Genius

by James Gleick

  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 leas
t 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.