Genius (19 page)

He turned on the air valve. The apparatus gave a slight tremble, and water started to dribble from the cork. More air—the flow of water increased and the rubber tube seemed to shake but not to twist, at least not with any confidence. Feynman opened the valve farther, and the bottle exploded, showering water and glass across the room. The head of the cyclotron banished Feynman from the laboratory henceforth.

Sobering though Feynman’s experimental failure was, for years to come he and Wheeler both delighted in telling the story, and they were both scrupulous about never revealing the answer to the original question. Feynman had worked it out correctly, however. His physical intuition had never been sharper, nor his ability to translate fluently between a palpable sense of the physics and the formal mathematical equations. His experiment had actually worked, until it exploded. Which way does the lawn sprinkler turn? It does not turn at all. As the nozzles suck water in, they do not pull themselves along, like a rope climber pulling himself up hand over hand. They have no purchase on the water ahead. And the idea of force exerted as a torque within the curve of the S is beside the point. In the normal version, water sprays forth in organized jets. The action and reaction are straightforward and measurable. The momentum of the water spraying in one direction equals the momentum that spins the nozzle in the opposite direction. But in the inverse case, when water is sucked in, there are no jets. The water is not organized. It enters the nozzle from all directions and therefore applies no force at all.

A development in twentieth-century entertainment technology—the motion picture—incidentally provided an advance in the technology of thought experiments. It was now natural for a scientist, in his mind’s laboratory, to
play the film backward
. In the case of the lawn sprinkler, reversibility proved to be an illusion. If the flow of the water were visible, a motion picture of an ordinary lawn sprinkler played backward would look distinctly different from the sucking lawn sprinkler played forward. Filmmakers themselves had been seduced by the new, often comical insights that could be gained by taking a strip of celluloid and running it backward through the projector. Divers sprang feet first from lakes as a spray of water collapsed into the space left behind. Fires drew smoke from the air and created a trail of new-made paper. Fragmented eggshells assembled themselves around shuddering chicks.

For Feynman and Wheeler reversibility was becoming a central issue at the level of atomic processes, where spins and forces interacted more abstractly than in a lawn sprinkler. It was well known that the equations describing the motions and collisions of objects ran equally well forward and backward. They were symmetrical with respect to time, at least where just a few objects were concerned. How embarrassing, therefore, that time seemed so one-way in the real world, where a small amount of energy could scramble an egg or shatter a dish and where unscrambling and unshattering were beyond the power of science. “Time’s arrow” was already the catchphrase for this directionality, so evident to common experience, yet so invisible in the equations of physicists. There, in the equations, the road from past to future looked identical to the road from future to past. “There is no signboard to indicate that it is a one-way street,” complained Arthur Eddington. The paradox had been there all along, since Newton at least, but relativity had highlighted it. The mathematician Hermann Minkowski, by visualizing time as a fourth dimension, had begun to reduce past-future to the status of any pair of directions: left-right, up-down, back-front. The physicist drawing his diagrams obtains a God’s-eye view. In the space-time picture a line representing the path of a particle through time simply exists, past and future visible together. The four-dimensional space-time manifold displays all eternity at once.

The laws of nature are not rules controlling the metamorphosis of what is into what will be. They are descriptions of patterns that exist, all at once, in the whole tapestry. The picture is hard to reconcile with our everyday sense that time is special. Even the physicist has his memories of the past and his aspirations for the future, and no space-time diagram quite obliterates the difference between them.

Philosophers, in whose province such speculations had usually belonged, were left with a muddy and senescent set of concepts. The distress of the philosophers of time spilled into their adverbs:
sempiternally
,
hypostatically
,
tenselessly
,
retrodictably
. Centuries of speculation and debate had left them unprepared for the physicists’ sudden demolition of the notion of simultaneity (in the relativistic universe it meant nothing to say that two events took place at the same time). With simultaneity gone, sequentiality was foundering, causality was under pressure, and scientists generally felt themselves free to consider temporal possibilities that would have seemed farfetched a generation before.

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.