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

Although he did not know it, his quantum-mechanics professor, Morse, had recommended in his junior year that the department graduate him a year early. The suggestion was turned down, and Slater himself became Feynman’s thesis adviser. Slater proposed a problem that at first seemed not much deeper than most senior theses. The question could almost have come from a physics and

chemistry handbook: Why does quartz expand so little when heated? Compared to metals, for example, why is its coefficient of expansion so smal ? Any substance expands because heat agitates its molecules—heat is the agitation of its molecules—but in a solid the details of the expansion depend on the actual molecular layout. A crystal, with its molecules in a regular geometrical array, can expand more along one axis than another. Typical y scientists would represent a crystal ine structure with a Tinkertoy model, bal s stuck on rods, but real matter is not so rigid. Atoms may be more or less locked in an array, or they may swing or float more or less freely from one place to another.

Electrons in a metal wil swarm freely about. The color, the texture, the rigidity, the frangibility, the conductivity, the softness, the taste of a substance al depend on the local habits of atoms. Those habits in turn depend on the forces at work within a substance—forces both classical and quantum mechanical—and when Feynman began his thesis work those forces were not wel understood, even in quartz, the most common mineral on earth.

An old-fashioned steam engine was regulated by a mechanical governor: a pair of iron bal s swinging outward from a spinning shaft. The faster it spun, the farther outward they would swing. But the farther they would swing, the harder they would make it to spin the shaft. Feynman started by imagining some analogous effect in the atoms of quartz, silicon dioxide, a pair of oxygen atoms clinging to each atom of silicon. Instead of spinning, the silicon atoms were vibrating; as the quartz grew warmer, he thought that

the oxygen atoms might provide a mechanical force that would pul inward against the increasing agitation of the molecules, thus compensating somehow for the ordinary expansion. But how could the forces within each molecule

—forces that varied in different directions—be calculated?

No straightforward method seemed to exist.

He had never thought about molecular structure in such detail before. He taught himself everything he could about crystals, their standard arrangements, the geometries and the symmetries, the angles between atoms. It al came down to one unknown, he realized: the nature of the forces pressing the molecules into particular alignments. In its search for fundamental laws ever farther down the hierarchy of sizes, physics had now reached a level where molecular forces should be coming into focus. Scientists could measure how much pressure it took to squeeze quartz a given distance in a given direction. With the stil -new technique of X-ray diffraction, they could look at the shadow patterns of a regular crystal and deduce its structure. As some theorists continued to look even deeper toward the atom’s core, others now tried applying the quantum techniques to questions of structure and chemistry. “A science of materials as distinct from matter became possible,” a scholar of structure, Cyril Stanley Smith, who worked with Feynman a few years later as the chief metal urgist on the secret project at Los Alamos, said of this time. From atomic forces to the stuff that feeds our senses—that was the connection waiting to be made. From abstract energy levels to three-dimensional forms. As

Smith added epigrammatical y, “Matter is a holograph of itself in its own internal radiation.”

Forces or energy—that was the choice for those seeking to apply the quantum understanding of the atom to the workings of real materials. At stake was not mere terminology but a root decision about how to conceive of a problem and how to proceed in calculating.

The conception of nature in terms of forces went back to Newton. It was a direct way of dealing with the world, envisioning firsthand interactions between objects. One exerts a force on another. A distinction between force and energy did not emerge clearly until the nineteenth century, and then, gradual y, energy began to take over as the fulcrum of scientists’ thinking. Force is, in modern terms, a vector quantity, with both a magnitude and a direction.

Energy is directionless, scalar—meaning that it has a magnitude only. With the rise of thermodynamics energy came to the fore. It began to seem more fundamental.

Chemical reactions could be neatly computed as operations designed to minimize energy. Even a bal rol ing down a hil —moving from a state of higher to lower potential energy—was seeking to minimize its energy. The Lagrangian approach that Feynman resisted in his sophomore-year physics class also used a minimum of energy to circumvent the laborious calculation of direct interactions. And the law of conservation of energy provided a tidy bookkeeping approach to a variety of calculations. No comparable law existed for forces.

Yet Feynman continued to seek ways of using the

language of forces, and his senior thesis evolved beyond the problem Slater had posed. As Feynman conceived the structure of molecules, forces were the natural ingredients.

He saw springlike bonds with varying stiffness, atoms attracting and repel ing one another. The usual energy-accounting

methods

seemed

secondhand

and

euphemistic. He titled his thesis—grandly—“Forces and Stresses in Molecules” and began by arguing that it would be more il uminating to attack molecular structure directly by means of forces, intractable though that approach had been considered in the past.

Quantum mechanics had begun with energy for two reasons, he contended. One was that the original quantum theorists had habitual y tested their formulas against a single type of application, the calculation of the observed spectra of light emitted by atoms, where forces played no obvious part. The other was that the wave equation of Schrödinger simply did not lend itself to the calculation of vector quantities; its natural context was the directionless measurement of energy.

In Feynman’s senior year, just over a decade after the three-year revolution of Heisenberg, Schrödinger, and Dirac, the applied branches of physics and chemistry had been drawn into an explosion of activity. To outsiders quantum mechanics might have seemed a nuisance, with its philosophical entanglements and computational nightmares. In the hands of those analyzing the structures of metals or chemical reactions, however, the new physics was slicing through puzzles that classical physics found

impenetrable. Quantum mechanics was triumphing not because a few leading theorists found it mathematical y convincing, but because hundreds of materials scientists found that it worked. It gave them insights into problems that had languished, and it gave them a renewed livelihood.

One had only to understand the manipulation of a few equations and one could final y compute the size of an atom or the precise gray sheen of a pewter surface.

Chief in the new handbook was Schrödinger’s wave equation. Quantum mechanics taught that a particle was not a particle but a smudge, a traveling cloud of probabilities, like a wave in that the essence was spread out. The wave equation made it possible to compute with smudges and accommodate the probability that a feature of interest might appear anywhere within a certain range.

This was essential. No classical calculation could show how electrons would arrange themselves in a particular atom: classical y the negatively charged electrons should seek their state of lowest energy and spiral in toward the positively charged nuclei. Substance itself would vanish.