Symmetries and Paraparticles as a Motivation for Structuralism

Jeremy Butterfield
Cambridge University
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
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Reprint years 2012
DOI 10.1093/bjps/axr034
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References found in this work BETA

Are Quantum Particles Objects?Simon Saunders - 2006 - Analysis 66 (1):52-63.
Discerning Fermions.Simon Saunders & F. A. Muller - 2008 - British Journal for the Philosophy of Science 59 (3):499 - 548.

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Citations of this work BETA

Unitary Inequivalence as a Problem for Structural Realism.Steven French - 2012 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 43 (2):121-136.
The Role of Symmetry in the Interpretation of Physical Theories.Adam Caulton - 2015 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 52 (Part B):153-162.
Entities Without Intrinsic Physical Identity.Vincent Lam - 2014 - Erkenntnis 79 (5):1157-1171.
Generalism and the Metaphysics of Ontic Structural Realism.David Glick - 2017 - British Journal for the Philosophy of Science:axy008.

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