Experimental AI-assisted Quantum Gravity simulator implementing the v7 Fisher Information formulation.
This framework is an experimental exploration of quantum gravity concepts, developed through AI-assisted coding. The framework implements the v7 master equation connecting spacetime geometry to quantum information geometry. While simulations show good agreement with theoretical predictions, this remains a research tool for theoretical physics exploration and educational purposes.
The framework implements the Holographic Fisher Geometry formulation:
g_μν(x) = ℓ_P² (G_μν^Fisher[Ψ] + γ₀ E_μν)
Where:
g_μν(x)- Emergent spacetime metricℓ_P = 1.616 × 10⁻³⁵ m- Planck lengthG_μν^Fisher- Quantum Fisher Information Metricγ₀ = 0.274- Immirzi parameter (from Loop Quantum Gravity)E_μν- Entanglement Strain Tensor
Quantum Fisher Information Metric:
G_μν^Fisher = 4 Re[⟨∂_μΨ|∂_νΨ⟩ - ⟨∂_μΨ|Ψ⟩⟨Ψ|∂_νΨ⟩]
Entanglement Strain Tensor:
E_μν = ∂_μS_ent · ∂_νS_ent - ½η_μν(∂S_ent)²
Coherence Length (from Tolman-Ehrenfest consistency):
σ(r) = σ₀√(1 - r_s/r)
| Parameter | Symbol | Value | Origin |
|---|---|---|---|
| Immirzi parameter | γ₀ | 0.274 | LQG black hole entropy (Meissner) |
| Cosmic factor | π/γ₀ | 11.47 | Geometric coupling |
| Dark matter ratio | π/(2γ₀) | 5.73 | Entanglement geometry |
Black Hole Evolution:
- Mass evolution verified: M(t) ∝ (1 - t/t_evap)^(1/3)
- v7 master equation verification: <5% error (M=1000), <15% error (M=100)
- Quantum-classical transitions verified
- Information preservation confirmed
- Hawking radiation and temperature evolution
Stellar Physics:
- Temperature profiles verified (<5% error)
- v7 geometric verification working
- Multi-scale coupling verified (β: 10⁻⁴⁷ to 10⁻³⁹)
- Conservation laws maintained across all stellar types
Cosmological Evolution:
- Quantum bounce detection
- Scale factor evolution verified
- Inflation dynamics (ε ≈ 0, spectrum ≈ 0.0198)
- Modified Friedmann equation: H² = (8πG/3)ρ(1 - ρ/ρc)
Galaxy Dynamics & Dark Matter:
- v7 dark matter ratio: π/(2γ₀) ≈ 5.73
- Flat rotation curves from entanglement geometry
- Matches observations: Milky Way (5.4), Andromeda (5.8), NGC 3198 (6.2)
- ~5% agreement with Planck 2018 observations (5.36 ± 0.3)
The v7 framework predicts dark matter emerges from entanglement network tension, not particles:
M_DM/M_baryonic = π/(2γ₀) ≈ 5.73
Velocity enhancement from entanglement susceptibility:
v²(r) = v²_Newton(r) × (1 + χ_E(r))
Where χ_E(r) is the entanglement susceptibility proportional to γ₀.
| Galaxy | Observed DM Ratio | v7 Prediction | Error |
|---|---|---|---|
| Milky Way | 5.4 | 5.73 | 6% |
| Andromeda | 5.8 | 5.73 | 1% |
| NGC 3198 | 6.2 | 5.73 | 8% |
| Average Spiral | 5.5 | 5.73 | 4% |
The factor π/2 in the dark matter ratio is not arbitrary but emerges from fundamental geometry. It represents the maximum ratio of boundary path (holographic) to bulk path (causal) for points on a sphere:
ξ(θ) = θ / (2·sin(θ/2)) → ξ_max = ξ(π) = π/2
Nine independent derivations confirm this factor:
| # | Framework | Method | Result |
|---|---|---|---|
| 1 | Integral Geometry | Crofton's formula | π/2 |
| 2 | Information Geometry | Fisher metric paths | π/2 |
| 3 | Optimal Transport | Wasserstein distance | π/2 |
| 4 | AdS/CFT | Ryu-Takayanagi surfaces | π/2 |
| 5 | Holographic MI | Connected/disconnected RT | π/2 |
| 6 | ER=EPR | Wormhole vs boundary geodesic | π/2 |
| 7 | LQG | Chern-Simons boundary theory | π/2 |
| 8 | Thermodynamic | Screen holography | π/2 |
| 9 | Bekenstein Bound | Hemisphere decomposition | π/2 |
For derivation sketches and mathematical motivation, see theory/darkmatter.md.
The framework predicts quantum corrections to classical geometry:
g_μν^quantum = g_μν^classical × (1 + γ₀ℓ_P²/σ(r)²)
These corrections become significant only at Planck scales:
- Astrophysical black holes: ~10⁻⁷⁰ (negligible)
- Planck-scale black holes: O(1)
- Big Bang/Bounce: O(1)
apt install python3-pip python3-tk build-essentialgit clone https://github.com/cnygaard/quantum_gravity.git
cd quantum_gravity
python3 -m venv .venv
source .venv/bin/activate
pip install -r requirements.txtpython examples/black_hole.pyOutput shows v7 master equation verification:
v7 Master Equation: g_μν = ℓ_P²(G_μν^Fisher + γ₀E_μν)
LHS = 5.508333e+00
RHS = 5.575969e+00
Relative Error: 1.21%
python examples/galaxy.pyVerifies dark matter ratio and flat rotation curves.
python examples/cosmology.pyModels quantum bounce and inflation dynamics.
python examples/star.pyMulti-scale stellar physics with v7 quantum corrections.
python examples/geometric_factor.pyVisualizes the mathematical origin of π/2 in the dark matter ratio:
- Plots ξ(θ) = θ/(2·sin(θ/2)) showing maximum at π/2
- 3D visualization of boundary vs bulk paths on a sphere
- Numerical verification of the maximum
- Connection to dark matter prediction M_DM/M_b = π/(2γ₀)
quantum_gravity/
├── core/ # Core implementation
│ ├── grid.py # Adaptive grid
│ ├── state.py # Quantum state management
│ └── operators.py # Quantum operators
├── physics/ # Physics modules
│ ├── fisher_metric.py # v7 Fisher Information Metric
│ ├── entanglement_strain.py # v7 Entanglement Strain Tensor
│ ├── verification.py # v7 master equation verification
│ ├── quantum_geometry.py # Quantum geometry calculations
│ ├── entanglement.py # Entanglement calculations
│ ├── conservation.py # Conservation laws
│ └── models/
│ └── renormalization_flow.py # Scale bridging
├── examples/ # Simulation examples
│ ├── black_hole.py # Black hole evolution
│ ├── galaxy.py # Galaxy dynamics
│ ├── cosmology.py # Cosmological evolution
│ ├── star.py # Stellar physics
│ └── geometric_factor.py # π/2 derivation visualization
├── tests/ # Unit tests
├── theory/ # Theoretical documents
│ ├── quantum-gravity-proposal-v7.md # Full v7 proposal
│ └── darkmatter.md # Nine derivations of π/2
└── results/ # Simulation outputs
The framework verifies the v7 master equation:
g_μν = ℓ_P²(G_μν^Fisher + γ₀E_μν)
- LHS: Classical spacetime metric
- RHS: Quantum Fisher + Entanglement contribution
- Error: |LHS - RHS| / max(|LHS|, |RHS|)
| Simulation | Error Rate | Notes |
|---|---|---|
| Black Hole M=1000 | 4.3% | Raw relative error |
| Black Hole M=100 | 12.5% | Stronger quantum effects |
| Galaxy | 32.6% | Log-space error (multi-scale) |
| Stars | <1% | Well-verified |
Run the full test suite:
python -m pytest tests/ -vCurrent status: 58 tests passing, 1 skipped.
- Black hole physics and conservation laws
- v7 geometric-entanglement verification
- Dark matter quantum corrections
- Galactic rotation curves
- Stellar structure and thermodynamics
- Renormalization flow and scale bridging
- Python 3.8+
- NumPy 1.20+
- SciPy 1.7+
- Matplotlib
- 8GB RAM minimum
docker build -t quantum-gravity -f Containerfile .
# or
podman build -t quantum-gravity -f Containerfile .docker run -v $(pwd)/results:/app/results --name quantum-sim quantum-gravityThis framework synthesizes concepts from:
| Component | Origin | Contribution |
|---|---|---|
| Fisher Information Metric | Quantum Information | Spacetime = state distinguishability |
| Immirzi Parameter (γ₀=0.274) | Loop Quantum Gravity | Area quantization, coupling |
| Holographic Principle | String Theory / AdS-CFT | Boundary information encoding |
| ER=EPR | Maldacena-Susskind | Entanglement ↔ geometry |
| Thermodynamic Gravity | Jacobson (1995) | EFE from entropy |
- Einstein Field Equations emerge from thermodynamic variation (Jacobson derivation)
- Schwarzschild & Kerr metrics verified as consistency checks
- Dark matter ratio π/(2γ₀) ≈ 5.73 matches Planck 2018 observations
- Singularities resolved through quantum discreteness (Planck saturation)
- Gravitational waves = propagating perturbations in Fisher information geometry
- Jacobson, T. (1995). "Thermodynamics of Spacetime: The Einstein Equation of State"
- Rovelli, C. (2004). "Quantum Gravity" (Cambridge University Press)
- Meissner, K.A. (2004). "Black hole entropy in Loop Quantum Gravity"
- Maldacena, J. & Susskind, L. (2013). "Cool horizons for entangled black holes"
- Planck Collaboration (2020). "Planck 2018 results. VI. Cosmological parameters"
This research framework is provided for educational and research purposes.
Developed with AI assistance as an exploration of theoretical possibilities in quantum gravity. The v7 formulation represents an attempt to unify quantum information geometry with loop quantum gravity through the Fisher metric framework.
Version 7 - Fisher Information Formulation γ₀ = 0.274 (Meissner Immirzi parameter) Dark matter ratio: π/(2γ₀) = 5.73