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

In effect the electron feels a resistance, cal ed radiation resistance, and extra force has to be applied to overcome it. A broadcasting antenna, radiating energy in the form of radio waves, encounters radiation resistance—extra current has to be sent through the antenna to make up for it.

Radiation resistance is at work when a hot, glowing object cools off. Because of radiation resistance, an electron in an atom, alone in empty space, loses energy and dies out; the lost energy has been radiated away in the form of light. To explain why this damping takes place, physicists assumed they had no choice but to imagine a force exerted by the electron on itself. By what else, in empty space?

One day, however, Feynman walked into Wheeler’s office with a new idea. He was “pie-eyed,” he confessed, from struggling with an obscure problem Wheeler had given him. Instead he had turned back to self-action. What if (he thought) an electron isolated in empty space does not emit radiation at al , any more than a tree makes a sound in an empty forest. Suppose radiation were to be permitted only when there is both a source and a receiver. Feynman imagined a universe with just two electrons. The first shakes. It exerts a force on the second. The second shakes and generates a force that acts back on the first. He computed the force by a familiar field equation of Maxwel ’s, but in this two-particle universe there was to be

no field, if the field meant a medium in which waves were freely spreading outward on their own.

He asked Wheeler, Could such a force, exerted by one particle on another and then back on the first, account for the phenomenon of radiation resistance?

Wheeler loved the idea—it was the sort of approach he might have taken, stripping a problem down to nothing but a pair of point charges and trying to build up a new theory from first principles. But he saw immediately that the numbers would come out wrong. The force coming back to the first charge would depend on how strong the second charge was, how massive it was, and how near it was. But none of those quantities influence radiation resistance. This objection seemed obvious to Feynman afterward, but at the time he was astonished by his professor’s fast insight. And there was another problem: Feynman had not properly accounted for the delay in the transmission of the force to and fro. Whatever force was exerted back on the first particle would come at the wrong time, too late to match the known effect of radiation resistance. In fact Feynman suddenly realized that he had been describing a different phenomenon altogether, a painful y simple one: ordinary reflected light. He felt foolish.

Time delay had not been a feature of the original electromagnetic theory. In Maxwel ’s time, on the eve of relativity, it stil seemed natural to assume, as Newton had, that forces acted instantaneously. An imaginative leap was needed to see that the earth swerves in its orbit not because the sun is there but because it was there eight minutes before, the time needed for gravity’s influence to cross nearly a hundred mil ion miles of space—to see that

if the sun were plucked away, the earth would continue to orbit for eight minutes. To accommodate the insights of relativity, the field equations had to be amended. The waves were now retarded waves, held back by the finite speed of light.

Here the problem of time’s symmetry entered the picture.

The electromagnetic equations worked magnificently when retarded waves were correctly incorporated. They worked equal y wel when the sign of the time quantities was reversed, from plus to minus. Translated back from mathematics into physics, that meant advanced waves—

waves that were received before they were emitted.

Understandably, physicists preferred to stay with the retarded-wave solutions. An advanced wave, running backward in time, seemed peculiar. Viewed in close-up it would look like any other wave, but it would converge on its source, like a concentric ripple heading toward the center of a pond, where a rock was about to fly out—the film played backward again. Thus, despite their mathematical soundness, the advanced-wave solutions to field equations stayed in the background, an unresolved but not especial y urgent puzzle.

Wheeler immediately proposed to Feynman that they consider what would happen if advanced waves were added to his two-electron model. What if the apparent time-symmetry of the equations were taken seriously? One would have to imagine a shaken electron sending its radiation outward symmetrical y in time. Like a lighthouse sending its beam both north and south, an electron might shine both forward and backward to the future and the past.

It seemed to Wheeler that a combination of advanced and

retarded waves might cancel each other in a way that would overcome the lack of any time delay in the phenomenon of radiation resistance. (The canceling of waves was wel understood. Depending on whether they were in or out of phase, waves of the same frequency would interfere either constructively or destructively. If their crests and troughs lined up exactly, the size of the waves would double. If crests lined up with troughs, then the waves would precisely neutralize each other.) He and Feynman, calculating excitedly over the next hour, found that the other difficulties also seemed to vanish. The energy arriving back at the original source no longer depended on the mass, the charge, or the distance of the second particle. Or so it seemed, in the first approximation produced by their rough computation on Wheeler’s blackboard.

Feynman set to work on this possibility. He was not troubled by the seemingly nonsensical meaning of it. His original notion contained nothing out of the ordinary: Shake a charge here—then another charge shakes a little later.

The new notion turned paradoxical as soon as it was expressed in words: Shake a charge here—then another charge shakes a little earlier . It explicitly required an action backward in time. Where was the cause and where was the effect? If Feynman ever felt that this was a deep thicket to enter merely for the sake of eliminating the electron’s self-action, he suppressed the thought. After al , self-action created an undeniable contradiction within quantum mechanics, and the entire profession was finding it insoluble. At any rate, in the era of Einstein and Bohr, what was one more paradox? Feynman already believed that it was the mark of a good physicist never to say, “Oh,

whaddyamean, how could that be?”

The work required intense calculation, working out the correct forms of the equations, always checking to make sure that the apparent paradox never turned into an actual mathematical contradiction. Gradual y the basic model became, not a system of two particles, but a system where the electron interacted with a multitude of other “absorber”

particles al around it. It would be a universe where al radiation eventual y reached the surrounding absorber. As it happened, that softened the most bizarre time-reversed tendencies of the model. For those who were squeamish about the prospect of effects anticipating their causes, Feynman offered a barely more palatable view: that energy is momentarily “borrowed” from empty space, and paid back later in exact measure. The lender of this energy, the absorber, was assumed to be a chaotic multitude of particles, moving in al directions so that almost al its effects on a given particle would cancel one another. The only time an electron would feel the presence of this absorbing layer would be when it accelerated. Then the effect of the source on the absorber would return to the source at exactly the right time, with exactly the right force, to account for radiation resistance. Thus, given that one cosmological assumption—that the universe has enough matter in every direction to soak up outgoing radiation—