Spins

Spins refer to a fundamental property of quantum particles known as intrinsic angular momentum. Unlike everyday objects, spin is not a literal rotation in space, but a quantum degree of freedom that exists independently of physical motion. It is quantified by a spin quantum number and associated with a magnetic moment, making spin observable through its interactions with magnetic fields.

Mathematically, spin is described by quantum numbers that specify possible states. The spin quantum number is denoted s, and the projection along a chosen axis, m_s, takes values from -s to +s in integer steps. For example, electrons have s = 1/2 and two possible spin projections, m_s = -1/2 and +1/2. Photons have s = 1 and, in practice, two observable helicity states corresponding to spin projections along their direction of motion. Spin systems form the basis of two-level quantum bit implementations and more complex multilevel schemes.

Experimentally, spin can be revealed by measurements that reveal discrete, quantized outcomes. The Stern-Gerlach experiment demonstrated beam splitting according to spin along a magnetic field direction, and techniques such as electron spin resonance and nuclear magnetic resonance exploit spin transitions induced by electromagnetic fields. Spin also couples to other degrees of freedom, such as orbital motion (spin-orbit coupling) and collective spin excitations (magnons) in magnetic materials.

In theory, spin is linked to fundamental principles of quantum statistics. Particles with half-integer spin are fermions and obey Fermi-Dirac statistics, while integer-spin particles are bosons and obey Bose-Einstein statistics, a relationship known as the spin-statistics theorem. Applications span quantum information, spintronics, and condensed matter physics.

Other uses of the word spin refer to rotation around an axis in everyday language and to presenting information with a biased slant in journalism, a usage known as spin.