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By Root 2159 0

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