Explanation of the Special Theory of Relativity by Analytical Geometry and Reformulation of the Inverse-Square-Law

TL;DR

This paper reformulates the inverse-square law using analytical geometry and space-time concepts, providing a relativistic perspective without relying on space-time curvature, and reveals new analogies between morphological and physical parameters.

Contribution

It introduces a novel geometric approach to inverse-square laws, deriving relativistic formulations without assuming light speed isotropy or space-time curvature.

Findings

Space-time length replaces spatial distance in inverse-square laws

Analytic relationship between position and field intensity established

New analogy between orbital eccentricity and momentum discovered

Abstract

The space-time length R between a moving source and the observation point is calculated in order to substitute with it the spatial distance D, normally used in the Newton's law of gravitation, as well as in any inverse-square-law. Fundamentally, three space-time amounts describe dynamics. The relationship between position and field intensity is analytic, estimable in euclidean space, and considering a linear reference system for the time parameter. The formulation shows compatibility with fundamental rules of classical mechanics, highlighting also hitherto unknown properties, as a perfect analogy between morphological and physical parameters, such as the complete correspondence between the eccentricity and the momentum in the orbital motion. Moreover, the procedure naturally contains relativistic formulation without introducing any special hypothesis on light speed isotropy, asking so the question about the actual need to introduce the concept of space-time curvature for the correct interpretation of physics phenomena.