How Natural Origin Achieves the Algebraization of Special and General Relativity

Abstract

This paper develops the algebraization of relativity by reconstructing the foundational expressions of both special relativity and general relativity. For special relativity, the paper does not begin with coordinate transformations. Instead, it begins with right handed light speed relay refresh of space units, interpreting the invariance of light speed as the limiting speed of space unit refresh. Through the step settlement mother equation, time dilation, length contraction, the Lorentz factor, and the absence of local time in the light state are directly derived. In this way, special relativity is reduced from the complexity of Lorentz forward and inverse transformations to a minimal algebraic relation of refresh budget allocation. For general relativity, the paper does not take Riemannian geometry, metric tensors, or curvature calculation as the ontological starting point. Instead, it further reduces the core scale of the Schwarzschild exterior field to the time element of the central source and uses time potential to uniformly reinterpret gravitational acceleration, Mercury perihelion precession, solar limb light bending, gravitational redshift, black hole closure, and quadrupole manifestation of gravitational waves. The paper argues that the classical success of general relativity is rooted in the time element readout revealed by the minimal Schwarzschild exterior field. Matter reads time potential as slope, orbits read it as phase, light reads it as direction, clocks read it as frequency ratio, and dynamic time element axes are read as gravitational waves. The entire paper ultimately forms a unified main line: space unit refresh gives the upper limit of light speed, the step settlement mother equation gives the algebraic structure of special relativity, and the time element and time potential give the algebraic structure of general relativity. Relativity is thereby advanced from the language of coordinate transformation and geometric curvature to the language of bottom layer refresh budget and time potential readout.