Abstract

The continued mathematical validity of the Einstein and Lorentz transformation equations has been mathematically challenged based on namespace analysis and on apparent violations of the rules of algebraic substitution. In addition, the Einstein-Lorentz Special Relativity equations do not properly incorporate frequency into the derivation because they overlook its bi-directional nature and do not account for superposition of waves principle. Furthermore, both Einstein and Lorentz use their equations to transform points instead of lengths. He we compare and contrast the essential characteristics of the Einstein-Lorentz models with the model of Complete and Incomplete Coordinate Systems, which introduces a revised set of length-based transformation equations, addresses the bi-directional nature of frequency, and adheres to the superposition of waves principles. The model of Complete and Incomplete Coordinate Systems is a wave medium (aether) based model that is generalize to apply to oscillating phenomena and moving systems, does not suffer from the same mathematical problems as the Einstein-Lorentz derivations, and uses equations that yield equal or better results that the existing Einstein-Lorentz equations.