From Kinetic Energy Relativity to Potential Energy Relativity

This paper establishes the LL equation---a novel relativistic quantum mechanical framework rigorously derived from first principles of energy conservation and energy equivalence. By introducing the renormalized mass field Meff = m0 1 + 2V/ (m0c2) with quantum gravity cutoff and gradient correction δH = ihc/2βα, we resolve the non-covariant potential coupling problem inherent in the Dirac equation. Theoretical consistency (probability conservation, Lorentz covariance, and classical correspondence) is proven analytically. Experimental validation across 42 high-precision tests demonstrates unprecedented accuracy with mean deviation 0. 28σ, outperforming Dirac (2. 10σ) and Klein-Gordon (8. 35σ) equations. The LL equation provides a unified framework for quantum mechanics and general relativity, with quantum gravity effects observed at 5. 2σ significance.