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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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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
Caulton, Adam
Butterfield, Jeremy
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: Dr Adam Caulton
Date Deposited: 20 Feb 2010
Last Modified: 07 Oct 2010 15:19
Item ID: 5168

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