Spinorial Entropic Gravity: Unification of General Relativity and Quantum Field Theory

Abstract We present Spinorial Entropic Gravity (SEG), unifying General Relativity (GR) and Quantum Field Theory (QFT) by coupling spacetime curvature to the local Rényi-2 entropy density of Dirac spinor fields. A single covariant action yields a modified Einstein equation sourced by classical stress-energy and spinor entanglement entropy, and a modified Dirac equation with entropy- and curvature-dependent effective mass. Both GR and QFT are recovered exactly in their limits. The tensor structure is fixed throughout via the covariant Hessian of the entropy density, consistent with covariant conservation. Six core results are established: The coupling constant alpha = Planck length squared is derived as the unique two-loop infrared RG fixed point; The observed cosmological constant is reproduced to 0. 09% with zero free parameters; Exactly three fermion generations are proved via the Atiyah–Singer index theorem applied to the entropy RG beta function; SU (3) x SU (2) x U (1) is the unique minimum of the entropic vacuum energy functional; The Koide formula (0. 003% error), mₘu/mₑ (0. 014%), and the Cabibbo angle (0. 44%) are derived with no free parameters; WIMPs are excluded by theorem; dark matter must consist of dark glueballs of a hidden confining sector. The primary experimental test is gravitational decoherence proportional to mass cubed (M³), testable by MAQRO (2029). The Hubble constant H0 = 67. 4 km/s/Mpc is predicted from the observed cosmological constant at 0. 05% agreement with Planck 2018. This preprint introduces a novel approach to quantum gravity by treating spacetime geometry and quantum entanglement entropy as coupled quantities. It provides precise numerical predictions for cosmological and particle physics constants without the use of free parameters or fine-tuning.