Electrons and Protons

Editor’s Note

Paul Dirac was one of the most creative physicists of the early twentieth century. In 1932 he was appointed Lucasian professor at Cambridge University, and his theory unifying quantum mechanics with Einstein’s theory of special relativity won him the 1933 Nobel Prize in physics. Here Nature reports on one of the implications of this theory, as Dirac outlined in a paper in the Proceedings of the Royal Society. His equations predicted “electrons of negative energy”, which meant, of positive charge. The report echoes Dirac’s initial suspicion that these predicted positively charged particles would behave like protons, but they soon proved to be “positive electrons” or positrons, made of antimatter.　　中文

A theory of positive electricity has been put forward by Dr. P. A. M. Dirac in the January number of the Proceedings of the Royal Society. The relativity quantum theory of an electron leads to a wave equation which possesses solutions corresponding to negative energies—the energy of the electron of ordinary experiment being reckoned as positive—and although there are serious difficulties encountered in any immediate attempt to associate these negative states with protons, the existence of positive electricity can be predicted by a fairly direct line of argument. Since the stable states of an electron are those of lowest energy, all the electrons would tend to fall into the negative energy states—with emission of radiation—were it not for the Pauli exclusion principle, which prevents more than one electron from going to any one state. If, however, it is assumed that “there are so many electrons in the world that… all the states of negative energy are occupied except perhaps a few…”, it may be supposed that the infinite number of electrons present in any volume will remain undetectable if uniformly distributed, and only the few “holes”, or missing states of negative energy will be amenable to observation. The step is then made of regarding these “holes” as “things of positive energy” which are identified with the protons. A difficulty now arises in ordinary electromagnetic theory which apparently has to cope with the presence of negative electricity of infinite density; this is met by supposing that for ordinary purposes volume-charges must be measured by departures from a “normal state of electrification”, which is “the one where every electronic state of negative energy and none of positive energy is occupied.” The problem of the large mass of the proton, as compared with that of the electron, is not discussed in detail, but a possible line of attack is indicated. Dr. Dirac has included the minimum of mathematical analysis in this paper, which can be followed in all essential points by anyone acquainted with the principles of the quantum theory.　　中文

(125, 182; 1930)