for no-collapse quantum theories.

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. This approach also provides a more general framework in which to consider no-collapse formulations of quantum mechanics more generally.