137 - Arthur I. Miller [21]
He had developed a keen interest in the theory of numbers and a year later entered the university. He had also tried studying Einstein’s relativity theory. The reigning power in the mathematics department, Professor Ferdinand von Lindemann, convinced that Heisenberg’s brush with relativity theory had spoiled his mind for a career in mathematics, rejected him outright. Sommerfeld, on the other hand, delighted with his enthusiasm and obvious brilliance, sent him straight to his graduate-level seminars, plunging him into advanced quantum physics.
Heisenberg and Pauli quickly struck up a friendship, cemented by their mutual passion for physics—although the two young men had diametrically opposite tastes when it came to what constituted a good time. Heisenberg recalled: “While I loved the daylight and spent as much of my free time as I could mountain-walking, swimming or cooking simple meals on the shore of one of the Bavarian lakes, Wolfgang was a typical night bird. He preferred the town, liked to spend his evenings in some old bar or café, and would then work on his physics through much of the night with great concentration and success.” It was often said that in Germany just after the war, in the pre-Hitler years of the Weimar Republic, there were two types of people: those who went in for night life and those who dedicated themselves to the youth movement. Pauli typified the former, Heisenberg the latter.
Whenever they were apart, they corresponded, though their letters were more like scientific articles as they bounced ideas off one another. Just as he had corrected Heisenberg’s homework in Münich, so Pauli continued to comment critically on Heisenberg’s ideas. “Pauli had a very strong influence on me,” Heisenberg recalled. “I mean Pauli was simply a strong personality…. He was extremely critical, I don’t know how frequently he told me, ‘You are a complete fool,’ and so on. That helped me a lot.”
“When I was young I believed I was the best formalist of my time,” Pauli said later in life, referring to his extraordinary understanding of mathematics and how to use it in solving problems in physics. Mathematics had served him well in his papers on relativity theory. Now Pauli was to apply his mathematical acumen to another puzzle that he was determined to crack and which formed the subject matter of his PhD thesis. It related to the great Danish physicist Niels Bohr and his seminal model of the “atom as universe.”
Niels Bohr and his theory of the atom
Bohr was another scientific prodigy. He arrived in England from Copenhagen in 1911, when he was twenty-six, and became fascinated by the work of Ernest Rutherford at Manchester University. Rutherford had just unraveled the structure of the atom in a series of experiments that suggested that the atom was made up of a nucleus with a positive charge, surrounded by enough negatively charged electrons to produce an electrically neutral atom.
In other words, it was a sort of miniature solar system. But the model was unstable. Science was out of step with nature.
Bohr set out to solve this problem. He showed that electrons in an atom could not revolve in just any orbit—like planets—but that only certain orbits were allowed. Given that atoms are generally stable, their planetary electrons cannot be pulled into the nucleus. If they did then the atom would collapse. Bohr interpreted the stability of atoms as proof that there had to be a lowest orbit. He found it by altering Newton’s theory of planetary motion using Planck’s constant.*
In his atomic “bookkeeping” Bohr assigned to each allowed orbit a whole number, which he called the “principal quantum number.” The lowest orbit was number one. As the principal quantum number increased, the orbits became closer and closer. Bohr called allowed orbits “stationary states.”
(a)
(a) This figure shows the hydrogen