What is Spin? A Geometric explanation

Otto Stern and Walther Gerlach conducted the 1922 experiment that identified a fundamental new property of particles. They sent silver atom beams through inhomogeneous magnetic fields, observing deflection patterns that revealed electrons exist in discrete quantum states.

Quantum field theory, the most advanced model of particle physics, describes fundamental particles as dimensionless points with intrinsic properties. Electrons, quarks, photons, and other elementary particles possess spin alongside mass and charge as defining characteristics.

Mathematicians classify symmetries using group theory—sets of operations that can be combined or reversed. Physicists apply these abstract structures to describe how particles transform under rotations, revealing spin’s geometric origin.

The Standard Model organizes fundamental particles by spin numbers, which determine mathematical descriptions and physical behaviors. Physicists classify bosons (integer spin) and fermions (half-integer spin) based on rotational transformation properties.

Quantum mechanics’ superposition principle allows particles to exist simultaneously in multiple states until measurement forces collapse onto definite outcomes. This principle resolves the paradox of spin-1/2 requiring 720° rotations.

Electrons, quarks, and all matter particles (fermions) possess spin-1/2, requiring two complete 360° rotations to return to their initial states. This bizarre property distinguishes matter from force-carrying particles like photons.

Spinors are abstract mathematical entities introduced to quantum mechanics to describe particles requiring two complete rotations to return to their starting point. Physicists model electrons, quarks, and all fermions using spinor fields.