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Symmetries and Paraparticles as a Motivation for Structuralism

Caulton, Adam and Butterfield, Jeremy (2009) Symmetries and Paraparticles as a Motivation for Structuralism. [Preprint]

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    Abstract

    This paper develops an analogy proposed by Stachel between general relativity (GR) and quantum mechanics (QM) as regards permutation invariance. Our main idea is to overcome Pooley's criticism of the analogy by appeal to paraparticles. In GR the equations are (the solution space is) invariant under diffeomorphisms permuting spacetime points. Similarly, in QM the equations are invariant under particle permutations. Stachel argued that this feature - a theory's "not caring which point, or particle, is which" - supported a structuralist ontology. Pooley criticizes this analogy: in QM the (anti-)symmetrization of fermions and bosons implies that each individual state (solution) is fixed by each permutation, while in GR a diffeomorphism yields in general a distinct, albeit isomorphic, solution. We define various versions of structuralism, and go on to formulate Stachel's and Pooley's positions, admittedly in our own terms. We then reply to Pooley. Though he is right about fermions and bosons, QM equally allows more general types of symmetry, in which states (vectors, rays or density operators) are not fixed by all permutations (called 'paraparticle states'). Thus Stachel's analogy is revived.


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    Item Type: Preprint
    Additional Information: Forthcoming in The British Journal for the Philosophy of Science.
    Keywords: Symmetry, identity, structuralism, paraparticles, hole argument, general covariance, permutation symmetry, Stachel, Pooley
    Subjects: Specific Sciences > Physics > Symmetries/Invariances
    Specific Sciences > Physics > Relativity Theory
    Specific Sciences > Physics > Quantum Mechanics
    Depositing User: Adam Caulton
    Date Deposited: 20 Feb 2010
    Last Modified: 07 Oct 2010 11:19
    Item ID: 5168
    URI: http://philsci-archive.pitt.edu/id/eprint/5168

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