Relativistic solutions to the falling body in a uniform gravitation field

Abstract

Many different solutions to the problem of the relativistic particle in a uniform gravitational field have been offered. The fact that different, apparently correct, solutions to the same problem exist is in itself a puzzle. A resolution to this puzzle is found by exploiting the equivalence principle to reduce the problem to the observations made by an accelerated observer of objects moving inertially in a background inertial frame. It is shown that some solutions, those arising from a truly curved space-time, cannot be treated in this manner. It is found that differences in the remaining solutions arise because the authors use coordinate displacement to describe the motion rather than proper distance. The coordinate systems of these different accelerated frames are distorted and produce different apparent motions of objects in the background frame. When the ‘‘right’’ variables are used all motions are identical.