Genius_ The Life and Science of Richard Feynman - James Gleick [76]
Least Action in Quantum Mechanics
Omega oil did nothing for Arline’s lumps and fevers, and she was admitted to the hospital in Far Rockaway with what her doctor feared was typhoid. Feynman began to glimpse the special powerlessness that medical uncertainty can inflict on a scientific person. He had come to believe that the scientific way of thinking brought a measure of calmness and control in difficult situations—but not now. However remotely, medicine was a part of the domain of knowledge he considered his. It belonged to science. At one time his father had hopefully studied a kind of medicine. Lately Richard had been sitting in on a physiology course, learning some basic anatomy. He read up on typhoid fever in Princeton’s library, and when he visited Arline in the hospital he started questioning the doctor. Had a Widal test been administered? Yes. The results? Negative. Then how could it be typhoid? Why were all of Arline’s friends and relatives wearing gowns to protect against supposed bacteria that even a sensitive laboratory test could not detect? What did the mysterious lumps appearing and disappearing in her neck and armpit have to do with typhoid? The doctor resented his questions. Arline’s parents pointed out that his status as fiancé did not entitle him to interfere in her medical care. He backed down. Arline seemed to recover.
With Wheeler, meanwhile, Feynman was trying to move their work a crucial step forward. So far, despite its modern, acausal flavor, it was a classical theory, not a quantum one. It treated objects as objects, not as probabilistic smudges. It treated energy as a continuous phenomenon, where quantum mechanics required discrete packets and indivisible jumps in well-defined circumstances. The problem of self-energy was as severe in classical electrodynamics as in quantum theory. Unwanted infinities predated the quantum. They appeared as soon as one faced the consequences of a pointlike electron. It was as simple as dividing by zero. Feynman had felt from the beginning that the natural route would be to start with the classical case and only then work toward a quantized electrodynamics. There were already standard recipes for translating classical models into their modern quantum cousins. One prescription was to take all the momentum variables and replace them with certain more complicated expressions. The problem was that in Wheeler and Feynman’s theory there were no momentum variables. Feynman had eliminated them in creating his simplified framework based on the principle of least action.
Sometimes Wheeler told Feynman not to bother—that he had already solved the problem. Later in the spring of 1941 he went so far as to schedule a presentation of the quantized theory at the Princeton physics colloquium. Pauli, still dubious, buttonholed Feynman on his way into Palmer Library one day. He asked what Wheeler was planning to say. Feynman said he didn’t know.
“Oh?” Pauli said. “The professor doesn’t tell his assistant how he has it worked out? Maybe the professor hasn’t got it worked out.”
Pauli was right. Wheeler canceled the lecture. He lost none of his enthusiasm, however, and made plans for not one but a grand series of five papers. Feynman, meanwhile, had a doctoral thesis to prepare. He decided to approach the quantizing of his theory just as he had approached complicated problems at MIT, by working out cases that were stripped to their bare essentials. He tried calculating the interaction of a pair of harmonic oscillators, coupled, with a time delay—just a pair of idealized springs. One spring would shake, sending out a pure sine wave. The other would bounce back, and out of their interaction new wave forms would evolve. Feynman made some progress but could not understand the quantum version. He had gone too far in the direction of simplicity.
Conventional quantum mechanics went from present to future by the solving of differential equations—the so-called Hamiltonian method. Physicists spoke of “finding