In quantum physics, what rule forbids two identical fermions from sharing all the same quantum numbers?

The Pauli exclusion principle forbids two identical fermions from sharing all the same quantum numbers.

Wolfgang Pauli proposed the principle in 1925 to explain patterns in atomic spectra and the structure of electron shells. Electrons are fermions, so each orbital can contain at most two electrons, and those two must have opposite spin quantum numbers. The rule is not simply a statement that electrons repel each other; it follows from the antisymmetric quantum state required for identical fermions.

The principle helps explain the periodic table, chemical bonding, and the stability of ordinary matter. It also supports the pressure inside white dwarfs and neutron stars. A common mix-up is applying it to all particles: identical bosons, such as photons, may occupy the same quantum state. The broader rule comes from quantum statistics, while the exclusion result specifically concerns fermions.