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 | ||||||
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| 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 |
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| 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 |
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| 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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