Wolfgang Pauli was born in Vienna in the same year in which Max Planck introduced quantization. He was five when Einstein printed the theory of relativity. At 19, a student at the University of Munich, he was asked to write an encyclopedia piece on Einstein’s theory. The article was actually so brilliant that as soon as Einstein read it he remarked that it could be Pauli understood even more regarding relativity than he himself did. In 1925, five years before postulating the neutrino, Pauli put forward his Exclusion Principle. He illustrated that the assorted atomic spectra would make sense when the electron states in an atom are summarized by four quantum digits moreover if each of these types of conditions is occupied by a single electron. In other words, the minute a given state is occupied, every one of the various other electrons will be excluded from that state. Pauli recognized that one of the digits had to correspond to energy, which in turn is related to the proximity from the center (when we consider the status as orbits), while at the same time two additional numerals illustrate angular momentum, which pertains to the shape and orientation pertaining to the orbit. Pauli could find no physical significance for the fourth quantum number, which was needed empirically. The significance was found that very same year by two Dutch physics scholars.
George Uhlenbeck and Samuel Goudsmit were researching a number of features in regard to spectral lines named the anomalous Zeeman effect. That subsequently led them to the realization that Pauli’s 4th quantum digit needs to relate to electron spin. Here is the story in Goudsmit’s wonderful and self-effacing words– a story that conveys the groping and uncertainty that exist in the struggle to understand nature, as contrasted with the logic and certainty that are imposed after the battle is won.
The Pauli principle was published early in 1925 … if I had been a good physicist, I would have noticed already in May 1925 that this implied that the electron possessed spin. But I was not a good physicist and I did not realize this …When Uhlenbeck appeared on the scene…he asked all the questions I never had…and the day came that I had to tell Uhlenbeck about the Pauli principle– he said to me: “But don’t you see what this implies? It means that there is a fourth degree of freedom for the electron. It means that the electron has a spin, that it rotates”…I asked “What is a degree of freedom?” In any case, he made his remark, and it was lucky that I knew all these things about the spectra…“That fits precisely into our hydrogen scheme which we wrote about four weeks ago. If one now allows the electron to be magnetic with the appropriate magnetic moment, then one can understand all those complicated Zeeman-effects.—S. Goudsmit
And so the idea that the electron spins on its axis was introduced (still thinking of the electron as a particle) and that this spin has a value of 1/2, as contrasted with the photon’s spin of 1.
The next step was to see if this is consistent with experimentation. During a course at Harvard University, Prof. Wendell Furry gave this amusing account of how this happened (as best as I can recall): After Uhlenbeck and Goudsmit had the idea that electron spin might explain the anomalous spectroscopic results, there remained the crucial task of determining if the effect is in the right direction. This involved the kind of calculation that all physics students have to suffer through in which polarity, direction of spin, direction of magnetic field, the “right-hand rule”, etc., get all confused and make the head spin (no pun intended). In other words, there are many opportunities to go wrong, and many do. Well, the story goes, each man did the calculation and when they compared notes they found they had opposite results. One of them had obviously made a mistake, so they went back to check their calculations. As it happened, each found an error, so they were still in disagreement. At this point they went to their mentor, Paul Ehrenfest, who happened to have a distinguished visitor named Albert Einstein. It was decided that the four of them would do the calculation independently (remember, we are talking about elementary physics here). When they got together the result was 2-2. They finally broke the deadlock by counting Einstein’s vote twice.— W. Furry (restructured).
I believe that this story is making light of the difficulty physicists have in keeping track of the proper sign. (It is said that the difference between a good and a bad physicist is that the good one makes an even number of errors, so the final sign is correct.) It also hints of the “papal” authority of Einstein, although Uhlenbeck did say that Einstein visited Leiden in 1925 and “gave us the essential hint” to complete the calculation.