The Geometric Derivation of the Transformation of Time and Position Coordinates in STE

Abstract

It is commonly thought that the Michelson-Morley experiment from 1887 (1) and Kennedy-Thorndike experiment from 1932 (2) demonstrated that the ether does not exist and that the velocity of light in vacuum is absolutely constant. The analysis of this experiment led to the creation of the special theory of relativity (STR). In this article, a different transformation of time and position than the Lorentz transformation is derived on the basis of the geometric analysis of the Michelson-Morley experiment. The transformation is derived based on the assumption that the universal frame of reference, called the ether, exists. Our concept states that the ether is not a substance with physical properties, as it was understood in the past, but a frame of reference in which the velocity of light is constant in every direction. In inertial frames of reference moving in the ether, the velocity of light may be different. The obtained transformations are transformations from the ether to the inertial frame and from the inertial frame to the ether. Based on the new transformation, the Special Theory of Ether (STE) was created (4), (5).