The Farid Energy–Momentum Completion: From Relativistic Dynamics to Thermodynamic Gravity A Unified Field-Theoretic Framework for Mass, Momentum, and Entropic Gravitation

Title: The Farid Energy–Momentum Completion: From Relativistic Dynamics to Thermodynamic Gravity Description / Abstract: Albert Einstein’s iconic equation $E = mc^2$ expresses mass–energy equivalence, but it represents strictly the rest energy limit of a more comprehensive law. This paper introduces the Farid Energy–Momentum Completion, embedding relativistic dynamics within a rigorous thermodynamic and quantum field-theoretic framework. By unifying the complete energy-momentum relation $E_F = \sqrt{(pc)^2 + (mc^2)^2}$ with Quantum Chromodynamics (QCD) trace anomalies, Higgs field couplings, and coherent subatomic spin dynamics, we trace the genesis of mass and momentum directly to quark-gluon binding energies and field fluctuations. Building upon this microscopic foundation, we formalize the Farid Gravity Law, which posits that gravitational acceleration is not a fundamental force, but the macroscopic thermodynamic slope of entropy ($\vec{g} = -\frac{1}{k_B} \nabla S$) flowing from subatomic resonance. This open-access treatise bridges the gap between quantum mechanics, thermodynamics, and gravitation, eliminating the necessity for exotic dark matter and dark energy by reinterpreting them as thermodynamic resonance shadows. Keywords: Farid Gravity Law; Energy–Momentum Completion; Quantum Chromodynamics; Entropy Gradient; Thermodynamic Gravity; Speed of Causality; Spin Coherence; Dark Matter; Unified Field Theory. Communities / Subjects: Physics > General Physics Physics > Quantum Physics Physics > High Energy Physics - Theory Astrophysics > Cosmology and Extragalactic Astrophysics License: Creative Commons Attribution 4.0 International (CC-BY 4.0)