The task ahead

If one tries to view the problem situation faced by Eddington from his point of view, it breaks into three parts. The expectation was that these three would prove connected in some way when the problem was solved. The first part of the problem is to make some connexion between 136 as a number of algebraic elements and 1/136 as related to (though by 1936 Eddington was aware that it was not equal to) e2/ħc. As I said in the last chapter, the fine-structure constant occurs in many different contexts. Ideally, if it is to be related to algebraic structures, it should be possible to use any of these contexts with the principle of identification to establish the relation. Eddington chose, naturally enough, the occurrence of α as a coefficient in Dirac's equation of the hydrogen atom. Hitherto I have been speaking only of Dirac's equation for the free electron; that is the simplest case. But, as will have been clear from Dirac's explanation quoted in Chapter 6, his work was inspired – like so much work in both the old and new quantum theories – by difficulties in explaining the hydrogen spectrum fully. The way in which the equation for the free electron was modified to take account of the electrostatic force between proton and electron was well known, if not at all understood, in the quantum wave mechanics of Schrödinger. Dirac took it over without question and Eddington followed Dirac. No-one has since questioned this method of introducing an electric force, so I shall do no more now than to remark that it is a little mysterious.