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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