Gravitation in Kinematic Relativity

Abstract

A CRUCIAL test of a relativity theory of gravitation is its ability to explain (a) the perihelion advance of a planetary orbit as observed in the case of Mercury, and (b) the deflexion of light in a gravitational field as observed in the field of the sun. Another, completing the trio of tests which Einstein's general theory satisfied with such notable success, is in a different category, since it involves some hypothesis concerning the ‘proper’ frequencies of atomic vibrations; this is (c) the shift of the spectral lines emitted by atoms near a massive body, as observed in the case of light from the sun and from the companion to Sirius. It is not difficult to apply tests a and b to the gravitational part of Milne's theory¹, assuming that the equations of motion given by Milne hold in the field of the sun. The results are that, first, there is a perihelion motion, but it is in the wrong direction, and secondly, there is no gravitational deflexion of light. The failure under the first test could perhaps be accounted for by the fact that the sun is not at rest in the substratum; but if this were so, the perihelion effect would depend critically upon the sun's velocity relative to the substratum and upon the orientation of the planetary orbit under consideration. On the whole, it appears that Milne's dynamical theory does not compare favourably with Einstein's general theory.