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

work il uminating the interstices of molecules.) New vacuum equipment and finely etched mirrors gave a high precision to the spectroscopic work. And a monstrous new electromagnet created fields more powerful than any on the planet.

Julius Stratton and Philip Morse taught the essential advanced theory course for seniors and graduate students, Introduction to Theoretical Physics, using Slater’s own text of the same name. Slater and his col eagues had created the course just a few years before. It was the capstone of their new thinking about the teaching of physics at MIT.

They meant to bring back together, as a unified subject, the discipline that had been subdivided for undergraduates into mechanics,

electromagnetism,

thermodynamics,

hydrodynamics, and optics. Undergraduates had been acquiring their theory piecemeal, in ad hoc codas to laboratory courses mainly devoted to experiment. Slater now brought the pieces back together and led students toward a new topic, the “modern atomic theory.” No course yet existed in quantum mechanics, but Slater’s students headed inward toward the atom with a grounding not just in classical mechanics, treating the motion of solid objects, but also in wave mechanics—vibrating strings, sound waves bouncing around in hol ow boxes. The instructors told the students at the outset that the essence of theoretical physics lay not in learning to work out the mathematics, but in learning how to apply the mathematics to the real phenomena that could take so many chameleon forms: moving bodies, fluids, magnetic fields and forces,

currents of electricity and water, and waves of water and light. Feynman, as a freshman, roomed with two seniors who took the course. As the year went on he attuned himself to their chatter and surprised them sometimes by joining in on the problem solving. “Why don’t you try Bernoul i’s equation?” he would say—mispronouncing Bernoulli because, like so much of his knowledge, this came from reading the encyclopedia or the odd textbooks he had found in Far Rockaway. By sophomore year he decided he was ready to take the course himself.

The first day everyone had to fil out enrol ment cards: green for seniors and brown for graduate students.

Feynman was proudly aware of the sophomore-pink card in his own pocket. Furthermore he was wearing an ROTC

uniform; officer’s training was compulsory for first- and second-year students. But just as he was feeling most conspicuous,

another

uniformed,

pink-card-carrying

sophomore sat down beside him. It was T. A. Welton.

Welton had instantly recognized the mathematics whiz from the previous spring’s open house.

Feynman looked at the books Welton was stacking on his desk. He saw Tul io Levi-Civita’s Absolute Differential Calculus , a book he had tried to get from the library.

Welton, meanwhile, looked at Feynman’s desk and realized why he had not been able to find A. P. Wil s’s Vector and Tensor Analysis . Nervous boasting ensued.

The Saratoga Springs sophomore claimed to know al about general relativity. The Far Rockaway sophomore

announced that he had already learned quantum mechanics from a book by someone cal ed Dirac. They traded several hours’ worth of sketchy knowledge about Einstein’s work on gravitation. Both boys realized that, as Welton put it, “cooperation in the struggle against a crew of aggressive-looking seniors and graduate students might be mutual y beneficial.”

Nor were they alone in recognizing that Introduction to Theoretical Physics now harbored a pair of exceptional young students. Stratton, handling the teaching chores for the first semester, would sometimes lose the thread of a string of equations at the blackboard, the color of his face shifting perceptibly toward red. He would then pass the chalk, saying, “Mr. Feynman, how did you handle this problem,” and Feynman would stride to the blackboard.

The Best Path

A law of nature expressed in a strange form came up again and again that term: the principle of least action. It arose in a simple sort of problem. A lifeguard, some feet up the beach, sees a drowning swimmer diagonal y ahead, some distance offshore and some distance to one side. The lifeguard can run at a certain speed and swim at a certain lesser speed. How does one find the fastest path to the swimmer?

The path of least time. The lifeguard travels faster on land than in water; the best path is a compromise. Light-which also travels faster through air than through water-seems somehow to choose precisely this path on its way from an underwater fish to the eye of an observer.

A straight line, the shortest path, is not the fastest. The lifeguard wil spend too much time in the water. If instead he angles far up the beach and dives in directly opposite the swimmer—the path of least water—he stil wastes time.

The best compromise is the path of least time, angling up the beach and then turning for a sharper angle through the water. Any calculus student can find the best path. A lifeguard has to trust his instincts. The mathematician Pierre de Fermat guessed in 1661 that the bending of a ray of light as it passes from air into water or glass—the

refraction that makes possible lenses and mirages—

occurs because light behaves like a lifeguard with perfect instincts. It fol ows the path of least time. (Fermat, reasoning backward, surmised that light must travel more slowly in denser media. Later Newton and his fol owers thought they had proved the opposite: that light, like sound, travels faster through water than through air. Fermat, with his faith in a principle of simplicity, was right.) Theology, philosophy, and physics had not yet become so distinct from one another, and scientists found it natural to ask what sort of universe God would make. Even in the quantum era the question had not ful y disappeared from the scientific consciousness. Einstein did not hesitate to invoke His name. Yet when Einstein doubted that God played dice with the world, or when he uttered phrases like the one later inscribed in the stone of Fine Hal at Princeton, “The Lord God is subtle, but malicious he is not,”

the great man was playing a delicate game with language.

He had found a formulation easily understood and imitated by physicists, religious or not. He could express convictions about how the universe ought to be designed without giving offense either to the most literal believers in God or to his most disbelieving professional col eagues, who were happy to read God as a poetic shorthand for whatever laws or principles rule this flux of matter and energy we happen to inhabit . Einstein’s piety was sincere but neutral, acceptable even to the vehemently antireligious Dirac, of whom Wolfgang Pauli once complained, “Our friend Dirac, too, has a religion, and its guiding principle is ‘There is no

too, has a religion, and its guiding principle is ‘There is no God and Dirac is His prophet.’”

Scientists of the seventeenth and eighteenth centuries also had to play a double game, and the stakes were higher. Denying God was stil a capital offense, and not just in theory: offenders could be hanged or burned. Scientists made an assault against faith merely by insisting that knowledge—some knowledge—must wait on observation and experiment. It was not so obvious that one category of philosopher should investigate the motion of fal ing bodies and another the provenance of miracles. On the contrary, Newton and his contemporaries happily constructed scientific proofs of God’s existence or employed God as a premise in a chain of reasoning. Elementary particles must be indivisible, Newton wrote in his Opticks , “so very hard as never to wear or break in pieces; no ordinary power being able to divide what God himself made one in the first creation.” Elementary particles cannot be indivisible, René Descartes wrote in his Principles of Philosophy : There cannot be any atoms or parts of matter which are indivisible of their own nature (as certain philosophers have imagined)… . For though God had rendered the particle so smal that it was beyond the power of any creature to divide it, He could not deprive Himself of the power of division, because it was absolutely impossible that He should lessen His own omnipotence… .