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- Title
A New Approach to Understanding Quantum Mechanics: Illustrated Using a Pedagogical Model over ℤ 2.
- Authors
Ellerman, David
- 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 Z 2 = { 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.
- Subjects
QUANTUM mechanics; EQUIVALENCE relations (Set theory); VECTOR spaces; SET theory; FEYNMAN, Richard Phillips, 1918-1988
- Publication
AppliedMath, 2024, Vol 4, Issue 2, p468
- ISSN
2673-9909
- Publication type
Article
- DOI
10.3390/appliedmath4020025