POLITE · Literature review
Every constraint relevant to optical Lorentz-invariance violation, vacuum dispersion, and birefringence — with its method, band, parametrization, assumptions, systematics, and the bound as reported.
1 of 9 rows has been checked against the original source and is marked verified. The rest are transcribed from the comparison table of the timing paper and are marked pending until independently checked. A review that claims to be source-verified has to show which rows are not yet.
| Source | Probe | Band | Parametrization | Reported constraint | Status |
|---|---|---|---|---|---|
| Keating (2026), this work
Assumptions. Quadratic limb-darkening law with Claret & Bloemen (2011) coefficients; Gaussian errors; simultaneous emission across bands at the stellar surface. Systematics. Limb-darkening model uncertainty dominates (1.37% of variance); distance uncertainty 0.55%; atmospheric DCR < 0.1%. Total systematic 2.0%.
|
Eclipsing binary timing | Optical, 440–800 nm | Model-independent Δc/c | |Δc/c| < 3.75 × 10-10 (95% CL, FC) | ✓ verified |
| Vasileiou et al. (2013)
Assumptions. Power-law dispersion relation; intrinsic source-frame emission lags negligible or bounded. Systematics. Intrinsic spectral lag at the source is the dominant and hardest-to-bound term.
|
GRB time-of-flight | GeV γ-ray, ~0.1–30 GeV | En LIV, n = 1 | |Δc/c| ≲ 10-20; ELIV > 7.6 EPlanck | ○ pending |
| Abdo et al. (2009)
Assumptions. Photon emission time bounded by the observed trigger; z ≈ 0.9. Systematics. Entirely dominated by the emission-time assumption for one photon.
|
Single-photon GRB limit | 31 GeV γ-ray | En LIV, n = 1 | |Δc/c| ≲ 2 × 10-18 | ○ pending |
| Schaefer (1999)
Assumptions. Observed lags attributed to propagation rather than emission physics. Systematics. Intrinsic lag degeneracy.
|
GRB spectral lag | MeV–GeV γ-ray | En LIV, n = 1 | |Δc/c| ≲ 10-17 | ○ pending |
| Ellis et al. (2006)
Assumptions. Population-level cancellation of intrinsic lags. Systematics. Source-population heterogeneity.
|
GRB time lags | MeV–GeV γ-ray | En LIV, n = 1 | |Δc/c| ≲ 10-17 | ○ pending |
| Wei et al. (2015)
Assumptions. Plasma contribution modelled and removed; dominant delay is astrophysical dispersion, not LIV. Systematics. Dispersion-measure modelling dominates and is itself the signal of interest for plasma studies.
|
Fast radio burst dispersion | Radio, ~1 GHz | Photon mass / LIV parameters | Photon-mass and LIV parameter bounds | ○ pending |
| Warner & Nather (1969)
Assumptions. Simultaneous emission of optical and radio pulse components. Systematics. Emission-mechanism differences between the optical and radio bands.
|
Crab pulsar arrival times | Optical–radio, 0.54 µm to 1.2 m | Model-independent Δc/c | |Δc/c| < 4 × 10-7 | ○ pending |
| Brecher (1977)
Assumptions. Keplerian orbital solution for the binary. Systematics. Orbital element uncertainties.
|
X-ray binary timing | X-ray | Source-velocity dependence (Ritz) | Δc/c < 2 × 10-9 | ○ pending |
| de Sitter (1913)
Assumptions. Binary orbits Keplerian; observed distortions attributable to emission theory. Systematics. Historical photographic astrometry limits.
|
Spectroscopic binary orbits | Optical | Source-velocity dependence (Ritz) | Ruled out simple Ritz emission theory | ○ pending |
Constraints at different photon energies probe different regions of any putative dispersion relation. They are complementary rather than directly interchangeable, and the table should not be read as a leaderboard.
Brian Keating 