Джеймс Глик - Genius - The Life and Science of Richard Feynman

Perhaps the universe bloomed and col apsed again and again in a cycle that ran through eternity.

The issue seemed linked to the nature of time itself.

Assumptions about time were built into the equations for the particle interactions that led to the creation and dissipation of light. If one thought about time as Wheeler and Feynman had, one could not escape a cosmic connection between these intimate interactions and the process of universal expansion. As Hermann Bondi said at the meeting’s outset, “This process leads to the dark night sky, to the disequilibrium between matter and radiation, and to the fact that radiated energy is effectively lost … we accept a very close connection between cosmology and the basic structure of our physics.” By their boldness in constructing a time-symmetrical theory of half advanced and half retarded waves, Wheeler and Feynman had been forced into boldness of a cosmological sort. If the equations were to balance properly, they had to make the

mathematical assumption that al radiation was eventual y absorbed somewhere. A beam of light heading forever into an eternal future, never to cross paths with a substance that would absorb it, would violate their assumption, so their theory mandated a certain kind of universe. If the universe were to expand forever, conceivably its matter might so thin out that light would not be absorbed.

Physicists had learned to distinguish three arrows of time. Feynman described them: the thermodynamic or

“accidents of life” arrow; the radiation or “retarded or advanced” arrow; and the cosmological arrow. He suggested keeping in mind three physical pictures: a tank with blue water on one side and clear water on the other; an antenna with a charge moving toward it or away; and distant nebulas moving together or apart. The connections between these arrows were connections between the pictures. If a film showed the water getting more and more mixed, must it also show the radiation leaving the antenna and the nebulas drifting apart? Did one form of time govern the others? His listeners could only speculate, and speculate they did.

“It’s a very interesting thing in physics,” said Mr. X, “that the laws tel us about permissible universes, whereas we only have one universe to describe.”

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 hopeful y 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 al 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

wel -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 al 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 col oquium. Pauli, stil 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 tel 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 oscil ators, 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-cal ed Hamiltonian method. Physicists spoke of “finding a Hamiltonian” for a system: if they could find one, then they could go ahead and calculate; if not, they were helpless. In Wheeler and Feynman’s view of direct action at a distance, the Hamiltonian method had no place. That was because of the introduction of time delays. It was not enough merely to write down a complete description of the present: the positions, momentums, and other quantities. One never knew when some delayed effect would hurtle into the picture out of the past (or in the case of Wheeler and Feynman, out of the future). Because past and future interacted, the customary differential-equation point of view broke down. The alternative least-action or Lagrangian approach was no luxury. It was a necessity.

With al this on his mind, Feynman went to a beer party at the Nassau Tavern. He sat with a physicist lately arrived from Europe, Herbert Jehle, a former student of Schrödinger in Berlin, a Quaker, and a survivor of prison camps in both Germany and France. The American scientific world was absorbing such refugees rapidly now, and the turmoil of Europe seemed more palpable and near.

Jehle asked Feynman what he was working on. Feynman explained and asked in turn whether Jehle knew of any application of the least-action principle in quantum

mechanics.

Jehle certainly did. He pointed out that Feynman’s own hero, Dirac, had published a paper on just that subject eight years before. The next day Jehle and Feynman looked at it together in the library. It was short. They found it, “The Lagrangian in Quantum Mechanics,” in the bound volumes of Physikalische Zeitschrift der Sowjetunion , not the best-read of journals. Dirac had worked out the beginnings of a least-action approach in just the style Feynman was seeking, a way of treating the probability of a particle’s entire path over time. Dirac considered only one detail, a piece of mathematics for carrying the wave function—the packet of quantum-mechanical knowledge—forward in time by an infinitesimal amount, a mere instant.