As is the case for uncertainty and complementary, the notion of indiscernibility is necessary in order to extend the use of classical concepts to quantum physics. The ordinary way to conceive particle is at odds with the quantum rule that indistinguishable paths don't contribute individually to the predictions, but rather interfere. Yet, under certain conditions, one is allowed to interpret quantum phenomena in terms of particles; but she has to give up the strong notion of individuality involved in the classical concept of material body.

Quantum field theory, which is the relativistic generalisation of quantum mechanics, does not contain any direct reference to labelled particles. It simply predicts a number of phenomena that can be partially understood in terms of interacting particles. It accounts, for example, for high energy processes which are interpreted as the creation and the annihilation of elementary particles.

Under some assumptions, the quantum treatment of identical particles can be derived from quantum field theory, which also provides a (not elementary!) explanation for the connection between spin and statistics (in particle language, the fact that particles with integer spin are bosons whereas particles with half-integer spin are fermions). As we show in the section on the Pauli's exclusion principle, the statistical pattern of ensembles of identical particles is determined by the symmetry properties imposed upon their global quantum state by the indiscernibility principle.