P-8: The Geometric Origin of Gravity — Torsion and Einstein-Cartan Theory from the Spatial Orientation Field(v1.1)

Abstract:How gravity can be reconciled with quantum mechanics is one of the deepest challenges in contemporary theoretical physics. Starting from the first principles of Space Ontology—the spatial orientation field equation—we demonstrate that gravity is not an independent "oddity" apart from the other interactions, but an inevitable consequence of the nonlinear dynamics of space itself. By coupling the complexified spatial orientation field to spacetime geometry, we show that the κ term in the field equation is exactly equivalent to the contraction of the torsion tensor with the superpotential current. The Einstein-Cartan equations derived from the variation of the unified action reveal that the source of torsion is precisely the spin angular momentum of the spatial motion modes. In the weak-field, low-velocity approximation, the theory reduces to Newtonian gravity and predicts a small correction arising from spin fluctuations. More fundamentally, the gravitational constant G is shown to be an emergent parameter: starting from the Planck vortex micro-element model, the expression for G contains an exponential suppression from instanton effects, e^(−2π²/κ) ≈ 10^(−504). This result provides, for the first time from first principles, an explanation for why gravity is so extraordinarily weak, and reveals the deep geometric unity among gravity and the strong, weak, and electromagnetic interactions.This paper is the eighth in the first series (17 papers total) of Space Ontology, establishing the geometric origin of gravity from torsion and Einstein-Cartan theory.