137 - Arthur I. Miller [30]
Sommerfeld supplied Heisenberg with the newest data as well as his own unpublished research, including speculation on new ways to combine the three quantum numbers at the very basis of Bohr’s theory of the atom. “All right, you have an interest in mathematics; it may be that you know something; it may be that you know nothing…. We will see what you can do,” he said. Heisenberg quickly came up with his own ideas on how to tackle the anomalous Zeeman effect. He rewrote one of Sommerfeld’s equations using half figures—1/2, 3/2, and so on—and discovered he could produce an equation that described most of the observed multiplets.
Then he turned to Bohr’s model of the atom—with the nucleus as a rigid core surrounded by filled shells of electrons, the whole thing spinning like a ball. Heisenberg made the audacious assumption that the core and the surrounding electron shared a half unit of angular momentum by means of an interaction that he left unspecified. (An object moving in a line has linear momentum [mass times velocity]. Similarly an object spinning like a top has angular momentum [which is related to mass times angular velocity].) The mysterious interaction between the core and the lone electron could be the explanation for the anomalous Zeeman effect. Sommerfeld was stunned, as was Pauli. Surely this would result in an atom emitting a half quanta of energy. But that had to be wrong because quanta were assumed to be indivisible. This was a basic postulate of the quantum theory. All the same, Heisenberg’s equation produced multiplets for the alkalis which precisely duplicated data from experiments. “Success sanctifies the means,” Heisenberg wrote to Pauli.
Sommerfeld was astonished that this novice dared take such a dramatically different approach to problems with which experienced scientists had struggled. Instead of getting tied up in endless complicated calculations, Heisenberg came up with instant solutions. Eventually Sommerfeld had to give in and accepted that there had to be half quantum numbers. After all, he reasoned, classical physics was frequently proved wrong. Why not atomic physics, too?
Bohr, however, insisted that while breakdowns in classical physics were fine, it was not acceptable when it came to his own theory of the atom. At the Bohr-Festspiele in Göttingen, he had discussed Heisenberg’s new approach and referred to it as “very interesting,” by which he meant that it was almost certainly wrong. Although it happened to fit existing data, Bohr argued, it was not an end in itself. Bohr was more interested in unraveling a problem than in instant solutions.
Bohr now suggested that there might be a force that linked the core and the lone outer electron in an alkali atom and that this force might distort the core in two different ways, giving rise to a “double-valuedness,” which he, too, was willing to include as a half quantum number. Thus Bohr was able to reproduce the required multiplets, while avoiding the other half quantum numbers that were essential to Heisenberg’s model. But what was this strange force? Pauli couldn’t accept it and argued tooth and nail with Bohr. He continued to torture himself over the problem of the anomalous Zeeman effect but could make no sense of it. Bohr insisted that Pauli publish his own contribution to these mathematical models and he did so “with a tear in my eye,” as he wrote to Sommerfeld. As for Heisenberg’s theory of the anomalous Zeeman effect, Pauli found it “unsightly” and “monstrous.” “I am deeply