Pushing‑Medium Gravity

Concise implementation of a refractive‑index + flow ("pushing‑medium") gravitational analogue together with a weak‑field General Relativity (GR) baseline and a reproducible testbench. The focus is parity with classical weak‑field observables (deflection, time delay, perihelion precession, frame‑drag, lensing scale, GW power) and incremental tooling for ray tracing and parameter extraction.

Repository Overview

src/
  pushing_medium/         # Medium index/flow, ray & deflection helpers, calibration hooks
  general_relativity/     # Weak-field GR comparison formulae
tests/                    # pytest suite (calibration, parity, convergence, PPN, strong-field trends)
docs/                     # LaTeX + Markdown technical notes
programs/demos/           # Example scripts (lensing, plasma index, skeleton flows, BNN demo)

Primary documentation sources: docs/markdown/ (readable) and docs/latex/ (original formula sheets).

Installation

Core (analysis/tests):

pip install -r requirements.txt  # if present, otherwise install numpy scipy matplotlib pytest

BNN demo (optional):

pip install torch torchvision torchaudio --index-url https://download.pytorch.org/whl/cpu

Testing

The repository includes a comprehensive test suite with 59 tests covering all aspects of the gravitational model:

# Run all tests (recommended)
pytest tests -v

# Quick test run  
pytest tests -q

# Run specific test categories
pytest tests/test_passed_benchmarks.py -v    # Core GR comparison tests
pytest tests/test_galaxy_rotation.py -v     # Galaxy dynamics tests

# Generate detailed test report
python test_results_table.py
pytest -q

Minimal BNN run:

HEADLESS=1 EPOCHS=1 NUM_WORKERS=0 python programs/demos/BNN/pmflow_bnn_always_plastic.py

Current Status: ✅ All 59 tests pass (100% success rate)

For detailed testing documentation, see TESTING.md.

Core Physical Model (outline)

1. Refractive index field: (n(\mathbf{r}) = 1 + \sum_i \mu_i/|\mathbf{r}-\mathbf{r}_i|) or continuous integral analogue.
2. Optional flow (\mathbf{u}_g) (rotational + translational placeholders) for frame‑drag analogues.
3. Light propagation: small‑angle Fermat updates using (\partial_x \ln n) integrals (several numeric variants).
4. Massive particle analogue: acceleration term (-c^2 \nabla \ln n) plus Newtonian superposition.

Packages & Calibration

pushing_medium (index, flows, deflection, iterative & moving‑lens integrators, Plummer helpers, effective metric, PPN estimates)

general_relativity (deflection, Shapiro delay, perihelion precession, frame‑drag, Einstein radius, GW speed/power, orbit energy)

Calibration (cached at tests/calibration.json):

• mu_coeff: fitted numeric deflection → analytic match (target 4GM/(c^2 b)).
• k_TT: quadrupole power normalization (≈1).
• k_Fizeau: provisional; presently near unity heuristic, numeric moving‑lens indicates negligible first‑order term.

Ray Bending Implementations

• Straight-line integral: index_deflection_numeric
• Fermat wrapper: fermat_deflection_static_index
• First-order moving lens: moving_lens_deflection_first_order
• Numeric moving lens (time-shifted lens): moving_lens_deflection_numeric
• Curved-path iterative refinement: curved_path_deflection_iterative

Limitations: small-angle assumption; near-critical (few R_s) behavior approximate; moving-lens path currently straight or first-order corrected only.

Galaxy Dynamics (Rotation Curves)

Module galaxy_dynamics.rotation provides utilities for preliminary disk + medium modified rotation curve modeling:

• Exponential disk mass interior: (M(<r)=M_d[1-(1+r/R_d)e^{-r/R_d}])
• Baryonic acceleration: (a_{bar}=G M(<r)/r^2)
• Phenomenological medium perturbation: (\delta n_{PM}= - (v_\infty^2/c^2) \ln(1+r/r_s) S(r)) with smoothing (S(r)=[1+(r_c/r)^m]^{-1/m})
• Medium acceleration (small perturbation): (a_{med}= -c^2,d\delta n_{PM}/dr) (sign chosen so outer contribution supports flattening)
• Circular speed: (v_c(r)=\sqrt{r(a_{bar}+a_{med})})

Example:

from galaxy_dynamics.rotation import DiskParams, MediumParams, rotation_curve
disk = DiskParams(M_d=5e40, R_d=5e19)
medium = MediumParams(v_inf=2.2e5, r_s=5e19, r_c=1e19, m=2.0)
radii = [1e19, 5e19, 1e20]
vc = rotation_curve(radii, disk, medium)

Tests cover mass convergence, acceleration signs, and approximate outer flattening behavior. SPARC ingestion and fitting pipeline are planned next.

Test Coverage (pytest)

• GR parity: deflection, Shapiro delay, redshift (potential), perihelion, frame-drag, Einstein radius, GW speed/power, orbit energy.
• Calibration: μ, k_TT, k_Fizeau presence.
• Convergence: step & domain extent (z_max) refinement.
• Moving lens: ratio consistency (first-order vs numeric).
• Iterative vs straight-line: accuracy sanity at moderate b.
• Strong-field trend: qualitative scaling (documentation only).
• PPN extraction: gamma, beta ≈ 1; metric signature checks.

Roadmap (short)

• Adaptive ray integration (near closest approach refinement)
• Path-corrected moving-lens calibration (refined k_Fizeau)
• Comprehensive error tables & benchmarking harness
• Effective metric higher-order terms (β beyond leading) & parameter scanning
• Wave / dispersion prototype (TT perturbations)

Effective Metric & PPN

Heuristic mapping: (g_{tt}\approx -1/n^2), (g_{rr}\approx n^2). Expansion for (n=1+\epsilon) gives matching leading coefficients ⇒ (\gamma\approx1). No non-linear term modeled ⇒ (\beta\approx1). Tests verify gamma, beta, and metric signature; higher-order refinement is future work.

Troubleshooting (selected)

• Headless plotting: set HEADLESS=1 (images saved to PNGs).
• Dataset issues: set DATA_DIR to a writable path.
• Slow BNN run: start with EPOCHS=1 and NUM_WORKERS=0.

License

Unrestricted use / public domain style (see repository for any clarifications).