On Lorentz transformation and special relativity: Critical mathematical analyses and findings

Abstract

In this paper, the Lorentz transformation equations are closely examined in connection with the constancy of the speed of light postulate of the special relativity. This study demonstrates that the speed of light postulate is implicitly manifested in the transformation under the form of space-to-time ratio invariance, which has the implication of collapsing the light sphere to a straight line, and rendering the frames of reference origin-coordinates undetermined with respect to each other. Yet, Lorentz transformation is shown to be readily constructible based on this conflicting finding. Consequently, the formulated Lorentz transformation is deemed to generate mathematical contradictions, thus defying its tenability. A rationalization of the isolated contradictions is then established. An actual interpretation of the Lorentz transformation is presented, demonstrating the unreality of the space-time conversion property attributed to the transformation.