What is spin?

In classic mechanics, the motion of an object is defined by 2 features: first, its extrinsic motion, it means its displacement, and secondly, its intrinsic motion: a rotation around itself. These 2 features are characterized by 2 physical quantities: momentum and angular momentum respectively. In quantum mechanics both physical quantities exist but with a more complex mathematical formalism. A quantum particle owns an angular momentum called spin whose values are quantified and must be either a whole multiple or a half integer multiple of ℎ/2*π according to the type of particle. The most important feature of the spin is its relationship with the global behavior of a population of same-kind particles. Particles with whole integer values of spin (bosons) can pile up in the same quantum state while particles with half-integer spin values (fermions) cannot be found in the same quantum state. This feature of spin explains collective behaviour of particles such as the electronic structure of atoms, or the electric conductivity of metals, or laser light, etc... (A.C.)