Джеймс Глик - Genius - The Life and Science of Richard Feynman

Welton became the fourth physicist in the group Feynman headed, now formal y known as T-4, Diffusion Problems. As a group leader Feynman was ebul ient and original. He drove his team hard in pursuit of his latest unorthodox idea for solving whatever problem was at hand.

Sometimes one of the scientists would object that a Feynman proposal was too complex or too bizarre.

Feynman would insist that they try it out, computing in groups with their mechanical calculators, and he had enough unexpected successes this way to win their loyalty to the cause of wide-ranging experimentation. They al tried to innovate in his fashion—no idea too wild to be considered. He could be ruthless with work that did not meet his high standards. Even Welton experienced the humiliation of a Feynman rebuke—“definitely ungentle humor” to which “only a fool would have subjected himself twice.” Stil Feynman managed to build esprit. He had taught himself to flip a pencil in one motion from a table into his hand, and he taught the same trick to his group. One day, amid a typical swirl of rumors that military uniforms were going to be issued to scientists working in the technical area, Bethe walked in to talk about a calculation.

Feynman said he thought they should integrate it by hand, and Bethe agreed. Feynman swiveled around and barked,

“Al right, pencils, calculate!”

A roomful of pencils flipped into the air in unison.

“Present pencils!” Feynman shouted. “Integrate!” And Bethe laughed.

Diffusion, that faintly obscure and faintly pedestrian

holdover from freshman physics, lay near the heart of the problems facing al the groups. Open a perfume bottle in a stil room. How long before the scent reaches a set of nostrils six feet away, eight feet away, ten feet away? Does the temperature of the air matter? The density? The mass of the scent-bearing molecules? The shape of the room?

The ordinary theory of molecular diffusion gave a means of answering most of these questions in the form of a standard differential equation (but not the last question—

the geometry of the containing wal s caused mathematical complications). The progress of a molecule dependedon a herky-jerky sequence of accidents, col isions with other molecules. It was progress by wandering, each molecule’s path the sum of many paths, of al possible directions and lengths. The same problem arose in different form as the flow of heat througha metal. And the central issues of Los Alamos, too, were problems of diffusion in a newguise.

The calculation of critical mass quickly became nothing more or less than a calculation of diffusion—the diffusion of neutrons through a strange, radioactive minefield, where now a col ision might mean more than a glancing, bil iard-bal change of direction. A neutron might be captured, absorbed. And it might trigger a fission event that would give birth to new neutrons. By definition, at critical mass the creation of neutrons would exactly balance the loss of neutrons through absorption or through leakage beyond the container boundaries. This was not a problem of arithmetic.

It was a problem of understanding the macroscopic spreading of neutrons as built up from the microscopic

individual wanderings.

For a spherical bomb the mathematics resembled another strange and beautiful diffusion problem, the problem of the sun’s limb darkening. Why does the sun have a crisp edge? Not because it has a solid or liquid surface. On the contrary, the gaseous bal of the sun thins gradual y; no boundary marks a division between sun and empty space. Yet we see a boundary. Energy diffuses outward from the roiling solar core toward the surface, particles scattering one another in tangled paths, until final y, as the hot gas thins, the likelihood of one more col ision disappears. That creates the apparent edge, its sharpness more an artifact of the light than a physical reality. In the language of statistical mechanics, the mean free path—the average distance a particle travels between one col ision and the next—becomes roughly as large as the radius of the sun. At that point photons have freed themselves from the pinbal game of diffusion and can fly in a straight line until they scatter again, in the earth’s atmosphere or in the sensitive retina of one’s eye. The difference in brightness between the sun’s center and its edge gave an indirect means of calculating the nature of the internal diffusion. Or should have—but the mechanics proved difficult until a bril iant young mathematician at MIT, Norbert Wiener, devised a useful method.

If the sun were a cool y radioactive metal bal a few inches across, with neutrons rattling about inside, it would start to look like a miniaturized version of the same problem. For a while this approach proved useful. Past a

certain point, however, it broke down. Too many idealizing assumptions had to be made. In a real bomb, cobbled together from mostly purified uranium, surrounded by a shel of neutron-reflecting metal, the messy realities would defy the most advanced mathematics available. Neutrons would strike other neutrons with a wide range of possible energies. They might not scatter in every direction with equal probability. The bomb might not be a perfect sphere.

The difference between these realities and the traditional oversimplifications arose in the first major problem assigned to Feynman’s group. Bethe had told them to evaluate an idea of Tel er’s, the possibility of replacing pure uranium metal with uranium hydride, a compound of uranium and hydrogen. The hydride seemed to have advantages. For one, the neutron-slowing hydrogen would be built into the bomb material; less uranium would be needed. On the other hand, the substance was pyrophoric

—it tended to burst spontaneously into flame. When the Los Alamos metal urgists got down to the work of making hydride chunks for testing, they set off as many as half a dozen smal uranium fires a week. The hydride problem had one virtue. It pushed the theorists past the limits of their methods of calculating critical masses. To make a sound judgment of Tel er’s idea they would have to invent new techniques. Before they considered the hydride, they had got by with methods based on an approximation of Fermi’s.

They been able to assume, among other things, that neutrons would travel at a single characteristic velocity. In pure metal, or in the slow reaction of the water boiler, that

assumption seemed to work out wel enough. But in the odd atomic landscape of the hydride, with its molecules of giant uranium atoms bonded to two or three tiny hydrogen atoms, neutrons would fly about at every conceivable velocity, from very fast to very slow. No one had yet invented a way of computing critical mass when the velocities spread over such a wide range. Feynman solved that problem with a pair of approximations that worked like pincers. The method produced outer bounds for the answer: one estimate known to be too large and another known to be too smal . The experience of actual computation showed that this would suffice: the pair of approximations were so close together that they gave an answer as accurate as was needed. As he drove the men in his group toward a new understanding of criticality (poaching sneakily, it seemed to them, on the territory of Serber’s group, T-2), he delivered up a series of insights that struck even Welton, who understood him best, as mystical. One day he declared that the whole problem would be solved if they could produce a table of so-cal ed eigenvalues, characteristic values of energies, for the simplified model that T-2 had been using. That seemed an impossible leap, and the group said so, but they soon found that he was right again. For Tel er’s scheme, the new model was fatal. The hydride was a dead end. Pure uranium and plutonium proved far more efficient in propagating a chain reaction.