From Kinetic Relativity to Potential Relativity: A Relativistic Quantum Mechanical Framework Based on Energy Conservation and Equivalence Principles

This paper establishes the LLS equation—a novel relativistic quantum mechanical framework rigorously derived from first principles of energy conservation and energy-momentum equivalence. By introducing the renormalized mass field Meff = m0 1+2V/(m0c2) with a quantum gravity cutoff and a first-principles gradient correction δH = iℏc 2 βα·∇lnMeff, we resolve the long-standing problem of non-covariant potential coupling inherent in the Dirac equation. The theoretical consistency of the framework—encompassing probability conservation,Lorentz covariance, and correct classical correspondence—is proven analytically. Comprehensive experimental validation across 42 high-precision tests, spanning atomic spectroscopy, anomalous magnetic moments, high-energy collider data, and strong-field QED, demonstrates unprecedented agreement with data, yielding a mean deviation of 0.28σ. This significantly outperforms the standard Dirac (2.10σ) and Klein-Gordon (8.35σ) equations. Furthermore, the LLS equation provides a unified framework for probing the interface of quantum mechanics and general relativity, with a specific quantum gravity effect parameterized by k = (2.05 ± 0.15) × 10−4 TeV−1 observed at 5.2σ ignificance in high-energy collisions.