Relativity in a Stationary Spherical or Elliptic Space

Abstract

The fundamentals of the theory of relativity in a stationary spherical or elliptic space are developed in continuation of a previous communication on the static Einstein space in a manner which enables visualization of relative motion. This particular stationary space appears to be the natural and simplest generalization of Einstein's space owing to the existence in both of the set of singularity-free motions previously introduced as Clifford translations. This stationary space is no longer spherically symmetrical in all directions, and there are shown to be two different types distinguished by right- and left-handed Clifford translations of the reference systems. Each stationary space when compared with the Einstein space has a right- or left-handed twist associated with it. The geodesics are distorted, except in a certain preferred direction, as compared with Einstein's space. This is due to the existence of a gravitational field which resembles in some ways that illustrated in Minkowski space by the "Einstein elevator." The Lorentz group links all these spaces, so that agreement between observers in any two spaces can be established with regard to a moving particle seen by both. Einstein's space is found to occupy a preferential position as compared with all the other stationary spaces of this type.