Relativistic coordinate shifting within three‐dimensional space

Let us consider that light, when viewed as a particle, forms a conic arc segment inscribed within the space viewed. The space (or frame) viewed is considered to exhibit a gravitational potential, and it is thus this potential that deforms the light path from a Euclidean/Newtonian derivation of a straight line to that of a relativistic curvilinear nature. Given a distance over this conic arc segment (assumed to form a parabolic arc segment) and a given time (considering the given distance involved), one derives a constancy of the speed of light of c, where c is considered as a constant regardless of the gravitational potential exhibited by the frame viewed. If we further consider that the Special Theory requires that light propagate on a linear measure as the velocity v (of necessity v being less than c on a comparable linear measure) between the axes concerned; then a displacement (in linear measure equal to c−v) occurs. The displacement evolved is then assumed to agree with the form of Maxwell. We assume that this linear displacement of c−v occurs upon the y‐axis of the frame viewed. Of necessity, a relative displacement must occur upon the x‐axis of the frame viewed. From the calculus, the dot products derived must vary in concept, in order to derive the totality of relative coordinate shifts occurring within any three‐dimensional space. One displacement is linear in nature, while the other is trigonometric in nature. We consider the displacement of Maxwell, Lorentz, Compton, and de Broglie to be linear in nature. Based on the principle of the Special Theory (and the other forms as mentioned), we consider the total displacement to be mechanically derivable. That derivation, once allowed, results the physics to agree with the observations complete to this moment in time. The paper concludes that the error in coordinate positioning shown by the global positioning satellite system (GPS satellite platform) is resolvable.