The Dual Pillars of the Farid Gravity Law: From Complete Relativistic Energy to Entropic Gravitation

Title The Dual Pillars of the Farid Gravity Law: From Complete Relativistic Energy to Entropic Gravitation Authors Prof. Dr. Md. Faridul Islam Chowdhury Neurosurgeon | Neuroscientist | Theoretical Cosmologist Founder & Director, Tanfarid Vision Research Institute (TVRI), Bogura, Bangladesh Inventor of the Tanfarid Quantum Thermodynamic Universe (TQTU) and the Farid Gravity Law Description This work presents the two foundational pillars of the Farid Gravity Law — a unified theoretical framework that connects quantum field dynamics, thermodynamics, and the physical origin of gravitational attraction. The first pillar is the complete relativistic energy–momentum functional: EF=(pc)2+(mc2)2 E_F = \sqrt{(pc)^2 + (mc^2)^2} EF=(pc)2+(mc2)2 This relation treats mass and momentum as complementary aspects of a single operational energy, moving beyond the rest-energy limit E=mc2 E = mc^2 E=mc2. It shows that the dominant contribution to nucleon mass arises from confined quark–gluon kinetic and field energy (approximately 99 %), consistent with the QCD trace anomaly. The second pillar is the thermodynamic definition of gravitational acceleration: g=−1kB∇S \mathbf{g} = -\frac{1}{k_B} \nabla S g=−kB1∇S Here gravity is reinterpreted not as a fundamental force or spacetime curvature, but as the macroscopic slope of entropy density. Local entropy gradients are generated by subatomic spin coherence and resonance, providing a microscopic origin for the gravitational field and a physical basis for the equivalence principle. Together these two equations form a continuous deductive chain: Quark–gluon energy → (m,p) (m, p) (m,p) → EF E_F EF → stress–energy tensor Tμν T_{\mu\nu} Tμν → entropy gradient ∇S \nabla S ∇S → gravitational acceleration g \mathbf{g} g. The framework offers a candidate explanation for gravitational phenomena without invoking dark matter or dark energy as independent entities, while remaining consistent with existing experimental constraints (MICROSCOPE equivalence-principle tests, CERN QGP data, and spin-coherence principles demonstrated in MRI). This deposit contains the full article presenting the dual-pillar formulation of the Farid Gravity Law within the broader Tanfarid Quantum Thermodynamic Universe (TQTU) research programme. Keywords Farid Gravity Law, Entropic Gravitation, Relativistic Energy–Momentum, Quantum Chromodynamics, Spin Coherence, Thermodynamic Gravity, Unified Field Theory, Tanfarid Quantum Thermodynamic Universe (TQTU)