137 - Arthur I. Miller [4]
But if this one number were so important, should it not be possible to deduce it from the mathematics of these theories? Disturbingly, no one could.
The fine structure constant turns out to be exquisitely tuned to allow life as we know it to exist on our planet. Perhaps it was not surprising, then, that physicists began referring to 137 as a “mystical number.”
By the time Sommerfeld stumbled across 137 in 1915, whole numbers were beginning to crop up everywhere in atomic physics. Two years before, the Danish physicist Niels Bohr had worked out that the energy levels of the electrons within atoms could be expressed with whole numbers, so-called quantum numbers. He assumed that only three quantum numbers were necessary to locate an electron in the atom, just as it takes only three numbers to locate an object in space: its coordinates in the three dimensions. But then ten years later the twenty-four-year-old Pauli showed that in fact a fourth quantum number was needed. The problem was that the fourth quantum number could not be visualized.
For Pauli the problem came down to numbers: to the “difficult transition from three to four.” And 137 turned out to be linked with this transition.
Three hundred years earlier, a full-scale row over a very similar issue had broken out between the mystic and scientist Johannes Kepler and the Rosicrucian Robert Fludd. Kepler argued that three was the fundamental number at the core of the universe, using arguments from Christian theology and ancient mysticism. Fludd, however, argued for four on the basis of the Kabbalah, of the four limbs, the four seasons, and the four elements (earth, water, air, and fire): God’s creation of the world was a transition from two to three to fourness, he asserted.
But where did 137 come in? Pauli became convinced that the number was so fundamental that it ought to be deducible from a theory of elementary particles. This quest took over his waking and sleeping life. Driven beyond endurance, he sought the help of Jung.
Jung’s theory of psychology offered Pauli a way to understand the deeper meaning of the fourth quantum number and its connection with 137, one that went beyond science into the realm of mysticism, alchemy, and archetypes. Jung, for his part, saw in Pauli a treasure trove of archaic memories, as well as a great scientist who could help him put his theories on a firm footing.
THE EARLY YEARS of the twentieth century were a watershed not unlike the Renaissance. Freud’s discovery of the mind as a field of study and Max Planck’s discovery of the quantum nature of matter were quickly followed by Einstein’s relativity theory and Bohr’s theory of the atom. Then came the horrors of the First World War, which inspired a trend toward spiritualism and a return to ancient beliefs, especially in Germany. Just before the war the great German physicist Werner Heisenberg was finding solace in reading Plato. In 1927 Sommerfeld, in response to a request by a periodical for an article on astrology, wrote:
Doesn’t it strike one as a monstrous anachronism that in the twentieth century a respected periodical sees itself compelled to solicit a discussion about astrology? That wide circles of the educated or half-educated public are attracted more by astrology than astronomy? [We] are thus evidently confronted once again with a wave of irrationality and romanticism like that which a hundred years ago spread over Europe as a reaction against the rationalism of the eighteenth century.
Yet he himself wrote ecstatically of the mystical qualities of 137.
The search for some point of contact between physics and the mind was of key interest to many physicists, including Max Born and Werner Heisenberg—two other pioneers of quantum physics—and Pauli and Bohr. As Pauli put it:
I do not