The concept of identical particles becomes important in the study of quantum mechanics. In a classical description from atomic physics--for instance, the one proposed by Ernest Rutherford--an atom resembles a miniature solar system. Protons and neutrons cluster together in the center like suns; electrons orbit around them like planets. In classical mechanics, each of the subatomic particles occupies a certain place in space and time, and (theoretically, at least) those places can be exactly defined. In quantum mechanics, however, the position of a given particle in space and time cannot be known exactly; it can only be predicted through probability. Under quantum mechanics, all particles of a given type become identical when they have the same probability of being in any particular space at any given time.

Quantum physicists divide all known particles into two basic types: fermions, which include all known particles of matter--quarks and leptons--and bosons, which include everything else: photons, gravitons, gluons, and others. There are some cases where collections of fermions can act like bosons because of their combined spin; the helium-4 isotope is an example. With respect to identical particles, bosons and fermions differ in a very important respect. According to the Pauli exclusion principle, no two fermions can occupy the same quantum state at the same time. According to Bose-Einstein statistics, however, any number of bosons can exist simultaneously in the same state. Under the system of investigation called wave mechanics, particles such as electrons behave in ways that can be predicted by a wave, a fermion must occupy a single point on the wave, but bosons can exist in quantity all along the wave form.

The theory of identical particles has had a great impact, not only on the study of atomic structure, but also in practical applications. The predicted behavior of fermions such as electrons has given rise to electron microscopy, new types of lasers, and solid-state computers.