PhilSci Archive

On the problem of emergence of classical space-time: The quantum-mechanical approach

Kryukov, Alexey (2003) On the problem of emergence of classical space-time: The quantum-mechanical approach. [Preprint]

[img]
Preview
PDF
Download (155Kb) | Preview

    Abstract

    The classical space-time structure is derived from the structure of an abstract infinite dimensional separable Hilbert space S. For this S is first realized as a Hilbert space H* of functions of abstract parameters. Such a realization is associated with the process of measuring position of macroscopic particles naturally occurring in the universe. The process of decoherence and collapse induced by the measurement is in return associated with the choice of a "decohered" submanifold M of realization H*. The submanifold M is then identified with the classical space-time. The mathematical formalism is developed which permits to recover the usual Riemannian geometry on space-time in terms of the Hilbert structure on S. The specific functional realizations of S are shown to produce space-times of different geometry and topology.


    Export/Citation:EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL
    Social Networking:

    Item Type: Preprint
    Keywords: Emergence, generalized functions, Hilbert space
    Subjects: Specific Sciences > Physics > Quantum Mechanics
    Depositing User: Alexey Kryukov
    Date Deposited: 18 Apr 2003
    Last Modified: 07 Oct 2010 11:11
    Item ID: 1141
    URI: http://philsci-archive.pitt.edu/id/eprint/1141

    Actions (login required)

    View Item

    Document Downloads