Mathematical Electron

Modern physicists are concerned with the infinitely large--the universe--and the indefinitely small--the electron. Accepted key to the puzzle of the universe is Einstein's theory of relativity. Crux of the theory is that: 1) nothing moves faster than the speed of light in empty space (186,000 miles per second); and 2) the speed of light is always the same, regardless of the motion of the light's source or of the observers. Most popular explanation of the workings of the electron is the quantum theory, which holds that energy is released and received not in a continuous stream but in separate little packets. For many years scientists have been trying to tie up relativity and the quantum theory, but even Einstein has met with no success (TIME, April 4). Chief difficulty is that practically nothing is known of the electron's structure.

In St. John's College, Cambridge, England sits a brilliant young mathematical physicist, Paul Adrien Maurice Dirac, who spends his days plotting a free-hand structure of the universe with paper & pencil. Experimental physicists have hung on his hunches ever since his blueprint of the positive electron pointed the way to its discovery in 1932. In the latest issue of the Proceedings of the Royal Society Physicist Dirac published his mathematical picture of what the electron may look like.

Two types of electrons have been visualized by physicists: the classical Lorentz model, a small but finite sphere charged with electricity, and the modern "point" model (used in quantum mechanics), which is a mere mathematical dot radiating infinite energy. The trouble with the Lorentz type is its assumption that all mass is of electromagnetic origin. Discovery of the neutron, a particle with no charge, disproved this. Trouble with the point model is that the infinite energy of the electron, too cumbersome to work with, has to be arbitrarily "reduced" to practical size.

Dirac offers "a new physical idea . . . an idea which should be intelligible both in the classical theory and in the quantum theory." Working with well-known equations he arrives at an electron which is a compound of the two old models: with point charge but a finite size, an interior and an exterior. A new element enters in his theory of the electron's radiation. When a Dirac electron, originally at rest, is disturbed by a pulse of electromagnetic radiation (such as a light-wave), "the electron seems to know about the pulse before it arrives and to get up an acceleration just sufficient to balance the effect of the pulse when it does arrive." Hence "it is possible for a signal to be transmitted faster than light" (through the interior of the electron). Does this represent a disproof of relativity? Not at all, said Mathematician Dirac, with the startling logic which only a mathematician can employ: the theory of relativity merely does not apply to the microcosm.

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