In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles (hadrons), and atomic nuclei.

All elementary particles of a given kind have the same spin quantum number, an important part of the quantum state of a particle. When combined with the spin-statistics theorem, the spin of electrons results in the Pauli exclusion principle, which in turn underlies the periodic table of chemical elements. The spin direction (also called spin for short) of a particle is an important intrinsic degree of freedom.

Wolfgang Pauli was the first to propose the concept of spin, but he did not name it. In 1925, Ralph Kronig, George Uhlenbeck, and Samuel Goudsmit suggested a physical interpretation of particles spinning around their own axis. The mathematical theory was worked out in depth by Pauli in 1927. When Paul Dirac derived his relativistic quantum mechanics in 1928, electron spin was an essential part of it.

There are two types of

:

, which is a generalization of

in

(

=

×

), and spin, which has no analogue in classical mechanics.

Since spin is a type of angular momentum, it has the same

:

•

in

. In practice, however, SI units are never used to describe spin: instead, it is written as a multiple of t

The head-on collision of a quark (the red ball) from one proton (the orange ball) with a gluon (the green ball) from another proton with opposite spin; spin is represented by the blue arrows circling the protons and the quark. The blue question marks circling the gluon represent the question: Are gluons polarised? The particles ejected from the collision are a shower of quarks and one photon of light (the purple ball).

he

. In

, the

is omitted, so spin is written as a unitless number.