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http://web.mit.edu/dikaiser/www/Kaiser.Weisskopf.pdf

**Excerpt:**

In Dirac’s earliest efforts with QED in the late 1920s and early 1930s, he had found unexpected solutions to his equations. Though baffling at first, in time physicists came to interpret these solutions to mean that every type of ordinary particle has an antimatter cousin carrying the same mass but opposite electric charge. Electrons, for example, should have companion particles (dubbed “positrons”) that each carry one unit of positive electric charge. His explanation remained quite controversial, even after the first experimental evidence for positrons was found in 1932. Further conceptual problems marred QED. As the early architects of QED had found to their dismay, straightforward application of their new equations yielded nonsensical results. Whenever they posed simple questions, such as the probability for two electrons to scatter, their formalism returned “infinity” rather than some finite number. Electrons might have a high probability to scatter (say, 75%), or a low one (10%), but whatever it was, it simply couldn’t be infinite! Yet try as they might, none of these physicists had found any way to complete meaningful calculations in QED.

Weisskopf re-analyzed one of these stubborn calculations, regarding how an electron would interact with its own electric field. Charged objects serve as the source for electric and magnetic fields; and their behavior is affected, in turn, by the presence of electric and magnetic fields. So how would an electron behave in its own self-field?

The problem seemed intractable because the strength of an object’s electric field grows the closer one approaches that object. This is rarely a problem for macroscopic objects, which always have some finite spatial extension. But physicists believed that electrons were point-like objects, with virtually no spatial extension at all. Indeed, the first attempts to calculate an electron’s self-energy found it to diverge—that is, blow up to infinity—as 1 r2 e , where re was the radius of the electron. A point particle, with re = 0, would have an infinite self-energy. These early calculations had ignored possible effects from the stillcontroversial positrons. By the time Weisskopf took up the problem, however, early evidence seemed to indicate that positrons might really exist after all. He reworked the self-energy calculation, taking into account the behavior of both electrons and positrons. Weisskopf’s calculation (with a little help from Wendell Furry, one of Oppenheimer’s postdocs, who’d corrected Viki’s sign error) showed a much more gradual breakdown of the equations than anyone had found previously: the electron’s self-energy diverged as the logarithm of the electron radius.

Such a function would still become infinite in the limit of a genuine point particle (with re = 0), but this gentle divergence seemed far less threatening to the entire QED edifice than the earlier results. Indeed, Weisskopf’s revised calculation, published in 1934, gave many physicists hope that the problems of QED might be conquered after all. That same year, Weisskopf teamed up with Pauli to scrutinize the behavior of antiparticles. They showed that even charged particles with zero spin—as yet entirely hypothetical, since no such spinless particles were known—would necessarily have antiparticle partners. Their conclusion, published in 1934, followed from the mathematical structure of quantized fields, and put Dirac’s conjectures about antiparticles on a more solid physical foundation. In 1936 Weisskopf completed another major article on QED. He returned to the behavior of an electron’s self-field. As many physicists knew by that time, the self-field was complicated because of Heisenberg’s uncertainty principle and the presence of “virtual” particles. In 1927, capping off years of work on quantum mechanics, Heisenberg had deduced that certain pairs of quantities, such as a particle’s position and its simultaneous momentum, could no longer be specified with unlimited precision in the quantum realm. The same held for the energy involved in a physical process, E, and the time excerpt ...