by James Gleick
In the fall of 1940 Feynman returned to the fundamental problem with which he had flirted since his undergraduate days. Could the ugly infinities of quantum theory be eliminated by forbidding the possibility that an electron acts on itself—by eliminating, in effect, the field? Unfortunately he had meanwhile learned what was wrong with his idea. The problem was a phenomenon that could only be explained, it seemed, in terms of the action of an electron on itself. When real electrons are pushed, they push back: an accelerating electron drains energy by radiating it away. In effect the electron feels a resistance, called 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 all, 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 Maxwell’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 painfully simple one: ordinary reflected light. He felt foolish.
Time delay had not been a feature of the original electromagnetic theory. In Maxwell’s time, on the eve of relativity, it still 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 million 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 equally well 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 especially 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 symmetrically 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 well 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 all, 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. Gradually the basic model became, not a system of two particles, but a system where the electron interacted with a multitude of other “absorber” particles all around it. It would be a universe where all radiation eventually 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 all directions so that almost all 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—Feynman found that a system of equations in which advanced and retarded waves were combined half and half seemed to withstand every objection.
Waves forward and backward in time. Wheeler and Feynman tried to work out a consistent scheme for the interactions of particles
, and they embroiled themselves in paradoxes of past and future . A particle shakes; its influence spreads outward like waves from a stone thrown into a pond. To make their theory symmetrical, they also had to use inward-traveling waves-implying action backward in time.
They found that they could avoid unpleasant paradoxes because these normal and time-reserved waves ("retarded" and "advanced") canceled each other out-but only if the universe was arranged so as to guarantee that all radiation would be absorbed somewhere, sometime. A beam of light traveling forever into infinite, empty space, never striking an absorber, would foil their theory's bookkeeping. Thus cosmologists and philosophers of time continued to consider their scheme long after it had been supplanted in the mainstream of quantum theory.
He described it to his graduate student friends and challenged them to find a paradox he could not explain his way through. For example, could one design a mechanism with a target that would shut a gate when struck by a pellet, such that the advanced field closed the gate before the pellet arrived, in which case the pellet could not strike the target, in which case the advanced field would not close the gate after all … He imagined a Rube Goldberg contraption that might have come straight from Wheeler’s old book of ingenious mechanisms and mechanical devices. Feynman’s calculations suggested that the model was surprisingly immune to paradox. As long as the theory relied on probabilities, it seemed to escape fatal contradictions. It did not matter where the absorber was or how it was shaped, as long as there were absorbing particles off at some distance in every direction. Only if there were “holes” in the surrounding layer, places where radiation could go forever without being absorbed, could the advanced effects make trouble, arriving back at the source before they had been triggered.
Wheeler had his own motive for pursuing this quixotic theory. Most physicists were now persuaded that the atom embodied at least three irreconcilably different particles, electrons, protons, and neutrons, and cosmic rays were providing intimations of several more. This proliferation offended Wheeler’s faith in the ultimate simplicity of the world. He continued to cherish a notion so odd that he was reluctant to discuss it aloud, the idea that a different kind of theory would reveal everything to be made of electrons after all. It was crazy, he knew. But if electrons were to be the ultimate building blocks, their radiative forces would have to provide the key, in ways that the standard theory was not prepared to explain. Within weeks he began pressing Feynman to write a preliminary paper. If they were going to make grand theories, Wheeler would make sure they publicized the work properly. Early in 1941 he told Feynman to prepare a presentation for the departmental seminar, usually a forum for distinguished visiting physicists, in February. It would be Feynman’s first professional talk. He was nervous about it.
As the day approached, Wigner, who ran the colloquiums, stopped Feynman in the hall. Wigner said he had heard enough from Wheeler about the absorber theory to think it was important. Because of its implications for cosmology he had invited the great astrophysicist Henry Norris Russell. John von Neumann, the mathematician, was also going to come. The formidable Wolfgang Pauli happened to be visiting from Zurich; he would be there. And though Albert Einstein rarely bestirred himself to the colloquiums, he had expressed interest in attending this one.
Wheeler tried to calm Feynman by promising to field questions from the audience. Wigner tried to brief him. If Professor Russell appears to fall asleep during your talk, Wigner said, don’t worry—Professor Russell always falls asleep. If Pauli appears to be nodding, don’t assume he agrees—he nods from palsy. (Pauli could be ruthless in dismissing work he considered shallow or flimsy: “ganz falsch,” utterly false—or worse, “not even false.”) Feynman prepared carefully. He collected his notes and put them into a brown envelope. He entered the seminar room early and covered the blackboard with equations. While he was writing, he heard a soft voice behind him. It was Einstein. He was coming to the lecture and first he wondered whether the young man might direct him to the tea.
Afterward Feynman could remember almost nothing: just the trembling of his hand as he pulled his notes from the envelope and then a feeling that his mind put itself at ease by concentrating on the physics and forgetting the occasion and the personalities. Pauli did object, perhaps sensing that the use of advanced potentials merely invoked a sort of mathematical tautology. Then, politely, Pauli said, “Don’t you agree, Professor Einstein?” Feynman heard that soft Germanic voice again—so pleasant, it seemed—saying no, the theory seemed possible, perhaps there was a conflict with the theory of gravitation, but after all the theory of gravitation was not so well established …
The Reasonable Man
He suffered spells of excessive rationality. When these struck it was not enough to make progress in his scientific work, nor to rectify his mother’s checkbook, nor to recompute his own equivocal balance sheet (eighteen dollars for laundry, ten dollars to send home … ), nor to lecture his friends, as they watched him repair his bicycle, on the silliness of believing in God or the supernatural. During one occurrence he wrote out an hourly schedule of his activities, both scholarly and recreational, “so as to efficiently distribute my time,” he wrote home. When he finished, he recognized that no matter how careful he was, he would have to leave some indeterminate gaps—“hours when I haven’t marked down just what to do but I do what I feel is most necessary then—or what I am most interested in—whether it be W.’s problem or reading Kinetic Theory of Gases, etc.” If there is a disease whose symptom is the belief in the ability of logic to control vagarious life, it afflicted Feynman, along with his chronic digestive troubles. Even Arline Greenbaum, sensible as she was, could spark flights of reason in him. He grew concerned about the potential for emotional disputes between husbands and wives. Even his own parents fought. He hated the battles and the anger. He did not see why two intelligent people, in love with each other, willing to converse openly, should get caught in arguments. He worked out a plan. Before revealing it to Arline, however, he decided to lay it out for a physicist friend over a hamburger at a diner on the Route 1 traffic circle. The plan was this. When Dick and Arline disagreed intensely about a matter of consequence, they would set aside a fixed time for discussion, perhaps one hour. If at the end of that time they had not found a resolution, rather than continue fighting they would agree to let one of them decide. Because Feynman was older and more experienced (he explained), he would be the one.
His friend looked at him and laughed. He knew Arline, and he knew what would really happen. They would argue for an hour, Dick would give up, and Arline would decide. Feynman’s plan was a sobering example of the theoretical mind at work.
Arline was visiting more and more often. They would have dinner with the Wheelers and go for long walks in the rain. She had the rare ability to embarrass him: she knew where his small vanities were, and she teased him mercilessly whenever she caught him worrying about other people’s opinions—how things might seem. She sent him a box of pencils emblazoned, “Richard darling, I love you! Putzie,” and caught him slicing off the incriminating legend, for fear of inadvertently leaving one on Professor Wigner’s desk. “What do you care what other people think?” she said again and again. She knew he prided himself on honesty and independence, and she held him to his own high standards. It became a touchstone of their relationship. She mailed him a penny postcard with a verse written across it:
If you don’t like the things I do
My friend, I say, Pecans to you!
If I irate with pencils new
My bosom pal, Pecans to you!
…
If convention’s mask is borne in view
…
If deep inside sound notions brew
And from without you take your cue
My sorry friend, Pecans to you!
Her words struck home. Meanwhile she had nagging health worries: a lump seemed to come and go on her neck, and she developed uncomfortable, unexplained fevers. Her uncle, a physicia
n, had her rub the lump with a nostrum called omega oil. (This style of treatment had had its heyday a hundred years before.)
The day after his presentation to the physics colloquium in February, Richard went up to Cambridge for a meeting of the American Physical Society, and she took the train from New York to Boston’s South Station to join him. An old fraternity friend picked her up and they crossed the bridge to MIT, catching a ride on a horse-drawn junk wagon. They found Richard in the corridor of building 8, the physics building. He walked by in animated conversation with a professor. Arline made eye contact with him, but he did not acknowledge her. She realized that it would be better not to speak.
When Richard returned to the fraternity house that evening he found her in the living room. He was ebullient; he grabbed her and swung her around, dancing. “He certainly believes in physical society,” one of the fraternity boys said. At Wheeler’s prodding Feynman had presented their space-time electrodynamics a second time, to a broader audience. The talk went well. After having faced a public of Einstein, Pauli, von Neumann, and Wigner, he had little to fear from the American Physical Society rank and file. Still, he worried that he might have bored his listeners by sticking nervously to his prepared text. There were a few polite questions, and Wheeler helped answer them.
