ExclusorPauli Exclusion Principle / Degeneracy Pressure

Exclusor works one door, and he does not check names. He checks states.

Behind him is a neon atom: ten electrons, seated 1s² 2s² 2p⁶. Each box on his chart is one orbital: two electrons at most, one spin-up, one spin-down. Every seat in the second shell is taken. Hence the sign.

Wolfgang Pauli wrote the rule in 1925, before anyone knew what the second seat in each box was for. To account for atomic spectra he needed a fourth quantum number with only two values, and he ruled that no two electrons in an atom could share all four. Later that year George Uhlenbeck and Samuel Goudsmit identified it as electron spin. Pauli received the 1945 Nobel Prize.

The modern form is the first three lines on this page. Swap two identical electrons and their joint wavefunction changes sign. Put both in the same state, a equal to b, and the determinant has two identical columns: the wavefunction is zero. That state does not exist.

The badge says ½ because the rule binds him too. Markus Fierz in 1939 and Pauli in 1940 showed that relativistic quantum theory makes every particle of half-integer spin obey it.

Neon has no stable negative ion. An eleventh electron would have to sit in 3s, and neon will not hold it.

Scale it up. In 1926 Ralph Fowler showed that electrons packed this tightly push back: degeneracy pressure, the last formula. It holds up white dwarfs, to about 1.4 solar masses, Chandrasekhar's limit. Exclusion is not a force. Together with electric attraction, it keeps bulk matter from collapsing, as Dyson and Lenard proved in 1967, and Lieb and Thirring, far more simply, in 1975.

Exclusor never shoves. He just knows who is already inside.