The problem of identity (synchronic and diachronic) in quantum mechanics

Tomasz Bigaj (University of Warsaw)

Abstract:  In my talk I will give an overview of the metaphysical problem of identity and indistinguishability arising in the quantum theory of many particles. According to the Received View (French, Redhead, Butterfield), quantum particles of the same type are never discernible by their properties (intrinsic and extrinsic) due to the inevitable symmetrization postulate.  This observation prompted a prolonged debate on the ontological status of elementary particles and the demise of the Principle of the Identity of Indiscernibles (PII). Alternative methods of discernibility have been proposed, including weak discernibility by symmetrical and irreflexive relations (Saunders, Muller). However, it has been pointed out that the Received View is based on some questionable assumptions, such as e.g. factorism, which states that particles constituting a composite system are individuated by the labels of the factors in the tensor product of Hilbert spaces. Yet factorism implies that properties of individual particles should be representable by non-permutation invariant operators, and this conflicts with the symmetrization postulate. An alternative approach, defended by Caulton, Dieks, Lubberdink and myself, is based on the assumption that the components of a collection of particles of the same type are to be identified by the symmetric projection operators representing permutation-invariant statements of the sort “Exactly n out of m particles possess property P”. This interpretation is not only fully permutation-invariant, but also restores the validity of the PII in the majority of cases involving bosonic and fermionic states. At the end of the talk I will compare the orthodox and unorthodox approaches to quantum individuation in regard to how they treat the relations between the synchronic and diachronic identities of quantum particles. I will use textbook cases of particle scatterings in order to argue that the orthodox analysis of the diachronic identities of particles before and after interactions is unsustainable, and that only the unorthodox approach gives a consistent picture of how particles retain (or don't retain) their identities in different experimental settings of mutual scatterings.