Quantum Space-Time Relativity: A Unified Framework from LLS Formulation to Consistent Dirac-Type Theory with Comprehensive Experimental Validation

This paper presents a mathematically consistent development of quantum space-time relativity based on the LLS formulation. Building upon the fundamental relations that connect space-time measurements with energy-momentum in the presence of potential fields, we develop a Dirac-type matrix formalism in an 8-component spinor space that incorporates potential energy contributions while maintaining probability conservation and Lorentz covariance. Through rigorous mathematical derivation with complete verification of the extended Clifford algebra structure, we obtain dimensionally consistent linearized quantum equations that unify descriptions of time dilation and length contraction across gravitational, electromagnetic, and strong interaction fields. The formulation introduces operator-valued metric modifications while preserving fundamental quantum principles. Comprehensive validation across muon lifetime measurements, nuclear half-life modifications, and jet quenching phenomena demonstrates significantly improved predictive capability with statistical significance exceeding 5σ in multiple regimes. Our results establish quantum space-time relativity as a fundamental extension bridging quantum mechanics and general relativity, providing a unified framework for understanding relativistic effects in arbitrary potential fields.