Identity of Quanta

Identity. From very early days of quantum theory it was recognized that quanta were statistically strange (see ► Bose-Einstein statistics). Suspicion fell on the identity of quanta, of how they are to be counted [1, 2]. It was not until Paul A. Dirac's (1902–1984) work of 1926 (and his discovery of ► Fermi-Dirac statistics [3]) that the nature of the novelty was clear: the quantum state of exactly similar particles of the same mass, charge, and ► spin must be symmetrized, yielding states either symmetric or antisymmetric under permutations. This is the symmetry postulate (SP).

The SP further implies that expectation values of particle ► observables are invariant under permutations. The latter looks temptingly like the sort of principle on which one might hope to found the theory of quantum identity. It is called the in-distinguishability postulate (IP) - see ► indistinguishability. But it turns out to be weaker than the SP, the principle we are interested in.