Page:The Meaning of Relativity - Albert Einstein (1922).djvu/120

in which

${\begin{aligned}{\mathfrak {F}}^{\mu \nu }&={\sqrt {-g}}g^{\mu \sigma }g^{\nu \tau }\phi _{\sigma \tau }\\{\mathfrak {J}}^{\mu }&={\sqrt {-g}}\rho {\frac {dx_{\nu }}{ds}}.\end{aligned}}$

If we introduce the energy tensor of the electromagnetic field into the right-hand side of (96), we obtain (115), for the special case ${\mathfrak {J}}^{\mu }=0$, as a consequence of (96) by taking the divergence. This inclusion of the theory of electricity in the scheme of the general theory of relativity has been considered arbitrary and unsatisfactory by many theoreticians. Nor can we in this way conceive of the equilibrium of the electricity which constitutes the elementary electrically charged particles. A theory in which the gravitational field and the electromagnetic field enter as an essential entity would be much preferable. H. Weyl, and recently Th. Kaluza, have discovered some ingenious theorems along this direction; but concerning them, I am convinced that they do not bring us nearer to the true solution of the fundamental problem. I shall not go into this further, but shall give a brief discussion of the so-called cosmological problem, for without this, the considerations regarding the general theory of relativity would, in a certain sense, remain unsatisfactory.

Our previous considerations, based upon the field equations (96), had for a foundation the conception that space on the whole is Galilean-Euclidean, and that this character is disturbed only by masses embedded in it. This conception was certainly justified as long as we were dealing with spaces of the order of magnitude of those