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:

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)