Genius: The Life and Science of Richard Feynman - James Gleick (1993)
The apostle of Niels Bohr at Princeton was a compact, gray-eyed, twenty-eight-year-old assistant professor named John Archibald Wheeler who had arrived the year before Feynman, in 1938. Wheeler had Bohr’s rounded brow and soft features, as well as his way of speaking about physics in oracular undertones. In the years that followed, no physicist surpassed Wheeler in his appreciation for the mysterious or in his command of the Delphic catchphrase:
A black hole has no hair was his. In fact he coined the term “black hole.”
There is no law except the law that there is no law.
I always keep two legs going, with one trying to reach ahead.
In any field find the strangest thing and then explore it.
Individual events. Events beyond law. Events so numerous and so uncoordinated that, flaunting their freedom from formula, they yet fabricate firm form.
He dressed like a businessman, his tie tightly knotted and his white cuffs starched, and he fastidiously pulled out a pocket watch when he began a session with a student (conveying a message: the professor will spare just so much time …). It seemed to one of his Princeton colleagues, Robert R. Wilson, that behind the gentlemanly façade lay a perfect gentleman—and behind that façade another perfect gentleman, and on and on. “However,” Wilson said, “somewhere among those polite façades there was a tiger loose; a reckless buccaneer … who had the courage to look at any crazy problem.” As a lecturer he performed with a magnificent self-assurance, impressing his audience with elegant prose and provocative diagrams. When he was a boy, he spent many hours poring over the drawings in a book called Ingenious Mechanisms and Mechanical Devices. He made adding machines and automatic pistols with gears and levers whittled from wood, and his blackboard illustrations of the most foggy quantum paradoxes retained that ingenious flavor, as though the world were a wonderful silvery machine. Wheeler grew up in Ohio, the son of librarians and the nephew of three mining engineers. He went to college in Baltimore, got his graduate degree at Johns Hopkins University, and then won a National Research Council Fellowship that brought him to Copenhagen in 1934 via freighter (fifty-five dollars one way) to study with Bohr.
He and Bohr worked together again, as colleagues this time, in the first months of 1939. Princeton had hired Wheeler and promoted the distinguished Hungarian physicist Eugene Wigner in a deliberate effort to turn toward nuclear physics. MIT had remained deliberately conservative about rushing to board the wagon train; Slater and Compton preferred to emphasize well-roundedness and links to more applied fields. Not so Princeton. Wheeler still remembered the magic of his first vision of radioactivity: how he had sat in a lightless room, staring toward the black of a zinc sulfide screen, counting the intermittent flashes of individual alpha particles sent forth by a radon source. Bohr, meanwhile, had left the growing tumult of Europe to visit Einstein’s institute in Princeton. When Wheeler met his ship at the pier in New York, Bohr was carrying news about what would now rapidly become the most propitious object in physics: the uranium atom.
Compared to the hydrogen atom, stark kernel with which Bohr had begun his quantum revolution, the uranium atom was a monster, the heaviest atom in nature, bulked out with 92 protons and 140-odd neutrons, so scarce in the cosmos that hydrogen atoms outnumber it by seventeen trillion to one, and unstable, given to decaying at quantum mechanically unpredictable moments down a chain of lighter elements or—this was the extraordinary news that kept Bohr at his portable blackboard all through the North Atlantic voyage—splitting, when slugged by a neutron, into odd pairs of smaller atoms, barium and krypton or tellurium and zirconium, plus a bonus of new neutrons and free energy. How was anyone to visualize this bloated nucleus? As a collection of marbles sliding greasily against one another? As a bunch of grapes squeezed together by nuclear rubber bands? Or as a “liquid drop”—the phrase that spread like a virus through the world of physics in 1939—a shimmering, jostling, oscillating globule that pinches into an hourglass and then fissures at its new waist. It was this last image, the liquid drop, that enabled Wheeler and Bohr to produce one of those unreasonably powerful oversimplifications of science, an effective theory of the phenomenon that had been named, only in the past year, fission. (The word was not theirs, and they spent a late night trying to find a better one. They thought about splitting or mitosis and then gave up.)
By any reasonable guess, a liquid drop should have served as a poor approximation for the lumpy, raisin-studded complex at the heart of a heavy atom, with each of two hundred-odd particles bound to each of the others by a strong close-range nuclear force, a force quite different from the electrical forces Feynman had analyzed on the scale of whole molecules. For smaller atoms the liquid-drop metaphor failed, but for large agglomerations like uranium it worked. The shape of the nucleus, like the shape of a liquid drop, depends on a delicate balance between the two opposing forces. Just as surface tension encourages a compact geometry in a drop, so do the forces of nuclear attraction in an atom. The electrical repulsion of the positively charged protons counters the attraction. Bohr and Wheeler recognized the unexpected importance of the slow neutrons that Fermi had found so useful at his laboratory in Rome. They made two remarkable predictions: that only the rarer uranium isotope, uranium 235, would fission explosively; and that neutron bombardment would also spark fission in a new substance, with atomic number 94 and mass 239, not found in nature and not yet created in the laboratory. To this pair of theoretical assertions would shortly be devoted the greatest technological enterprise the world had ever seen.
The laboratories of nuclear physics were spreading rapidly. Considerable American inventive spirit had gone into the development of an arsenal of machinery designed to accelerate beams of particles, smash them into metal foils or gaseous atoms, and track the collision products through chambers of ionizing gas. Princeton had one of the nation’s first large “cyclotrons”—the name rang proudly of the future—completed in 1936 for the cost of a few automobiles. The university also kept smaller accelerators working daily, manufacturing rare elements and new isotopes and generating volumes of data. Almost any experimental result seemed worthwhile when hardly anything was known. With all the newly cobbled-together equipment came difficulties of measurement and interpretation, often messy and ad hoc. A student of Wheeler’s, Heinz Barschall, came to him in the early fall of 1939 with a typical problem. Like so many new experimenters Barschall was using an accelerator beam to scatter particles through an ionizing chamber, where their energies could be measured. He needed to gauge the different energies that would appear at different angles of recoil. Barschall had realized that his results were distorted by the circumstances of the chamber itself. Some particles would start outside the chamber; others would start inside and run into the chamber’s cylindrical wall, and in neither case would the particle have its full energy. The problem was to compensate, find a way to translate the measured energies into the true energies. It was a problem of awkward probabilities in a complicated geometry. Barschall had no idea where to start. Wheeler said that he was too busy to think about it himself but that he had a very bright new graduate student …
Barschall dutifully sought out Dick Feynman at the residential Graduate College. Feynman listened but said nothing. Barschall assumed that would be the end of it. Feynman was adjusting to this new world, much smaller, for a physicist, than the scientific center he had left. He shopped for supplies in the stores lining Nassau Street on the west edge of the campus, and an older graduate student, Leonard Eisenbud, saw him in the street. “You look like you’re going to be a good theoretical physicist,” Eisenbud said. He gestured toward Feynman’s new wastebasket and blackboard eraser. “You’ve bought the right tools.” The next time Feynman saw Barschall, he surprised him with a sheaf of handwritten pages; he had been riding on a train and had time to write out a full solution. Barschall was overwhelmed, and Feynman had added another young physicist to the growing group of his peers with a weighty private appreciation for his ability.
Wheeler himself was already beginning to appreciate Feynman, who had been assigned to him—neither of them quite knew why—as a teaching assistant. Feynman had expected to be working with Wigner. He was surprised at their first meeting to see that his professor was barely older than he was. Then he was surprised again by Wheeler’s pointed display of a pocket watch. He took in the message. At their second meeting he pulled out a dollar pocket watch of his own and set it down facing Wheeler’s. There was a pause; then both men laughed.
A Quaint Ceremonious Village
Princeton’s gentility was famous: the eating clubs, the arboreal lanes, the ersatz-Georgian carved stone and stained glass, the academic gowns at dinner and punctilious courtesies at tea. No other college so keenly delineated the social status of its undergraduates as Princeton did with its club system. Although the twentieth century had begun to intrude—the graduate departments were growing in stature, and Nassau Street had been paved—Princeton before the war remained, as F. Scott Fitzgerald described it adoringly a generation earlier, “lazy and good-looking and aristocratic,” an outpost for New York, Philadelphia, and Southern society. Its faculty, though increasingly professional, was still sprinkled with Fitzgerald’s “mildly poetic gentlemen.” Even the kindly genius who became the town’s most famous resident on arriving in 1933 could not resist a gibe: “A quaint ceremonious village,” Einstein wrote, “of puny demigods on stilts.”
Graduate students, on track to a professional world, were partly detached from the university’s more frivolous side. The physics department in particular was moving decisively with the times. It had seemed to Feynman from a distance that Princeton’s physicists were disproportionately represented in the current journals. Even so he had to adjust to a place which, even more than Harvard and Yale, styled itself after the great English universities, with courtyards and residential “colleges.” At the Graduate College a “porter” monitored the downstairs entranceway. The formality genuinely frightened Feynman, until slowly he realized that the obligatory black gowns hid bare arms or sweaty tennis clothes. The afternoon he arrived at Princeton in the fall of 1939, Sunday tea with Dean Eisenhart turned his edginess about social convention into anxiety. He dressed in his good suit. He walked through the door and saw—worse than he had imagined—young women. He could not tell whether he was supposed to sit. A voice behind him said, “Would you like cream or lemon in your tea, sir?” He turned and saw the dean’s wife, a famous lioness of Princeton society. It was said that when the mathematician Carl Ludwig Siegel returned to Germany in 1935 after a year in Princeton he told friends that Hitler had been bad but Mrs. Eisenhart was worse.
Feynman blurted, “Both, please.”
“Heh-heh-heh-heh-heh,” he heard her say. “Surely you’re joking, Mr. Feynman!” More code—the phrase evidently signaled a gaffe. Whenever he thought about it afterward, the words rang in his ears: surely you’re joking. Fitting in was not easy. It bothered him that the raincoat his parents sent was too short. He tried sculling, the Ivy League sport that seemed least foreign to his Far Rockaway experience—he remembered the many happy hours spent rowing in the inlets of the south shore—and promptly fell from the impossibly slender boat into the water. He worried about money. When he entertained guests in his room they would share rice pudding and grapes, or peanut butter and jelly on crackers with pineapple juice. As a first-year teaching assistant he earned fifteen dollars a week. Cashing several savings certificates to pay a bill for $265, he spent twenty minutes calculating what combination would forfeit the least interest. The difference between the worst case and the best case, he found, came to eight cents. Outwardly, though, he cultivated his brashness. Not long after he arrived, he had his neighbors at the Graduate College convinced that he and Einstein (whom he had not met) were on regular speaking terms. They listened with awe to these supposed conversations with the great man on the pay phone in the hallway: “Yeah, I tried that … yeah, I did … oh, okay, I’ll try that.” Most of the time he was actually speaking with Wheeler.
As Wheeler’s teaching assistant—first for a course in mechanics, then in nuclear physics—Feynman quickly found himself taking over in the professor’s absence (and it began to sink in that facing a roomful of students was part of the profession he had chosen). He also met with Wheeler weekly on research problems of their own. At first Wheeler assigned the problems. Then a collaboration took shape.
The purview of physics had exploded in the first four decades of the century. Relativity, the quantum, cosmic rays, radioactivity, the nucleus—these new realms held the attention of leading physicists to the virtual exclusion of such classical topics as mechanics, thermodynamics, hydrodynamics, statistical mechanics. To a smart graduate student fresh on the theoretical scene these traditional fields seemed like textbook science, already part of history and—in their applied forms—engineering. Physics was “inward bound,” as its chronicler Abraham Pais put it; into the core of the atom the theorists went. All the superlatives were here. The experimental apparatus was the most expensive (machines could now cost thousands or even tens of thousands of dollars). The necessary energies were the highest. The materials and “particles” (this word was acquiring a specialized meaning) were the most esoteric. The ideas were the strangest. Relativity notoriously changed astronomers’ sense of the cosmos but found its most routine application in the physics of the atom, where near-light speeds made relativistic mathematics essential. As experimenters learned to ply greater levels of energy, the basic constituents gave way to new units even more basic. Through quantum mechanics, physics had established a primacy over chemistry—itself formerly the most fundamental of sciences, if the most fundamental was the one responsible for nature’s basic constituents.
As the thirties ended and the forties began, particle physics had not established its later dominance of the public relations of science. In choosing a theme for the annual Washington Conference on theoretical physics in 1940, organizers considered “The Elementary Particles” and the quaintly geophysical “Interior of the Earth”—and chose the interior of the earth. Still, neither Feynman nor Wheeler had any doubt about where a pure theorist’s focus must turn. The fundamental issue in the fundamental science was the weakness in the heart of quantum mechanics. At MIT Feynman had read Dirac’s 1935 text as a cliffhanger with the most thrilling possible conclusion: “It seems that some essentially new physical ideas are here needed.” Dirac and the other pioneers had taken their quantum electrodynamics—the theory of the interplay of electricity, magnetism, light, and matter—as far as they could. Yet it remained incomplete, as Dirac well knew.
The difficulty concerned the electron, the fundamental speck of negative charge. As a modern concept, the electron was still young, although many high-school students now performed (as Feynman had in Far Rockaway) a tabletop experiment showing that electric charge came in discrete units. What exactly was the electron? Wilhelm Röntgen, the discoverer of X rays, forbade the use of this upstart term in his laboratories as late as 1920. The developers of quantum mechanics, attempting to describe the electron’s charge or mass or momentum or energy or spin in almost every new equation, nevertheless maintained a silent agnosticism about certain issues of its existence. Particularly troubling: Was it a finite pellet or an infinitesimal point? In his model of the atom, already obsolete, Niels Bohr had imagined electrons as miniature planetoids orbiting the nucleus; now the atom’s electron seemed more to reverberate in an oscillatory harmony. In some formulations it assumed a wavelike cloak, the wave representing a distribution of probabilities that it would appear in particular places at particular times. But what would appear? An entity, a unit—a particle?
Even before quantum mechanics, a worm had gnawed at the heart of the classical understanding. The equations linking the electron’s energy (or mass) and charge implicated another quantity, its radius. As its size diminished, the electron’s energy grew, just as the pressure transmitted by a carpenter’s hammer becomes thousands of pounds per square inch when concentrated at the point of a nail. Furthermore, if the electron was to be imagined as a little ball of finite size, then what force or glue kept it from bursting from its own charge? Physicists found themselves manipulating a quantity called the “classical electron radius.” Classical in this context came to mean something like make-believe. The problem was that the alternative—a vanishingly small, pointlike electron—left the equations of electrodynamics plagued with divisions by zero: infinities. Infinitely small nails, infinitely energetic hammers.
In a sense the equations were measuring the effect of the electron’s charge on itself, its “self-energy.” That effect would increase with proximity, and how much nearer could the electron be to itself? If the distance were zero, the effect would be infinite—impossible. The wave equation of quantum mechanics only made the infinities more complicated. Instead of the grade-school horror of a division by zero, physicists now contemplated equations that grew out of bounds because they summed infinitely many wavelengths, infinitely many oscillations in the field—although even now Feynman did not quite understand this formulation of the infinities problem. Temporarily, for simple problems, physicists could get reasonable answers by the embarrassing expedient of discarding the parts of the equations that diverged. As Dirac recognized, however, in concluding his Principles of Quantum Mechanics, the electron’s infinities meant that the theory was mortally flawed. It seems that some essentially new physical ideas are here needed.
Feynman quietly nursed an attachment to a solution so radical and straightforward that it could only have appealed to someone ignorant of the literature. He proposed—to himself—that electrons not be allowed to act on themselves at all. The idea seemed circular and silly. As he recognized, however, eliminating self-action meant eliminating the field itself. It was the field, the totality of the charges of all electrons, that served as the agent of self-action. An electron contributed its charge to the field and was influenced by the field in turn. Suppose there was no field. Then perhaps the circularity could be broken. Each electron would act directly on another. Only the direct interaction between charges would be permitted. One would have to build a time delay into the equations, for whatever form this interaction took, it could hardly surpass the speed of light. The interaction was light, in the form of radio waves, visible light, X rays, or any of the other manifestations of electromagnetic radiation. “Shake this one, that one shakes later,” Feynman said later. “The sun atom shakes; my eye electron shakes eight minutes later because of a direct interaction across.”
No field; no self-action. Implicit in Feynman’s attitude was a sense that the laws of nature were not to be discovered so much as constructed. Although language blurred the distinction, Feynman was asking not whether an electron acted on itself but whether the theorist could plausibly discard the concept; not whether the field existed in nature but whether it had to exist in the physicist’s mind. When Einstein banished the ether, he was reporting the absence of something real—at least something that might have been—like a surgeon who opened a chest and reported that the bloody, pulsing heart was not to be found. The field was different. It had begun as an artifice, not an entity. Michael Faraday and James Clerk Maxwell, the nineteenth-century Britons who contrived the notion and made it into an implement no more dispensable than a surgeon’s scalpel, started out apologetically. They did not mean to be taken literally when they wrote of “lines of force”—Faraday could actually see these when he sprinkled iron filings near a magnet—or “idle wheels,” the pseudomechanical, invisible vortices that Maxwell imagined filling space. They assured their readers that these were analogies, though analogies with the newly formidable weight of mathematical rectitude.
The field had not been invented without reason. It had unified light and electromagnetism, establishing forever that the one was no more or less than a ripple in the other. As an abstract successor to the now-defunct ether the field was ideal for accommodating waves, and energy did seem to ripple wavelike from its sources. Anyone who played with electrical circuits and magnets as intently as Faraday and Maxwell could feel the way the “vibrations” or “undulations” could twist and spin like tubes or wheels. Crucially, the field also obviated the unpleasantly magical idea of action at a distance, objects influencing one another from afar. In the field, forces propagated sensibly and continuously from one place to the next. There was no jumping about, no sorcerous obeying of faraway orders. As Percy Bridgman, an American experimental physicist and philosopher, said, “It is felt to be more acceptable to rational thought to conceive of the gravitational action of the sun on the earth, for example, as propagated through the intermediate space by the handing on of some sort of influence from one point to its proximate neighbor, than to think of the action overleaping the intervening distance and finding its target by some sort of teleological clairvoyance.” By then scientists had efficiently forgotten that the field, too, was a piece of magic—a wave-bearing nullity, or empty space that was not quite empty (and more than space). Or in the elegant phrase of a later theorist, Steven Weinberg: “the tension in the membrane, but without the membrane.” The field grew so dominant in physicists’ thinking that even matter itself sometimes withdrew to the status of mere appendage: a “knot” of the field, or a “blemish,” or as Einstein himself said, merely a place where the field was especially intense.
Embrace the field or abhor it—either way, by the nineteen-thirties the choice seemed more one of method than reality. The events of 1926 and 1927 had made that clear. No one could be so naïve now as to ask whether Heisenberg’s matrices or Schrödinger’s wave functions existed. They were alternative ways of viewing the same processes. Thus Feynman, looking for a new eyepiece himself, began drifting back to a classical notion of unfieldlike particle interaction. The wavelike transmission of energy and the hocus-pocus of action at a distance were issues that he would have to address. In the meantime, Wheeler, too, had reasons to be drawn toward this implausibly pure conception. Electrons might interact directly, without the mediation of the field.
Folds and Rhythms
Feynman tended to associate more with the mathematicians than the physicists at the Graduate College. Students from the two groups joined each afternoon for tea in a common lounge—more English tradition transplanted—and Feynman would listen to an increasingly alien jargon. Pure mathematics had swerved away from the fields of direct use to contemporary physicists and toward such seeming esoterica as topology, the study of shapes in two, three, or many dimensions without regard to rigid lengths or angles. An effective divorce had occurred between mathematics and physics. By the time practitioners reached the graduate level, they shared no courses and had nothing practical to say to one another. Feynman listened to the mathematicians standing in groups or sitting on the couch at tea, talking about their proofs. Rightly or wrongly he felt he had an intuition for what theorems could be derived from what lemmas, even without quite understanding the subject. He enjoyed the strange rhetoric. He enjoyed trying to guess the counterintuitive answers to their nearly unvisualizable questions, and he enjoyed applying the physicist’s favorite needle, the claim that mathematicians spent their time proving the obvious. Although he teased them, he thought they were an exciting group—happy and interested in a kind of science that was getting beyond him. One friend was Arthur Stone, a patient young man attending Princeton on a fellowship from England. Another was John Tukey, who later became one of the world’s leading statisticians. These men spent their leisure time in curious ways. Stone had brought with him English-standard loose-leaf notebooks. The American-standard paper he bought at Woolworth’s overhung the notebooks by an inch, so he presently found himself with a supply of inch-wide paper ribbons, suitable for folding and twisting in different configurations. He tried diagonal folds at the 60-degree angle that produced rows of equilateral triangles. Then, following these folds, he wrapped a strip into a perfect hexagon.
Flexing a hexaflexagon.
When he closed the loop by taping the ends together, he found that he had created an odd toy: by pinching opposite corners of the hexagon, he could perform a queer origami-like fold, producing a new hexagon with a different set of triangles exposed. Repeating the operation exposed a third face. One more “flex” brought back the original configuration. In effect, he had a flattened tube that he was steadily turning inside out.
He considered this overnight. In the morning he took a longer strip and confirmed a new hypothesis: that a more elaborate hexagon could be made to cycle through not three but six different faces. The cycling was not so straightforward this time. Three of the faces tended to come up again and again, while the other three seemed harder to find. This was a nontrivial challenge to his topological imagination. Centuries of origami had not produced such an elegantly convoluted object. Within days copies of these “flexagons”—or, as this subspecies came to be more precisely known, “hexahexaflexagons” (six sides, six internal faces)—were circulating across the dining hall at lunch and dinner. The steering committee of the flexagon investigation soon comprised Stone, Tukey, a mathematician named Bryant Tuckerman, and their physicist friend Feynman. Honing their dexterity with paper and tape, they made hexaflexagons with twelve faces buried amid the folds, then twenty-four, then forty-eight. The number of varieties within each species rose rapidly according to a law that was far from evident. The theory of flexigation flowered, acquiring the flavor, if not quite the substance, of a hybrid of topology and network theory. Feynman’s best contribution was the invention of a diagram, called in retrospect the Feynman diagram, that showed all the possible paths through a hexaflexagon.
Seventeen years later, in 1956, the flexagons reached Scientific American in an article under the byline of Martin Gardner. “Flexagons” launched Gardner’s career as a minister to the nation’s recreational-mathematics underground, through twenty-five years of “Mathematical Games” columns and more than forty books. His debut article both captured and fed a minor craze. Flexagons were printed as advertising flyers and greeting cards. They inspired dozens of scholarly or semischolarly articles and several books. Among the hundreds of letters the article provoked was one from the Allen B. Du Mont Laboratories in New Jersey that began:
Sirs: I was quite taken with the article entitled “Flexagons” in your December issue. It took us only six or seven hours to paste the hexahexaflexagon together in the proper configuration. Since then it has been a source of continuing wonder.
But we have a problem. This morning one of our fellows was sitting flexing the hexahexaflexagon idly when the tip of his necktie became caught in one of the folds. With each successive flex, more of his tie vanished into the flexagon. With the sixth flexing he disappeared entirely.
We have been flexing the thing madly, and can find no trace of him, but we have located a sixteenth configuration of the hexahexaflexagon… .
The spirits of play and intellectual inquiry ran together. Feynman spent slow afternoons sitting in the bay window of his room, using slips of paper to ferry ants back and forth to a box of sugar he had suspended with string, to see what he could learn about how ants communicate and how much geometry they can internalize. One neighbor barged in on Feynman sitting by the window, open, on a wintry day, madly stirring a pot of Jell-O with a spoon and shouting “Don’t bother me!” He was trying to see how the Jell-O would coagulate while in motion. Another neighbor provoked an argument about the motile techniques of human spermatozoa; Feynman disappeared and soon returned with a sample. With John Tukey, Feynman carried out a long, introspective investigation into the human ability to keep track of time by counting. He ran up and down stairs to quicken his heartbeat and practiced counting socks and seconds simultaneously. They discovered that Feynman could read to himself silently and still keep track of time but that if he spoke he would lose his place. Tukey, on the other hand, could keep track of the time while reciting poetry aloud but not while reading. They decided that their brains were applying different functions to the task of counting: Feynman was using an aural rhythm, hearing the numbers, while Tukey visualized a sort of tape with numbers passing behind his eyes. Tukey said years later: “We were interested and happy to be empirical, to try things out, to organize and reduce to simple things what had been observed.”
Once in a while a small piece of knowledge from the world outside science would float Feynman’s way and stick like a bur from a chestnut. One of the graduate students had developed a passion for the poetry of Edith Sitwell, then considered modern and eccentric because of her flamboyant diction and cacophonous, jazzy rhythms. He read some poems aloud, and suddenly Feynman seemed to catch on; he took the book and started reciting gleefully. “Rhythm is one of the principal translators between dream and reality,” the poet said of her own work. “Rhythm might be described as, to the world of sound, what light is to the world of sight.” To Feynman rhythm was a drug and a lubricant. His thoughts sometimes seemed to slip and flow with a variegated drumbeat that his friends noticed spilling out into his fingertips, restlessly tapping on desks and notebooks. “While a universe grows in my head,—” Sitwell wrote,
I have dreams, though I have not a bed—
The thought of a world and a day
When all may be possible, still come my way.
Forward or Backward?
For a while the tea-time conversation among the physicists both at Princeton and at the Institute for Advanced Study was dominated by the image of a rotating lawn sprinkler, an S-shaped apparatus spun by the recoil of the water it sprays forth. Nuclear physicists, quantum theorists, and even pure mathematicians were consumed by the problem: What would happen if this familiar device were placed under water and made to suck water in instead of spewing it out? Would it spin in the reverse direction, because the direction of the flow was now reversed, pulling rather than pushing? Or would it spin in the same direction, because the same twisting force was exerted by the water, whichever way it flowed, as it was bent around the curve of the S? (“It’s clear to me at first sight,” a friend of Feynman’s said to him some years later. Feynman shot back: “It’s clear to everybody at first sight. The trouble was, some guy would think it was perfectly clear one way, and another guy would think it was perfectly clear the other way.”) In an increasingly sophisticated time the simple problems still had the capacity to surprise. One did not have to probe far into physicists’ understanding of Newton’s laws before reaching a shallow bottom. Every action produces an equal and opposite reaction—that was the principle at work in the lawn sprinkler, as in a rocket. The inverse problem forced people to test their understanding of where, exactly, the reaction wielded its effects. At the point of the nozzle? Somewhere in the curve of the S, where the twisted metal forces the water to change course? Wheeler was asked for his own verdict one day. He said that Feynman had absolutely convinced him the day before that it went around backward; that Feynman had absolutely convinced him today that it went around forward; and that he did not yet know which way Feynman would convince him the next day.
If the mind was the most convenient of laboratories, it was not proving the most trustworthy. Because the Gedankenexperiment was failing, Feynman decided to bring the lawn-sprinkler problem back into the world of matter—stiff metal and wet water. He bent a piece of tubing into an S. He ran a piece of soft rubber hose into it. Now he needed a convenient source of compressed air.
The Palmer Physical Laboratory at Princeton housed a magnificent array of facilities, though not quite up to the standards of MIT. There were four large laboraories and several smaller ones, with a total floor space of more than two acres. Machine shops supplied electrical charging devices, storage batteries, switchboards, chemical equipment, and diffraction gratings. The third floor was devoted to a high-voltage laboratory capable of direct currents at 400,000 volts. A low-temperature laboratory had machinery for liquefying hydrogen. Palmer’s pride, however, was its new cyclotron, built in 1936. Feynman had made a point of wandering over the day after he arrived at Princeton and had tea with the Dean. By comparison, MIT’s even newer cyclotron was an elegant futuristic masterpiece of shiny metal and geometrically arrayed dials; when MIT had finally decided to invest in high-energy physics, it had not stinted. Princeton’s gave Feynman a shock. He made his way down into the basement of Palmer, opened the door, and saw wires hanging like cobwebs from the ceiling. Safety valves for the cooling system were exposed, and water dripped from them. Tools were scattered on tables. It could not have looked less like Princeton. He thought of his wooden-crate laboratory at home in Far Rockaway.
The mystery of the lawn sprinkler. When it sprays water, it spins counterclockwise.But what happens when it is made to suck water in?
Amid the chaos, it seemed reasonable enough for Feynman to borrow the use of an outlet for compressed air. He attached the rubber tube and pushed the end through a large cork. He lowered his miniature lawn sprinkler through the neck of a giant glass water bottle and sealed the bottle with the cork. Rather than try to suck water from the tube, he was going to pump air into the top of the bottle. That would increase the pressure of the water, which would then flow backward into the S-shaped pipe, up the rubber hose, and out the bottle.
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.
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 physician, 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.
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 light 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.
—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.”
The absorber theory of Wheeler and Feynman had by then lost the interest of an increasingly single-minded particle physics, but it held center stage in this eclectic gathering. It had been born of their concern with reversible and irreversible processes, and now it served as common ground for three different approaches to understanding time’s flow, the arrow of time. As particle physicists had passed the absorber theory by, a new generation of cosmologists had taken it up. Their field had begun a transition from mere stargazing astronomy to an enterprise asking the grandest questions about the universe: whence and wherefore. It was beginning to stand out among the modern sciences as an enterprise not fully scientific, but an amalgam of philosophy, art, faith, and not a little hope. They had so few windows through the murky atmosphere—a few overworked glass contraptions on mountain tops, a few radio antennae—yet they believed they could peer far enough, or guess shrewdly enough, to uncover the origins of space and time. Already their space was not the flat, neutral stuff of their parents’ pre-Einsteinian intuition, but an eerily plastic medium that somehow embodied both time and gravity. Some of them, but not all, believed that space was expanding at high speed and dragging its contents farther and farther apart, on account of an explosive big bang ten or fifteen billion years before. It no longer seemed safe to assume that the universe was the same everywhere, infinite, static, Euclidean, ageless, and homogeneous: world without end, amen. The strongest evidence for an expanding universe was still, in 1963, Edwin Hubble’s 1929 discovery that other galaxies are streaming away from ours, and that the farther away they are, the faster they seem to be moving. Whether this expansion would continue forever or whether it would reverse itself was—and would remain—an open question. Perhaps the universe bloomed and collapsed again and again in a cycle that ran through eternity.
The issue seemed linked to the nature of time itself. Assumptions about time were built into the equations for the particle interactions that led to the creation and dissipation of light. If one thought about time as Wheeler and Feynman had, one could not escape a cosmic connection between these intimate interactions and the process of universal expansion. As Hermann Bondi said at the meeting’s outset, “This process leads to the dark night sky, to the disequilibrium between matter and radiation, and to the fact that radiated energy is effectively lost … we accept a very close connection between cosmology and the basic structure of our physics.” By their boldness in constructing a time-symmetrical theory of half advanced and half retarded waves, Wheeler and Feynman had been forced into boldness of a cosmological sort. If the equations were to balance properly, they had to make the mathematical assumption that all radiation was eventually absorbed somewhere. A beam of light heading forever into an eternal future, never to cross paths with a substance that would absorb it, would violate their assumption, so their theory mandated a certain kind of universe. If the universe were to expand forever, conceivably its matter might so thin out that light would not be absorbed.
Physicists had learned to distinguish three arrows of time. Feynman described them: the thermodynamic or “accidents of life” arrow; the radiation or “retarded or advanced” arrow; and the cosmological arrow. He suggested keeping in mind three physical pictures: a tank with blue water on one side and clear water on the other; an antenna with a charge moving toward it or away; and distant nebulas moving together or apart. The connections between these arrows were connections between the pictures. If a film showed the water getting more and more mixed, must it also show the radiation leaving the antenna and the nebulas drifting apart? Did one form of time govern the others? His listeners could only speculate, and speculate they did.
“It’s a very interesting thing in physics,” said Mr. X, “that the laws tell us about permissible universes, whereas we only have one universe to describe.”
Least Action in Quantum Mechanics
Omega oil did nothing for Arline’s lumps and fevers, and she was admitted to the hospital in Far Rockaway with what her doctor feared was typhoid. Feynman began to glimpse the special powerlessness that medical uncertainty can inflict on a scientific person. He had come to believe that the scientific way of thinking brought a measure of calmness and control in difficult situations—but not now. However remotely, medicine was a part of the domain of knowledge he considered his. It belonged to science. At one time his father had hopefully studied a kind of medicine. Lately Richard had been sitting in on a physiology course, learning some basic anatomy. He read up on typhoid fever in Princeton’s library, and when he visited Arline in the hospital he started questioning the doctor. Had a Widal test been administered? Yes. The results? Negative. Then how could it be typhoid? Why were all of Arline’s friends and relatives wearing gowns to protect against supposed bacteria that even a sensitive laboratory test could not detect? What did the mysterious lumps appearing and disappearing in her neck and armpit have to do with typhoid? The doctor resented his questions. Arline’s parents pointed out that his status as fiancé did not entitle him to interfere in her medical care. He backed down. Arline seemed to recover.
With Wheeler, meanwhile, Feynman was trying to move their work a crucial step forward. So far, despite its modern, acausal flavor, it was a classical theory, not a quantum one. It treated objects as objects, not as probabilistic smudges. It treated energy as a continuous phenomenon, where quantum mechanics required discrete packets and indivisible jumps in well-defined circumstances. The problem of self-energy was as severe in classical electrodynamics as in quantum theory. Unwanted infinities predated the quantum. They appeared as soon as one faced the consequences of a pointlike electron. It was as simple as dividing by zero. Feynman had felt from the beginning that the natural route would be to start with the classical case and only then work toward a quantized electrodynamics. There were already standard recipes for translating classical models into their modern quantum cousins. One prescription was to take all the momentum variables and replace them with certain more complicated expressions. The problem was that in Wheeler and Feynman’s theory there were no momentum variables. Feynman had eliminated them in creating his simplified framework based on the principle of least action.
Sometimes Wheeler told Feynman not to bother—that he had already solved the problem. Later in the spring of 1941 he went so far as to schedule a presentation of the quantized theory at the Princeton physics colloquium. Pauli, still dubious, buttonholed Feynman on his way into Palmer Library one day. He asked what Wheeler was planning to say. Feynman said he didn’t know.
“Oh?” Pauli said. “The professor doesn’t tell his assistant how he has it worked out? Maybe the professor hasn’t got it worked out.”
Pauli was right. Wheeler canceled the lecture. He lost none of his enthusiasm, however, and made plans for not one but a grand series of five papers. Feynman, meanwhile, had a doctoral thesis to prepare. He decided to approach the quantizing of his theory just as he had approached complicated problems at MIT, by working out cases that were stripped to their bare essentials. He tried calculating the interaction of a pair of harmonic oscillators, coupled, with a time delay—just a pair of idealized springs. One spring would shake, sending out a pure sine wave. The other would bounce back, and out of their interaction new wave forms would evolve. Feynman made some progress but could not understand the quantum version. He had gone too far in the direction of simplicity.
Conventional quantum mechanics went from present to future by the solving of differential equations—the so-called Hamiltonian method. Physicists spoke of “finding a Hamiltonian” for a system: if they could find one, then they could go ahead and calculate; if not, they were helpless. In Wheeler and Feynman’s view of direct action at a distance, the Hamiltonian method had no place. That was because of the introduction of time delays. It was not enough merely to write down a complete description of the present: the positions, momentums, and other quantities. One never knew when some delayed effect would hurtle into the picture out of the past (or in the case of Wheeler and Feynman, out of the future). Because past and future interacted, the customary differential-equation point of view broke down. The alternative least-action or Lagrangian approach was no luxury. It was a necessity.
With all this on his mind, Feynman went to a beer party at the Nassau Tavern. He sat with a physicist lately arrived from Europe, Herbert Jehle, a former student of Schrödinger in Berlin, a Quaker, and a survivor of prison camps in both Germany and France. The American scientific world was absorbing such refugees rapidly now, and the turmoil of Europe seemed more palpable and near. Jehle asked Feynman what he was working on. Feynman explained and asked in turn whether Jehle knew of any application of the least-action principle in quantum mechanics.
Jehle certainly did. He pointed out that Feynman’s own hero, Dirac, had published a paper on just that subject eight years before. The next day Jehle and Feynman looked at it together in the library. It was short. They found it, “The Lagrangian in Quantum Mechanics,” in the bound volumes of Physikalische Zeitschrift der Sowjetunion, not the best-read of journals. Dirac had worked out the beginnings of a least-action approach in just the style Feynman was seeking, a way of treating the probability of a particle’s entire path over time. Dirac considered only one detail, a piece of mathematics for carrying the wave function—the packet of quantum-mechanical knowledge—forward in time by an infinitesimal amount, a mere instant.
Infinitesimal time did not amount to much, but it was the starting point of the calculus. That limitation was not what troubled Feynman. As he looked over the few bound pages, he kept stopping at a single word: analogue. “A very simple quantum analogue,” Dirac had written. “… They have their classical analogues… . It is now easy to see what the quantum analogue of all this must be.” What kind of word was that, Feynman wondered, in a paper on physics? If two expressions were analogous, did it mean they were equal?
No, Jehle, said—surely Dirac had not meant that they were equal. Feynman found a blackboard and started working through the formulas. Jehle was right: they were not equal. So he tried adding a multiplication constant. Calculating more rapidly than Jehle could follow, he substituted terms, jumped from one equation to the next, and suddenly produced something extremely familiar: the Schrödinger equation. There was the link between Feynman’s Lagrangian-style formulation and the standard wave function of quantum mechanics. A surprise—by analogous Dirac had simply meant proportional.
But now Jehle had produced a small notebook. He was rapidly copying from Feynman’s blackboard work. He told Feynman that Dirac had meant no such thing. In his view Dirac’s idea had been strictly metaphorical; the Englishman had not meant to suggest that the approach was useful. Jehle told Feynman he had made an important discovery. He was struck by the unabashed pragmatism in Feynman’s handling of the mathematics, so different from Dirac’s more detached, more aesthetic tone. “You Americans!” he said. “Always trying to find a use for something.”
This was Richard Feynman nearing the crest of his powers. At twenty-three he was a few years shy of the time when his vision would sweep hawklike across the breadth of physics, but there may now have been no physicist on earth who could match his exuberant command over the native materials of theoretical science. It was not just a facility at mathematics (though it had become clear to the senior physicists at Princeton that the mathematical machinery emerging in the Wheeler-Feynman collaboration was beyond Wheeler’s own ability). Feynman seemed to possess a frightening ease with the substance behind the equations, like Einstein at the same age, like the Soviet physicist Lev Landau—but few others. He was a sculptor who sleeps and dreams with the feeling of clay alive in his fingers. Graduate students and instructors found themselves wandering over to the afternoon tea at Fine Hall with Feynman on their minds. They anticipated his bantering with Tukey and the other mathematicians, his spinning of half-serious physical theories. Handed an idea, he always had a question that seemed to pierce toward the essence. Robert R. Wilson, an experimentalist who arrived at Princeton from the famous cauldron of Ernest Lawrence’s Berkeley laboratory, talked casually with Feynman only a few times before making a mental note: Here is a great man.
The Feynman aura—as it had already become—was strictly local. Feynman had not yet finished his second year of graduate school. He remained ignorant of the basic literature and unwilling even to read through the papers of Dirac or Bohr. This was now deliberate. In preparing for his oral qualifying examination, a rite of passage for every graduate student, he chose not to study the outlines of known physics. Instead he went up to MIT, where he could be alone, and opened a fresh notebook. On the title page he wrote: Notebook Of Things I Don’t Know About. For the first but not the last time he reorganized his knowledge. He worked for weeks at disassembling each branch of physics, oiling the parts, and putting them back together, looking all the while for the raw edges and inconsistencies. He tried to find the essential kernels of each subject. When he was done he had a notebook of which he was especially proud. It was not much use in preparing for the examination, as it turned out. Feynman was asked which color was at the top of a rainbow; he almost got that wrong, reversing in his mind the curve of refraction index against wavelength. The mathematical physicist H. P. Robertson asked a clever question about relativity, involving the apparent path of the earth as viewed through a telescope from a distant star. Feynman did get that wrong, he realized later, but in the meantime he persuaded the professor that his answer was correct. Wheeler read a statement from a standard text on optics, that the light from a hundred atoms, randomly phased, would have fifty times the intensity of one atom, and asked for the derivation. Feynman saw that this was a trick. He replied that the textbook must be wrong, because by the same logic a pair of atoms would glow with the same intensity as one. All this was a formality. Princeton’s senior physicists understood what they had in Feynman. In writing up course notes on nuclear physics, Feynman had been frustrated by a complicated formula of Wigner’s for particles in the nucleus. He did not understand it. So he worked the problem out for himself, inventing a diagram—a harbinger of things to come—that enabled him to keep a tally of particle interactions, counting the neutrons and protons and arranging them in a group-theoretical way according to pairs that were or were not symmetrical. The diagram bore an odd resemblance to the diagrams he invented for understanding the pathways of folded-paper flexagons. He did not really understand why his scheme worked, but he was certain that it did, and it proved to be a considerable simplification of Wigner’s own approach.
In high school he had not solved Euclidean geometry problems by tracking proofs through a logical sequence, step by step. He had manipulated the diagrams in his mind: he anchored some points and let others float, imagined some lines as stiff rods and others as stretchable bands, and let the shapes slide until he could see what the result must be. These mental constructs flowed more freely than any real apparatus could. Now, having assimilated a corpus of physical knowledge and mathematical technique, Feynman worked the same way. The lines and vertices floating in the space of his mind now stood for complex symbols and operators. They had a recursive depth; he could focus on them and expand them into more complex expressions, made up of more complex expressions still. He could slide them and rearrange them, anchor fixed points and stretch the space in which they were embedded. Some mental operations required shifts in the frame of reference, reorientations in space and time. The perspective would change from motionlessness to steady motion to acceleration. It was said of Feynman that he had an extraordinary physical intuition, but that alone did not account for his analytic power. He melded together a sense of forces with his knowledge of the algebraic operations that represented them. The calculus, the symbols, the operators had for him almost as tangible a reality as the physical quantities on which they worked. Just as some people see numerals in color in their mind’s eye, Feynman associated colors with the abstract variables of the formulas he understood so intimately. “As I’m talking,” he once said, “I see vague pictures of Bessel functions from Jahnke and Emde’s book, with light tan j’s, slightly violet-bluish n’s, and dark brown x’s flying around. And I wonder what the hell it must look like to the students.”
In the past eight years neither Dirac nor any other physicist had been able to follow up on the notion of a Lagrangian in quantum mechanics—a way of expressing a particle’s history in terms of the quantity of action. Now Dirac’s idea served as an explosive release in Feynman’s imagination. The uneasy elements of quantum mechanics broke loose and rearranged themselves into a radically new formulation. Where Dirac had pointed the way to calculating how the wave function would evolve in an infinitesimal slice of time, Feynman needed to carry the wave function farther, through finite time. A considerable barrier separated the infinitesimal from the finite. Making use of Dirac’s infinitesimal slice required a piling up of many steps—infinitely many of them. Each step required an integration, a summing of algebraic quantities. In Feynman’s mind a sequence of multiplications and compounded integrals took form. He considered the coordinates that specify a particle’s position. They churned through his compound integral. The quantity that emerged was, once again, a form of the action. To produce it, Feynman realized, he had to make a complex integral encompassing every possible coordinate through which a particle could move. The result was a kind of sum of probabilities—yet not quite probabilities, because quantum mechanics required a more abstract quantity called the probability amplitude. Feynman summed the contributions of every conceivable path from the starting position to the final position—though at first he saw more a haystack of coordinate positions than a set of distinct paths. Even so, he realized that he had burrowed back to first principles and found a new formulation of quantum mechanics. He could not see where it would lead. Already, however, his sense of paths in space-time seemed somehow cleaner—more direct. There seemed something quaint now about the peculiarly constrained oscillations of the post-ethereal field, the wavy inheritance of the 1920s.
The White Plague
Twentieth-century medicine was struggling for the scientific footing that physics began to achieve in the seventeenth century. Its practitioners wielded the authority granted to healers throughout human history; they spoke a specialized language and wore the mantle of professional schools and societies; but their knowledge was a pastiche of folk wisdom and quasi-scientific fads. Few medical researchers understood the rudiments of controlled statistical experimentation. Authorities argued for or against particular therapies roughly the way theologians argued for or against their theories, by employing a combination of personal experience, abstract reason, and aesthetic judgment. Mathematics played no role in a biologist’s education. The human body was still largely a black box, its contents accessible only by means of the surgeon’s knife or the crepuscular outlines of the early X rays. Researchers were stumbling toward the first rudimentary understanding of diet. The modern-sounding word vitamin had been coined and a few examples isolated in laboratories, but Feynman’s father, Melville, having been diagnosed with chronic high blood pressure, was being slowly poisoned with an enriched, salty diet of eggs, milk, and cheese. Immunology and genetics were nothing but wells of ignorance. The prevailing theory of the mind was less a science than a collection of literary conceits blended with the therapeutic palliative of the confessional. Cancers, viruses, and diseases of the heart and brain resisted even the first glimmers of understanding. They would continue to mock medical science throughout the century.
Yet medicine was within reach of its first planetwide triumphs against bacterial epidemics, with the twin weapons of vaccination and antibiotic drugs. The year Feynman entered graduate school, Jonas Salk became a medical doctor; his assault on polio was just a few years away. Still, the habits of large clinical trials and statistical thinking had yet to become engrained in medical research. Alexander Fleming had noticed the antibacterial effect of the mold Penicillium notatum a decade before and then failed to take what a later era would consider the obvious next steps. He published his observation in a paper titled “A Medium for the Isolation of Pfeiffer’s Bacillus.” He tried rubbing his mold onto the open wounds of a few patients, with unclear results, but it never occurred to him to attempt a systematic study of its effects. A full decade passed, while biologists (and Fleming himself) dreamed futilely of a magic antibacterial agent that would save millions of lives, before finally two researchers happened upon his paper, extracted penicillin, and in 1940 crossed the line separating anecdote from science: they injected it into four sick mice, leaving another four untreated. In the context of 1930s medical science the lost decade was hardly noteworthy. Fleming’s contemporaries did not deride him as a bungler. They hailed him as a hero and awarded him the Nobel Prize.
Tuberculosis—consumption, the wasting disease, scrofula, phthisis, the white plague—killed more people at its prime, in more parts of the globe, than any other disease. To novelists and poets it carried a romantic aura. It was a disease of pale aesthetes. It was a disease of rarefaction, of the body squandering itself. Its long, slow fevers gave the false impression of life intensified, the metabolism heightened, the processes of existence stimulated. Thomas Mann, allowing tuberculosis to inspire his most famous novel, associated the ruin and inflammation of the tubercles with sin, with the Fall, with the creation of life itself from cool inorganic molecules—“that pathologically luxuriant morbid growth, produced by the irritant of some unknown infiltration … an intoxication, a heightening and unlicensed accentuation of the physical state.” He wrote those words in 1924, when the Magic Mountain resort-style sanatoriums of Europe were already dinosaurs of the past. To American public-health authorities faced with the reality of the disease, even then tuberculosis was more simply a disease of the poor.
Tuberculosis had infected Arline Greenbaum’s lymphatic system, perhaps having been carried by unpasteurized milk. Swelling reappeared in the lymph nodes on her neck and elsewhere, the lumps rubbery and painless. She suffered fevers and fatigue. But an accurate diagnosis remained beyond the abilities of her doctors. Arline did not strike them as the typical tuberculosis victim; she was not poor enough or young enough. Nor was lymphatic tuberculosis as common as tuberculosis that began in the lung (it was twenty to thirty times rarer). When they abandoned the notion of typhoid fever and considered the other standard possibilities, they focused on cancerous outbreaks: lymphoma, lymphosarcoma, Hodgkin’s disease.
Feynman was back in the library at Princeton, reading everything he could find. One standard book listed the possibilities. First was local infection. This was out of the question because the swellings were traveling too far. Second was lymphatic tuberculosis. This was easy to diagnose, the book said. Then came the cancers, and these, he read to his horror, were almost invariably fatal. For a moment he mocked himself for jumping to the most morbid possibility. Everyone who reads such catalogues must start thinking about death, he thought. He went off to the Fine Hall tea, where the conversation seemed unnaturally normal.
Those months in 1941 were a blur of visits to hospitals, symptoms appearing and fading, consultations with more and more doctors. He hovered on the outside, hearing most news secondhand through Arline’s parents. He and Arline promised each other that they would face whatever came, bravely and honestly. Arline insisted, as she had when less was at stake, that honesty was the bedrock of their love and that what she treasured in Richard was his eagerness to confront the truth, his unwillingness to be embarrassed or evasive. She said she did not want euphemisms or pretense about her illness. Few patients did, but the weight of medical practice opposed forthrightness in the face of terminal illness. Honest bad news was considered antitherapeutic. Richard faced a dilemma, because the doctors were finally settling on a grim diagnosis of Hodgkin’s disease. There would be periods of remission, they said, but the course of the illness could not be reversed.
For Arline’s benefit they proposed a camouflage diagnosis of “glandular fever.” Richard refused to go along with it. He explained that he and Arline had a pact—no lies, not even white ones. How would he be able to face her with this biggest lie of all?
His parents, Arline’s parents, and the doctors all urged him not to be so cruel as to tell a young woman she was dying. His sister, Joan, sobbing, told him he was stubborn and heartless. He broke down and bowed to tradition. In her room at Farmingdale Hospital, with her parents at her side, he confirmed that she had glandular fever. Meanwhile, he started carrying around a letter—a “goodbye love letter,” as he called it—that he planned to give her when she discovered the truth. He was sure she would never forgive the unforgivable lie.
He did not have long to wait. Soon after Arline returned home from the hospital she crept to the top of the stairs and overheard her mother weeping with a neighbor down in the kitchen. When she confronted Richard—his letter snug in his pocket—he told her the truth, handed her the letter, and asked her to marry him.
Marriage was not so simple. It had not occurred to universities like Princeton to leave such matters to their students’ discretion. The financial and emotional responsibilities were considered grave in the best of circumstances. He was supporting himself as a graduate student with fellowships—he was the Queen Junior Fellow and then the Charlotte Elizabeth Proctor Fellow, entitling him to earn two hundred dollars a year as a research assistant. When he told a university dean that his fiancée was dying and that he wanted to marry her, the dean refused to permit it and warned him that his fellowship would be revoked. There would be no compromise. He was dismayed at the response. He considered leaving graduate school for a while to find work. Before he made his decision, more news came from the hospital.
A test had found tuberculosis in Arline’s lymph glands. She did not have Hodgkin’s disease after all. Tuberculosis was not treatable—or rather it was treatable by any of dozens of equally ineffectual methods—but its onslaught was neither swift nor certain. Relief came over Richard in a flood. To his surprise the first note he heard in Arline’s voice was disappointment. Now they would have no reason to marry immediately.
Preparing for War
As the spring of 1941 turned to summer, the prospect of war was everywhere. For scientists it seemed especially real. The fabric of their international community was already tearing. Refugees from Hitler’s Europe had been establishing themselves in American universities for more than half a decade, often in roles of leadership. The latest refugees, like Herbert Jehle, had increasingly grim stories to tell, of concentration camps and terror. War work began to swallow up scientists long before the Japanese attack on Pearl Harbor. A Canadian colleague of Feynman’s returned home to join the Royal Air Force. Others seemed to slip quietly away: the technologies of war were already drawing scientists into secret enterprises, as advisers, engineers, and members of technical subcommittees. It was going to be a physicists’ war. When scientists were covertly informed about the Battle of Britain, the critical details included the detection of aircraft by reflected radio pulses—“radar” did not yet have a name. A few even heard about the breaking of codes by advanced mathematical techniques and electromechanical devices. Alert physicists knew from the published record that nuclear fission had been discovered at the Kaiser Wilhelm Institutes outside Berlin; that great energies could be released by a reaction that would proceed in a neutron-spawning chain; that any bomb, however, would require large quantities of a rare uranium isotope. How large? A number in the air at Princeton was 100 kilograms, more than the weight of a man. That seemed forbidding. Not so much as a grain of uranium 235 existed in pure form. The world’s only experience in separating radioactive isotopes on a scale greater than the microscopic was in Norway—now a German colony—where a distilling plant tediously produced “heavy,” deuterium-enriched, water. And uranium was not water.
Scientists picked up tidbits from casual conversation or found themselves fortuitously introduced into inner circles of secret activity. While Feynman remained mostly oblivious, his senior professor Eugene Wigner had for two years been a part of “the Hungarian conspiracy,” with Leo Szilard and Edward Teller, conniving to alert Einstein and through him President Franklin D. Roosevelt to the possibility of a bomb. (“I never thought of that!” Einstein had told Wigner and Szilard.) Another Princeton instructor, Robert Wilson, had been drawn in by a sequence that began with a telegram from his old mentor at the Berkeley cyclotron, Ernest Lawrence. At MIT, under cover of a conventional scientific meeting, Wilson and several other physicists learned about the new Radiation Laboratory, already called the Rad Lab, formed to turn the nascent British experience with radar into a technology that would guide ships, aim guns, hunt submarines, and altogether transform the nature of war. The idea was to beam radio waves in pulses so strong that targets would send back detectable echoes. Radar had begun at wavelengths of more than thirty feet, which meant fuzzy resolution and huge antennae. Clearly a practical radar would need wavelengths measured in inches, down toward the microwave region. The laboratory would have to invent a new electronics combining higher intensities, higher frequencies, and smaller hardware than anything in their experience. The British had invented a “magnetron” producing a microwave beam so concentrated that it could light cigarettes—enough to confound the Americans. (“It’s simple—it’s just a kind of whistle,” I. I. Rabi told one of the first groups of physicists to gather uneasily around the British prototype. One of them snapped back, “Okay, Rabi, how does a whistle work?”) These scientists acted long before the American public accepted the inevitability of the conflict. Wilson agreed to join the Rad Lab, though he had considered himself a pacifist at Berkeley. But when he tried to leave Princeton, Wigner and the department chairman, Smyth, decided it was time for another initiation. They told Wilson that Princeton would soon take on a project to create a nuclear reactor, and they told him why.
Fueling the prewar collaboration of scientists and weapons makers was a patriotic ethos that no subsequent war would command. It easily overcame Wilson’s pacifism. Feynman himself visited an army recruitment office and offered to join the Signal Corps. When he was told he would have to start with unspecialized basic training—no promises—he backed down. That spring, in 1941, after three years of frustration, he finally got a job offer from Bell Laboratories in New York, and he wanted to accept. When his friend William Shockley showed him around, he was thrilled by the atmosphere of smart, practical science in action. From their windows the Bell researchers could see the George Washington Bridge going up across the Hudson River, and they had traced the curve of the first cable on the glass. As the bridge was hung from it, they were marking off the slight changes that transformed the curve from a catenary to a parabola. Feynman thought it was just the sort of clever thing he might have done. Still, when a recruiter from the Frankford Arsenal nearby in Philadelphia—an army general—visited Princeton seeking physicists, Feynman did not hesitate to turn down Bell Laboratories and sign up with the army for the summer. It was a chance to serve his country.
In one way or another, by the time the United States entered the war in December, one-fourth of the nation’s seven-thousand-odd physicists had joined a diffuse but rapidly solidifying military-research establishment. A generation brought up with the understanding that science meant progress, the harnessing of knowledge and the empowerment of humanity, now found a broad national purpose. A partnership was already forming between the federal establishment and the leaders of scientific institutions. The government created in the summer of 1941 an Office of Scientific Research and Development, subsuming the National Defense Research Committee, charged with coordinating research in what MIT’s president, Karl Compton, the epitome of the new partnership, called “the field of mechanisms, devices, instrumentalities and materials of warfare.” Not just radar and explosives but calculating machines and battlefield medicines occupied the urgent war effort. An area like artillery was no longer a matter of haphazard trial-and-error lobbing of randomly designed shells. The nuclear physicist Hans Bethe had turned on his own initiative to a nascent theory of armor penetration; he also took on the issue of the supersonic shock waves that would shudder from the edge of a projectile. Less glamorously, Feynman spent his summer at the Frankford Arsenal working on a primitive sort of analog computer, a combination of gears and cams designed to aim artillery pieces. It all seemed mechanical and archaic—later he thought Bell Laboratories would have been a better choice after all.
Still, even in his college workshops, he had never confronted such an urgent blending of mathematics and metal. To aim a gun turret meant converting sines and tangents into steel gears. Suddenly trigonometry had engineering consequences: long before the tangent of a near-vertical turret diverged to infinity, the torque applied to the teeth of the gears would snap them off. Feynman found himself drawn to a mathematical approach he had never considered, the manipulation of functional roots. He divided a sine into five equal subfunctions, so that the function of the function of the function of the function of the function equaled the sine. And the gears could handle the load. Before the summer ended he was given a new problem as well: how to make a similar machine calculate a smooth curve—the path of an airplane, for example—from a sequence of positions coming in at regular intervals of a few seconds. Only later did he learn where this problem had arisen—from radar, the new technology from the MIT Radiation Laboratory.
After the summer he returned to Princeton, nothing remaining in his graduate education except the final task of writing his thesis. He worked slowly, trying out his least-action view of quantum mechanics on a variety of basic, illustrative problems. He considered the case of two particles or particle systems, A and B, which do not interact directly but through an intermediary system with wavelike behavior, a harmonic oscillator, O. A causes O to oscillate; O in turn acts on B. Complicated time delays enter the picture because, once O is set in motion, B will feel an influence that depends on A’s behavior some time in the past—and vice versa. This case was a carefully reduced version of the familiar problem of two particles interacting through the mediation of the field. He asked himself in what circumstances the equations of motion could be derived from a principle of least action, strictly from the available information about the two particles A and B, completely disregarding O, the stand-in for the field. The least-action principle had come to seem like more than merely a useful shortcut. He now felt that it bore directly on the issues on which physics traditionally turned, such principles as the conservation of energy.
“This preoccupation with …” he wrote—then reconsidered.
“This desire for a principle of least action is besides the simplicity gained that, when the motions can be so represented, conservation of energy, momentum, etc. are guaranteed.”
One morning Wilson came into his office and sat down. Something secret was going on, he said. He was not supposed to reveal the secret, but he needed Feynman and there was no other way. Furthermore, there were no rules about this secret. The military still did not take the physicists completely seriously. Physicists had decided on their own not to discuss certain matters, and now Wilson had decided to take it on himself to discuss one. It was time for Feynman’s initiation.
There was a possibility of a nuclear bomb, Wilson said. British physicists had heard the message of Bohr and Wheeler about uranium 235 two years earlier and had arrived at a new estimate for the critical mass of material that would be needed. An expatriate German chemist on the British team, Franz Simon, had made the Atlantic crossing by “flying boat” with the latest news from their Birmingham laboratory. Perhaps a pound or two would be enough. Perhaps even less. The British were working hard on the problem of separating the uranium isotopes, winnowing the rare lighter isotope, uranium 235, from the far more common chaff, uranium 238. The two forms of uranium are chemically indistinguishable—a chemical reaction sees just one kind of atom. But the atoms of different isotopes have different masses, a fact that theorists could exploit in several plausible ways. Simon himself was investigating a scheme of slow gaseous diffusion through metal foil riddled with pinpoint holes; the uranium 238 molecules, ever so slightly heavier, would lag behind as the gas drifted through. Secret committees and directorates were forming around the uranium problem. The British had a code name: tube alloy, soon contracted to tubealloy. The Americans were building a nuclear reactor; other Princeton professors were involved. And Wilson said he had come up with an idea of his own. He had invented a device—so far existing only in his head—that he hoped would solve the separation problem much faster. Where Simon was thinking about holes in metal—one morning he had gone into his kitchen and attacked a wire strainer with a hammer—Wilson had in mind a combination of novel electronics and cyclotron technology.
He had persuaded Harry Smyth to let him assemble a team from among the instructors, graduate students, and engineers. A sort of countrywide “body shop” trading in the available technical talent was taking shape with the help of the National Defense Research Council; that would help him find some necessary staff. Graduate students were being pressed into service with the help of a simple expedient—Princeton called a halt to most degree work. Students were asked to choose from among three war-related projects: Wilson’s; an effort to develop a new blast gauge for measuring explosive pressure; and a dully irrelevant-sounding investigation of the thermal properties of graphite. (Only later did it become clear that this meant the thermal-neutron properties of a material destined for nuclear reactors.) Wilson wanted to sign Feynman first. It occurred to him that Feynman’s persistent skepticism, his unwillingness to accept any assertion on authority, would be useful. If there was any baloney or self-deception in the idea, he thought, Feynman would find it. He wanted Feynman in place when he presented the plan to the other graduate students.
To his dismay Feynman turned him down flat. He was too deep in his thesis; also, though he did not say so, the Frankford Arsenal had left him slightly disillusioned with war work. He said that he would keep the secret but that he wanted no part of it. Wilson asked him at least to come to the meeting.
Long afterward, after all the bomb makers had taken second looks back at their moments of decision, Feynman remembered the turmoil of that afternoon. He had not been able to go back to work. As he recalled it, he thought about the importance of the project; about Hitler; about saving the world. Elsewhere a few physicists already guessed, making delicate inferences from university rosters and published papers, that Germany was mounting no more than a cursory nuclear-weapons research project. Still, among the physicists who had disappeared from view was Werner Heisenberg. The threat seemed real enough. Later Feynman remembered the decisive physical act of opening his desk drawer and placing in it the loose sheets of his thesis.
The Manhattan Project
Chicago, Berkeley, Oak Ridge, Hanford: the first outposts of the Manhattan Project eventually became permanent capitals of a national nuclear establishment. To produce purified uranium and plutonium on a scale of mere pounds would require the rapid establishment of the largest single-purpose industrial enterprise ever. General Electric, Westinghouse, Du Pont, Allis-Chalmers, Chrysler, Union Carbide, and dozens of smaller companies combined in an effort that would see giant new factory towns rising from the earth. Yet in the first uncertain months after the attack on Pearl Harbor nothing in the modest scale of nuclear research even remotely foreshadowed the impending transformation of the nation’s war-making capacity. Workshops were converted according to happenstance and convenience. At Princeton no more than a few thousand dollars was available for Wilson’s project. To get help with the electronics he resorted to throwing a near tantrum in I. I. Rabi’s office at the MIT Rad Lab. Including shop workers and technicians, his team grew to number about thirty. The experimental division amounted to one ungainly tube the length of an automobile, sprouting smaller tubes and electrical wiring. The theoretical division comprised, in its entirety, two cocky graduate students sitting side by side at roll-top desks in a small office.
They found they were able to bear the pressure of working on the nation’s most fateful secret research project. The senior theoretician crumpled a piece of paper one day, passed it to his assistant, and ordered him to throw it in the wastebasket.
“Why don’t you?” the assistant replied.
“My time is more valuable than yours,” said Feynman. “I’m getting paid more than you.” They measured the distances from scientist to wastebasket; multiplied by the wages; bantered about their relative value to nuclear science. The number-two man, Paul Olum, threw away the paper. Olum had considered himself the best undergraduate mathematician at Harvard. He arrived at Princeton in 1940 to be Wheeler’s second research assistant. Wheeler introduced him to Feynman, and within a few weeks he was devastated. What’s happening here? he thought. Is this the way physicists are, and I missed it? No physicist at Harvard was like this. Feynman, a cheerful, boyish presence spinning across the campus on his bicycle, scornful of the formalisms of modern advanced mathematics, was running mental circles around him. It wasn’t that he was a brilliant calculator; Olum knew the tricks of that game. It was as if he were a man from Mars. Olum could not track his thinking. He had never known anyone so intuitively at ease with nature—and with nature’s seemingly least accessible manifestations. He suspected that when Feynman wanted to know what an electron would do under given circumstances he merely asked himself, “If I were an electron, what would I do?”
Feynman found a vast difference between intuiting the behavior of electrons in rarefied theoretical contexts and predicting the behavior of a bulky jury-rigged assemblage of metal and glass tubing and electronics. He and Olum worked hastily. They could see from the start that Wilson’s idea sat somewhere near the border between possible and hopeless—but on which side of the border? The calculations were awkward. Often they had to resort to guesswork and approximation, and it was hard to see which pieces of the work could accommodate guesses and which demanded rigorous exactitude. Feynman realized that he did not completely trust theoretical physics, now that its procedures were put to such an unforgiving test. Meanwhile the technicians moved forward; they could not afford to wait for the theorists’ numbers. It was like a cartoon, Feynman thought; every time he looked around, the apparatus had sprouted another tube or a new set of dials.
Wilson called his machine an isotron (a near-meaningless name; his old mentor, Ernest Lawrence, was calling a competing device a calutron, California + tron). Of all the separation schemes, Wilson’s isotron owed the least to ordinary intuition about physical objects. It came the closest to treating atoms as denizens of a wavy electromagnetic world, rather than miniature balls to be pushed about or squeezed through holes. The isotron first vaporized and ionized chunks of uranium—heated them until they gave up an electron and thus became electrically charged. Then a magnetic field set them in motion. The stream of atoms passed through a hole that organized it into a tight beam. Then came the piece of wizardry that set the isotron apart from all the other separation schemes, the piece Feynman was struggling to evaluate.
A particularly jagged, sawtooth oscillation would be set up in the magnetic field. The voltage would swing sharply up and down, at radio wavelengths. Some of the uranium atoms would hit the field just as the energy fell to zero. Then some later atoms would enter the field as the energy rose, and they would accelerate enough to catch up with the first atoms. Then the energy would fall off again, so that the next atoms would travel more slowly. The goal was to make the beam break up into bunches, like traffic clumping on a highway. Wilson estimated that the bunches would be about a yard long. Most important, the uranium 235 and uranium 238 atoms, because of their differing masses, would accelerate differently in the magnetic field and would therefore bunch at different points. If the experimenters could get the timing right, Wilson thought, the bunches of each isotope should be distinct and separable. As they reached the end of the tube another precisely timed oscillating field, like a flag man at a detour, would deflect the bunches alternately left and right into waiting containers.
Complications appeared. As the ions’ own momentum pushed them together, their tendency to repel one another came into play. Furthermore some atoms lost not one but two or more electrons when ionized, doubling or tripling their electric charge and sabotaging Feynman’s calculations. When experimenters tried higher voltages than Feynman had initially calculated, they found that the bunches were springing back, the waves rebounding and forming secondary waves. It was with something like shock that Feynman realized that these secondary effects appeared in his equations, too—if only he could persuade himself to trust them. Nothing about the isotron project was simple. The physicists had to invent a way of feeding the machine with uranium powder instead of uranium wire, because the wire had a tendency to alloy with the electrodes, destroying them spectacularly. One of the experimenters found that, by setting a flame to the end of the uranium wire, he could create a shower of dazzling stars—an unusually expensive sparkler.
Meanwhile the project’s worst enemy was proving to be its closest competitor, Lawrence, at Berkeley. He wanted to absorb the isotron into his own project, shutting down the Princeton group and taking on its staff and equipment for his calutron. The California-tron similarly used the new accelerator technology to create a beam of uranium ions but accelerated them instead around a three-foot racetrack. The heavier atoms swung farther out. The light atoms made the tight turn into a carefully positioned collector. Or so they would in theory. When General Leslie R. Groves, the new head of the Manhattan Project, first made the drive up the winding road from San Francisco Bay to Berkeley’s Radiation Hill, he was appalled to find that the entire product of Lawrence’s laboratory could barely be seen without the aid of a magnifying glass. Worse, the microgram samples were not even half pure. Even so, they outweighed the total output of the Princeton group. Feynman carried the isotron’s flyspeck sample by the train to Columbia for analysis late in 1942; Princeton had no equipment capable of measuring the proportions of the isotopes in a tiny piece of uranium. Wearing his battered sheepskin coat, he had trouble finding anyone in the building who would take him seriously. He wandered around with his radioactive fragment until finally he saw a physicist he knew, Harold Urey, who took him in hand. Urey was a distinguished physicist who, as it happened, had delivered the first scientific lecture Feynman had ever heard, a public talk in Brooklyn on the subject of heavy water, sharing the bill with the wife of the Belgian balloonist Auguste Piccard. More recently Feynman had come to know Urey by attending meetings of the Manhattan Project’s de facto steering committee. In that way he also met for the first time I. I. Rabi, Richard Tolman, and the physicist, so like Feynman and yet so unlike him, who would control his destiny for the next three years, J. Robert Oppenheimer.
Soon after Feynman’s trip to Columbia bearing uranium, these men made their final decision on Princeton’s adventure with the isotron. On the recommendation of Lawrence, nominally in charge of all electromagnetic separation research, they closed the Princeton project down. Operationally the calutron seemed a full year ahead, and money had to be committed as well to the more conventional diffusion approach, with pumps and pipes instead of magnets and fields, the atoms drifting in random trajectories, at ever-so-slightly different speeds, through many miles of metal barriers pricked with billions of microscopic holes. Wilson was stunned. He thought the committee was acting not just hastily but hysterically. To his senior colleagues it seemed that Wilson had lost to the personal strength and promotional skill of his former mentor Lawrence. Smyth and Wigner both felt privately that, given a fuller trial, the isotron might conceivably have shortened the war. “Lawrence’s calutron simply used raw brute force to pry the beam a little way apart,” a younger team member said. “Our method was elegant.” Blown up to the scale needed for mass production—thousands of giant machines—the isotron promised a yield many times greater. Feynman had produced detailed calculations for the design of a vast manufacturing plant, with isotrons working in a “cascade” of increasing purity. He took into account everything from wall-scrapings to uranium that would be lost in workers’ clothing. He conceived arrays of several thousand machines—yet that proved a modest scale, in light of the later reality.
For Feynman one legacy of the Princeton effort was the friendship with Olum, a friendship, like many that followed, intellectually rich and emotionally unequal. Encounters with Feynman left marks on a series of young physicists and mathematicians, in the glare of a bright light, out-thought for the first time in their lives. They found different ways of adapting to this new circumstance. Some subordinated their own abilities to his and accepted his occasional bantering abuse in exchange for the surprising pleasure that came with his praise. Some found their self-image enough changed that they abandoned physics altogether. Olum himself eventually returned to mathematics, where he was more comfortable. He worked with Feynman throughout the war and then Feynman drifted away. They met only a few times in the next forty years. Olum thought of his old friend often, though. He was president of the University of Oregon when he heard of Feynman’s death. He realized that the young genius he had met at Princeton had become a part of him, impossible to extricate. “My wife died three years ago, also of cancer,” he said.
… I think about her a lot. I have to admit I have Dick’s books and other things of Dick’s. I have all of the Feynman lectures and other stuff. And there are things that have pictures of Dick on them. The article in Science about the Challenger episode. And also some of the recent books.
I get a terrible feeling every time I look at them. How could someone like Dick Feynman be dead? This great and wonderful mind. This extraordinary feeling for things and ability is in the ground and there’s nothing there anymore.
It’s an awful feeling. And I feel it—— A lot of people have died and I know about it. My parents are both dead and I had a younger brother who is dead. But I have this feeling about just two people. About my wife and about Dick.
I suppose, although this wasn’t quite like childhood, it was graduate students together, and I do have more—— I don’t know, romantic, or something, feelings about Dick, and I have trouble realizing that he’s dead. He was such an extraordinarily special person in the universe.
Absent from Princeton’s nuclear effort was John Wheeler. He had already departed for Chicago, where Enrico Fermi and his team at the Metallurgical Laboratory—that enigmatic laboratory employing no metallurgists—were driving toward the first nuclear reactor. They intended to use less-than-bomb-grade uranium to produce slow fission. In the spring of 1942 Chicago was the place where it was easiest to gain a sense of what the future held. Wheeler knew how deeply his former student was mired in the isotope-separation work. In March he sent Feynman a message. It was time to finish his thesis, no matter how many questions remained open. Wigner—who was also more and more a part of the Chicago work—agreed that Feynman had accomplished enough for his degree.
Feynman heard the warning. He requested a short leave from the isotron project. Even now he did not feel quite ready to write, especially under such pressure. Later he remembered spending the first day of his leave lying on the grass, guiltily looking at the sky. Finally, writing with fountain pen in his fast adolescent scrawl, he filled sheaves of scratch paper—but paper was expensive, so he used the stationery of the Lawrencian, the Lawrence High School newspaper (Arline Greenbaum, editor in chief) or surplus order forms of G. B. Raymond & Company, sewer pipe, flue linings, etcetera, of Glendale, Long Island. He had now thoroughly assimilated Wheeler’s revolutionary attitude, the stance that declared a break with the past. When the quantum mechanics of Max Planck was applied to the problem of light and the electromagnetic field, he wrote, “great difficulties have arisen which have not been surmounted satisfactorily.” Other interactions, with more recently discovered particles, were creating similar difficulties, he pointed out: “Meson field theories have been set up in analogy to the electromagnetic field theory. But the analogy is unfortunately all too perfect; the infinite answers are all too prevalent and confusing.” So he disposed of the field—at least the old idea of the field as a free medium for carrying waves. The field is a “derived concept,” he wrote. “The field in actuality is entirely determined by the particles.” The field is a mere “mathematical construction.” Just as radically, he deprecated the wave function of Schrödinger, the now-orthodox means of describing the full state of a quantum-mechanical system at a given time. It was practically useless, after all, when the interaction of particles involved a time delay. “We can take the viewpoint, then, that the wave function is just a mathematical construction, useful under certain conditions”—no, “certain particular conditions … but not generally applicable.”
He also took pains to leave his collaboration with Wheeler decisively behind. He wanted his thesis to be his own; he may already have sensed that the absorber theory in itself was leading toward a quirky dead end. It was his conception of the principle of least action that now consumed him. Wheeler-Feynman had been only a starting point, he wrote. It happened to provide most of the “illustrative examples” that would fill out the thesis. But he declared that his least-action method “is in fact independent of that theory, and is complete in itself.”
When he was done, the first part of the thesis looked deceptively old-fashioned. It worked out some nearly textbook equations for the description of mechanical systems, such as springs, coupled together by means of another oscillator. Then this intermediate oscillator disappeared. A stroke of mathematical ingenuity eliminated it. A shorthand calculation appeared, very much like the classical Lagrangian. Soon the ground shifted, and the subject was quantum mechanics. The classical machinery of the first part turned into something quite modern. Where there had been two mechanical systems coupled by an oscillator, now there were two particles interacting through the medium of an oscillating field. The field, too, was now eliminated. A new quantum electrodynamics arose from a blank slate.
Feynman concluded with a blunt catalog of the flaws in his thesis. It was a theory untested by any connection to experiment. (He hoped to find an application to laboratory problems in the future.) The quantum mechanics remained nonrelativistic: a working version would have to take into account the distortions of Newtonian physics that occur near the speed of light. Above all he felt dissatisfied with the physical meaning of his equations. He felt they lacked a clear interpretation. Although few concepts in science seemed more frightening or abstruse than Schrödinger’s wave function, in fact the wave function had achieved a kind of visualizability for physicists, if only as a sort of probabilistic smudge at the edge of consciousness. Feynman acknowledged that his scheme discarded even that fragment of a mental picture. Measurement was a problem: “In the mathematics we must describe the system for all times, and if a measurement is going to be made in the interval of interest, this fact must be put somehow into the equations from the start.” Time was a problem: his approach required, as he said, “speaking of states of the system at times very far from the present.” In the long run this would prove a virtue. For now it seemed to turn the method into a formalism with no ready physical interpretation. For Feynman, an unvisualizable formalism was anathema. The official thesis readers, Wheeler and Wigner, were unperturbed. In June Princeton awarded Feynman his doctoral degree. He attended the ceremony wearing the academic gown that had made him so uncomfortable three years before. He was proud in the presence of his parents. Fleetingly he was annoyed at sharing the platform with honorary-degree recipients; always pragmatic, he thought it was like giving an “honorary electrician’s license” to people who had not done the work. He imagined being offered such an honor and told himself that he would turn it down.
Graduation removed one obstacle to marriage, but only one. According to medical and quasi-medical dogma, tuberculosis was a burden on love. “Should Consumptives Marry?” was the title of a chapter in Dr. Lawrence F. Flick’s 1903 monograph, Consumption a Curable and Preventable Disease. Not without gravely weighing the “risks and burdens,” he warned. And:
The relationship between husband and wife is so intimate that even with great care there may be given opportunity in moments of forgetfulness for conveyance of the disease.
Many a young consumptive mother gets her shroud shortly after she has purchased the christening frock for her babe.
A 1937 Manual of Tuberculosis for Nurses and Public Health Workers declared that marriage should be forbidden:
Marriage is apt to be a very expensive and dangerous luxury to those who are suffering, or have recently suffered, from tuberculosis of the lungs… . If the patient is a woman, she has not only to face the risk of infecting her husband and her children, but she must take into consideration the fact that pregnancy is liable to aggravate existing disease.
As late as 1952 an authoritative text cited Somerset Maugham’s short story “Sanatorium,” about a young couple in love who disregard the customary strictures.
They were both so young and brave that it was a great pity… . One could wish the novelist would rewrite the story with the boy and girl sensibly waiting for several years… . I am addicted to happy endings.
The textbook phrases gave no hint of the howling whirlpool of emotions that came when love and tuberculosis combined. Richard’s parents dreaded his marriage to Arline. Lucille Feynman, especially, found the idea impossible to bear. Her dealings with her son became harsher as she realized how serious his intention was. In the late spring she sent him a cold, handwritten screed bristling with her fear for his health, her fear for his career, her worry about money, and, indirectly, her revulsion at the possibility of sexual relations. She held nothing in reserve.
“Your health is in danger, no I should say your life is in danger,” she wrote. “It is only natural that when you are married you will see more of her.” She worried about what other people would think (an enemy against which Richard and Arline were learning to circle the wagons). Tuberculosis carried a stigma, and the stigma would attach to Richard. “People dread T.B. When you have a wife in a T.B. sanatorium, no one knows it is not a real marriage. & I know the world considers such a man dangerous to associate with.” She told Richard that he was not earning enough money, that he had been loyal enough already, and that Arline “should be satisfied with the status of ‘engagement’ instead of ‘marriage,’ because in such a marriage you are not getting any of the pleasures of marriage, but only the severe burden.” She warned that she and Melville would not help the couple with money under any circumstances. She appealed to his patriotism, saying that the burden of a sick wife would compromise his ability to serve his country. She reminded him that his grandparents had fled European persecution and pogroms for a country whose freedom he took for granted. “Your marriage at this time, seems a selfish thing to do, just to please one person.” She doubted that he sincerely wanted to marry Arline; she asked whether he was not merely trying to please her, “just as you used to occasionally eat spinach to please me.” She said that she loved him and hated to see him make a noble but useless gesture. She said, “I was surprised to learn such a marriage is not unlawful. It ought to be.”
Melville took a calmer tack. He asked Richard to get professional advice at Princeton, and Richard obeyed, consulting his department chairman, Smyth, and the university doctor. Smyth merely said he preferred to keep out of his staff’s private affairs. He kept to that position even when Feynman went to the extreme of pointing out that he would be in contact both with a tubercular wife and with students. The doctor was concerned to make sure that Feynman understood the danger of pregnancy, and Feynman told him they did not intend to make love. (The doctor noted that tuberculosis was an infectious rather than a contagious disease, and Feynman, typically, pressed him on that point. He had a suspicion that the distinction was an artifact of unscientific medical jargon—that, if there was a difference at all, it was a difference of degree only.)
He told his father that he and Arline did not plan to marry any time within the next year. But just a few days later, having received his degree and his new status, he wrote back to his mother, proudly updating his letterhead by penning “Ph.D.” after the printed “Richard Feynman.” He tried to respond reasonably to each argument. Neither Smyth nor the university physician were concerned about any danger to his health, he said. If marriage to Arline would be a burden, it was a burden he coveted. He had realized one day, arranging Arline’s transfer to the sanatorium nearby, that he was actually singing aloud with the sheer pleasure of planning their life together. As far as his duty to country was concerned, he would do whatever was necessary and go wherever he was sent. It was not that he wanted to be noble, he told his mother. Nor was it that he felt obliged to keep a promise he had made years before under different circumstances.
Marrying Arline was distinctly different from spinach. He did not like spinach. Anyway, he said, he had not eaten spinach out of love for his mother. “You misunderstood my motives as a small boy—I didn’t want you angry at me.”
He had made up his mind. He moved into a flat at 44 Washington Road immediately after graduation and for a while did not even tell his mother the address. He rapidly made the final arrangements—as Arline said, “in no time flat”:
I guess maybe it is like rolling off of a log—my heart is filled again & I’m choked with emotions—and love is so good & powerful—it’s worth preserving—I know nothing can separate us—we’ve stood the tests of time and our love is as glorious now as the day it was born—dearest riches have never made people great but love does it every day—we’re not little people—we’re giants … I know we both have a future ahead of us—with a world of happiness—now & forever.
With his parents frightened and unreconciled, he borrowed a station wagon from a Princeton friend, outfitted it with mattresses for the journey, and picked up Arline in Cedarhurst. She walked down her father’s hand-poured concrete driveway wearing a white dress. They crossed New York Harbor on the Staten Island ferry—their honeymoon ship. They married in a city office on Staten Island, in the presence of neither family nor friends, their only witnesses two strangers called in from the next room. Fearful of contagion, Richard did not kiss her on the lips. After the ceremony he helped her slowly down the stairs, and onward they drove to Arline’s new home, a charity hospital in Browns Mills, New Jersey.