Genius_ The Life and Science of Richard Feynman - James Gleick [208]
From QED to Genetics
“Hello, my sweetheart,
“Murray and I kept each other awake arguing until we could stand it no longer. We woke up over Greenland …”
They were off to Brussels together for a conference, partly nostalgic, on “the present state of quantum electrodynamics.” Dirac was there, and Feynman spoke once again with his old hero—Dirac still wholly unreconciled to the renormalization program for evading the infinities that had plagued his old theory. Renormalization seemed an ugly gimmick, an arbitrary and unphysical device for merely discarding inconvenient quantities in one’s equations. To most physicists Dirac’s qualms sounded like the intolerance of the old in the face of new ideas—in this case ideas that succeeded where Dirac’s own theory had broken down. He reminded them of Einstein, with his famous crotchety unwillingness to accept quantum mechanics, and like Einstein he could hardly be dismissed. Honest physicists at least understood his qualms, even if they attributed them, ultimately, to a generational hardening of the intuitions. Age was no friend of the physicist. Wisdom counted for nothing. Feynman was acutely and painfully aware of the truth expressed in a ditty sometimes attributed to Dirac himself; it appeared from time to time, over the years, on Caltech office doors:
Age is, of course, a fever chill
That every physicist must fear.
He’s better dead than living still
When once he’s past his thirtieth year.
Feynman also sympathized with Dirac’s qualms about renormalization, more so than any of his coinventors of the modern methods. Quantum electrodynamics had become a singular triumph of theoretical physics. The computations that had taken Feynman and Schwinger hours or weeks to accomplish in their first and second approximations could now be extended to many deeper levels of accuracy, using electronic computers and hundreds of Feynman diagrams to organize the work. Some theorists and their graduate students spent years on these calculations. They added and subtracted hundreds of terms, deeper and deeper into infinite series. It struck some of them as bizarrely unsatisfying work: some of the terms were enormous, positive or negative, compared to the final result. Yet presumably they would cancel out in the end, leaving a small, finite number. The mathematical status of such computation remained uneasy. It was not mathematically certain that the calculations would converge. Yet for practical calculations in quantum electrodynamics they always seemed to, and when the increasingly precise results were compared with the results of increasingly sensitive experiments, they matched. To convey a sense of how “delicately” experiment and theory agreed, Feynman would say it was like measuring the distance from New York to Los Angeles to within the thickness of a single hair. Yet the unphysical nature of the computing process troubled him, the corrections upon corrections with no sense of whether the next correction must be large or small. “We have been computing terms like a blind man exploring a new room,” he said in his keynote talk in Brussels.
Other theorists, meanwhile, had begun to use the very concept of “renormalizability” as a way of distinguishing between possible theories for the esoteric particles to which quantum electrodynamics did not apply. Dyson had first recognized that it might be fruitful to think of renormalizability this way, as a criterion for judgment. A renormalizable theory was one by which, practically speaking, calculations could be made. “Note the cunning of reason at work,” said the physicist and historian Silvan S. Schweber. “The divergences