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

Schrödinger’s point was that, while physicists now glibly calculated such events as probabilities—half yes and half no, perhaps—they stil could not visualize a cat as anything but alive or dead.

Physicists made a nervous truce with their own inability to construct unambiguous mental models for events in the very smal world. When they used such words as wave or particle —and they had to use both—there was a silent, disclaiming asterisk, as if to say: not really . As a

consequence, they recognized that their profession’s relationship to reality had changed. Gone was the luxury of supposing that a single reality existed, that the human mind had reasonably clear access to it, and that the scientist could explain it. It was clear now that the scientist’s work product—a theory, a model—interpreted experience and construed experience in a way that was always provisional.

Scientists relied on such models as intensely as someone crossing a darkened room relies on a conjured visual memory. Stil , physicists now began to say explicitly that they were creating a language—as though they were more like literary critics than investigators. “It is wrong to think that the task of physics is to find out how nature is,” said Bohr.

“Physics concerns only what we can say about nature.” This had always been true. Never before, though, had nature so pointedly rubbed physicists’ noses in it.

Yet in the long run most physicists could not eschew visualization. They found that they needed imagery. A certain kind of pragmatic, working theorist valued a style of thinking based on a kind of seeing and feeling. That was what physical intuition meant. Feynman said to Dyson, and Dyson agreed, that Einstein’s great work had sprung from physical intuition and that when Einstein stopped creating it was because “he stopped thinking in concrete physical images and became a manipulator of equations.” Intuition was not just visual but also auditory and kinesthetic. Those who

watched

Feynman

in

moments

of

intense

concentration came away with a strong, even disturbing sense of the physicality of the process, as though his brain

did not stop with the gray matter but extended through every muscle in his body. A Cornel dormitory neighbor opened Feynman’s door to find him rol ing about on the floor beside his bed as he worked on a problem. When he was not rol ing about, he was at least murmuring rhythmical y or drumming with his fingertips. In part the process of scientific visualization is a process of putting oneself in nature: in an imagined beam of light, in a relativistic electron. As the historian of science Gerald Holton put it,

“there is a mutual mapping of the mind … and of the laws of nature.” For Feynman it was a nature whose elements interacted with palpable, variegated, fluttering rhythms.

He thought about it himself. Once—uninterested though he was in fiction or poetry—he careful y copied out a verse fragment by Vladimir Nabokov: “Space is a swarming in the eyes; and time a singing in the ears.”

“Visualization—you keep repeating that,” he said to another historian, Silvan S. Schweber, who was trying to interview him.

What I am real y trying to do is bring birth to clarity, which is real y a half-assedly thought-out pictorial semi-vision thing. I would see the jiggle-jiggle-jiggle or the wiggle of the path. Even now when I talk about the influence functional, I see the coupling and I take this turn—like as if there was a big bag of stuff—and try to col ect it away and to push it. It’s al visual. It’s hard to explain.

“In some ways you see the answer——?” asked Schweber.

——the character of the answer, absolutely. An inspired method of picturing, I guess. Ordinarily I try to get the pictures clearer, but in the end the mathematics can take over and be more efficient in communicating the idea of the picture.

In certain particular problems that I have done it was necessary to continue the development of the picture as the method before the mathematics could be real y done.

The field itself presented the ultimate chal enge.

Feynman once told students, “I have no picture of this electromagnetic field that is in any sense accurate.” In seeking to analyze his own way of visualizing the unvisualizable he had learned an odd lesson. The mathematical symbols he used every day had become entangled with his physical sensations of motion, pressure, acceleration … Somehow he invested the abstract symbols with physical meaning, even as he gained control over his raw physical intuition by applying his knowledge of how the symbols could be manipulated.

When I start describing the magnetic field moving through space, I speak of the E- and B- fields and wave my arms and you may imagine that I can see them. I’l tel you what I see. I see some kind of vague,

shadowy, wiggling lines … and perhaps some of the lines have arrows on them—an arrow here or there which disappears when I look too closely… . I have a terrible confusion between the symbols I use to describe the objects and the objects themselves.

Yet he could not retreat into the mathematics alone.

Mathematical y the field was an array of numbers associated with every point in space. That, he told his students, he could not imagine at al .

Visualization did not have to mean diagrams. A complex, half-conscious, kinesthetic intuition about physics did not necessarily lend itself to translation into the form of a stick-figure drawing. Nor did a diagram necessarily express a physical picture. It could merely be a chart or a memory aid.

At any rate diagrams had been rare in the literature of quantum physics. One typical example used a ladder of horizontal lines to represent the notion of energy levels in the atom:

The “quantum jump” visualized as a sort of ladder.

The quantum jump from one level down to another accompanied the emission of a photon; the absorption of a photon would bring a jump upward. No depiction of the photons appeared in these diagrams; nor in another, more awkward schematic for the same process.

Feynman never used such diagrams, but he often fil ed his note pages with drawings of a different sort, recal ing the space-time paths that had been so crucial a feature of his Princeton work with Wheeler. He drew the paths of electrons as straight lines, moving across the page to represent motion through space and up the page to represent progress through time. At first he, too, left the emission of a photon out of his pictures: that event would appear as the deflection of an electron from one path to another. The absence of photons did reflect an implicit choice from among the available pictorial landscapes: Feynman was stil thinking mainly in terms of electrons interacting with the electromagnetic field as a field, rather than with the field as incarnated in the form of particles, photons.

In mid-1947 friends of Feynman persuaded him—threats and cajoling were required—to write for publication the theoretical ideas they kept hearing him explain. When he final y did, he used no diagrams. The result was partly a

reworking of his thesis, but it also showed the maturing and broadening of his command of the issues of quantum electrodynamics. He expressed the tenets of his new vision with an unabashed plainness. For some physicists this would be the most influential set of ideas Feynman ever published.

He said he had developed an alternative formulation of quantum mechanics to add to the pair of formulations produced two decades before by Schrödinger and Heisenberg. He defined the notion of a probability amplitude for a space-time path . In the classical world one could merely add probabilities: a batter’s on-base percentage is the 30 percent probability of a base hit plus the 10 percent probability of a base on bal s plus the 5