Author: Dimitar Kretski 0000-0001-5108-2243
Affiliation: Center for Hydro- and Aerodynamics, Institute of Metal Science, Equipment and Technologies "Acad. A. Balevski", Bulgarian Academy of Sciences, Varna, Bulgaria
This repository contains code and analyses for the one-parameter dispersion relation ω² = c² k² (1 + Λ k²)
applied separately to a laboratory analog system, to gravitational-wave propagation, and to near-horizon photon orbits. No result here detects a non-zero Λ, and no single value of Λ is assumed to apply across these systems.
The authoritative, detailed status is paper3/PAPER3_VALIDATION_STATUS.md. Where this page and that document differ, that document is correct.
1. Giant quantum vortex (laboratory analog system). An independent reimplementation of the quasinormal-mode calculation for the superfluid-helium giant vortex of Švančara et al., using their dispersion relation and the flow parameters from their Table SI (arXiv:2308.10773), compared with the measured EXP B resonances (arXiv:2502.11209). The resonance frequencies were not fitted.
- q=1: mean relative deviation 0.021% (max 0.036%) over m = −21 … −4.
- q=2: 0.01–0.06% for m ≤ −10, growing smoothly to 1.0% at m = −4. This trend is a property of the branch, not of the numerical method.
- q=3 and q=4: no corresponding branch identified. The search is closed unless a new method or candidate appears.
- No statistical test is reported yet: measured frequency uncertainties are not available.
Details: paper3/PAPER3_ADDENDUM_BLIND_2D.md, paper3/STAGE6_5B4_3_ROOTB_FREEZE.md.
2. Gravitational-wave propagation. The propagation phase used here is identical to the LVK α=4 modified-dispersion parametrization, with Λ_GW = ħ²c³A₄. The published GWTC-4.0 bound (arXiv:2603.19020) translates to Λ_GW ∈ [−7.2×10⁻³, +2.2×10⁻³] m³/s (90%), consistent with Λ = 0. The same translation was published independently in arXiv:2607.17431. A separate analysis of GW150914 gives z = −0.43σ against an off-source null, also consistent with Λ = 0.
3. Photon sector. LHAASO observations of GRB 221009A (Yang, Bi & Yin, JCAP 04 (2024) 060, arXiv:2312.09079) constrain the quadratic (n=2) photon dispersion, which maps onto this model as Λ = −S·(ħc/E_QG,2)², with Λ > 0 superluminal. The maximum-likelihood 95% limits give Λ < 7.5×10⁻⁵⁶ m² (superluminal) and |Λ| < 2.7×10⁻⁵⁶ m² (subluminal); the weakest of the paper's three spectral models gives Λ < 2.0×10⁻⁵⁵ m². This supersedes the earlier Fermi-LAT bound (Λ < 1.44×10⁻⁵³ m²). The limits assume no intrinsic energy-dependent emission delay and vary by tens of percent with the light-curve model. The near-horizon photon-ring solver is regression-tested against Paper 2 but has not been applied to observational data.
- BEC data. Steinhauer et al. 2002 (13 measured points extracted from the vector EPS in the arXiv source,
paper3/bec_validation/steinhauer2002/): the LDA Bogoliubov spectrum needs no additional k⁴ term; the Bogoliubov k⁴ coefficient is constrained to −3% ≲ g_extra ≲ +6% (95%). This tests Bogoliubov theory in this condensate, not the Λ-model: the BEC quartic term ξ²/4 is standard quantum pressure. Ozeri et al. 2002 (digitized, N = 3–4 points) is consistent but too small to be a confirmation. A cavity-QED control dataset (Guo et al. 2021) gives a clean null. - Path-dependence test for GW events: not feasible with current sky localisations (reliability 0 on all three axes, 174 events). Closed before any anomaly statistic was computed.
- Dirac-material mapping: not supported by the cited literature.
- Photonic and fiber mappings: not connected to any measured quantity. The fiber module (
paper3/dispersion/) currently runs only on synthetic demonstration arrays (omega ~ k^4 plus noise), so it produces no physical result.
- The three systems above use separate parameters. The relation Λ_NH = Λ_GW/c is a dimensional observation, not a derivation, and the laboratory coefficients are properties of those media.
- The laboratory results test the numerical methods against real spectra. They are not tests of gravitational dispersion, and no mapping from the vortex to a Kerr black hole has been derived.
These checks confirm that the code is correct. They are not physical results.
- Spectral PDE solver: exact in space; O(1/N) in time; second-order spatial convergence of the full leapfrog integration for N = 64–128 (N < 64 unreliable).
- Recovery of a known Λ from synthetic data and a Λ = 0 control:
paper3/dispersion/tests/. - GW matched-filter pipeline: injection/recovery and off-source null tests on real LIGO noise (
paper3/gw/matched_filter/). - QNM roots: reproduced by an experiment-blind 2D search and by an independent Newton solver (14/14; same physical residual function).
All current code uses ω² = c²k²(1 + Λk²). Some older files (paper3/STATUS.md, paper3/dispersion/README.md, fiber_event_horizon_structural_test.py, gwosc_zero_crossing_injection_recovery.py) write 1 + 2Λk², which defines a Λ smaller by a factor of 2. For BEC, Λ = ħ²/(4m²c_s²), which equals ξ²/4 for ξ = ħ/(m c_s).
| Topic | Location |
|---|---|
| Status and claim boundaries | paper3/PAPER3_VALIDATION_STATUS.md |
| Giant-vortex QNM code | paper3/gw/matched_filter/_archive/qnm_branch_work/ |
| GW analyses | paper3/gw/matched_filter/ |
| GW path-dependence test | paper3/gw/path_test/ |
| BEC checks | paper3/bec_validation/ |
| Fitting tool for your own (k, ω) data | paper3/lambda_experimental_validator.py |
| Solver and convergence tests | paper3/wave_equation_2D_solver.py, paper3/paper3_h_convergence_test.py |
| Earlier full draft (August 2026) | paper3/paper3_final.tex |
Quick start:
pip install -r requirements.txt
python paper3/lambda_experimental_validator.py --omega data_omega.csv --k data_k.csv
python paper3/gw/matched_filter/convention_check.py
fits a single Λ with no medium-specific baseline; for real media use a residual test against the known dispersion, as in bec_validation/steinhauer2002/Further commands are listed in each subdirectory.
- Kretski, D. (2026). A Hamiltonian Oscillator Extension of Wave Propagation in Schwarzschild Spacetime. Zenodo preprint. https://doi.org/10.5281/zenodo.22018715
- Kretski, D. (2026). A Hamiltonian Dispersion Framework for Kerr Photon Rings, Frequency-Dependent Shadow Sensitivity, Superradiance, and Eikonal Quasinormal Modes. Zenodo. https://doi.org/10.5281/zenodo.22051427
- Kretski, D. (2026). [FULL TITLE]. Submitted to Physical Review D.
Please also cite the work this repository depends on:
- Smaniotto, F., Solidoro, V., Patrick, R., Švančara, P. et al. Black-hole spectroscopy from a giant quantum vortex. arXiv:2502.11209. Resonance data kindly provided by P. Švančara (CNRS Institut Néel).
- Švančara, P. et al. Rotating curved spacetime signatures from a giant quantum vortex. arXiv:2308.10773.
- Abac, A. G. et al. (LVK) (2026). GWTC-4.0: Tests of General Relativity. II. Parameterized Tests. arXiv:2603.19020.
- Araújo Filho, A. A. et al. (2026). Gravitational wave propagation in Hořava–Lifshitz gravity. arXiv:2607.17431.
- Mirshekari, S., Yunes, N. & Will, C. M. (2012). Phys. Rev. D 85, 024041.
- Steinhauer, J., Ozeri, R., Katz, N. & Davidson, N. (2002). Phys. Rev. Lett. 88, 120407. arXiv:cond-mat/0111438.
- Ozeri, R. et al. (2002). Phys. Rev. Lett. 88, 220401.
- Guo, Y. et al. (2021). Nature 599, 211. Data: Harvard Dataverse, DOI:10.7910/DVN/LGT5O6.
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