Genius_ The Life and Science of Richard Feynman - James Gleick [143]
The existing theory “explained” the existence of different energy levels in the atom. It gave physicists their only workable means of calculating them. The different energies arose from different combinations of crucial quantum numbers, the angular momentum of the electron orbiting the nucleus, and the angular momentum of the electron spinning around itself. A certain symmetry built into the equation made it natural for a pair of the resulting energy levels to coincide exactly. But they did not coincide in Willis Lamb’s laboratory, so something must be missing and, as Bethe surmised, that something was the theorists’ old bugbear, the self-interaction of the electron.
This extra energy or mass was created by the snake-swallowing-its-tail interplay of the electron with its own field. This quantity had been a tolerable nuisance when it was theoretically infinite and experimentally negligible. Now it was theoretically infinite and experimentally real. Bethe had in mind a suggestion that the Dutch physicist Hendrik Kramers had made at Shelter Island: that the “observed” mass of the electron, the mass the theorists tended to think of as a fundamental quantity, should be thought of as a combination of two other quantities, the self-energy and an “intrinsic” mass. These masses, intrinsic and observed, also known as “bare” and “dressed,” made an odd couple. The intrinsic mass could never be measured directly, and the observed mass could not be computed from first principles. Kramers proposed a method by which the theorists would pluck a number from experimental measurements and correct it, or “renormalize” it. This Bethe did, crudely but effectively. Meanwhile, as the mass went, so went the charge—this formerly irreducible quantity, too, had to be renormalized. Renormalization was a process of adjusting terms of the equation to turn infinite quantities into finite ones. It was almost like looking at a huge object through an adjustable lens, and turning a knob to bring it down to size, all the while watching the effect of the knob turning on other objects, one of which was the knob itself. It required great care.
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 all 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 gradually 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 enthrall 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