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A New Approach to Understanding Quantum Mechanics: Illustrated Using a Pedagogical Model over ℤ2

Ellerman, David (2024) A New Approach to Understanding Quantum Mechanics: Illustrated Using a Pedagogical Model over ℤ2. AppliedMath (MDPI), 4 (2). pp. 468-494.

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Abstract

The new approach to quantum mechanics (QM) is that the mathematics of QM is the linearization of the mathematics of partitions (or equivalence relations) on a set. This paper develops those ideas using vector spaces over the field ℤ2={0.1}
as a pedagogical or toy model of (finite-dimensional, non-relativistic) QM. The 0,1
-vectors are interpreted as sets, so the model is “quantum mechanics over sets” or QM/Sets. The key notions of partitions on a set are the logical-level notions to model distinctions versus indistinctions, definiteness versus indefiniteness, or distinguishability versus indistinguishability. Those pairs of concepts are the key to understanding the non-classical ‘weirdness’ of QM. The key non-classical notion in QM is the notion of superposition, i.e., the notion of a state that is indefinite between two or more definite- or eigen-states. As Richard Feynman emphasized, all the weirdness of QM is illustrated in the double-slit experiment, so the QM/Sets version of that experiment is used to make the key points.


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Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
Ellerman, Daviddavid@ellerman.org0000-0002-5718-618X
Keywords: mathematics of quantum mechanics; partitions; equivalence relations; vector spaces over ℤ2; objective indefiniteness; indistinguishability
Subjects: Specific Sciences > Mathematics > Foundations
General Issues > Philosophers of Science
Specific Sciences > Physics > Quantum Mechanics
General Issues > Science Education
Depositing User: David Ellerman
Date Deposited: 16 May 2024 16:12
Last Modified: 16 May 2024 16:12
Item ID: 23410
Journal or Publication Title: AppliedMath (MDPI)
Publisher: MDPI
Official URL: https://doi.org/10.3390/appliedmath4020025
DOI or Unique Handle: 10.3390/appliedmath4020025
Subjects: Specific Sciences > Mathematics > Foundations
General Issues > Philosophers of Science
Specific Sciences > Physics > Quantum Mechanics
General Issues > Science Education
Date: 2 May 2024
Page Range: pp. 468-494
Volume: 4
Number: 2
URI: https://philsci-archive.pitt.edu/id/eprint/23410

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