Complete Electromagnetism from Lattice Field Medium: Electric Force from Phase, Magnetic Force from Momentum Density

This paper demonstrates that complete electromagnetism—both electric and magnetic phenomena—emerges from the fundamental Lattice Field Medium (LFM) governing equations GOV-01 and GOV-02, without any external physics injected. Electric Force (Review):Electric charge is identified with wave function phase (θ = 0 for negative, θ = π for positive). The Coulomb force emerges from phase interference: same-phase charges experience constructive interference (higher energy → repulsion), while opposite-phase charges experience destructive interference (lower energy → attraction). Magnetic Force (New):The magnetic force emerges from the momentum density term j = Im(Ψ*∇Ψ) in GOV-02. Moving charges create anisotropic χ perturbations, with B ∝ curl(j). A second moving charge experiences perpendicular forces through this anisotropic field, yielding the complete Lorentz force F = q(E + v × B). Key Results: All four Maxwell equations map to LFM mechanisms Helicity coupling ε_W = 2/(χ₀+1) = 0.1 controls magnetic strength The j term serves dual roles: magnetism AND weak force parity violation Numerical experiments confirm velocity-dependent perpendicular forces LFM-Maxwell Correspondence: Maxwell Equation LFM Mechanism ∇·E = ρ/ε₀ χ sourced by |Ψ|² (GOV-02 energy term) ∇×B = μ₀j χ anisotropy from momentum density j ∇×E = -∂B/∂t GOV-01/02 coupled wave dynamics ∇·B = 0 Topological (curl has zero divergence) This completes the electromagnetic sector of LFM's four-force unification, with gravity, strong force, weak force, electric force, and magnetic force all emerging from GOV-01 + GOV-02. New Equations Documented: CALC-29: Magnetic field from current density CALC-30: Complete Lorentz force emergence Keywords: electromagnetism, magnetic field, Lorentz force, Maxwell equations, lattice field medium, LFM, phase interference, momentum density, probability current, emergent forces, unification, GOV-01, GOV-02 Related Papers: LFM-PAPER-045: Canonical Governing Equations (v9.2) LFM-PAPER-046: Fundamental Constants from χ₀ = 19 LFM-PAPER-061: Definitive Formula Catalog LFM-PAPER-065: Electric Force from Phase Interference LFM-PAPER-066: Nuclear Forces (Strong/Weak)