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The British Journal for the Philosophy of Science 1999 50(3):325-347; doi:10.1093/bjps/50.3.325
© 1999 by British Society for the Philosophy of Science
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On the significance of permutation symmetry

N Huggett

Department of Philosophy, M/C267, University of Illinois at Chicago, Chicago, IL 60607, USA. E-mail: huggett@uic.edu

There has been considerable recent philosophical debate over the implications of many particle quantum mechanics for the metaphysics of individuality (cf. Huggett [1997]). In this paper I look at things from a rather different perspective: by investigating the significance of permutation symmetry. I consider how various philosophical positions link up to the physical postulate of the indistinguishability of permuted states-permutation invariance-and how this postulate is used to explain quantum statistics. I offer an explanation of the statistics that relies on the neglected parallel between permutations and covariant spatial transformation. And I explore the parallel, showing that a further kind of symmetry explains why permutations are invariant when spatial symmetries are not.


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