Quantum Electrodynamics and Photons

QED, as we shall call it, is generally considered to be synonymous with the interaction of electrons and "photons", and the names most commonly associated with the theory are Paul Dirac and Richard Feynman (see the first two references below) who treated both entities, quite unambiguously, as elementary particles.

QED achieved its most notable success in the period 1947-49, when the Dirac equation was modified to include the interaction of electrons with the vacuum electromagnetic field, thereby explaining, with enormous accuracy, some small effects in the spectrum of atomic hydrogen (Lamb shift) and in the electron's magnetic moment. This was first achieved by Julian Schwinger, who, building on Victor Weisskopf's ideas developed in the 1930s, described the electronic current by means of another field, so that the electron was no longer a point, but an extended object with a diameter of the order of a few picometers (the Compton wavelength). Schwinger's achievement was largely hidden from public view, though, jointly with Feynman and Tomonaga, he was awarded the Nobel Prize for it. Feynman's contribution was to show that Schwinger's very formidable calculations could be "simplified" by reverting to a pointlike description of both electrons and photons. Today any clever undergraduate knows how to calculate, using the famous "Feynman diagrams", all the processes of QED. But Schwinger knew that this was an example of the maxim "A little knowledge is a dangerous thing". He refused to teach his students Feynman diagrams, because he saw Feynman's pointlike particles as a dangerous oversimplification.

Today we can see, more precisely than in 1949, the price paid for this "simplification". The diagrams of Feynman play fast-and-loose with the direction of time. The recipe that "a positron is an electron travelling backwards in time" (see the second reference below) may help us to calculate, but not to understand. It should not surprise us that, persisting with such exotic language, we go first to faster-than-light communication between the two light detectors of Aspect's experiment, and then to H.G.Wells-type Time Travel.

  1. P. A. M. Dirac, Principles of Quantum Mechanics, Oxford, 1958
  2. R. P. Feynman, Quantum Electrodynamics, Benjamin, 1961
  3. S. S. Schweber, QED and the Men who Made It, Princeton, 1994
  4. T. W. Marshall, Is there a bridge connecting stochastic and quantum electrodynamics?, in Fundamental Problems in Quantum Physics, eds. M. Ferrero and A. van der Merwe (Kluwer, Dordrecht, 1995) pp187-198.

The latter article is available by email