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14 Balmer’s simple formula described the spectrum of the hydrogen atom perfectly, but not its cause. By luck or judgment, Balmer had stumbled upon a great truth. The question was: Why does his magical rule work? In 1912 Niels Bohr found the explanation, courtesy of quantum theory. In quantum theory any particle can take on a wavelike character. 15 Bohr visualized the waves for electrons in atoms as if they were wobbles on a length of rope. When coiled in a circle, like a lasso, for a wave to fit perfectly into its circumference, the number of wavelengths in the circuit has to be an integer.

You could read the full literary version, as in a conventional book, or instead you could skim a cartoon strip, where the text was minimal, restricted to essential speech bubbles and atmospheric illustrations. The latter were more popular. Years later, even students who studied English literature in college admit that they started with the comic-strip version. If Schwinger’s development of QED was akin to reading Proust, then Feynman’s was the cartoon version. Today students meet Feynman’s pic- Shelter Island and QED 41 torial approach and from these diagrams deduce the mathematical expressions appropriate to the situation; Schwinger’s methods have by and large been consigned to history.

This technology gives far greater electric fields than in a simple battery, but in turn is trifling compared to what occurs within atoms. Inside an atom of hydrogen, some ten volts is the gap between the The Point of Infinity 29 electron and proton, which are separated on the average by only a tenth of a billionth of a meter. 30 Now we meet the enigma. In Dirac’s equation, the electron appears as a fundamental indivisible point of electric charge, and in the immediate vicinity of an electron with no physical extent, the field becomes infinitely strong.

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