The theory of the transformations of coordinates connected to massive reference frames

Abstract

The paper presents a new local group of transformations of coordinates of reference frames connected to massive bodies such as the earth, sun, etc., which in the kinematic respect are fairly inertial but do possess different gravitational fields [Eq. (6)]. Account has been taken of the gravitational field of the reference body on the metric of the frame. For identical frames it goes over into the Lorentz group. Relativistic effects in reference frames connected to massive bodies, reference bodies, are usually described by the equations of the general theory of relativity (1)-(3). However, among massive bodies one can always distinguish a particular group of bodies which are sufficiently inertial in the kinematic respect even though they do possess various gravitational fields. From the computational point of view, the application of the complex apparatus of the general theory of relativity to such systems is not justified and the group of Lorentz transformations in the given case is not applicable. Thus, it would be advantageous, without going beyond the framework of the principle of relativity, to find a group of coordinate transformations which would take account of the influence of the reference bodies in the description of relativity effects. The present paper is devoted to this problem. The physical considerations at the basis of the theory will be expounded below as required.