On Eddington's Treatment of Dirac's Equation

Eddington, in his book Relativity Theory of Protons and Electrons, makes statements to the effect that the invariance of Dirac's equation is an elementary consequence of the tensor form which it acquires in the new wave tensor calculus, in which it is merely an identity derivable on epistemological principles and not on physical hypothesis. It is shown in this article that the invariance of Dirac's equation referred to by Eddington is a purely formal one, while the invariance which is of particular interest in quantum mechanics depends upon the physical interpretation of the wave function. The generalization of physical interpretation suggested by Eddington's work, however, has the desirable quality of leaving Dirac's equation invariant in the physical sense. It is further shown that in the derivation of Dirac's equation Eddington makes use of the usual physical assumptions, but in somewhat disguised form.