Symmetries and Paraparticles as a Motivation for Structuralism

TL;DR

This paper revisits the analogy between general relativity and quantum mechanics regarding permutation invariance, proposing paraparticles as a way to strengthen the structuralist interpretation of these theories.

Contribution

It introduces paraparticles into the analogy, addressing criticisms and reinforcing the structuralist view of permutation invariance in GR and QM.

Findings

Paraparticles allow more general symmetries in QM.

The analogy between GR and QM is strengthened by considering paraparticles.

Structuralist interpretations are supported by these symmetry considerations.

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.