Maverick Genius Read online

  The materials of art, said one of Dyson’s favorite poets, T. S. Eliot, keep changing, but the quality of art doesn’t improve.9 How about science? Well, the material conditions of science keep changing (better detectors, faster computers). The “quality” of science, you might say, depends on its ability to explain more phenomena. At its best, art enchants. At its best, science enlightens. It might seem that quantum science, with its themes of uncertainty and indeterminacy, represented something like the opposite of enlightenment. Heisenberg responded by saying that quantum mechanics was only revealing what nature had decreed, namely a blurred reality at the most fundamental level of existence. Knowing what you don’t—or can’t—know is itself a form of knowledge.

  AIRY NOTHING

  No scientific accounting of nature can ever be complete. Further measurements uncover new things to explain. So no sooner had quantum mechanics begun to emerge as the fundamental description of microscopic reality than it too began to spring leaks. One of the first problems concerned calculations of how electrons interact with themselves.* When some calculations were slotted into the quantum equations, the theoretical answers that came back (such as: What was the energy of an electron in some circumstances?) were equal to infinity! What had gone wrong? Here is where Freeman Dyson would make his mark, helping to choreograph the dance of electrons and light.

  Dyson had traveled to Ithaca to be where the action was, and he wouldn’t be disappointed. Seminarians learn by studying venerable texts. He had been recruited into physics by his reading of those important quantum gospels, Heitler’s and Wentzel’s textbooks. These books had warned of the deficiencies in quantum science leading to the infinities. This was Dyson’s hint that something troubling and wonderful was happening.

  If we could picture this world what would it look like? It’s comparatively easy to think of electrons by the trillion racing through metal wires as electricity. But try visualizing electrons one or two at a time. Each flings out its own electric force, and a magnetic force too, on any charged object passing by. But the electron itself is a charged object, so it ought to feel its own electromagnetic field. And so it does. One way of visualizing this self-interaction is to suppose that an electron is continually shooting out tiny parcels of electromagnetic energy—bundles called virtual photons—which it then promptly reabsorbs.

  We don’t have spacecraft small enough to journey in toward a single electron to see what happens on this tiny scale. With pencil and paper, however, theorists can go anywhere they like. They can imagine—or with their equations they can predict—what happens when you view the electron (in its guise as a particle) from a distance of a millionth of a meter and then a billionth and then a trillionth, and so on indefinitely, closer and closer.

  And the closer you get to the electron, the more crowded this inner space becomes. That is, as you fly along in your minuscule space odyssey in the direction of the electron, as if it were some exotic ball of electric charge, things would get more and more frenzied. First of all, the electron does not have an atmosphere, like our Earth. It doesn’t have a surface. There’s no reachable center. Instead what you encounter as you go closer is only an ever denser storm of virtual light. These virtual photons could themselves shoot forth particles—such as virtual electrons accompanied by virtual antielectrons—and these virtual particles, in turn, could unleash still more virtual photons, and so forth.

  The idea of virtual particles is no stranger than the idea of virtual money. Many people receive their salaries electronically, pay their bills electronically, accrue investment interest electronically, and purchase goods electronically. “Money” in this case is no more than disembodied digits moving about from one place to another, while keeping a proper balance. That’s what virtual particles do. They move about, undergo transformation, slip in and out of existence, and keep a balance.

  If you took into account all the activity of virtual particles cloaking the electron, and tried to calculate something practical such as the strength of the electron’s magnetism, you got an answer that looked like infinity. And that’s just for one electron. What about all the rest of them? An inexhaustible supply of electrons in the universe, each with an apparently infinite storehouse of energy: this was infinity squared!

  Stop to consider the near fantastical status of this microscopic description of nature, one that calls forth a vapor of virtual particles capering about in the recesses of the atom. It sounds a bit like the story in Shakespeare’s A Midsummer Night’s Dream, which takes place mostly in a forest enchanted by fairies who confound the thinking of all who enter there. Near the end of the play, Theseus, the wise duke, summarizes the delightful power of the events just witnessed:

  And as imagination bodies forth

  The forms of things unknown, the poet’s pen

  Turns them to shapes, and gives to airy nothing

  A local habitation and a name.

  Scientists spin out equations in order to account adroitly for the complexities of nature, such as an electron’s local habitation, while playwrights spin out dramas that colorfully account for human complexity. Shakespeare summons fairies to perform magic. Physicists “body forth” electrons and photons out of the airy nothing of empty space. The effectiveness of Shakespeare’s play depends on the charm by which he reveals human nature. The effectiveness of quantum science depends on its accuracy in predicting phenomena detected in apparatus, even if we never personally witness quantum fields at work.

  CHASING INFINITY

  The quantum equations, which looked so clever in the 1920s, now were in danger of being spoiled by nonsensical results. An explanation was needed. Surely, electrons cannot be shrouded in an infinite fog of energy. They are not miniature suns. Infinity, if it is there staring at us from within an atom, from within every atom, must somehow be disguised or modified in some way. The quantum catechism needed reforming.

  In the late 1930s quantum progress was stymied by this specter of infinity. Then the Second World War arrived and physicists’ attention was drawn to radar and nuclear matters, freezing out consideration of nonessential issues. But in the spring of 1947, a great thaw occurred. It was possible to do quantum physics again. A call went out for a new ecumenical council. This time the bishops of physics, at least those concerned with quantum infinity, were summoned to a resort on a hard-to-reach island wedged between the eastern arms of Long Island, a hundred miles from New York City. Not as international as the Solvay conferences had been, the Shelter Island conference brought together mostly American scientists, reflecting the difficulty of postwar travel and also the growing importance of research in the United States.

  Indeed, most of the twenty-four participants had been involved with the Manhattan Project or one of the other wartime ventures. The presiding presence on Shelter Island, as he had been at Los Alamos, was J. Robert Oppenheimer. This was the first open physics meeting anyone had attended for many years, and it was a pleasure to talk freely without the encumbrance of security clearances. No barbed wire hemmed them in. They would be pondering not the explosion of uranium nuclei flying apart in the atmosphere but the hypothetical typhoon of virtual photons that swarmed around the electron.

  The elite group, which included Bethe and Feynman, started out on the morning of June 2, 1947, by boarding a bus in Manhattan. Led by a police motorcade through Long Island, the bus stopped en route for a festive banquet offered by a patriotic local businessman who wanted to honor the bomb-making and war-ending accomplishments of the nuclear scientists.

  The council on Shelter Island consisted chiefly of theorists, but the most important presentation was made by an experimentalist. Willis Lamb, who during the war was absorbed in perfecting a radar scheme in the interest of shooting down German fighters, was now shooting microwaves into a tiny vial of hydrogen at Columbia University. Lamb had the attention of everyone in the room.10

  What he’d found concerned the light coming out of heated hydrogen. Hydrogen, like all other elements, posses
ses a unique set of inner energy levels. These quantum levels can be sensitively catalogued by observing the light waves emitted when the atoms are heated. Lamb, using apparatus of unprecedented precision, discovered that at least one of the levels wasn’t where it was supposed to be. One type of light ray emitted by hydrogen atoms wasn’t at quite the expected frequency. The discrepancy, which became known as the Lamb shift, caused a sensation in physics, and was the prime subject of conversation at Shelter Island.

  Here was a vital piece of factual reality. It provided a fixed target to aim at. Many physicists felt that an explanation of this misplaced atomic energy level would offer a clue to the unwanted infinities. Explain the Lamb shift and maybe you would restore, or at least refresh, confidence in the quantum explanation of the cosmos.

  THE NOVITIATE ENDS

  When Hans Bethe left the Shelter Island meeting, he already had drawn up a rough hypothesis explaining how the electron interacts with itself, and he was able to make a rudimentary calculation of the Lamb shift. Bethe assigned Dyson, a new student in the fall of 1947, a world-class problem: improve Bethe’s own explanation of the Lamb shift by attaching the machinery of Einstein’s special relativity to the quantum equations. That is, Dyson was to build into the theory the proper relation between the mass and energy of particles moving at high speed.

  Dyson threw himself into the work. He had to do a good job, since everyone was watching. Dyson didn’t return after four years with the answer and write up a Ph.D. dissertation. Instead he came back after a month, done. He hadn’t fully explained why hydrogen atoms were out of tune, but he had nudged Bethe’s equations into a more useful form. The professors were delighted, but the other students were appalled. If this guy, who had practically no physics background and who read newspapers half the day, could perform these kinds of calculations so quickly, then what chance was there for them to succeed?11

  At Bethe’s urging, Dyson wrote up his notes for publication in Physical Review. This was his first physics paper.12 Already his days as a novice were coming to an end.

  In numerous letters home Dyson kept his parents abreast of his exploits. He never felt so close to them, he said, as when he was away in the United States.13 More able to gauge his abilities in the world of mathematics than in his adopted field of physics, he understated his new work in comparison to the masterful paper about the Minkowski conjecture he had written to win admittance to Cambridge:

  I have done nothing in the past two months that you could call very clever or difficult; nothing one-tenth as hard as my fellowship thesis; but because the problems I am now dealing with are public problems and all the theoretical physicists have been racking their brains over them for ten years with such negligible results, even the most modest contributions are at once publicized and applauded.14

  Oh well, he was saying, I might as well be the one to fix things. Note his use of the word “public.” Mathematics had been something private, while physics was public. His effort at encompassing the universe, at least the electron part, was modest so far, he insisted, but it had caused at least a small positive disturbance among onlookers.

  Indeed, others had started to take notice of Dyson. A follow-up to the Shelter Island meeting was planned. The next invitation-only ecumenical council would take place at a resort in the Pocono Mountains of Pennsylvania. With Oppenheimer again acting as leader, two dozen premier physicists assembled to attack the infinity problem. Bethe requested an invitation for Dyson, who had, after all, cleared some new territory in the study of electrodynamics, the science devoted to the electromagnetic force. Oppie said no. Keeping the attendance elite was necessary if the proper focus was to be maintained. So Dyson was not asked along. He would be a seminarian just a bit longer.

  MOUNTAINTOP PHYSICS

  At the 1948 Pocono conference the focus would be on the substance of infinity. Specifically, how did the interaction between an electron and the ubiquitous electromagnetic field keep from amplifying itself into an infinite feedback blowup? This was going to be the most important conference of Freeman Dyson’s career. Even though he would not be there in person—he would only follow the battle from afar as if it were some distant artillery duel—the ideas to be exchanged over the next few days were to shape his own thinking for years to come.

  At Pocono, the showcase matchup would be between Richard Feynman and Julian Schwinger. Both were about thirty years old, so another energetic, youthful battle of ideas was expected, reminiscent of the Knaben Physik quantum breakthroughs in the 1920s. Both Feynman and Schwinger had grown up in New York City, had shown brilliance early, and had quickly become professors at Ivy League colleges. Feynman was a professor at Cornell, while Schwinger had beat out Bethe for a job at Harvard. But everything else about them was different.

  Feynman was boisterous, while Schwinger was reserved. Feynman drove a grubby Oldsmobile, Schwinger a plush Cadillac. Feynman spent the war years working on the atomic bomb in Los Alamos, while Schwinger had worked on radar at MIT.

  Schwinger, in lecture mode, was polished; at the risk of being exhausting he impressed his audiences with comprehensiveness. When he finished speaking you knew you had heard just about everything there was to hear on that subject. The matter had been thought out and presented with the precision of a district attorney.

  Feynman, by contrast, was more animated, colloquial. In the sequence of his explanations he cut corners.

  Each man had come up the mountain in Pennsylvania to offer his own comprehensive theory of quantum electrodynamics, or QED, the framework that combines the nineteenth-century theory of electromagnetic forces with twentieth-century quantum science. Each took his turn trying to impress a very discriminating audience. Those in attendance included Niels Bohr, who had been so conspicuous at the 1927 Solvay conference and who even now was the very godfather of quantum orthodoxy; Enrico Fermi, who had done pioneering work in nuclear physics and who had built the first working nuclear reactor; Edward Teller, who had been working for many years on plans for a thermonuclear bomb; Paul Dirac, one of the founders of field theory; and even the authors of Dyson’s two favorite quantum textbooks, Gregor Wentzel and Walter Heitler.

  The topic of discussion was worthy of this august audience. Two rival efforts to chase down the persistent quantum infinities were being offered. Like two politicians rolling up at the party convention to make their cases before the delegates, Julian Schwinger and Richard Feynman arrived amid high expectation. One presentation would be a mesmerizing triumph, the other an embarrassing failure.

  Schwinger, speaking first, outlined his attempt to reform quantum science. His scheme, based on a mathematical expression called a Green’s function, looked a bit like the sort of field theory already pioneered by Heisenberg and Dirac. Two months before, at the New York meeting of the American Physical Society, Schwinger had presented an early version of the theory. Extra lectures and larger rooms were needed to accommodate the crush of viewers. In the months since, he’d finished his work.

  Now came the full Schwinger. Previously physicists had believed the infinities could be fixed by somehow redefining the mass and charge of the electron, and this is what Schwinger had now done.15 If the electron’s mass and charge were infinite it wouldn’t matter, since the electron—at least the electron we encounter in actual measurements—would be surrounded by that countervailing blizzard of electromagnetic fields. Schwinger’s process of cosmic mitigation at the submicroscopic level, neutralizing the infinities, made electrons—every electron—normal again, fit to participate in atomic society. This domestication of the electron was therefore called renormalization.

  Schwinger’s lecture went on for hours. This masterful expositor, who in a long teaching career at Harvard would supervise the candidacy of eighty physics Ph.D.’s, including future Nobelists, bedazzled and benumbed his audience of experts. Few questions came up during the onslaught of Schwinger’s logic. At the end, the auditors, still anesthetized by the extreme density of equations, couldn’t
be sure, but it looked as if he had done it. Schwinger had tamed the infinities in a consistent way. Oppie was pleased.

  Then the second part of the double feature started up. Feynman was different. He became legendary for his wayward habit of assembling ideas from the ground up. He didn’t work up his explanations from others’ equations. He started fresh, sought a physical view of things, as opposed to being merely mathematical, and frequently made death-defying, mountain-goat leaps from crag to crag, leaving out lots of steps in the proof in order to get to the point sooner. That’s the way his mind worked. Those observing the display were worried not because of the math but because here was a man performing high-wire maneuvers without a net beneath.

  Feynman didn’t deny that Schwinger’s field approach to understanding electrons was useful. But he preferred, somewhat quaintly, to imagine electrons as things moving about. To calculate how an electron gets from place to place, from a to b, you should take into account all the possible ways of going, he said, and then add up the possibilities for all those possible paths—each weighted by its relative likelihood—to arrive at a final answer. Driving from New York to Los Angeles, for example, you could take a northern route through Denver or a southern route through Phoenix, or maybe somewhere in between. An electron, going from here to there, does the same thing. But for the electron there are an infinite number of alternative paths to take.

  Feynman offered a gigantic form of bookkeeping that kept track of each path by conjuring an associated picture. Quantum rules, solidified into a secular canon at previous conclaves like Solvay, insisted that we never know precisely which way an electron had gone; in a way, the electron had taken all available paths. Feynman seized on this every-which-way reality to describe quantum reality, not for making a cross-country journey but for explaining the perpetual dance of matter with light.