From Space-Time Relativity to Energy-Momentum Relativity: A First-Principles Derivation from the Equivalence of All Forms of Energy

This paper presents a comprehensive theoretical framework derived from a single first principle: the Principle of Total Energy Equivalence. This principle posits that in a complete physical theory, the rest energy (m0c2), kinetic energy (pc), and potential energy (V ) must contribute symmetrically and on an equal footing to the total relativistic energy of a system. We begin by postulating the fundamental energy-momentum relation E = (m0c2 +V)2 +p2c2. Through rigorous mathematical derivation, we demonstrate that this relation naturally generalizes the Dirac equation to include potential energy relativistically, resulting in a novel wave equation termed the LL Equation. We show that this framework seamlessly incorporates and extends both Quantum Mechanics and General Relativity. Crucially, we provide detailed derivations of two cornerstone predictions of GR–the anomalous precession of Mercury’s perihelion and the gravitational deflection of light–directly from our energy-based formalism, without invoking the full apparatus of Riemannian geometry. The theoretical values obtained, ∆ϕmercury = 43.0′′ per century and ∆ϕlight = 1.75′′, are in exact agreement with experimental observations. Further more, we address the quantum mechanical consistency of the theory by introducing a modified inner product that ensures probability conservation for the non-Hermitian terms in the Hamiltonian. This work establishes a unified foundation for modern physics, resolving long-standing tensions and offering novel insights into quantum gravity.