The Standard Form of General Potential Relativity: A Comprehensive Framework with Experimental Verification and Mathematical Refinements

This paper presents a fundamental reformulation of relativistic physics based on the principle of energy conservation and a novel equivalence principle between kinetic and potential energy. We demonstrate that the LLG mass-energy relation provides a more foundational framework than both special and general relativity, which emerge as special cases when potential energy is zero or corresponds to gravitational fields, respectively. Through rigorous mathematical development, we derive the exact linearization of the nonlinear relativistic wave equation, yielding the LLG equation as a first-order linear differential equation. Two complementary approaches—Lie algebra linearization using sl(3,C) representation theory and matrix linearization with generalized Dirac matrices—are developed, both maintaining Lorentz covariance, probability conservation, and unitary evolution without approximation. We further develop the complete quantum field theory formulation including second quantization and renormalization. Comprehensive experimental verification across hydrogen spectroscopy, electron anomalous magnetic moment, proton charge radius, and gravitational wave observations demonstrates the LLG framework’s superior agreement with empirical data compared to established theories.