Hiding near the back of the hall, Shinichiro Tomonaga was one of the few to understand Heisenberg’s lectures. He had just spent a year and a half as an undergraduate teaching himself quantum mechanics from all the original papers. On the last day of lectures, Nagaoka scolded that Heisenberg and Dirac had discovered a new theory in their 20s, whereas Japanese students were still pathetically copying lecture notes. “Nagaoka’s pep talk really did not get me anywhere,” Tomonaga later confessed.
Sons of Samurai
He was, however, destined to go places, along with his high school and college classmate Hideki Yukawa. Both men’s fathers had traveled abroad and were academics: Tomonaga’s a professor of Western philosophy, Yukawa’s a professor of geology. Both were of samurai lineage. Even before going to school, the younger Yukawa had learned the Confucian classics from his maternal grandfather, a former samurai. Later he encountered the works of Taoist sages, whose questioning attitude he would liken to the scientific pursuit. Tomonaga was inspired to study physics by hearing Albert Einstein lecture in Kyoto in 1922, as well as by reading popular science books written in Japanese.
The two men obtained their bachelor’s degrees in 1929 from Kyoto University, at the start of the worldwide depression. Lacking jobs, they stayed on as unpaid assistants at the university. They taught each other the new physics and went on to tackle research projects independently. “The depression made scholars of us,” Yukawa later joked.
In 1932 Tomonaga joined Nishina’s lively group at Riken. Yukawa moved to Osaka University and, to Tomonaga’s annoyance, confidently focused on the deepest questions of the day. (Yukawa’s first-grade teacher had written of him: “Has a strong ego and is firm of mind.”) One was a severe pathology of quantum electrodynamics, known as the problem of infinite self-energy. The results of many calculations were turning out to be infinity: the electron, for instance, would interact with the photons of its own electromagnetic field so that its mass—or energy—increased indefinitely. Yukawa made little progress on this question, which was to occupy some of the world’s brilliant minds for two more decades. “Each day I would destroy the ideas that I had created that day. By the time I crossed the Kamo River on my way home in the evening, I was in a state of desperation,” he later recalled.
Eventually, he resolved to tackle a seemingly easier problem: the nature of the force between a proton and a neutron. Heisenberg had proposed that this force was transmitted by the exchange of an electron. Because the electron has an intrinsic angular momentum, or spin, of one half, his idea violated the conservation of angular momentum, a basic principle of quantum mechanics. But having just replaced classical rules with quantum ones for the behavior of electrons and photons, Heisenberg, Bohr and others were all too willing to throw out quantum physics and assume that protons and neutrons obeyed radical new rules of their own. Unfortunately, Heisenberg’s model also predicted the range of the nuclear force to be 200 times too long.
Yukawa discovered that the range of a force depends inversely on the mass of the particle that transmits it. The electromagnetic force, for instance, has infinite range because it is carried by the massless photon. The nuclear force, on the other hand, is confined within the nucleus and should be communicated by a particle of mass 200 times that of the electron. He also found that the nuclear particle required a spin of zero or one to conserve angular momentum.
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