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Autograph postcard signed 'W. Pauli' to Samuel A. Goudsmit, Hamburg, postmarked 13 March, 1926.[Hamburg: 1926].
An iconic artefact of twentieth-century physics of great historical significance, this is the postcard in which the 26-year old Pauli finally acknowledges that Goudsmit and George Uhlenbeck were correct in their discovery of electron spin. Known as the 'conscience of physics', Pauli's imprimatur was essential before the concept of spin could be accepted by the wider physics community. Spin is now one of the key concepts in quantum physics. Pauli's bitter initial opposition to spin is doubly ironic: its discovery was based on Pauli's exclusion principle, formulated less than a year earlier, for which Pauli received the Nobel Prize (Goudsmit and Uhlenbeck did not receive the Nobel); and it was Pauli himself who eventually showed how to incorporate spin into quantum mechanics, which had been invented by Werner Heisenberg just nine months earlier.

Translated, the postcard reads, in full:

"Dear Goudsmit,
First of all I am writing to you today to inform you that because of recent communications from Copenhagen I have realized that I have been wrong in my objections against Thomas and that his deliberations about relativity can be put into an entirely correct and faultless form. Therefore the questions referring to fine structure can really be satisfactorily answered!
Secondly I would like to urge you once more to check thoroughly whether the Danish Zeeman measurement on He+ can be reconciled with an alkali-like concept of these Zeeman effects. Please write to me as soon as you know anything about this! It was very good to see you in Hamburg.
With best regards to you personally and to Professor Ehrenfest [i.e. Paul Ehrenfest, Goudsmit's teacher]."

"Pauli was an exceptional man in many respects. Not only did he enter physics as a prodigy and contribute outstanding discoveries under his own name but he contributed also to the success of others through personal discussions and through an extensive correspondence ... His criticism was sought but also dreaded. He has therefore been called the 'Conscience of Physics' (Gewissen der Physik). Ehrenfest, who was very fond of him, conferred on him the title 'God's Whip' (Geissel Gottes), because he would not relent in a discussion until all the weak points had been made perfectly clear" (Brandt, p. 203).

When the visible lines of the spectrum of hydrogen are observed in a powerful spectroscope, they appear as close doublets. In atoms having two electrons outside the closed core, or shell, of electrons the lines are split into triplets. Higher multiplets are also possible. This phenomenon, known as fine structure, was established experimentally around 1890 but did not receive an explanation until Sommerfeld's theory of 1915-16, which had wide influence through its detailed treatment in Sommerfeld's classic textbook Atombau und Spektrallinien (1919). Sommerfeld's theory was accepted by most physicists until near the end of the reign of the 'old' quantum theory in 1925, but by that time a number of discrepancies had been found between experiment and the theory's predictions. In attempting to explain these discrepancies, Pauli had found it necessary to postulate a 'particular two-valuedness of the quantum-theoretic properties of the electron, which cannot be described from the classical point of view.' "Within a few months this property of the electron was given a physical description which, it is true, is not satisfactory from the viewpoint of classical physics. This description is regarded as the discovery of the intrinsic angular momentum or spin of the electron. In fact the description was given twice. Already in January [Ralph] Kronig discussed it with Pauli who was completely opposed to the idea so that Kronig did not publish it. The concept of the electron spin was independently proposed and published by Uhlenbeck and Goudsmit, who thus became the discoverers of spin ... In a lecture given in 1955, Uhlenbeck recalled: 'Goudsmit and I hit upon this idea by studying a paper by Pauli, in which the famous exclusion principle was formulated and in which, for the first time four quantum numbers were ascribed to the electron. This was done rather formally; no concrete picture was connected with it. To us, this was a mystery. We were so conversant with the proposition that every quantum number corresponds to a degree of freedom, and on the other hand with the idea of a point electron, which obviously had three degrees of freedom only, that we could not place the fourth quantum number. We could understand it only if the electron was assumed to be a small sphere which could rotate'" (Brandt, pp. 148-150).

Uhlenbeck and Goudsmit published their discovery in a one-page note in Naturwissenschaften in November 1925 ['Ersetzung der Hypothese vom unmechanischen Zwang durch eine Forderung bezglich des inneren Verhaltens jedes einzelnen Elektrons,' p. 953]. A problem quickly arose. Heisenberg calculated the splitting of the energy levels based on Uhlenbeck and Goudsmit's idea and found that it was twice as large as the experimentally observed value. "In December 1925 the golden jubilee of Lorentz' doctorate was celebrated. Among many others Bohr attended and he urged Uhlenbeck and Goudsmit to write a more detailed paper. This they completed in the same month. It is entitled 'Spinning Electrons and the Structure of Spectra' [Nature, 117, pp. 264-5], has two pages, and mentions the missing factor of two. Bohr was very much in favour of spin. In a letter to Ehrenfest, who had been his host in Leiden, he wrote that on his way back to Copenhagen he felt 'wie ein Profet des Elektromagnet-Evangeliums [like a prophet of the spin gospel]' when meeting with Pauli and Heisenberg.

"The missing factor of two was found by [the British physicist Llewellyn] Thomas early in 1926, then working in Bohr's institute. The transformation between the two reference systems (orbiting electron and electron at rest) is, of course, a Lorentz transformation. After all, in his first paper on special relativity Einstein had used it to connect the electric field of a charge at rest with the magnetic field of a moving charge. But a Lorentz transformation can be applied only if the two reference systems are in uniform (unaccelerated) motion with respect to each other. The circular motion appearing here, however, is accelerated. By taking this fact properly into account Thomas was able to explain the mysterious factor of two, later called the Thomas factor" (Brandt, p. 151).

Pauli "was first informed of Thomas's calculation in a letter from Bohr of 20 February 1926 where Bohr writes: 'even your being alarmed about my frivolous enthusiasm for the 'new heresy' didn't discourage me.' And he continues, not without irony: 'Now comes the surprise for the learned theoreticians of relativity and responsibility-carrying scientists [i.e. Heisenberg and Pauli]. Indeed, a young Englishman, Thomas, who during the last half year was in Copenhagen, has found out these days that the whole question of the unlucky factor 2 probably is due exclusively to a mistake in the calculation of the relative motion of the electron and the nucleus.' Having got Thomas's manuscript from Bohr, Pauli replied on 26 February. His rejection was complete: 'I consider the publication of the present note by Thomas in Nature to be a blunder and would be glad if you could block it or else see to it that essential modifications are made in the text of the note.'

"But Bohr was unwavering in his optimism, while Pauli repeated his criticism in long letters to Bohr on 5 March and to [Hendrik] Kramers on 8 March 1926. In the latter Pauli writes: 'Today Herr Goudsmit was here [i.e., in Hamburg, as Pauli mentions in the postcard], and I was delighted to see him. What he told me about the calculations of Thomas and the manuscripts of Thomas which he brought along have utterly strengthened me in the view that with my objections ... I am totally right.' It was in this letter also that Pauli referred to himself as 'God's whip' striking the Copenhagen Institute again" (Enz, pp. 114-115). Bohr addressed Pauli's criticisms in a letter of 9 March, and this time Pauli was convinced. "To Goudsmit he wrote on 13 March [in the offered postcard]: 'Today I write you, first, to inform you that, based on recent information from Copenhagen, I now indeed have come to the conviction that I was wrong with my objections against Thomas and that his relativistic consideration may be brought into a totally correct and unobjectionable form. The question of the fine structure therefore is now truly satisfactorily clarified.'

"Looking back it is obvious that Pauli's 'two-valuedness' referred to the spin, the electron's fourth degree of freedom which became of fundamental importance in the announcement of the exclusion principle. Indeed, some two years later Pauli showed in another fundamental paper ['Zur Quantenmechanik des magnetischen Elektrons,' Zeitschrift für Physik 43, 12 July 1927, pp. 601-623] that it was possible to describe the spinning electron by two-component wave functions. With this, the problem of the electron spin was completely solved, at least in the framework of non-relativistic wave mechanics, and it yielded, as another manifestation of the two-valuedness, the well-known Pauli matrices" (Enz, pp. 115-116).

C. P. Enz, No Time to be Brief, 2006; S. Brandt, Harvest of a century, 2009.. Autograph postcard signed 'W. Pauli' to Samuel A. Goudsmit, Hamburg, postmarked 13 March, 1926. 140 x 90 mm, written on both sides, in German (margin with two punch-holes, catching a few letters but not affecting legibility)

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