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Algebraic aspects of quantum indiscernibility

Krause, Decio and Feitosa, Hercules de Araujo (2008) Algebraic aspects of quantum indiscernibility. [Preprint]

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    Abstract

    We show that using quasi-set theory, or the theory of collections of indistinguishable objects, we can define an algebra that has most of the standard properties of an orthocomplete orthomodular lattice, which is the lattice of all closed subspaces of a Hilbert space. We call the mathematical structure so obtained $\mathfrak{I}$-lattice. After discussing (in a preliminary form) some aspects of such a structure, we indicate the next problem of axiomatizing the corresponding logic, that is, a logic which has $\mathfrak{I}$-lattices as its Lindembaum algebra, which we postpone to a future work. Thus we conclude that the initial intuitions by Birkhoff and von Neumann that the ``logic of quantum mechanics" would be not classical logic (a Boolean algebra), is consonant with the idea of considering indistinguishability right from the start, that is, as a primitive concept. In the first sections, we present the main motivations and a ``classical'' situation which mirrors that one we focus on the last part of the paper. This paper is our first analysis of the algebraic structure of indiscernibility.


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    Item Type: Preprint
    Keywords: indiscernibility, non-individuality, quantum logic, quasi-sets
    Subjects: General Issues > Structure of Theories
    Specific Sciences > Mathematics
    Specific Sciences > Physics > Quantum Mechanics
    Depositing User: D├ęcio Krause
    Date Deposited: 25 Jun 2008
    Last Modified: 07 Oct 2010 11:16
    Item ID: 4086
    URI: http://philsci-archive.pitt.edu/id/eprint/4086

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