Correspondence principle as equivalence of categories

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    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.

    Original languageEnglish
    Pages (from-to)309-314
    Number of pages6
    JournalQuantum Studies: Mathematics and Foundations
    Issue number4
    StatePublished - 1 Dec 2017


    • Category theory
    • Computability
    • Constructive mathematics
    • Functors
    • Ising models of a spin glass
    • Number partitioning problem
    • Quantum–classical correspondence

    ASJC Scopus subject areas

    • Atomic and Molecular Physics, and Optics
    • Mathematical Physics


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