Quantum Mechanics and Relativity – The Dirac Equation (1928)

Abstract

Abstract Dalitz, who relates this story, adds that ‘this has been preserved to this day’ [1]. It was this philosophy that Dirac used when he found the equation that now bears his name. Unlike many results in theoretical physics it was neither inspired by unexplained measurements nor by physical insight but only by considerations of mathematical ‘beauty’ or, in other words, simplicity. In the Dirac equation not only quantum mechanics and the special theory of relativity were married, but also the spin of the electron is contained in it without any ad hoc assumption. So far, so good. But the equation not just beautifully described known phenomena, it did more. It predicted the existence of electrons with negative energy. This was at first held to be a severe problem of the theory but was finally understood as great progress, because negative-energy electrons could be interpreted as hitherto unknown particles. Thus, the existence of new particles was predicted which had all properties of the electron except for the electric charge, which must be positive rather than negative. These particles were indeed found four years after the equation. Dirac is often quoted to have said that his equation ‘contains most of physics and all of chemistry’. This, however, is not the case, although in a paper on the (non-relativistic) Quantum Mechanics of Many-Electron Systems, quite unrelated to the Dirac equation, similar words appear [2]: ‘The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much to complicated to be soluble.’ We begin this episode by mentioning briefly the work, previous to Dirac’s, on the reconciliation of quantum mechanics with special relativity and with spin, respectively.