The Theory of Entropicity (ToE) Validates Einstein’s General Relativity (GR) Prediction for Solar Starlight Deflection via an Entropic Coupling Constant η

This paper demonstrates that the Theory of Entropicity (ToE), a novel framework grounded in entropy-driven dynamics, successfully reproduces the deflection of starlight by the Sun as originally predicted by Einstein’s General Relativity (GR). Unlike GR, which attributes light bending to spacetime curvature, ToE derives the deflection angle from an entropic variational principle that governs particle trajectories through entropy-constrained geodesic fields. By introducing a fundamental entropic coupling constant η, we show that the resulting light trajectory yields a deflection angle numerically identical to Einstein’s prediction of 1.75 arcseconds for solar grazing incidence. This result emerges naturally from the entropic Binet equation of ToE, without requiring the metric tensor formalism of GR, thereby highlighting entropy as a fundamental generator of gravitational phenomena. To further validate the universality of η, we apply the same entropic framework to the perihelion precession of Mercury’s orbit. By dynamically adapting its interaction based on the system’s massless or massive nature, ToE predicts that the perihelion precession correction matches the observed relativistic value of 43 arcseconds per century. Crucially, we establish that η follows the scaling relation: ηperihelion = ηlight × α|ΓGM/2 which naturally accounts for the distinct behaviors of null and timelike geodesic fields within the entropy field. Our findings not only validate Einstein’s results from a non-metric, entropy-based perspective but also reveal that entropy acts as a universal field whose interaction dynamically adapts based on the presence or absence of mass, strengthening internal consistency and predictive power of the Theory of Entropicity in weak-field relativistic regimes.