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Quantum Physics in Non-Separable Hilbert Spaces

Earman, John (2020) Quantum Physics in Non-Separable Hilbert Spaces. [Preprint]

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Abstract

In Mathematical Foundations of Quantum Mechanics (1932) von Neumann made separability of Hilbert space an axiom. Subsequent work in mathematics (some of it by von Neumann himself) investigated non-separable Hilbert spaces, and mathematical physicists have sometimes made use of them. This note discusses some of the problems that arise in trying to treat quantum systems with non-separable spaces. Some of the problems are "merely technical" but others point to interesting foundations issues for quantum theory, both in its abstract mathematical form and its applications to physical systems. Nothing new or original is attempted here. Rather this note aims to bring into focus some issues that have for too long remained on the edge of consciousness for philosophers of physics.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Earman, Johnjearman@pitt.edu
Keywords: foundations of quantum mechanics, non-separable Hilbert spaces
Subjects: General Issues > Models and Idealization
Specific Sciences > Physics > Quantum Mechanics
General Issues > Structure of Theories
Depositing User: John Earman
Date Deposited: 08 Nov 2020 15:12
Last Modified: 17 Jun 2023 11:32
Item ID: 18363
Subjects: General Issues > Models and Idealization
Specific Sciences > Physics > Quantum Mechanics
General Issues > Structure of Theories
Date: 6 November 2020
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/18363

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