A well-known particle physicist’s adage:
Ever since the fundamental paper of Wigner on the irreducible representations of the Poincaré group, it has been a (perhaps implicit) deﬁnition in physics that an elementary particle ‘is’ an irreducible representation of the group, G, of ‘symmetries of nature’ (Ne’eman and Sternberg 1991, pp. 327.)
But what exactly does that mean? Many would agree that Wigner’s seminal work on the Poincaré group has some deep metaphysical implication. But what? Wigner himself provided very little indication as to what it might be, even in his later work in the philosophy of physics.
However, there seems to be what Arthur Fine would call a “core position” about Wigner’s result. That is: there is a tight mathematical connection between the symmetry groups of nature, and the measurable quantities of quantum theory. You can even diagram it:
However, as I’ve argued before (and in a forthcoming article), a certain realist addition to this core position just doesn’t make sense. So what, if anything, can be said about Wigner’s result beyond the core position?
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