Ellerman, David (2024) A New Approach to Understanding Quantum Mechanics: Illustrated Using a Pedagogical Model over Z2. Applied Math, 4 (2). 468-494..
|
Text
_MDPI-AppliedMath-Simplified Model.pdf Download (1MB) | Preview |
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.
| Export/Citation: | EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL |
| Social Networking: |
| Item Type: | Published Article or Volume | ||||||
|---|---|---|---|---|---|---|---|
| Creators: |
|
||||||
| Keywords: | mathematics of quantum mechanics; partitions; equivalence relations; vector spaces over Z2; objective indefiniteness; indistinguishability | ||||||
| Subjects: | Specific Sciences > Mathematics > Logic General Issues > Philosophers of Science Specific Sciences > Physics > Quantum Mechanics General Issues > Science Education |
||||||
| Depositing User: | David Ellerman | ||||||
| Date Deposited: | 14 Apr 2024 17:10 | ||||||
| Last Modified: | 14 Apr 2024 17:10 | ||||||
| Item ID: | 23284 | ||||||
| Journal or Publication Title: | Applied Math | ||||||
| Publisher: | MDPI Inc. | ||||||
| DOI or Unique Handle: | https://doi.org/10.3390/ appliedmath4020025 | ||||||
| Subjects: | Specific Sciences > Mathematics > Logic General Issues > Philosophers of Science Specific Sciences > Physics > Quantum Mechanics General Issues > Science Education |
||||||
| Date: | 2024 | ||||||
| Page Range: | 468-494. | ||||||
| Volume: | 4 | ||||||
| Number: | 2 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/23284 |
Monthly Views for the past 3 years
Monthly Downloads for the past 3 years
Plum Analytics
Altmetric.com
Actions (login required)
 |
View Item |
![[feed]](http://philsci-archive.pitt.edu/style/images/feed-icon-32x32.png){kind=icon}