## Abstract

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 language | English |
---|---|

Pages (from-to) | 309-314 |

Number of pages | 6 |

Journal | Quantum Studies: Mathematics and Foundations |

Volume | 4 |

Issue number | 4 |

DOIs | |

State | Published - 1 Dec 2017 |

## Keywords

- 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