Quarticles and the Identity of Indiscernibles

In sections 5.3-4 of their paper in this volume, French and Rickles raise the question of the logical relations between the indistinguishability postulate (IP) and the various senses in which particles might fail to be individuals. In section 5.3 they refer to the convincing arguments of French and Redhead (1988) and of Butterfield (1993) that IP does not logically entail non-individuality, understood several ways – even though, as all seem to concede, there is something perverse about taking bosons and fermions to be individuals. Going the other way, as Huggett and Imbo show, if non-individuality is taken to mean the absence of continuous distinguishing trajectories, characteristic of standard quantum mechanics (QM), then non-individuality does not entail IP. Nor, as French and Rickles point out, do substance or haecceity views of individuality. But what if we conceive of individuality in terms of the principle of the identity of indiscernibles (PII)? First, French and Redhead (1988) and Butterfield (1993) have given theorems showing that bosons and fermions violate PII, while the former have also demonstrated violations of PII in the case of a certain paraparticle state. But these cases, as I will explain (and as French and Rickles point out), cover just a very few of the possible kinds of quantum particles, and so for each kind the question arises as to whether it violates PII. I will give an answer to this question here, rather more general than – though based on – those previously offered. So consider the theorems proven about PII. Suppose one has an n-particle system. The states of such a system lie in the Hilbert space that is the tensor product of n Hilbert spaces, one for each of the particles. Suppose further that the Hilbert space for particle i or j – appearing as the i and the j factors of To appear in K.A. Brading and E. Castellani (eds.), ”Symmetries in Physics: Philosophical Reflections”, CUP 2003. Contact the author at [email protected] K.A. Brading and E. Castellani (eds.), Symmetries in Physics: Philosophical Reflections, CUP 2003 N. Huggett and T. Imbo, “Identicality and indistinguishability”, in preparation.