Pauli and Bohr watch a spinning top. Photograph by Erik Gustafson, courtesy of AIP Emilio Segrè Visual Archives, Margrethe Bohr Collection.
By 1920, physicists were still struggling to make sense of the splitting of atomic spectral lines in a magnetic field, discovered by Pieter Zeeman (Milestone 1). With the Bohr atom of 1913 had come the notion of quantized orbits for electrons around the atomic nucleus. Perhaps, it was thought, the Zeeman splitting arose from the interaction between the angular momenta of the 'core' of electrons in closed shells and of the 'radiant electron' in the outermost unclosed shell. Yet calculations made on this basis — notably by Arnold Sommerfeld and Alfred Landé, using an Ersatzmodell — failed to match experimental data. The helium atom posed a particular problem: which of its two electrons should be considered 'core' and which 'radiant'? Also, no one could explain why, if an atom were in its ground state, all its electrons were not bound into the innermost shell. In 1924, Landé gave up the struggle as "impossible once and for all".
Wolfgang Pauli, however, was undeterred. He dropped the notion of an interaction between core and radiant electron and proposed instead that line splitting arose as a consequence of an intrinsic property of the electron: "eine klassisch nicht beschreibbare Art von Zweideutigkeit" — a classically indescribable two-valuedness — as he wrote in the first of his two 1925 Zeitschrift für Physik papers.
Ralph Kronig, a young physicist in Landé's laboratory, suggested to Pauli that this might be imagined as the rotation of an electron about its own axis with one half-unit of angular momentum — in other words, spin. Pauli disliked the idea: it was still 'classically indescribable' and, moreover, the calculations of level splitting by Kronig were a factor of two out from measured values. Kronig did not publish, but later that year George Uhlenbeck and Samuel Goudsmit did — the same idea, beset by the same problems. Pauli still didn't like it.
Nevertheless, it was a short step from the 'two-valuedness' of an intrinsic electron quantum number for Pauli to realize why all electrons in an atom are not bound in the innermost state. Guided by comments made by Edmund C. Stoner, Pauli saw that, if the four numbers used to describe line splitting (denoted n, k, m and j) were thought of as quantum numbers of the electron, then once an electron existed in some state defined by particular values of n, k, m and j, no other electron could enter that state. Using this 'exclusion principle', Pauli could derive the exact shell structure of the atom — two electrons to close the innermost shell, eight to close the next, and so on.
Pauli's 'two-valuedness' was indeed due to the spin of the electron.
The deal was sealed early in 1926, with the publication by Llewellyn H. Thomas of what became known as the 'Thomas factor' — the missing factor of two. Thomas' classical analysis finally won over Pauli the perfectionist (Paul Dirac would soon supply the full quantum relativistic formalism; Milestone 4). Pauli's 'two-valuedness' was indeed due to the spin of the electron. Probably the great man was cheered, having written to Kronig in May 1925, "At the moment physics is again terribly confused. In any case, it is too difficult for me, and I wish I had been a movie comedian or something of the sort and had never heard of physics."
der Geschwindigkeitsabhängigkeit der Elektronenmasse auf den Zeemaneffekt
