The spin-statistics theorem establishes a fundamental connection between the spin of a particle and its statistical behavior. Particles with half-integer spin are fermions and obey the Pauli exclusion principle, meaning that they cannot occupy the same quantum state. Particles with integer spin are bosons and obey Bose-Einstein statistics, allowing them to occupy the same quantum state. This theorem plays a crucial role in understanding the behavior of matter, from the properties of atoms and molecules to the formation of stars and galaxies.
