Simulation Controls
Random phase blobs — instant structure
Field Statistics
Complex Field Dynamics
Ψ = A·e^(iθ) — Complex wave with amplitude and phase
Phase θ — Encodes charge; gradient creates current
|Ψ|² — Energy density; creates χ depression (gravity)
How It Works
Complex Wave Field Ψ
Unlike a real scalar field, the complex field Ψ = A·e^(iθ) carries both amplitude (matter density) and phase (charge/spin).
Phase differences between regions create currents: j = Im(Ψ*∇Ψ). This enables angular momentum, charge flows, and swirling patterns that break the symmetry seen in real-field simulations.
Gravity from χ Depression
The χ field responds to matter via GOV-02: regions with high |Ψ|² cause χ to decrease. Lower χ means slower wave propagation — this IS gravity in LFM.
Matter accumulates in wells (low χ), repels from voids (high χ). The Mexican hat V(χ)=λ_H(χ²−χ₀²)² makes χ₀=19 a dynamical attractor; black hole interiors settle at −χ₀ = −19 (Z₂ second vacuum).
Simulation of LFM coupled wave equations on a 128² lattice with complex Ψ field.
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