As part of the formulation of quantum mechanics in the first third of the 20th century, it was discovered that elementary particles has a quantity besides mass, electric charge, etc. That quantity was given the name spin, since it was somewhat analogous to the traditional concept of angular momentum. (The particles do not actually rotate, so the name is also somewhat misleading.) The electron, for example, was found to have a spin value of ½, as did the positron, proton, and neutron. The photon has spin of 1, and alpha particles have spin 0. These spins can combine to produce other net spins in atoms and their nucleii, according to the complex rules of quantum mechanics.

Particles with spins of 0, 1, 2, etc. are called bosons,, while particles with spins ½, 3/2, 5/2, etc. are called fermions. It was found that collections of bosons behaved quite differently from collections of fermions. In particular, two...