Geometric Unification of Physical Interactions

Abstract This work presents a geometric framework in which gravitation and electrostatic behavior emerge as distinct regimes of the same underlying radial geometric interaction. The model is constructed from a unified intrinsic acceleration equation derived from volumetric scaling, geometric projection, and relativistic saturation constraints. The framework predicts two asymptotic interaction regimes: a_g ~ m^(1 / 3) and: a_e ~ m^(-5 / 3) which are shown to emerge naturally from a continuous geometric attenuation law. In this interpretation, gravitation corresponds to the coherent volumetric redistribution of radial geometric tension, while the electrostatic regime appears when this redistribution collapses near the geometric penetration scale λ, producing a dimensional amplification of radial attenuation across spatial degrees of freedom. The model further demonstrates that the characteristic mesoscopic scale m_φ is not imposed externally, but emerges dynamically as the equilibrium point between coherent volumetric shielding and amplified radial tension. The resulting formulation produces a unified geometric response: T_3(R) = R + R^(-5) recovering both asymptotic regimes from a single continuous expression. The unified intrinsic acceleration equation can then be rewritten in the compact geometric form: a_i = (a_z · T_3(R)) / (1 - (L_t / r)) where the numerator represents the geometrically redistributed radial tension of the object and the denominator represents the remaining unsaturated spatial metric available for interaction. Physical interaction is interpreted not as force propagation through an inert background, but as the geometric response of space to volumetric projection, radial attenuation, and metric saturation. Consequently, several fundamental constants — including the gravitational constant G and the reduced Planck constant ħ — are reinterpreted not as primitive quantities, but as emergent scaling parameters associated with finite geometric resolution. The unified geometric response is also interpreted informationally, with mass emerging as an effective coherence cost associated with maintaining stable volumetric propagation across a discrete spatial metric. v32: Conceptual refinements, new sections, typographical corrections.