how we discovered electrons spin

The Mechanism

By 1925 spectroscopists could photograph the emission lines of every element and read patterns in the wavelengths that atomic theory could not explain. Two problems in particular were pressing. First, when a sodium atom was placed in a magnetic field, single spectral lines split into two rather than three — the "anomalous Zeeman effect," which Wolfgang Pauli in Hamburg had reduced to an unavoidable "two-valuedness" of the electron that no classical picture could describe. Second, Alkali atoms showed doublets in their spectra — spontaneous splittings, even without a magnetic field, that suggested the electron carried some intrinsic angular momentum around itself. In January 1925 a 20-year-old Columbia PhD student named Ralph Kronig, then travelling through Europe, worked out the necessary two-valuedness with an explicit picture: an electron spinning on its own axis, generating an intrinsic magnetic moment. He showed it to Pauli in Hamburg, who ridiculed it — "it is indeed very clever but of course has nothing to do with reality" — because the surface of a classical spinning electron would have to move faster than light for the numbers to work. Kronig withdrew the idea and never published. That autumn in Leiden, two graduate students of Paul Ehrenfest — George Uhlenbeck, 24, and Samuel Goudsmit, 23 — arrived at the same picture independently. Ehrenfest, who was Einstein's closest correspondent and Bohr's most respected critic, made them write it up in a two-page note. They took the draft to Hendrik Lorentz — sixty-two, Nobel laureate, the elder statesman of Dutch theoretical physics — who worked through the classical picture over the following week and returned with the same objection Pauli had raised: the equatorial speed of a spinning electron would exceed the speed of light. Uhlenbeck and Goudsmit wanted to withdraw the paper. Ehrenfest replied that he had already mailed it. As Uhlenbeck later recalled his advisor telling them: "You are both young enough to be able to afford a stupidity!" The paper appeared in *Naturwissenschaften* in November 1925, and an even shorter English version in *Nature* on 20 February 1926, titled "Spinning Electrons and the Structure of Spectra." There was a factor-of-two discrepancy with observation that Kronig's version had also carried, and which Pauli used against them; it was fixed by Llewellyn Thomas at Bohr's institute in Copenhagen a few weeks later with a relativistic correction now called the Thomas precession. Once the factor of two came out right, Pauli conceded — and by 1927 he had built the electron's two-valuedness into his own formalism as the Pauli spin matrices. Two years after that, Paul Dirac's 1928 relativistic wave equation for the electron produced spin as an automatic consequence of relativity and quantum mechanics, so that "electron spin" was no longer a hypothesis but a theorem. Every fermion — the electron and every other elementary particle of matter — carries spin ½. The Pauli exclusion principle, which says no two identical fermions can share a quantum state, follows directly from this spin: it is why atoms have shells, why chemistry has periods, why matter takes up space. Uhlenbeck and Goudsmit had two more careers each. Uhlenbeck became a leading statistical-mechanics theorist at Michigan and later Rockefeller University; Goudsmit ran the scientific arm of the American Alsos Mission at the end of World War II — the intelligence effort that captured Werner Heisenberg and dismantled the German uranium program — and later became editor of *Physical Review Letters*, the journal where most twentieth-century particle-physics discoveries were first announced. Neither ever won a Nobel Prize; the citation was blocked in 1927 by Pauli's own priority claim, and the Kronig priority question hung over the award until it was too late to give.