At the same time, Tomonaga was tackling the problem of infinite self-energy that Yukawa had given up. To this end, he developed a means of describing the behavior of several interacting quantum particles, such as electrons, moving at near the speed of light. Generalizing an idea due to Dirac, he assigned to each particle not just space coordinates but also its own time coordinate and called the formulation “super-many-time theory.” This work, which became a powerful framework for quantum electrodynamics, was published in 1943 in Riken’s science journal.
By this time most students had been mobilized for war. Nambu was among those assigned to radar research for the army. (Intense rivalry between the army and the navy led each to duplicate the other’s efforts). Resources were short and the technology often very primitive: the army could not develop mobile radar systems to pinpoint enemy targets. Nambu was once handed a piece of Permalloy magnet, about three by three inches, and told to do what he could with it for aerial submarine detection. He was also told to steal from the navy Tomonaga’s paper on waveguides, labeled “Secret,” which he accomplished by visiting an unsuspecting professor [see “Strings and Gluons—The Seer Saw Them All,” by Madhusree Mukerjee, News and Analysis; Scientific American, February 1995].
(Curiously, Japan’s past technical contributions included excellent magnetrons designed by Kinjiro Okabe and an antenna; the latter, invented by Hidetsugu Yagi and Shintaro Uda in 1925, still projects from many rooftops. The Japanese armed forces learned about the importance of the “Yagi array” from a captured British manual.)
Younger physicists around the Tokyo area continued their studies when they could; professors from the University of Tokyo, as well as Tomonaga, held special courses for them on Sundays. In 1944 a few students (including Satio Hayakawa, whose quote begins this article) were freed from war research and returned to the university campus. Even so, times were difficult. One student’s house was burned down, another was drafted, and a third had his house burned down just before he was drafted. The venue for the seminars shifted several times. Tomonaga, who had always been physically weak, would sometimes instruct his students while lying sick in bed.
Meanwhile Nishina had been instructed by the army to investigate the possibility of making an atomic bomb. In 1943 he concluded that it was feasible, given enough time and money. He assigned a young cosmic-ray physicist, Masa Takeuchi, to build a device for isolating the lighter form of uranium required for a bomb. Apparently Nishina thought the project would help keep physics research alive for when the war ended. Taketani, back in prison, was also forced to work on the problem. He did not mind, knowing it had no chance of success.
Across the Pacific, the Manhattan Project was employing some 150,000 men and women, not to mention a constellation of geniuses and $2 billion. In contrast, when the Japanese students realized they would need sugar to make uranium hexafluoride (from which they could extract the uranium) they had to bring in their own meager rations. A separate effort, started by the navy in 1943, was also far too little, too late. By the end of the war, all that the projects had produced was a piece of uranium metal the size of a postage stamp, still unenriched with its light form.
And two atom bombs had exploded in Japan. Luis W. Alvarez of the University of California at Berkeley was in the aircraft that dropped the second bomb over Nagasaki, deploying three microphones to measure the intensity of the blast. Around these instruments he wrapped a letter (with two photocopies) drafted by himself and two Berkeley colleagues, Philip Morrison and Robert Serber. They were addressed to Riokichi Sagane, Nagaoka’s son and a physicist in Tomonaga’s group. An experimenter, Sagane had spent two years at Berkeley learning about cyclotrons, enormous machines for conducting studies in particle physics. He had become acquainted with the three Americans who now sought to inform him of the nature of the bomb. Although the letter was recovered by the military police, Sagane learned of it only after the war. After the Japanese surrender in August 1945, the country was effectively under American occupation for seven years. General Douglas MacArthur’s administration reformed, liberalized and expanded the university system. But experimental research in nuclear and related fields was essentially prohibited. All cyclotrons in Japan were dismantled and thrown into the sea, for fear that they might be used to research an atomic bomb.