James Wills (LSE): “Classical Particle Indistinguishability, Precisely.”

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Abstract: I present an analysis of classical particle indistinguishability as ‘observational indistinguishability’ in a certain mathematically precise sense. I will argue that this leads to three interesting and welcome consequences in the foundations of statistical mechanics: (1) The identification and resolution of shortcomings in the ongoing debate concerning the solution to the N! problem: the problem in statistical mechanics of justifying the inclusion of a factor N! in a probability distribution over the phase space of N indistinguishable classical particles. (2) A reinterpretation of the quotienting procedure typically used to justify the N! term and a rigorous derivation of the N! factor which does not appeal to the metaphysics of particles and which rather draws only on facts about observables. (3) A reconstruction of Gibbs’ own argument as a special case of my analysis in which particles are observationally indistinguishable with respect to the Hamiltonian. I call this ‘dynamical indistinguishability’.