Demonstrating that gravitational lensing emerges from first principles in the Lattice Field Medium framework using proper substrate dynamics.
LFM is a substrate theory. Everything IS the substrate—you don't put things "on top of" it. Light in LFM is not something that propagates through the substrate; light IS the substrate oscillating.
This experiment demonstrates gravitational lensing using the full coupled dynamics where both E and χ evolve together, and radiation emerges naturally from oscillating matter.
GOV-01 (E wave): ∂²E/∂t² = c²∇²E − χ²E
GOV-02 (χ wave): ∂²χ/∂t² = c²∇²χ − κ(E² − E₀²)
- E: Wave amplitude (energy density) at each lattice point
- χ (chi): Local substrate property—evolves dynamically, not static!
- κ: Coupling constant between E² and χ dynamics
- Create "matter": Bound E-structures (like atoms) on the lattice
- Create a "star": Massive E-structure that creates a χ-well via GOV-02
- Excite the atom: Kick the electron so it oscillates → naturally radiates
- Radiation propagates: The substrate oscillations spread outward
- Measure lensing: Does radiation bend toward the star?
- Radiation from oscillating matter bends toward massive objects
- Lensing ratio: 15× more radiation toward star than away
- χ-well depth: 90% reduction at star center
For frequencies above the mass gap (ω ≥ χ₀):
| ω/χ₀ | Lensing Ratio |
|---|---|
| 1.0 | 3438 |
| 2.0 | 3339 |
| 4.0 | 3253 |
Coefficient of variation: 2.3% — lensing is essentially achromatic!
Power law slope: -0.04 (flat)
For real photons where ω/χ₀ ~ 10¹⁵, any dispersion is unmeasurably small.
# Clone the repo
git clone https://github.com/gpartin/lensingexperiment.git
cd lensingexperiment
# Install dependencies
pip install numpy matplotlib
# Run the main lensing experiment
python lfm_substrate_lensing.py
# Run frequency dependence test
python lfm_substrate_frequency_scan.py| File | Description |
|---|---|
lfm_substrate_lensing.py |
Main experiment: star + radiating atom, measures lensing |
lfm_substrate_frequency_scan.py |
Frequency test: confirms achromatic lensing |
figures/ |
Output figures from experiments |
REDDIT_RESPONSE.md |
Response to Klein-Gordon dispersion critique |
dev/ |
Development/auxiliary scripts (not needed to run main experiments) |
✅ Gravitational lensing emerges from coupled GOV-01 + GOV-02 dynamics
✅ No static fields — both E and χ evolve dynamically
✅ Light is substrate oscillations — radiation emerges naturally from matter
✅ Achromatic for ω >> χ₀ — only 2.3% variation over 4× frequency range
✅ Fully reproducible — run the code yourself
Previous tests were flawed: we computed a static χ field and injected artificial "test waves" to see how they bent. This is wrong for a substrate theory.
Correct approach: Let the full coupled system evolve. Matter (bound E-structures) oscillates and naturally radiates. The radiation IS the substrate oscillating. No separation between "light" and "medium."
When done correctly, lensing emerges and chromatic dispersion becomes negligible.
This experiment addresses concerns about Klein-Gordon dispersion:
"The dispersion relation ω² = c²k² + χ² implies frequency-dependent behavior..."
The key insight: this concern applies when testing a frozen background with artificial waves. In true substrate dynamics with coupled E-χ evolution, the physics is different—and achromatic lensing emerges naturally for high-frequency radiation.
See REDDIT_RESPONSE.md for the full discussion.
MIT License
- Repository: https://github.com/gpartin/lensingexperiment
- LFM Paper Series: https://github.com/gpartin/Papers