The Theory of Entropicity (ToE): An Entropy-Driven Derivation of Mercury’s Perihelion Precession Beyond Einstein’s Curved Spacetime in General Relativity (GR)

We present a novel derivation of the perihelion precession (shift) of Mercury using the Entropic Force-Field Hypothesis (EFFH), now formulated as the Theory of Entropicity (ToE). Unlike Einstein’s General Relativity (GR), which attributes perihelion precession to spacetime curvature, we show that it arises naturally from entropy-driven modifications to Newtonian gravity. By introducing higher-order entropy corrections to the gravitational potential of Newton, with inputs from the Unruh Effect, Hawking Temperature, Bekenstein-Hawking Entropy, the Holographic Principle, the Binet Equation, and the Vis-viva Equation, we derive a modified orbital equation that leads to an identical perihelion shift of 43 arcseconds per century, which Einstein derived in 1915 from his momentous General Theory of Relativity (GTR). This result further demonstrates that entropy constraints, rather than curved spacetime, are the fundamental driver of gravitational interactions. Newton’s Classical Theory of Gravitation describes gravity as a force, while Einstein’s General Relativity describes gravity as being as a result of spacetime curvature; but our Theory of Entropicty (ToR) describes gravity as an emergent field from the constraints prescribed by the fundamental Entropic Field.