The puzzle was a pattern in the allowed states
Why do atomic shells close, instead of every electron settling into the same lowest arrangement? Drawing more planetary orbits could not answer that. The periodic pattern of chemistry, multiplet spectra and magnetic line splitting all had to fit one way of counting electron states.
The ETH archive ties Pauli’s fourth quantum number to multiplet structure and the anomalous Zeeman effect. Each spectral line marks a jump between two terms, so counting states means first sorting the terms. The evidence was an ordered network of lines, not a direct image of which electron places were filled.
Read the evidence: ETH Library, The Pauli Principle — Pauli archive and institutional account
The rule came before an intuitive picture
Looking back, Pauli recalls rejecting the idea that alkali doublets come from the angular momentum of the atomic core. Instead he gave the electron a two-valued property that classical physics could not describe. Stoner’s comparison between the number of states counted in spectra and the closed subgroups helped link the two counts.
The exclusion rule then allowed at most one electron in each fully specified one-electron state. The rule came before spin was accepted as its interpretation. Projecting modern spin labels onto every step of the discovery hides why the fourth degree of freedom looked so hard to understand at first.
Read the evidence: W. Pauli (1946), Exclusion Principle and Quantum Mechanics — Nobel lecture, December 13; readable copyETH Library, The Pauli Principle — Pauli archive and institutional account
The complete state includes spin
Two electrons can share a spatial orbital if their spins differ, because they then occupy different spin-orbitals. Likewise, two states need not differ in location to be distinct. What counts is the full spatial and spin description.
A single determinant treats the electrons as independent particles. It is useful, but it does not describe every interacting atom exactly. Correlated electron states can need a superposition of several determinants, and the superposition is still antisymmetric. The exclusion requirement holds in that better calculation; the simple picture of filling orbitals may not.
Read the evidence: W. Pauli (1946), Exclusion Principle and Quantum Mechanics — Nobel lecture, December 13; readable copy
The formula cancels when two electrons share a spin-orbital
The normalized antisymmetric state below is built from two orthonormal spin-orbitals. Each label stands for a complete set of position and spin. Swapping the labels flips the sign of the state and leaves every probability unchanged. The labels name the arguments of the state; they do not mark which electron is which.
Put the same spin-orbital in both slots and the numerator cancels to zero everywhere, so no normalized state is left. Once antisymmetry is assumed, this algebra shows exclusion directly. It does not explain, within nonrelativistic mechanics alone, why electrons must belong to this symmetry class.
Read the evidence: W. Pauli (1946), Exclusion Principle and Quantum Mechanics — Nobel lecture, December 13; readable copy
Spin–statistics adds assumptions, not a repulsive force
Pauli’s 1940 paper takes up the link between spin and statistics in relativistic theory. Its abstract names the conditions it relies on, including positive energy and observables that commute at spacelike separation. This is a further theoretical argument, not a tidier version of the earlier spectral counting.
So exclusion should not be drawn as a new classical force that pushes labeled particles apart. Coulomb interactions, antisymmetry and the set of available states together shape how matter behaves. The occupation rule alone is not enough to calculate a real material’s pressure, bonding or energy spectrum.
Read the evidence: W. Pauli (1940), The Connection Between Spin and Statistics, Phys. Rev. 58, 716 — author abstract
Use the Labs to see what each model assumes
The exchange Lab shows how distinguishability changes the comparison; the occupation Lab compares quantum state counting in an ideal gas. Neither rebuilds the spectral evidence that led Pauli to his rule. When a model forbids an occupation in its code, it is showing an assumption and what follows from it.
Historically the path ran from sorting spectral terms to a rule on occupation, then to antisymmetric many-electron states and a relativistic spin–statistics argument. Taking these steps one at a time shows what each one explains, and makes clear that no single experiment established them all.
Read the evidence: ETH Library, The Pauli Principle — Pauli archive and institutional accountW. Pauli (1940), The Connection Between Spin and Statistics, Phys. Rev. 58, 716 — author abstract