This repository houses two distinct, high-performance physics simulations related to advanced propulsion concepts:
- Toroidal PIC Simulation: A Particle-in-Cell simulation of Xe⁺ ions in a toroidal magnetic field.
- Warp Drive QI Audit: A numerical evaluation of the physical feasibility of Alcubierre, White-Natário, Rodal (2025), and Fuchs (2024) warp metrics against the Ford–Roman quantum inequality.
Warning
Lentz (2021) is NOT included in this audit. The Lentz metric requires a full Einstein–Maxwell–plasma coupling to achieve T₀₀ ≥ 0. The simple sign-flip of the Alcubierre ADM Hamiltonian formula is physically invalid and has been removed. See Lentz (2021) §IV and Bobrick & Martire (2021) for context.
Warning
EXPERIMENTAL — not yet peer-validated, use results with caution. This simulation code is currently unvalidated and should not be treated with the same confidence as the Zenodo-cited QI Audit below.
toroidal_pic.py is a self-contained, experimental Particle-in-Cell (PIC) simulation of 100,000 Xe⁺ ions confined in a toroidal magnetic field (2.6 T peak, major radius 3 m, minor radius 0.5 m).
| Component | Method |
|---|---|
| Particle integrator | Boris pusher + leapfrog (3-D Cartesian) |
| Magnetic field | Toroidal B = B₀(R₀/R) φ̂ + Bz ẑ (1/R decay + vertical) |
| Electric field | Self-consistent via 2-D (R,Z) Poisson solve |
| Poisson solver | DST (Type-I) in Z + tridiagonal (Thomas) in R |
| Charge deposition | Area-weighted (CIC) on cylindrical grid |
| Boundaries | Conducting walls; particles absorbed on contact |
- Kinetic energy vs. time
- Cyclotron resonance peak (FFT of total axial current)
- Density maps (R, Z) saved as PNG every 1 µs
python toroidal_pic.pyAll configuration lives in the CFG dictionary at the top of the script. All output goes to the pic_output/ directory.
An open-source quantum-inequality audit of Alcubierre, White-Natário, Rodal (2025), and Fuchs (2024) warp metrics evaluating their physical feasibility using the Ford-Roman Quantum Inequality (QI) bound and the ADM Hamiltonian constraint for extrinsic curvature.
| Metric | Energy type | Key result |
|---|---|---|
| Alcubierre (1994) | Negative (exotic) | Exceeds QI by ~68–69 orders of magnitude |
| White-Natário | Negative (exotic) | Peak reduced 70%, total comparable to Alcubierre |
| Rodal (2025)† | Predominantly positive, net ≈ 0 | Peak deficit reduced ~38× vs. Alcubierre; global Type I; QI exceeded by ~10⁶³ |
| Fuchs (2024)* | Positive only (shell) | Zero negative energy – passes QI audit trivially. Requires ~1.8 M☉ of positive-energy shell. Subluminal only. |
* Fuchs is subluminal; QI gap is trivial because no negative energy is present.
† Rodal QI gap computed using the actual diffuse negative-energy volume V₋ (numerically integrated).
Important
Precise conclusion: None of the audited superluminal warp metrics satisfy the Ford–Roman quantum inequality bound. This tool has not yet evaluated all known solutions; notably, the Bobrick–Martire class of "positive-energy warp drives" has not been audited.
Bottom line: No known warp metric is physically feasible within current physics. This repository makes the math explicit and reproducible.
The Rodal (2025) irrotational warp drive [arXiv:2512.18008] is the first fully explicit, continuous, analytically derived solution with vanishing spatial vorticity. Our implementation reproduces its published canonical results. Despite classical improvements, the QI bound is still exceeded by a factor ~10⁶³.
The Fuchs (2024) constant-velocity subluminal warp drive [Class. Quantum Grav. 41 (2024) 095013] is the only known metric that completely avoids negative energy, satisfying all classical energy conditions. Our independent audit (powered by warpax) confirms this across the full subluminal parameter space.
Run the full QI audit with the command-line interface:
python testfisico.py --delta 0.2614 --radius 3.0 --velocity_c 1.1 --mass_ship 100000This produces:
- Console output: QI bound, gap analysis, hypothetical Δ, subluminal comparison
qi_vs_Delta.png/.pdf— QI energy vs wall thicknessqi_vs_Radius.png/.pdf— QI energy vs bubble radiusqi_vs_Radius_with_SHIP.png/.pdf— QI limit vs ship requirementenergy_vs_velocity.png/.pdf— Required energy vs ship speedmetric_comparison.png/.pdf— Four-panel metric comparisonrodal_energy_map.png/.pdf— 2-D polar map of Rodal proper energy density
from metric_explorer import run_metric_comparison
run_metric_comparison(
v_s = 1.1 * 2.99792458e8, # 1.1c in m/s
R = 3.0, # bubble radius [m]
Delta = 0.2614, # wall thickness [m]
include_rodal=True
)python convergence_fuchs.py # prove E_minus = 0 is converged
python sweep_fuchs.py # generate fuchs_phase_space.png
python warpax_qi_audit.py # single-point auditpytest tests/- Lentz Metric: Not evaluated. Lentz (2021) requires a full Einstein–Maxwell–plasma coupling to achieve T₀₀ ≥ 0 everywhere. The sign-flip of the Alcubierre ADM formula is physically invalid and has been removed from this codebase. Future work would need to implement the full Lentz stress-energy tensor.
- Bobrick–Martire class: Not yet audited. These solutions may have different energy properties and are a target for future work.
- Rodal Metric: The proper energy density is computed from the spatial Hessian of the scalar potential Φ(r,θ). The QI gap for Rodal uses the actual diffuse negative-energy volume V₋ rather than a thin-shell model.
- Alcubierre & White-Natário: The QI volume now uses the numerically integrated negative-energy volume V_minus = ∫_{ρ<0} 4π r² dr, replacing the thin-shell approximation 4πR²Δ previously used.
- Fuchs Metric: Results obtained via warpax (MIT-licensed). The audit confirms zero negative energy for the canonical subluminal parameters.
- QI Bound: The QI bound applied here is the Ford-Roman (1995) flat-spacetime result; curved-spacetime corrections exist but do not change the order-of-magnitude gap.
- E_req_total: The total energy requirement is now the numerically integrated ADM result for the Alcubierre metric, not a dimensional estimate.
A requirements.txt is provided with pinned versions for scientific reproducibility:
git clone https://github.com/mabgresearch/warp-qi-audit.git
cd warp-qi-audit
pip install -r requirements.txt(Note: Numba is optional but strongly recommended for the Toroidal PIC Simulation performance.)
MIT — see LICENSE.
Contributions, issues, and pull requests welcome.