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

He drew electrons as solid lines with arrows. For photons he used wavy lines without arrows: no directionality needed because the photon’s anti-particle is itself. “The fundamental interaction” reinterpreted the basic textbook process of electromagnetic repulsion. Two negative charges, electrons, repel. A standard picture, showing lines of force or merely two bal s pressing apart from each other, would beg the question of how an entity feels the force of another entity at a distance. It would imply that force can be transmitted instantly, when in truth, as Feynman’s diagrams

automatical y made explicit, whatever carries force can move only as fast as light. In the case of electromagnetism, it is light—in the form of fugitive “virtual” particles that flash into existence just long enough to help quantum theorists balance their books.

These

were

space-time

diagrams,

of

course,

representing time as one direction on the page. Typical y the past sat at the bottom and the future at the top; one way to read the diagram would be to cover it with a sheet of paper, pul the paper slowly upward, and watch the history unfold. An electron changes course as it emits a photon.

Another electron changes course when it absorbs the photon. Yet even the idea that the earlier event is emission and that the later is absorption represented a prejudice about time. It was built into the language. Feynman stressed how free his approach was from customary intuitions: these events are interchangeable.

The Feynman diagram: “The fundam ental interaction.” It is a space-time diagram: the progress of time is shown upward on the page. If one covers it with a sheet of paper and then draws the paper slowly upward:

•A pair of electrons-their paths shown as solid lines-move toward each other.

•When (6) is reached , a virtual photon is emitted by the right-hand electron (wiggly line), and the electron is deflected outward.

•At (5) the photon is reabsorbed by the other electron , and it, too, is deflected outward.

Thus this diagram depicts the ordinary force of repulsion between two electrons as a force carried by a quantum of light. Because it is a virtual particle, coming into existence for a mere ghostly instant, it can temporarily violate the laws that govern the system as a whole—the exclusion principle or the conservation of energy, for example. And Feynman noted that it is arbitrary to think of the photon as being emitted in one place and absorbed in the other: one can say just as correctly that it is emitted at (5), travels

backward in time, and is then (earlier) absorbed at (6).

The diagram is an aid to visualization. But it serves physicists mainly as a bookkeeping device. Each diagram is associated with a complex number, an amplitude that is squared to produce a probability for the process shown.

In fact each diagram represented not a particular path, with specified times and places, but a sum of al such paths. There were other simple diagrams. He represented the self-energy of an electron—its interaction with itself—by showing a photon line returning to the same electron that spawned it. There was a grammar of permissible diagrams, corresponding, as Dyson had emphasized, to the permissible mathematical operations. Stil , the diagrams could grow arbitrarily complicated, virtual particles appearing and disappearing in an intricate, recursive mesh. Feynman’s first H-shaped diagram for interacting electrons was the only such diagram with one virtual photon. Drawing al the possible diagrams with two virtual photons showed how quickly the permutations grew.

Each made a contribution to the final computation, and more complicated diagrams became enormously difficult to calculate. Fortunately the greater the complication the less the probability and the smal er, therefore, the effect on the answer. Even so, physicists would shortly find themselves agonizing over pages of diagrams resembling catalogs of knots. They found it was worth the effort; each diagram could replace an effective lifetime of Schwingerian algebra.

Self-interaction. It is necessary to sum the amplitudes corresponding tomany Feynman diagrams to add the contributions for every way an event can occur. The continual possibility of virtual particles materializing and vanishing causes increasing complexity.

Here an electron interacts with itself, in effect- the self-energy problem that first troubled Feynman in his work with Wheeler. It emits and absorbs its own virtual photon.

Feynman diagrams seemed to depict particles, and they had sprung from a mind focused on a particle-centered style of visualization, but the theory they anchored—

quantum field theory—gave center stage to the field. In a sense the paths of the diagrams, and the paths summed in the path integrals, were the paths of the field itself.

Feynman read the Physical Review more avidly than ever in the past, watching for citations. For a while it was al Schwinger—a paper would be pages of glyphs and would culminate in a neat expression that Feynman felt he could

simply have written down as a starting point. He was sure this could not last. It did not. Feynman’s method, Feynman’s rules, began to take over. In the summer of 1950 a paper appeared with smal “Feynman diagrams” on the first page

—“fol owing the simplified methods introduced by Feynman.” A month later came another: “a technique due to Feynman… . The calculation of matrix elements can be simplified greatly by use of the Feynman-Dyson methods.”

The unreasonable power of the diagrams in the hands of students frustrated some of the elders, who felt that physicists were waving a sword that they did not understand. As the flood of papers began to cite Feynman, Schwinger went into what he described as his retreat. “Like the silicon chip of more recent years, the Feynman diagram was bringing computation to the masses,” he said. Later, people who overlooked the note of hoi pol oi quoted this remark as though Schwinger had intended a tribute. He had not. This was “pedagogy, not physics.”

Yes, one can analyze experience into individual pieces of topology. But eventual y one has to put it al together again. And then the piecemeal approach loses some of its attraction.

Making the increasingly precise calculations for which quantum electrodynamics became famous requi red formidable exercises in combinatorics.

Schwinger’s students at Harvard were put at a competitive disadvantage, or so it seemed to their fel ows elsewhere, who suspected them of surreptitiously using the

diagrams anyway. This was sometimes true. (They revered him, though—his night-owl ways, his Cadil ac, his theatrical y impeccable lecture performances. They emulated his way of saying, “We can effectively regard …”

and they tried to construct the perfect Schwinger sentence: one graduate student, Jeremy Bernstein, liked a prototype that began, “Although ‘one’ is not perfectly ‘zero,’ we can effectively regard …” They also worried about Schwinger’s ability to materialize silently beside them at the lunch table; a group of his graduate students protected themselves with a conversational convention in which Schwinger meant Feynman and Feynman meant Schwinger .) Murray Gel -Mann later spent a semester staying in Schwinger’s house in Cambridge and loved to say afterward that he had searched everywhere for the Feynman diagrams. He had not found any, but one room had been locked …

Away to a Fabulous Land

Bethe worried that Feynman was growing restless after four years at Cornel . There were entanglements with women: Feynman pursued them and dropped them, or tried to, with increasingly public frustration—so it seemed even to undergraduates, who knew him as the least professorial of professors, likely to be found beating a rhythm on a dormitory bench or lying supine and greasy beneath his Oldsmobile. He had never settled into any house or