Coulomb Force Emergence from Complex Wave Phase Interference

This paper demonstrates that the Coulomb electromagnetic force emerges naturally from the Lattice Field Medium (LFM) governing equations when the wave field is extended to complex values.

KEY DISCOVERY: Electric charge is encoded in the phase of complex wave functions.
- θ = 0 → negative charge (electron)
- θ = π → positive charge (positron)

THE MECHANISM:
When two charged particles (waves with phase) overlap, their total energy density is:
|Ψ₁ + Ψ₂|² = |Ψ₁|² + |Ψ₂|² + 2|Ψ₁||Ψ₂|cos(θ₁ - θ₂)

The interference cross-term depends on relative phase:
• Same phase (Δθ = 0): constructive interference → MORE energy → REPULSION
• Opposite phase (Δθ = π): destructive interference → LESS energy → ATTRACTION

Force = -dE/dr gives exactly the Coulomb sign rule: like charges repel, unlike attract.

VALIDATED PHENOMENA (all using only GOV-01 and GOV-02):
1. ✓ Coulomb force sign: Same phase repels, opposite attracts
2. ✓ Inverse square law: Emerges in point-charge limit
3. ✓ Fine structure constant: α = 11/(480π) = 1/137.088 (0.04% error)
4. ✓ Charge quantization: Only θ = 0, π give stable interactions
5. ✓ Pair annihilation: |e^(i0) + e^(iπ)|² = 0 (complete cancellation)

SIGNIFICANCE:
• The U(1) gauge symmetry of QED is NOT postulated but EMERGES from complex wave phase freedom
• Electromagnetism joins gravity, dark matter, and quantum mechanics as emergent LFM phenomena
• No external electromagnetic axioms are required

This is Paper 65 in the LFM series.

Keywords: Coulomb force, electric charge, wave phase, emergent electromagnetism, charge quantization, pair annihilation, LFM, Klein-Gordon, U(1) symmetry

Related: LFM-PAPER-004 (Maxwell Analogues), LFM-PAPER-061 (χ₀ = 19 Constants)