The Foundations of Local Interaction Field Equilibrium (LIFE Theory): From Minkowski Spacetime and Wheeler GEONs to Unified Volumetric Force Densities and Subatomic Quantum Eigenmodes

This paper presents the formal mathematical foundations and unified synthesis of the Local Interaction Field Equilibrium (LIFE) framework. By expanding Minkowski’s four-dimensional spacetime continuum into a unified volumetric force-density equilibrium (∑ B_i ≡ 0 N/m³), we resolve several longstanding paradoxes in classical electrodynamics, quantum foundations, and elementary particle physics.Through standing-wave envelope regularization coupled to an intrinsic gravito-inertial mass-energy term (Term B-6), elementary leptons and hadrons—such as the electron and proton—are substantiated not as point-charge singularities, but as self-binding, three-dimensional electromagnetic cavity eigenmodes. This framework naturally eliminates the infinite electrostatic self-energy divergence (∫ E² dV → ∞) and Poincaré self-stresses without requiring ad-hoc non-electrical hypotheses. The 1836:1 mass disparity between the proton (938.27 MeV) and electron (0.511 MeV) is resolved via geometric cavity compaction: because the proton encapsulates a vastly higher energy density, non-linear gravito-inertial self-compression forces it into an ultra-compact femtometer cavity (R₀ ≈ 0.8 fm), whereas the electron occupies an extended picometer enclosure (R₀ ≈ 1.21 pm).Furthermore, complete three-dimensional quantization yields a parameter-free mass spectrum governed by spherical Bessel roots (xn,l/π) that accurately predicts baryonic excitations (including the spin-flip Δ(1232) and the radial breathing Roper N(1440) resonances) and resolves the Standard Model Yukawa hierarchy problem (y_f ∝ 1/R₀). Finally, the formation of the ground-state hydrogen atom is derived as a stationary cavity equilibrium: destructive field interference in the intermediate shell induces an effective metric-inertial repulsive gradient that permanently stabilizes the electron envelope at the Bohr radius (a₀ ≈ 52.9 pm), providing a deterministic alternative to classical radiation collapse and unphysical quantum jump postulates.