Genius_ The Life and Science of Richard Feynman - James Gleick [45]
“Now I know I’m right … In my theory there are a lot more ‘fundamental’ invariants than in the other theory.”
And on they went. “Hot dog! after 3 wks of work … I have at last found a simple proof,” Feynman wrote. “It’s not important to write it, however. The only reason I wanted to do it was because I couldn’t do it and felt that there were some more relations between the An & their derivatives that I had not discovered … Maybe I’ll get electricity into the metric yet! Good night, I have to go to bed.”
The equations came fast, penciled across the notebook pages. Sometimes Feynman called them “laws.” As he worked to improve his techniques for calculating, he also kept asking himself what was fundamental and what was secondary, which were the essential laws and which were derivative. In the upside-down world of early quantum mechanics, it was far from obvious. Heisenberg and Schrödinger had taken starkly different routes to the same physics. Each in his way had embraced abstraction and renounced visualization. Even Schrödinger’s waves defied every conventional picture. They were not waves of substance or energy but of a kind of probability, rolling through a mathematical space. This space itself often resembled the space of classical physics, with coordinates specifying an electron’s position, but physicists found it more convenient to use momentum space (denoted by Pα), a coordinate system based on momentum rather than position—or based on the direction of a wavefront rather than any particular point on it. In quantum mechanics the uncertainty principle meant that position and momentum could no longer be specified simultaneously. Feynman in the August after his sophomore year began working with coordinate space (Qα)—less convenient for the wave point of view, but more directly visualizable.
“Pα is no more fundamental than Qα nor vice versa—why then has Pα played such an important role in theory and why don’t I try Qα instead of Pα in certain generalizations of equations …” Indeed, he proved that the customary approach could be derived directly from the theory as cast in terms of momentum space.
In the background both boys were worrying about their health. Welton had an embarrassing and unexplained tendency to fall asleep in his chair, and during the summer break he was taking naps, mineral baths, and sunlamp treatments—doses of high ultraviolet radiation from a large mercury arc light. Feynman suffered something like nervous exhaustion as he finished his sophomore year. At first he was told he would have to stay in bed all summer. “I’d go nuts if it were me I,” T. A. wrote in their notebook. “Anyhow, I hope you get to school all right in the fall. Remember, we’re going to be taught quantum mechanics by no less an authority than Prof. Morse himself. I’m really looking forward to that.” (“Me too,” Feynman wrote.)
They were desperately eager to be at the front edge of physics. They both started reading journals like the Physical Review. (Feynman made a mental note that a surprising number of articles seemed to be coming from Princeton.) Their hope was to catch up on the latest discoveries and to jump ahead. Welton would set to work on a development in wave tensor calculus; Feynman would tackle an esoteric application of tensors to electrical engineering, and only after wasting several months did they begin to realize that the journals made poor Baedekers. Much of the work was out of date by the time the journal article appeared. Much of it was mere translation of a routine result into an alternative jargon. News did sometimes break in the Physical Review, if belatedly, but the sophomores were ill equipped to pick it out of the mostly inconsequential background.
Morse had taught the second half of the theoretical physics course that brought Feynman and Welton together, and he had noticed these sophomores, with their penetrating questions about quantum mechanics. In the