Explicit-Field-Resistance Gravity : Microscopic Properties, Coarse-Grained Bridge, and Unification of the Four Fundamental Forces

Abstract

Abstract This paper proposes a new gravitational theory framework—Explicit-Field-Resistance Gravity (EFRG)—which explicitly embeds the field-resistance parameter into the gravitational equations. The core innovation lies in establishing a micro-macro unified framework: the microscopic property relation (xi_micro(sigma) = xi_0 * sigma^(-4/3)) (where xi_0 = 851.63 m^-1 is the vacuum intrinsic field resistance, and sigma is the vacuum coherent compression degree), through the coarse-grained bridge sigma(r) = (r/r_0)^(9/4) (where r_0 = 2L_0 = 3.89 mm), naturally derives the macroscopic manifestation xi(r) proportional to r^-3, perfectly matching the three-scale phenomenological model (deviation < 0.01%). From a strict variational principle, the nonlinear Poisson equation is derived, and the interpolation function nu(x) = (sqrt(1+4x^2)-1)/(sqrt(1+4x^2)+1) reproduces MOND behavior in the low-acceleration limit. Numerical verification shows a solar system deviation < 10^-16%, a galaxy rotation curve asymptotic velocity V_infinity = 176 km/s, and an effective mass enhancement in the weak lensing region of M_eff approximately 1.0-1.8 x M_GR. Core Addition: A unified picture of the four fundamental forces on the field-resistance master scale is established. The strong nuclear force, electromagnetic force, and weak force "penetrate" the field-resistance layer at microscopic scales with ratios a_actual / a_xi ~ 10^13-10^42, while gravity at microscopic scales is completely submerged by field resistance (a_N / a_xi ~ 10^-58). This explains why the microscopic world "does not feel" gravitational corrections, while at galactic scales (a_N ~ a_xi) MOND effects emerge. Keywords: Field resistance; Modified gravity; MOND; Dark matter alternative; T_3 algebra; Vacuum coherent compression degree; Unification of four fundamental forces