137 - Arthur I. Miller [36]
Spin was undeniably a property of an electron but it was entirely impossible to visualize it in a way consistent with relativity theory. Scientists had to accept that the fourth quantum number had no accompanying visual image. It was time for atomic physics to move on from trying to visualize everything in images relating to the world in which we live.
Intermezzo—Three versus Four: Alchemy, Mysticism, and the Dawn of Modern Science
My branch of science, physics, has got somewhat bogged down. The same thing can be said in a different way: When rational methods in science reach a dead end, a new lease on life is given to those contents that were pushed out of time consciousness in the 17th century and sank into the unconscious.
—WOLFGANG PAULI
SINCE his student days and before, Pauli had been interested not just in the rational world of physics but also in the role of the irrational. Arnold Sommerfeld, his professor and lifelong mentor, was fascinated by the sixteenth-century pioneer of modern science, Johannes Kepler. Science, Sommerfeld reminded his students, emerged out of mysticism and had never completely separated itself. Besides his purely scientific work, Sommerfeld also pursued kabbalistic lines of research based on pure numbers and spoke of Kepler as his precursor.
In fact, he saw a direct connection between the developments of modern science and the harmony that Kepler had been searching for. Writing of his own research into spectral lines, the “fingerprint” of the atom, he said, “What we are nowadays hearing of the language of the spectra is a true music of the spheres within the atom, chords of integral relationships, an order and harmony that becomes even more perfect in spite of manifold variety.”
Pauli, too, sought out links between his work and these ancient esoteric systems of understanding the universe. Many years later he was to write to Sommerfeld that he had finally succeeded in using the exclusion principle to establish the reason why the electron shells fill up as they do in the series 2, 8, 18, 32, a grouping that Sommerfeld had described as “somewhat kabbalistic.” In 1923, when Sommerfeld wrote those words, no one had been able to find any reason why electron shells should fill up in this way and not some other. There was, in fact, no firm basis for almost all of the rules of atomic physics. “Some of the rules recall irresistibly the teaching of the alchemists or the witches’ kitchen of Faust,” wrote one physicist. Writings on the subject were nearly as mysterious as the Kabbalah, the Jewish book of mysticism that claimed that numbers could yield insight into the world beyond sense perceptions, just as Bohr’s theory of the atom promised.
From time to time Pauli could not resist poking fun at his mentor’s obsession with numbers. Once he noticed an advertisement posted around Munich, promoting an optical firm: “If you have trouble with your eyes, see Herr Runke.” Pauli added the coda, “For integers, go to Sommerfeld.”
In a tribute to Sommerfeld on his eightieth birthday, Pauli wrote that he “would not hesitate to set as a superscription over Sommerfeld’s works in a wider sense the title of Kepler’s magnum opus—Harmonices Mundi.”
Inspired by Sommerfeld, Pauli became fascinated by Kepler and may well have read him in the original Latin. In Hamburg he could have followed up his interest by attending lectures by Erwin Panofsky. A historian of art who specialized in symbolism and iconography, Panofsky had a great deal of knowledge about early science, particularly Kepler.
But what was it about Kepler that particularly piqued Pauli’s interest?
It seems likely that Pauli read Kepler’s Harmonices Mundi (Harmonics of the World) at this early stage of his life, when he was working on the exclusion principle. If so, he could not fail to have noticed the Appendix to Book V, about