Dirac's New Classical Theory of Electrons

Abstract

Similarities are pointed out between Dirac's theory and certain equations belonging to the projective theory of relativity. The latter include an electromagnetic potential of fixed gauge and are such that if one reduces them to special relativity in the conventional way by taking $g_{\mathrm{ab}}$ to be Galilean, one can extract from them equations closely corresponding to those of Dirac's theory. However, it is shown that taking $g_{\mathrm{ab}}$ to be Galilean ignores quantities that may not be negligible relative to Dirac's gauge-fixing constant $k^2=\frac{m^2}{e^2}$; thus, effects arising from non-Galilean $g_{\mathrm{ab}}$ may be important in a theory of the type proposed by Dirac. When $g_{\mathrm{ab}}$ is not Galilean one apparently loses the central characteristic of Dirac's theory that all electric currents have $\frac{m}{e}$ of electronic value. Equations of motion are still present, however. And since the gauge-fixed electromagnetic potential can be zero without contradicting the field equations, one need not postulate an ether for the reasons that arise from Dirac's theory.