Physical uniformity of the Universe

The question of the spatial homogeneity of the Universe is re-examined from the viewpoint of the hypothesis on the physical unity of the universe. It is shown that the demand for the universal validity of the theory of relativity implies that the average value of the Newtonian world potential is constant everywhere in the universe which is spatially homogeneous on a large scale. It turns out that Mach's principle is compatible with the special theory of relativity if the average value of the normalized world potential is exactly equal to–c ². This fact may be interpreted as a consequence of the fundamental idea of the general relativity that cosmic matter determines the space-time metric in agreement with Mach's principle.