Quantum_ Einstein, Bohr and the Great Debate About the Nature of Reality - Manjit Kumar [89]
Throughout the summer of 1925 Goudsmit taught Uhlenbeck everything he knew about spectral lines. Then one day they discussed the exclusion principle, which Goudsmit thought was no more than another ad hoc rule that brought a little more order to the unholy mess of atomic spectra. However, Uhlenbeck immediately hit upon an idea that Pauli had already dismissed.
An electron could move up and down, back and forth, and side to side. Each of these different ways of moving physicists called a 'degree of freedom'. Since each quantum number corresponds to a degree of freedom of the electron, Uhlenbeck believed that Pauli's new quantum number must mean that the electron had an additional degree of freedom. To Uhlenbeck, a fourth quantum number implied that the electron must be rotating. However, spin in classical physics is a rotational motion in three dimensions. So if electrons spin in the same way, like the earth about its axis, there was no need for a fourth number. Pauli argued that his new quantum number referred to something 'which cannot be described from the classical point of view'.38
In classical physics, angular momentum, everyday spin, can point in any direction. What Uhlenbeck was proposing was quantum spin – 'two-valued' spin, spin 'up' or spin 'down'. He pictured these two possible spin states as an electron spinning either clockwise or anti-clockwise about a vertical axis as it orbits the atomic nucleus. As it did so, the electron would generate its own magnetic field and act like a subatomic bar magnet. The electron can line up either in the same or in the opposite direction as an external magnetic field. Initially it was believed that any allowed electron orbit could accommodate a pair of electrons provided that one had spin 'up' and the other spin 'down'. However, these two spin directions have very similar but not identical energies, resulting in the two slightly different energy levels that gave rise to the alkali doublet lines – two closely spaced lines in the spectra instead of one.
Uhlenbeck and Goudsmit showed that electron spin could be either plus or minus half, values that satisfied Pauli's restriction for the fourth quantum number to be 'two-valued'.39
By the middle of October, Uhlenbeck and Goudsmit had written a one-page paper and showed it to Ehrenfest. He suggested that the normal alphabetical order of names be reversed. Since Goudsmit had already published several well-received papers on atomic spectra, Ehrenfest was concerned that readers would think that Uhlenbeck was the junior partner. Goudsmit agreed, as 'it was Uhlenbeck who had thought of spin'.40 But as to the soundness of the concept itself, Ehrenfest was unsure. He wrote to Lorentz asking for 'his judgement and advice on a very witty idea'.41
Although 72, retired and living in Haarlem, Lorentz still travelled to Leiden once a week to teach. Uhlenbeck and Goudsmit met him one Monday morning after his lecture. 'Lorentz was not discouraging', said Uhlenbeck. 42 'He was a little bit reticent, said that it was interesting and that he would think about it.' A week or two later, Uhlenbeck went back to receive Lorentz's verdict and was given a stack of papers full of calculations in support of an objection to the very notion of spin. A point on the surface of a spinning electron, Lorentz pointed out, would move faster than the speed