splits up into a symmetrical and an anti-symmetrical part; these two parts are given by
and
. In other words, the world tensor splits up of its own accord into gravitation and electricity, showing thereby the deep union between the two.
As late as 1922, Einstein did not show much enthusiasm for these new generalisations, but subsequently he appears to have modified his views, going so far as to investigate the problem of the world-action in the light of Eddington’s geometry.
He first studied a possible mathematical expression for the action, one which had already been suggested by Eddington. It was a strikingly simple expression representing certain of the generalised space-time curvatures; no longer a mere stringing together of the various actions. When the principle of stationary action was applied to it, it fell apart, yielding the law of gravitation on one side and the laws of electricity on the other. The mathematical results obtained by Einstein in this respect point to a general diffusion of electricity throughout the world; and as in the case of Weyl’s treatment, magnetic and not electric charges appear to lie at the basis of matter. Subsequently, Einstein proved that other expressions for the action would yield the same results.
Yet, in spite of all these remarkable successes, the outlook is none too promising. The problem of matter is no nearer a solution than before. Indeed, it is highly probable that some totally new departure will have to be considered. Here it must be remarked that the attempts we have been outlining follow the methods of field physics; that is to say, the entire physical universe is assumed to be built up of the
’s and