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

From one perspective, renormalization amounted to subtracting infinities from infinities, with a silent prayer.

Ordinarily such an operation could be meaningless: infinity (the number of integers, 0, 1, 2, 3, …) minus infinity (the number of even integers, 0, 2, 4, …) equals infinity (the remaining, odd integers, 1,3, 5, …), and al three of those infinities are the same, unlike, for example, the distinctly greater infinity representing the number of real numbers.

The theorists implicitly hoped that when they wrote infinity –

infinity = zero nature would miraculously make it so, for once. That their hope was granted said something important about the world. For a while it was not clear just what.

Bethe assigned Dyson a stripped-down, toy version of

the Lamb shift, asking him to calculate the Lamb shift for an electron with no spin. It was a way for Dyson to find a quick way into a problem of the most timely importance and for Bethe to continue his own prodding. Dyson could see that the calculation Bethe had published was both a swindle and a piece of genius, a bad approximation that somehow coughed up the right answer. More and more, too, Dyson talked with Feynman, who gradual y began to come into clearer focus for him. He watched this wild American dash from the dinner table at the Bethes’ to play with their five-year-old son, Henry. Feynman did have an extraordinary affinity for his friends’ children. He would entertain them with gibberish, or with juggling tricks, or with what sounded to Dyson like a one-man percussion band. He could enthral them merely by borrowing someone’s eyeglasses and slowly putting them on, taking them off, and putting them on.

Or he would engage them in conversation. He once asked Henry Bethe, “Did you know there are twice as many numbers as numbers?”

“No, there are not!” Henry said.

Feynman said he could prove it. “Name a number.”

“One mil ion.”

Feynman said, “Two mil ion.”

“Twenty-seven!”

Feynman said, “Fifty-four,” and kept on countering with the number that was twice Henry’s, until suddenly Henry saw the point. It was his first real encounter with infinity.

For a while, because Feynman did not seem to take his work seriously, neither did Dyson. Dyson wrote his parents

that Feynman was “half genius and half buffoon” (a description he later regretted). Just a few days later Dyson heard an account from Weisskopf, visiting Cornel , of Schwinger’s progress at Harvard. He sensed a connection with the very different notions he was hearing from Feynman. He had begun to see a method beneath Feynman’s flash and wildness. The next time he wrote his parents, he said:

Feynman is a man whose ideas are as difficult to make contact with as Bethe’s are easy; for this reason I have so far learnt much more from Bethe, but I think if I stayed here much longer I should begin to find that it was Feynman with whom I was working more.

A Half-Assedly Thought-Out Pictorial

Semi-Vision Thing

By the physicists’ own lights their difficulties were mathematical: infinities, divergences, unruly formalisms.

But another obstacle lay in the background, rarely surfacing in the standard published or unpublished rhetoric: the impossibility of visualization. How was one to perceive the atom, or the electron in the act of emitting light? What mental picture could guide the scientist? The first quantum paradoxes had so shattered physicists’ classical intuitions that by the 1940s they rarely discussed visualization. It

seemed a psychological issue, not a scientific one.

The atom of Niels Bohr, a miniature solar system, had become an embarrassingly false image. In 1923, on the tenth anniversary of Bohr’s conception, the German quantum physicist Max Born hailed it: “the thought that the laws of the macrocosmos in the smal reflect the terrestrial world obviously exercises a great magic on mankind’s mind”—but already he and his col eagues could see the picture fading into anachronism. It survived in the language o f angular momentum

and spin —as wel as in the

standard high-school physics and chemistry curriculums—

but there was no longer anything plausible in the picture of electrons orbiting a nucleus. Instead there were waves with modes of resonance, particles that smeared out probabilistical y, operators and matrices, mal eable spaces with extra dimensions, and physicists who forswore the idea of visualization altogether. Bohr himself had set the tone. In accepting the Nobel Prize for his atomic model, he said it was time to give up the hope of explanations in terms of analogies with everyday experience. “We are therefore obliged to be modest in our demands and content ourselves with concepts which are formal in the sense that they do not provide a visual picture of the sort one is accustomed to require… .” This progress had not been altogether free of tension. “The more I reflect on the physical portion of Schrödinger’s theory, the more disgusting I find it,” was Heisenberg’s 1926 comment to Pauli. “Just imagine the rotating electron whose charge is distributed over the entire space with axes in 4 or 5

dimensions. What Schrödinger writes on the visualizability of his theory … I consider trash.” As much as physicists valued the conceptualizing skil they cal ed intuition, as much as they spoke of a difference between physical understanding and formal understanding, they had nevertheless learned to mistrust any picture of subatomic reality that resembled everyday experience. No more basebal s, artil ery shel s, or planetoids for the quantum theorists; no more idle wheels or wavy waves. Feynman’s father had asked him, in the story he told so many times: “I understand that when an atom makes a transition from one state to another, it emits a particle of light cal ed a photon…

. Is the photon in the atom ahead of time? … Wel , where does it come from, then? How does it come out?” No one had a mental image for this, the radiation of light, the interaction of matter with the electromagnetic field: the defining event of quantum electrodynamics.

Where this image should have been, instead there was a void, as frothy and alive with possibility as the unquiet vacuum of the new physics. Unable to let their minds fix on even a provisional picture of quantum events, some physicists turned to a new kind of philosophizing, characterized by paradoxical thought experiments and arguments about reality , consciousness , causality , and measurement . Such arguments grew to form an indispensable part of the late twentieth century’s intel ectual atmosphere; they trailed the rest of physics as a cloud of smoke and flotsam trails a convoy. They were provocative and irresolvable. The paper of Einstein, Podolsky, and

and irresolvable. The paper of Einstein, Podolsky, and Rosen in 1935—the paper that provided the seventeen-year-old Schwinger with his first opportunity to impress Rabi—became an enduring example. It posed the case of two quantum systems—atoms, perhaps—linked by a particle interaction in their past but now separated by a great distance. The authors showed that the plain act of measuring one atom of this pair would affect what one could measure about the other atom, and the effect would be instantaneous—faster than light and thus retroactive, as it were. Einstein considered this a damning commentary on the laws of quantum mechanics. Bohr and younger theorists maintained a more sanguine attitude, noting that Einstein himself had already placed past and distance into the class of concepts about which one could no longer speak with comfortable, classical certainty. In the same vein was Schrödinger’s famous cat: a poor hypothetical animal sitting in a box with a vial of poisonous gas attached to a detector, its fate thus linked to that same quantum-mechanical event, the emission of a photon from an atom.