by James Gleick
When Feynman talked about fluid flow, he knew he was returning to a childlike, elemental fascination with the world as it is. The pleasure of watching water in bathtubs or mud puddles on the sidewalk, of trying to dam a curbside rivulet after a rainstorm, of contemplating the movement in waterfalls and whirlpools—that was what made every child a physicist, he felt. In trying to understand superfluidity, he began once again with first principles. What was a fluid? A substance, liquid or gas, that cannot withstand a shear stress, but moves under the force. The tendency of a fluid to resist the shear is its viscosity, its internal friction—honey being more viscous than water, water more than air. Nineteenth-century physicists creating the first effective equations for fluid flow found viscosity especially troublesome, so uncomputable were its consequences. For the sake of simplicity, they often created models that ignored viscosity—and for that John von Neumann later mocked them. Modelers always tried to omit unnecessary complication—that was one thing. But classical fluid dynamicists had omitted what seemed an essential, defining quality. Sarcastically von Neumann called them theorists of “dry water.” Superfluid helium, Feynman said, resembled that impossible idealization, fluid without viscosity. It was dry water.
Superfluidity had an equally bizarre twin, superconductivity, the flow of electricity with no dissipation or resistance. Both were phenomena of low-temperature experimentation. Superconductivity had been discovered in 1911; superfluidity not until 1938, because of the difficulties of watching the behavior of a liquid inside a pinhead-size container in a supercooled cryostat. Esoteric though they were, by the fifties this pair of phenomena had become crown jewels of the side of theoretical physics not devoted to elementary particles. Little progress had been made in understanding the perpetual-motion machinery that seemed to be at work. It seemed to Feynman that they were like “two cities under siege … completely surrounded by knowledge although they themselves remained isolated and unassailable.” Besides Landau, the chief contributor to the theorizing on superfluidity was Lars Onsager, the distinguished Yale chemist whose notoriously difficult courses in statistical mechanics were sometimes called (in allusion to Onsager’s accent) Norwegian I and Norwegian II.
Nature had exhibited another kind of perpetual motion, familiar to quantum physicists: motion at the level of electrons in the atom. No friction or dissipation slowed electrons. Only in the interactions of crowds of atoms did the energy drain of friction arise. Were these super phenomena somehow escaping the incoherent tumult of classical matter? Was this a case of quantum mechanics writ large? Could the whole apparatus of wave functions, energy levels, and quantum states translate itself onto macroscopic scales? The most basic clue that this was indeed large-scale quantum behavior came from the apparent unwillingness of helium to freeze into hard crystals at any temperature. Classically, absolute zero was often described as the temperature at which all motion ceases. Quantum mechanically, there is no such temperature. Atomic motion never does cease. That precise a zero would violate the uncertainty principle.
Landau and others had set the stage with a handful of useful conceptions of liquid helium. One powerful idea, which continued to dominate all kinds of solid-state physics, was the notion of new entities—“quasiparticles” or “elementary excitations”—collective motions that traveled through matter and interacted with one another as if they were particles. Quantum sound waves, now called phonons, were one example. Another: liquid helium seemed to contain units of rotational motion christened rotons. Feynman tried to work out the implications of these ideas. He also explored the notion that liquid helium acts as though it were (here, as elsewhere, the old-fashioned is had to be permanently replaced by the provisional acts as though it were) a mixture of two coexisting substances, a normal liquid and a pure superfluid.
One of the strangest of all the liquid-helium manifestations demonstrated how the mixture would work. A circular tube like a bicycle tire was packed with powder and then filled with liquid helium. It was set spinning and then abruptly halted. The powder would halt the flow of any normal liquid. But the superfluid component of liquid helium would continue to flow, around and around, passing through the microscopic interstices in the powder, in effect ignoring the presence of another, normal liquid. Students could sense the flow by feeling the tire’s resistance to torque, as a spinning gyroscope resists sidelong pressure. And, once set in motion, the superflow would persist as long as the universe itself.
At a meeting in New York of the American Physical Society in 1955 Feynman startled a Yale group, students of Onsager, who described a new experiment they were conducting with rotating buckets. (In the low-temperature business “buckets” tended to be glass tubes the size of a thimble.) Feynman rose and said that a rotating bucket of superfluid would be filled with peculiar vortices, whirlpools hanging down like strings. The speakers had no idea what he was talking about. This peculiar image was the essence of his visualization of the atomic behavior of liquid helium. He had tried to picture how individual atoms would move together within the fluid; he calculated the forces between them as directly as he could, with tools dating back to his undergraduate research with John Slater. He saw that rotational motions would arise, just as Landau had suggested, and he applied the quantum-mechanical restriction that such motion would have to come in indivisible units. For a while he struggled to find the right image for an elementary excitation in a superfluid. He considered an atom in a cage, oscillating. A pair of atoms revolving one around the other. A tiny rotating ring of atoms. The challenge was to drive toward a solution of a many-particle problem in quantum mechanics without being able to begin with a formal, mathematical line of reasoning. It was a challenge in pure visualization.
He lay awake in bed one night trying to imagine how rotation could arise at all. He imagined a liquid divided by a thin sheet, an imaginary impermeable membrane. On one side the liquid was motionless; on the other side it flowed. He knew how to write the old-fashioned Schrödinger wave function for both sides. Then he imagined the sheet disappearing. How could he make the wave functions join? He thought about the different phases combining. He imagined a kind of surface tension, energy proportional to the surface area of his sheet. He considered what would happen when an individual atom moved across the boundary—at what point in the rising and falling wave of energy the surface tension would fall to zero and the atom would be able to move freely. He was starting to see a surface divided into strips of glue, where the atoms could not mix, and other narrow strips where atoms would be able to change places. He calculated how little energy it would take to distort the wave function until the atoms would be held back, and realized that the strips of free motion would be no more than the width of a single atom. Then he realized that he was seeing lines, vortex lines around which the atoms circulated in rings. The rings of atoms were like rings of children waiting to use a playground slide. As each child descended—the wave function changing from plus to minus—another would slip into position at the top. But the fluid version was more than just a two-dimensional ring. It also wound back on itself through the third dimension—like a smoke ring, Feynman concluded, twenty years after he had led an investigation of smoke-ring dynamics in his high school physics club. These quantum smoke rings, or vortex lines, would circle about the tiniest conceivable hole, just one atom’s width across.
In a succession of articles spanning five years he worked out the consequences of his view of the interplay of energy and motion in this quantum fluid. The vortex lines were the fundamental units, the indivisible quanta of the system. They set limits on the ways in which energy could be exchanged within the fluid. In a thin enough tube, or a slow enough flow, the lines would not be able to form, and the flow would just coast, unchanging, losing no energy, and thus absolutely free of resistance. He showed when vortex lines would arise and when they would vanish. He showed when they would begin to entangle one another and ball up, creating another unexpected phenomenon that no one had yet seen in the laboratory
: superfluid turbulence. Caltech hired low-temperature experimental specialists, and Feynman worked with them closely. He learned all the details of the apparatus, vacuum pumps for cooling by lowering the vapor pressure; rubber O-rings for ensuring tight seals. Before long, word was spreading of an experiment that struck physicists as “typical Feynman.” Tiny wings, airfoils, were attached to a thin quartz fiber hanging down through a tube. The superfluid was pulled through vertically. A normal fluid would have spun the wings like a tiny propeller, but the superfluid refused to cause twisting. Instead it slipped frictionlessly past. In their search for lighter and lighter airfoils, the experimenters finally killed some local flies, or so they claimed, and the investigation became known as the flies’-wings experiment.
Physicists who had worked in the area of condensed matter for longer than Feynman—and who would remain there after Feynman had once again departed—were struck by his method as much as by his success. He used none of the technical apparatus for which he was now famous: no Feynman diagrams, no path integrals. Instead he began with mental pictures: this electron pushes that one; this ion rebounds like a ball on a spring. He reminded colleagues of an artist who can capture the image of a human face with three or four minimal and expressive lines. Yet he did not always succeed. As he worked on superfluidity, he also struggled with superconductivity, and here, for once, he failed. (Yet he came close. At one point, about to leave on a trip, he wrote a single page of notes, beginning, “Possibly I understand the main origin of superconductivity.” He was focusing on a particular kind of phonon interaction and on one of the experimental signatures of superconductivity, a transition in a substance’s specific heat. He could see, as he jotted to himself, that there was “something still a little haywire,” but he thought he would be able to work out the difficulties. He signed the page: “In case I don’t return. R. P. Feynman.”) Three younger physicists, intensely aware of Feynman’s competitive presence—John Bardeen, Leon Cooper, and Robert Schrieffer—invented a successful theory in 1957. The year before, Schrieffer had listened intently as Feynman delivered a pellucid talk on the two phenomena: the problem he had solved, and the problem that had defeated him. Schrieffer had never heard a scientist outline in such loving detail a sequence leading to failure. Feynman was uncompromisingly frank about each false step, each faulty approximation, each flawed visualization.
No tricks or fancy calculations would suffice, Feynman said. The only way to solve the problem would be to guess the outline, the shape, the quality of the answer.
We have no excuse that there are not enough experiments, it has nothing to do with experiments. Our situation is unlike the field, say, of mesons, where we say, perhaps there aren’t yet enough clues for even a human mind to figure out what is the pattern. We should not even have to look at the experiments… . It is like looking in the back of the book for the answer … The only reason that we cannot do this problem of superconductivity is that we haven’t got enough imagination.
It fell to Schrieffer to transcribe Feynman’s talk for journal publication. He did not quite know what to do with the incomplete sentences and the frank confessions. He had never read a journal article so obviously spoken aloud. So he edited it. But Feynman made him change it all back.
New Particles, New Language
In the mere half-decade since the triumph of the new quantum electrodynamics the culture of high-energy physics had made and remade itself again and again. The language, the interests, and the machinery seemed to undergo a new transformation monthly. Experimentalists and theorists assembled yearly for meetings called Rochester conferences (after their initial site, Rochester, New York), descendants of the already mythic-seeming Shelter Island–Pocono–Oldstone meetings, but far larger and better financed, scores and then hundreds of participants. By the first of these meetings, at the close of 1950, quantum electrodynamics itself was already passé; it was so perfect experimentally and so far from the frontier of new forces and particles. That year had seen a kind of milestone, the discovery of a new particle not in cosmic rays but in an experimentalist’s accelerator. This was a neutral pi meson, or pion—“neutral” because it carried no charge. Actually, the experimenters did not so much detect the neutral pion as the pair of gamma rays into which it immediately decayed. This particle’s ephemerality made it less consequential in the everyday world of tables and chairs, chemistry and biology, than on this exciting frontier: it typically vanished after a lifetime of a tenth of a millionth of a billionth of a second. This qualified as a short time by 1950 standards. Yet standards were changing. Within a few years particle tabulations would list this fleeting entity in the category of STABLE. And meanwhile the legions of cosmic-ray explorers, many of them British, hoisting their photographic plates skyward with balloons, would find their specialty declining as spectacularly as it had risen. “Gentlemen, we have been invaded,” one of their leaders declared. “The accelerators are here.”
Of necessity physicists dispensed with their earlier squeamishness about the prospect of adding yet another particle to the already rich stew. On the contrary, an experimentalist could hardly aspire to more than the creation and discovery of a new particle. What it meant to measure these particles had also changed dramatically since the days when electrons had held center stage. Inferring the mass of a particle from the arcing traces left in a cloud chamber by its second- and third-generation decay products was not so simple. An enormous range of error had to be tolerated. It had become a serious and worthwhile intellectual challenge merely to identify the particles, to name them, to write down the rules of which particles could decay into which other particles. These rules were pithy new equations: π + p→π0 + n,, a pion with negative charge and a proton produce a neutral pion and a neutron. Never mind assessing the mass; it was hard enough to identify the objects of study. Declaring the existence or nonexistence of a certain particle became a delicate rite imbued with as much anticipation and judgment as declaring a rain delay at a baseball game.
This was the experimenters’ art, but, as the accelerator era began, Feynman took a special interest in the methodologies and pitfalls. He was influenced by Bethe, who always wanted to ground his theory in his own intuitions about the numbers, and by Fermi, the field’s last great combination of experimenter and theorist. Bethe spent time working out formulas for the probabilities of various wrong curvatures in cloud-chamber photographs. One experimentalist, Marcel Schein, set off a typical commotion with the announcement that he had discovered a new particle in cyclotron experiments. Bethe was suspicious. The energies seemed far too low to produce the kind of particle Schein described. Feynman forever remembered the confrontation between the two men, their faces eerily illuminated by the glow from the light table used to view the photographic plates. Bethe looked at one plate and said that the gas of the cloud chamber seemed to be swirling, distorting the curvatures. In the next plate, and the next, and the next, he saw different sources of potential error. Finally they came to a clean-looking photograph, and Bethe mentioned the statistical likelihood of errors. Schein said that Bethe’s own formula predicted only a one-in-five chance of error. Yes, Bethe replied, and we’ve already looked at five plates. To Feynman, looking on, it seemed like classic self-deception: a researcher believes in the result he is seeking, and he starts to overweight the favorable evidence and underweight the possible counterexamples. Schein finally said in frustration: You have a different theory for every case, while I have a single hypothesis that explains all at once. Bethe replied, Yes, and the difference is that each of my many explanations is right and your one explanation is wrong.
A few years later Feynman happened to be visiting Berkeley when experimenters excitedly thought they had discovered an antiproton—a particle clearly destined to be found at higher energies, but impossible, Feynman thought, at the mere hundreds of millions of electron volts available that year. As Bethe had, he went into a dark room to examine the photographs, a dozen questionable images and one that seemed ab
solutely perfect, the cornerstone of the discovery, with its track curving backward just as the antiparticle must.
There must be matter somewhere in the vacuum chamber, Feynman said.
Absolutely not, the experimenters told him—just thin glass walls on either side.
Feynman asked what held the upper and lower plates together. They said there were four small bolts.
He looked again at the white arc curving through the magnetic field. Then he jabbed his pencil down onto the table, inches away from the edge of the photograph. Right here, he said, must be one of those bolts.
The blueprint, retrieved from the files and laid out over the photograph, showed that his pencil had found the exact spot. An ordinary proton had struck the bolt and scattered backward into the picture. Later, experimenters at Caltech felt that Feynman’s very presence exerted a sort of moral pressure on their findings and methods. He was mercilessly skeptical. He loved to talk about the famous oil-drop experiment of Caltech’s first great physicist Robert Millikan, which revealed the indivisible unit charge of the electron by isolating it in tiny, floating oil drops. The experiment was right but some of the numbers were wrong—and the record of subsequent experimenters stood as a permanent embarrassment to physics. They did not cluster around the correct result; rather, they slowly closed in on it. Millikan’s error exerted a psychological pull, like a distant magnet forcing their observations off center. If a Caltech experimenter told Feynman about a result reached after a complex process of correcting data, Feynman was sure to ask how the experimenter had decided when to stop correcting, and whether that decision had been made before the experimenter could see what effect it would have on the outcome. It was all too easy to fall into the trap of correcting until the answer looked right. To avoid it required an intimate acquaintanceship with the rules of the scientist’s game. It also required not just honesty, but a sense that honesty required exertion.
