Arbitrary Character of World-Geometry

Abstract

PROF. E. A. MILNE, in the important paper¹ in which he gives an account of an invariant distribution of particles forming an expanding universe in flat space-time, has stated that the geometry adopted in cosmological theories may be chosen arbitrarily, the expression of the laws of Nature being relative to the geometry assumed. A similar view has also been expressed by myself². The first enunciation of the idea, however, seems to have been due to Poincaré in quite the early days of relativity. It is interesting in this connexion to observe that there is a very simple method of converting the law of motion of a particle expressed in the geometry of Einstein's theory to the corresponding law expressed in any other geometry.