E-QFT v5.0: Full General Relativity from Emergent Quantum Field Theory

Overview

This repository contains the complete implementation of E-QFT (Emergent Quantum Field Theory) v5.0, which demonstrates the emergence of full General Relativity from quantum projector fields. Starting from quantum information-theoretic principles, we recover:

• Causal structure: Light cones with Lieb-Robinson velocity v_LR → c
• Lorentz invariance: Systematically vanishing violations α_n ∝ a^(n-2)
• Einstein equations: Via stable BSSN evolution
• Gravitational waves: Matching numerical relativity to < 10^-14
• Matter coupling: Klein-Gordon fields and Oppenheimer-Snyder collapse

Key Results

| Test | Result | Publication Figure | |------|--------|-------------------| | Lieb-Robinson velocity | v_LR = (0.96 ± 0.01)c | Fig. 1 | | Lorentz violation | α₄ = (σa)²/12 → 0 | Fig. 2 | | BSSN constraints | ||H||₂ < 4×10⁻⁴ | Fig. 3 | | Waveform mismatch | < 10⁻¹⁴ | Fig. 4 | | OS collapse error | 9.9% → 0% as σ/a → ∞ | Fig. 6 |

Installation

Requirements

• Python 3.8+
• NumPy >= 1.20
• SciPy >= 1.7
• Matplotlib >= 3.4
• Numba >= 0.54
• h5py >= 3.0

Setup

bash git clone https://github.com/eqft-collaboration/egravity-v5.git cd egravity-v5 pip install -r requirements.txt

Quick Start

Run All Tests

bash python run_all_tests.py

This will execute all priority tests and generate: - test_summary.png - Visual test results - test_results.json - Detailed test data - PUBLICATION_CHECKLIST.txt - Publication readiness

Individual Priority Tests

```python

Priority 1: Lieb-Robinson velocity

from physics.lrmeasurementfinal import measureliebrobinsonvelocity vLR, vLRerr = measureliebrobinson_velocity(L=32, sigma=4.0)

Priority 2: Lorentz invariance

from physics.lorentzfinal import testlorentzinvariance results = testlorentz_invariance()

Priority 3: BSSN constraints

from physics.constraintdampingsimple import main main() # Runs full constraint analysis

Priority 4: Waveform validation

from physics.waveformvalidation import validatewaveforms mismatch = validate_waveforms()

Priority 5: Matter coupling

from physics.mattercouplingoptimized import testkleingordon kgpassed = testklein_gordon() ```

Repository Structure

V5.0/ ├── core/ # Core 4D implementation │ ├── projectors_4d.py # 4D covariant projectors │ ├── symplectic_4d.py # Symplectic evolution │ └── adm_evolution.py # ADM formalism ├── geometry/ # Geometric structures │ ├── dec_4d.py # Discrete exterior calculus │ └── bssn.py # BSSN evolution ├── physics/ # Physics tests & validation │ ├── lr_measurement_final.py # Priority 1 │ ├── lorentz_final.py # Priority 2 │ ├── constraint_damping_simple.py # Priority 3 │ ├── waveform_validation.py # Priority 4 │ └── matter_coupling_optimized.py # Priority 5 ├── tex/ # LaTeX publication │ └── full_gr.tex # Main manuscript └── run_all_tests.py # Master test suite

Reproducing Publication Results

Figure 1: Lieb-Robinson Light Cone

```bash python physics/generatelrplot.py

Output: lrpropagationsigma4.png

```

Figure 2: Lorentz Invariance

```bash python physics/lorentz_final.py

Output: lorentz_final.png

```

Figure 3: BSSN Constraints

```bash python physics/constraintdampingsimple.py

Output: constraint_evolution.png

```

Figure 4: Waveform Comparison

```bash python physics/waveform_validation.py

Output: waveform_comparison.png

```

Figure 5: Klein-Gordon Field

```bash python physics/mattercouplingoptimized.py testkleingordon

Output: kleingordontest.png

```

Figure 6: Oppenheimer-Snyder Collapse

```bash python physics/mattercouplingoptimized.py

Output: oscollapseoptimized.png

```

Theoretical Background

E-QFT posits that spacetime emerges from quantum projector overlaps:

g_μν(x) = Σ_αβ c_α c*_β ⟨P_α|ĝ_μν|P_β⟩ exp(-|x-x_α|²/4σ²) exp(-|x-x_β|²/4σ²)

where: - |P_α⟩ are 4D covariant projector states - σ is the projector width - c_α are quantum amplitudes

The continuum limit (a → 0, σ/a fixed) recovers exact GR.

Performance Notes

• Default lattice size: L = 32³
• Typical runtime: ~10 min for full test suite
• Memory usage: ~2 GB for L = 32³
• GPU acceleration: Planned for v6.0

Citation

If you use this code, please cite:

bibtex @article{EQFT2025, Barreiro, L. (2025). Emergent Classical General Relativity from E-QFT Quantum Projector Fields (5.0). Zenodo. https://doi.org/10.5281/zenodo.16743665 }

License

This project is licensed under GPL-3.0. See LICENSE for details.

Contact

• Corresponding Author: Lionel Barreiro (lionel.barreiro@eqft-institute.org)
• GitHub Issues: https://github.com/E-QFT-Team/E-QFT_e-gravity-v5/issues

Acknowledgments

We thank the E-QFT collaboration for valuable discussions. Computations were performed using the E-QFT v5.0 framework. This work was supported by [funding sources].

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Note: This is research code accompanying a scientific publication. While we strive for correctness, use at your own risk. Please report any issues.