Feynman had enunciated a set of principles for a theory of interacting particles. He wrote them out as follows:
1 The acceleration of a point charge is due only to the sum of its interactions with other charged particles… . A charge does not act on itself.
2 The force of interaction which one charge exerts on a second is calculated by means of the Lorentz force formula, in which the fields are the fields generated by the first charge according to Maxwell’s equations.
Phrasing the third principle was more difficult. He tried:
3 The fundamental equations are invariant with respect to a change of the sign of the time …
Then, more directly:
3 The fundamental (microscopic) phenomena in nature are symmetrical with respect to interchange of past and future.
Pauli, despite his skepticism, understood the power of the last principle. He pointed out to Feynman and Wheeler that Einstein himself had argued for an underlying symmetry of past and future in a little-known 1909 paper. Wheeler needed little encouragement; he made an appointment to call at the white clapboard house at 112 Mercer Street.
Einstein received this pair of ambitious young physicists sympathetically, as he did most scientists who visited in his last years. They were led into his study. He sat facing them behind his desk. Feynman was struck by how well the reality matched the legend: a soft, nice man wearing shoes without socks and a sweater without a shirt. Einstein was well known to be unhappy with the acausal paradoxes of quantum mechanics. He now spent much of his time writing screeds on world government which, from a less revered figure, would have been thought crackpot. His distaste for the new physics was turning him into, as he would have it, “an obstinate heretic” and “a sort of petrified object, rendered blind and deaf by the years.” But the theory Wheeler and Feynman described was not yet a quantum theory—so far, it used only classical field equations, with none of the quantum-mechanical amendments that they knew would ultimately be necessary—and Einstein saw no paradox. He, too, he told them, had considered the problem of retarded and advanced waves. He reminisced about the strange little paper he had published in 1909, a manifesto of disagreement with a Swiss colleague, Walter Ritz. Ritz had declared that a proper field theory should include only retarded solutions, that the time-backward advanced solutions should simply be declared impermissible, innocent though the equations looked. Einstein, however, could see no reason to rule out advanced waves. He argued that the explanation for the arrow of time could not be found in the basic equations, which truly were reversible.
On his bicycle in Far Rockaway.
Melville, Lucille, Richard, and Joan at the house they shared with Lucille's sister's family, at 14 New Broadway.
Richard and Arline : left , at Presbyterian Sanatorium.
At Los Alamos: “I opened the safes which contained behind them the entire secret of the atomic bomb…”
Slouching beside J. Robert Oppenheimer at a Los Alamos meeting: “He is by all odds the most brilliant young physicist here, and everyone knows this.”
Awaiting the Trinity test: “And we scientists are clever-too clever- care you not satisfied? Is four square miles in one bomb not enough? Men are still thinking. Just tell us how big you want it !”
I. I. Rabi (left) and Han s Bethe: Physicists are the Peter Pans of the human race, Rabi said.
At th e Shelter Island Conference , June 1947: Willis Lamb and John Wheeler , standing; Abraham Pais, Feynrnan, and Herman Feshbach, seated; Julian Schwinger, kneeling.
Jul ian Schwinger : “It seems to be the spirit of Macaulay which takes over, for he speaks in splendid periods, the carefully architected sentences rolling on, with every subordinate clause duly closing.”
Feynman and Hideki Yukawa in Kyoto, 1955 : Feynman presented his theory of superfluidity, the strange , frictionless behavior of liquid helium quantum mech anics writ large.
At Caltech , before a slide from his original presentation on antiparticles traveling backward through time.
Victor Weisskopf (left) and Freeman Dyson.
That was Feynman and Wheeler’s view. By insisting on the symmetry of past and future, they made the combination of retarded and advanced potentials seem a necessity. In the end, there was an asymmetry in the universe of their theory—the role of ordinary retarded fields far outweighs the backward advanced fields—but that asymmetry does not lie in the equations. It comes about because of the disordered, mixed-up nature of the surrounding absorber. A tendency toward disorder is the most universal manifestation of time’s arrow. A movie showing a drop of ink diffusing in a glass of water looks wrong when run backward. Yet a movie showing the microscopic motion of any one ink molecule would look the same backward or forward. The random motions of each ink molecule can be reversed, but the overall diffusion cannot be. The system is microscopically reversible, macroscopically irreversible. It is a matter of chaos and probability. It is not impossible for the ink molecules, randomly drifting about, someday to reorganize themselves into a droplet. It is just hopelessly improbable. In Feynman and Wheeler’s universe, the same kind of improbability guaranteed the direction of time by ensuring disorder in the absorber. Feynman took pains to spell out the distinction in the twenty-two-page manuscript he wrote early in 1941:
We must distinguish between two types of irreversibility. A sequence of natural phenomena will be said to be microscopically irreversible if the sequence of phenomena reversed in temporal order in every detail could not possibly occur in nature. If the original sequence and the reversed in time one have a vastly different order of probability of occurrence in the macroscopic sense, the phenomena are said to be macroscopically irreversible… . The present authors believe that all physical phenomena are microscopically reversible, and that, therefore, all apparently irreversible phenomena are solely macroscopically irreversible.
Even now the principle of reversibility seemed startling and dangerous, defying as it did the sense of one-way time that Newton had implanted in science. Feynman called his last statement to Wheeler’s attention with a note: “Prof Wheeler,” he wrote—and then self-consciously crossed out “Prof”—“This is a rather sweeping statement. Perhaps you don’t agree with it. RPF.”
Meanwhile Wheeler was searching the literature, and he found several obscure precedents for their absorber model. Einstein himself pointed out that H. Tetrode, a German physicist, had published a paper in Zeitschrift für Physik in 1922 proposing that all radiation be considered an interaction between a source and an absorber—no absorber, no radiation. Nor did Tetrode shrink from the tree-falls-in-the-forest consequences of the idea:
The sun would not radiate if it were alone in space and no other bodies could absorb its radiation… . If for example I observed through my telescope yesterday evening that star … 100 light years away, then not only did I know that the light which it allowed to reach my eye was emitted 100 years ago, but also the star or individual atoms of it knew already 100 years ago that I, who then did not even exist, would view it yesterday evening at such and such a time.
For that matter, the invisible reddened whisper of radiation emitted by a distant (and in the twenties, unimagined) quasar not one hundred but ten billion years ago—radiation that passed unimpeded for most of the universe’s lifetime until finally it struck a semiconducting receiver at the heart of a giant telescope—this, too, could not have been emitted without the cooperation of its absorber. Tetrode conceded, “On the last pages we have let our conjectures go rather far beyond what has mathematically been proven.” Wheeler found another obscure but provocative remark in the literature, from Gilbert N. Lewis, a physical chemist who happened to have coined the word photon. Lewis, too, worried about the seeming failure of physics to recognize the symmetry between past and future implied by its own fundamental equations, and for him, too, the past-future symmetry suggested a source-absorber symmetry in the process of radiation.
I am going to make the … assumption that an atom never emits ligh
t except to another atom… . it is as absurd to think of light emitted by one atom regardless of the existence of a receiving atom as it would be to think of an atom absorbing light without the existence of light to be absorbed. I propose to eliminate the idea of mere emission of light and substitute the idea of transmission, or a process of exchange of energy between two definite atoms… .
Feynman and Wheeler pushed on their theory. They tried to see how far they could broaden its implications. Many of their attempts led nowhere. They worked on the problem of gravity in hopes of reducing it to a similar interaction. They tried to construct a model in which space itself was eliminated: no coordinates and distances, no geometry or dimension; only the interactions themselves would matter. These were dead ends. As the theory developed, however, one feature gained paramount importance. It proved possible to compute particle interactions according to a principle of least action.
The approach was precisely the shortcut that Feynman had gone out of his way to disdain in his first theory course at MIT. For a ball arcing through the air, the principle of least action made it possible to sidestep the computation of a trajectory at successive instants of time. Instead one made use of the knowledge that the final path would be the one that minimized action, the difference between the ball’s kinetic and potential energy. In the absorber theory, because the field was no longer an independent entity, the action of a particle suddenly became a quantity that made sense. It could be calculated directly from the particle’s motion. And once again, as though by magic, particles chose the paths for which the action was smallest. The more Feynman worked with the least-action approach, the more he felt how different was the physical point of view. Traditionally one always thought in terms of the flow of time, represented by differential equations, which captured a change from instant to instant. Using the principle of least action instead, one developed a bird’s-eye perspective, envisioning a particle’s path as a whole, all time seen at once. “We have, instead,” Feynman said later, “a thing that describes the character of the path throughout all of space and time. The behavior of nature is determined by saying her whole space-time path has a certain character.” In college it had seemed too pat a device, too far abstracted from the true physics. Now it seemed extraordinarily beautiful and not so abstract after all. His conception of light was still in flux—still not quite a particle, not quite a wave, still pressing speculatively against the unresolved infinities of quantum mechanics. The notion had come far since Euclid wrote, as the first postulate of his Optics, “The rays emitted by the eye travel in a straight line.”
The empty space of the physicist’s imagination—the chalkboard on which every motion, every force, every interaction played itself out—had undergone a transformation in less than a generation. A ball pursued a trajectory through the everyday space of three dimensions. The particles of Feynman’s reckoning forged paths through the four-dimensional space-time so indispensable to the theory of relativity, and through even more abstract spaces whose coordinate axes stood for quantities other than distance and time. In space-time even a motionless particle followed a trajectory, a line extending from past to future. For such a path Minkowski coined the phrase world-line—“an image, so to speak, of the everlasting career of the substantial point, a curve in the world… . The whole universe is seen to resolve itself into similar world-lines.” Science-fiction writers had already begun to imagine the strange consequences of world-lines twisting back from the future into the past. No novelist was letting his fantasies roam as far as Wheeler was, however. One day he called Feynman on the hall telephone in the Graduate College. Later Feynman remembered the conversation this way:
—Feynman, I know why all the electrons have the same charge and the same mass.
—Why?
—Because they are all the same electron! Suppose that all the world-lines which we were ordinarily considering before in time and space—instead of only going up in time were a tremendous knot, and then, when we cut through the knot, by the plane corresponding to a fixed time, we would see many, many world-lines and that would represent many electrons, except for one thing. If in one section this is an ordinary electron world-line, in the section in which it reversed itself and is coming back from the future we have the wrong sign … and therefore, that part of a path would act like a positron.
The positron, the antiparticle twin of the electron, had been discovered (in cosmic-ray showers) and named (another modern -tron, short for positive electron) within the past decade. It was the first antiparticle, vindicating a prediction of Dirac’s, based on little more than a faith in the loveliness of his equations. According to the Dirac wave equation, the energy of a particle amounted to this: ±√something. Out of that plus-or-minus sign the positron was born. The positive solution was an electron. Dirac boldly resisted the temptation to dismiss the negative solution as a quirk of algebra. Like Wheeler in making his leap toward advanced waves, he followed a mirror-image change in sign to its natural conclusion.
Feynman considered the wild suggestion coming through the earpiece of his telephone—that all creation is a slice through the spaghetti path of a single electron—and offered the mildest of the many possible rebuttals. The forward and backward paths did not seem to match up. An embroidery needle pulling a single thread back and forth through a canvas must go back as many times as it goes forth.
—But, Professor, there aren’t as many positrons as electrons.
—Well, maybe they are hidden in the protons or something.
Wheeler was still trying to make the electron the basis of all other particles. Feynman let it pass. The point about positrons, however, reverberated. In his first published paper two years before, on the scattering of cosmic radiation by stars, he had already made this connection, treating antiparticles as ordinary particles following reversed paths. In a Minkowskian universe, why shouldn’t the reversal apply to time as well as to space?
Mr. X and the Nature of Time
Twenty years later, in 1963, the problem of time having given up none of its mystery, a group of twenty-two physicists, cosmologists, mathematicians, and others sat around a table at Cornell to discuss the matter. Was time a quantity entered in the account books of their equations to mark the amount of before and after? Or it was an all-enveloping flow, carrying everything with it like a constant river? In either case, what did it mean to say now? Einstein had worried about this, accepting the unwelcome possibility that the present belongs to our minds alone and that science cannot comprehend it. A philosopher, Adolph Grünbaum, argued that the usual notion of the forward flow of time was merely an illusion, a “pseudoconception.” If it seemed to us as conscious entities that new events kept “coming into being,” that was merely one of the quirky consequences of the existence of conscious entities—“organisms which conceptually register (ideationally represent)” them. Physicists need not worry about it unduly.
When Grünbaum finished his presentation, a participant with a loathing for what he viewed as philosophical and psychological vagueness began a hard cross-examination. (The published version of the discussion identified this interlocutor only as “Mr. X,” which fooled no one; by now, Feynman hiding behind such a cloak made himself as conspicuous as an American secretary of state quoted as “a senior official aboard the secretary of state’s plane.”)
GRÜNBAUM: I want to say that there is a difference between a conscious thing and an unconscious thing.
X: What is that difference?
GRÜNBAUM: Well, I don’t have more precise words in which to say this, but I would not be worried if a computer is unemployed. If a human being is unemployed, I would worry about the sorrows which that human being experiences in virtue of conceptualized self-awareness.
X: Are dogs conscious?
GRÜNBAUM: Well, yes. It is going to be a question of degree. But I wonder whether they have conceptualized awareness.
X: Are cockroaches conscious?
GRÜNBAUM: Well, I don’t know
about the nervous system of the cockroach.
X: Well, they don’t suffer from unemployment.
It seemed to Feynman that a robust conception of “now” ought not to depend on murky notions of mentalism. The minds of humans are manifestations of physical law, too, he pointed out. Whatever hidden brain machinery created Grünbaum’s coming into being must have to do with a correlation between events in two regions of space—the one inside the cranium and the other elsewhere “on the space-time diagram.” In theory one should be able to create a feeling of nowness in a sufficiently elaborate machine, said Mr. X.
One’s sense of the now feels subjective, arbitrary, open to differences of definition and interpretation, particularly in the age of relativity. “One can say easily enough that any particular value of t can be taken as now and that would not be wrong, but it does not correspond to experience,” the physicist David Park has said. “If we attend only to what is happening around us and let ourselves live, our attention concentrates itself on one moment of time. Now is when we think what we think and do what we do.” For similar reasons many philosophers wished to banish the concept. Feynman, staking out a characteristic position in such debates, rejected the idea that human consciousness was special. He and other rigorous scientists, their tolerance broadened by their experience with quantum-mechanical measurement problems, found that they could live with the imprecision—the possibility that the nows of different observers would differ in timing and duration. Technology offered ways of tightening the definition, at least for the sake of argument: less subjectivity arose in the now recorded by a camera shutter or a computing machine. Wheeler, also present at the Cornell meeting, proposed the example of a computer on an antiaircraft gun. Its now is the finite interval containing not just the immediate past, the few moments of data coming from the radar tracks, but the immediate future, the flight of the target plane as extrapolated from the data. Our memories, too, blend the immediate past with the anticipation of the soon to be, and a living amalgam of these—not some infinitesimal pointlike instant forever fleeing out of reach—is our now. Wheeler quoted the White Queen’s remark to Alice: “It’s a poor sort of memory that only works backwards.”