General Quantum Spacetime Relativity: Unification of Special Relativity, General Relativity, and Quantum Mechanics via the LLG Framework

This paper establishes a comprehensive theoretical framework termed General Quantum Spacetime Relativity (GQSR), founded upon the fundamental principles of energy conservation and the kinetic-potential energy equivalence. We extend the LLG (Liu-Liu-Generalized) mass-energy momentum relation to incorporate general potentials V , from which we derive generalized time dilation and length contraction formulas. These classical relations are subsequently quantized through a non-canonical scheme that promotes measured temporal and spatial intervals to operators conjugate to energy and momentum, while maintaining energy and momentum as classical variables in the initial representation. This yields a system of second-order differential equations governing quantum spacetime observables. By employing both generalized Dirac matrices and sl(3,C) Lie algebra representation theory, we achieve exact linearization into a first-order, multi-component wave equation. The resulting framework demonstrably encompasses Special Relativity (V = 0) and General Relativity (with V as the gravitational potential) as natural limiting cases, while extending predictive validity to regimes of strong electromagnetic and chromodynamic fields. Rigorous confrontation with experimental data—including muon lifetime modifications in strong magnetic fields, quarkonium suppression patterns in heavy-ion collisions, precision atomic spectroscopy, the proton charge radius puzzle, and gravitational wave phase shifts—confirms the theory’s enhanced predictive accuracy and consistency across multiple physical domains. The theory is shown to be mathematically self-consistent, possessing Lorentz covariance, unitary evolution, probability conservation, and a renormalizable quantum field theory formulation.