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Symmetries and paraparticles as a motivation for structuralism

Caulton, Adam and Butterfield, J. (2012) Symmetries and paraparticles as a motivation for structuralism. British Journal for the Philosophy of Science, 63 (2). pp. 233-285. ISSN 0007-0882

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Identification Number: 10.1093/bjps/axr034

Abstract

This article 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 particle symmetry, in which states (vectors, rays, or density operators) are not fixed by all permutations (called ‘paraparticle states’). Thus Stachel's analogy is revived.

Item Type: Article
Official URL: http://bjps.oxfordjournals.org/
Additional Information: © 2011 The Author
Divisions: Philosophy, Logic and Scientific Method
Subjects: B Philosophy. Psychology. Religion > B Philosophy (General)
Q Science > Q Science (General)
Sets: Departments > Philosophy, Logic and Scientific Method
Date Deposited: 19 Dec 2013 14:46
Last Modified: 20 Apr 2019 01:00
URI: http://eprints.lse.ac.uk/id/eprint/55071

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