Correspondence principle as equivalence of categories
| Autor: | Arkady Bolotin |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Quantum Physics
Pure mathematics Functor Equivalence of categories Computability Hilbert space FOS: Physical sciences Mathematical Physics (math-ph) Atomic and Molecular Physics and Optics symbols.namesake Mathematics::Category Theory Thermodynamic limit symbols Ising model Quantum Physics (quant-ph) Category theory Finite set Mathematical Physics Mathematics |
| Zdroj: | Quantum Studies: Mathematics and Foundations. 4:309-314 |
| ISSN: | 2196-5617 2196-5609 |
| Popis: | If quantum mechanics were to be applicable to macroscopic objects, classical mechanics would have to be a limiting case of quantum mechanics. Then the category Set that packages classical mechanics has to be in some sense a 'limiting case' of the category Hilb packaging quantum mechanics. Following from this assumption, quantum-classical correspondence can be considered as a mapping of the category Hilb to the category Set, i.e., a functor from Hilb to Set, taking place in the macroscopic limit. As a procedure, which takes us from an object of the category Hilb (i.e., a Hilbert space) in the macroscopic limit to an object of the category Set (i.e., a set of values that describe the configuration of a system), this functor must take a finite number of steps in order to make the equivalence of Hilb and Set verifiable. However, as it is shown in the present paper, such a constructivist requirement cannot be met in at least one case of an Ising model of a spin glass. This could mean that it is impossible to demonstrate the emergence of classicality totally from the formalism of standard quantum mechanics. Major revision of the previous draft; 8 pages |
| Databáze: | OpenAIRE |
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