The difficulty was a pattern of allowed states
Why do atomic shells close, instead of all electrons settling into the same lowest arrangement? This was not answered by drawing more planetary orbits. Chemical periodicity, multiplet spectra and magnetic splitting had to be reconciled with one way of counting electronic possibilities.
The ETH archive connects Pauli’s fourth quantum number to multiplet structure and the anomalous Zeeman effect. A spectral line records a transition between terms; extracting a count of states requires their classification. The evidence is an organized network of lines, rather than a photograph of occupied electron seats.
Read the evidence: ETH Library, The Pauli Principle — Pauli archive and institutional account
The restriction came before a comfortable picture
In his later account, Pauli recalls rejecting an explanation of alkali doublets based on angular momentum of the atomic core. He introduced a classically indescribable two-valued property of the electron. Stoner’s comparison between spectral-state counts and closed subgroups helped connect the bookkeeping.
The exclusion rule then restricted occupation of a fully specified one-electron state. It preceded the accepted spin interpretation. Reading modern spin labels back into every step of the discovery conceals why the fourth degree of freedom initially seemed so difficult to understand.
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
A spatial orbital is not the complete state
Two electrons can share a spatial orbital when their spin states differ. They do not then occupy the same complete spin-orbital. Conversely, different locations are not needed to make two states distinct: the full spatial and spin information matters.
A single determinant is a useful independent-particle construction, not an exact description of every interacting atom. Correlated electronic states can require superpositions of determinants while retaining antisymmetry. The exclusion requirement survives that improvement; a simple orbital filling diagram need not.
Read the evidence: W. Pauli (1946), Exclusion Principle and Quantum Mechanics — Nobel lecture, December 13; readable copy
The cancellation expresses the forbidden occupation
For two orthonormal spin-orbitals, the normalized antisymmetric state below exchanges the complete position-and-spin labels. Interchanging the particle labels reverses the sign without changing any probability. The labels track arguments of the state, not distinguishable electron identities.
If both orbitals are replaced by the same one, the numerator cancels identically and cannot describe a normalized state. That algebra displays exclusion once antisymmetry is imposed. It does not prove, from 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 tackles the connection in relativistic theory. Its abstract explicitly invokes conditions involving positive energy and commutation of observables at spacelike separation. This is a further theoretical argument, not simply the earlier spectral counting written more neatly.
Exclusion therefore should not be drawn as a new classical force that pushes labeled particles apart. Coulomb interactions, antisymmetry and the choice of available states jointly affect matter. An occupation rule alone does not 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 models to ask what has been assumed
The exchange Lab lets distinguishability change the comparison; the occupation Lab compares quantum state counting in an ideal gas. Neither reconstructs the spectral evidence that led Pauli to his rule. A model that forbids an occupation in its code is demonstrating an assumption and its consequences.
The historical bridge runs from spectral classification to an occupation restriction, then to antisymmetric many-electron states and a relativistic spin–statistics argument. Keeping these steps separate makes the explanatory gain visible without pretending they were all established by one experiment.
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