POLITE · Memo
A plain statement of where optical tests of Lorentz invariance stand, and what a dedicated optical program contributes that existing measurements do not. Written to be argued with.
What is established
In absolute terms, gamma-ray bounds dominate and it is not close. Fermi-LAT observations of gamma-ray bursts constrain |Δc/c| at the 10-20 level within the standard En parametrization, roughly eight orders of magnitude tighter than anything achievable at optical wavelengths. The reason is the energy lever arm: at ~10 GeV the fractional speed difference needed to produce a detectable delay is suppressed by (E/ELIV)n, which buys exquisite sensitivity to any power-law dispersion.
Radio constraints from fast radio bursts are complementary but entangled with plasma dispersion, which must be modelled and subtracted and which is far larger than any putative LIV term. X-ray binary timing (Brecher 1977) and the classical spectroscopic binary tests (de Sitter 1913) bound a different hypothesis — dependence of light speed on source velocity rather than on frequency.
What is not established is anything within the optical window. The most-cited optical-adjacent result, Warner & Nather’s 1969 Crab pulsar measurement, spans optical to radio — a frequency ratio of about two million. It is a superb measurement of something slightly different. Before the eclipsing-binary work, no purely optical-band constraint on vacuum dispersion appears in the literature at all.
What remains uncertain
Whether the En extrapolation is the right frame. Comparing an optical bound to a GeV bound requires assuming a monotonic power law across fifteen decades of photon energy. Non-standard models exist in which the energy dependence is non-monotonic, resonant, or has threshold structure — massive hidden-sector photon mixing, certain extra-dimensional scenarios. In those cases optical dispersion could be present while gamma-ray dispersion is suppressed. I am not aware of a specific published model predicting |Δc/c| ~ 10-12–10-10 at eV energies while remaining below 10-20 at GeV, and constructing or excluding one is a theory problem. But the possibility is the general argument for multi-wavelength coverage.
Limb-darkening model fidelity. The chromatic correction rests on tabulated quadratic coefficients. That model uncertainty is the dominant systematic, and it is estimated from the Algol calibrator residual as an empirical floor rather than derived from first principles. Better stellar atmosphere models, or an empirical calibration across many nearby systems, would tighten it.
Intrinsic polarization in Algol systems. For the polarimetric channel this is the open question. Algol-type binaries have circumstellar material, mass transfer streams, and scattering envelopes, all of which produce intrinsic polarization varying with orbital phase. Separating that from any propagation-induced rotation requires knowing the intrinsic signal well — and the literature on phase-resolved polarimetry of these systems is thinner than the timing literature.
Starspot-induced timing variation. With a single epoch per target this cannot be assessed from epoch-to-epoch scatter, so it enters the budget as zero — a placeholder, not a measurement. Multi-epoch data is required to bound it honestly.
What POLITE adds
An optical channel that does not exist yet. Filling the eV portion of the multi-wavelength constraint landscape has value precisely because the model-independent comparison across energies is where non-power-law dispersion would reveal itself.
A distance-scaling discriminant. Most systematics in optical timing are distance-independent. A genuine dispersion signal must scale linearly with distance. Observing a sample spanning a factor of ~16 in distance — extensible to far more — turns that into a direct test rather than an assumption, with a nearby calibrator providing an empirical null.
A birefringence channel timing cannot reach. Dispersion and birefringence are separate consequences of Lorentz violation. The polarimeter targets the second, where the observable is position-angle rotation growing with path length, and where the limiting systematic is absolute angle calibration rather than photon noise.
A reusable methodology. The chromatic correction is not specific to this problem. Any multi-band timing study of eclipsing binaries or transiting exoplanets must contend with wavelength-dependent eclipse morphology. The same approach applies to precision transit timing across bands, to interacting binaries where mass transfer produces chromatic effects, and to calibrating photometric timing systematics in large time-domain surveys such as LSST.
Headroom. A measurement that is 98% statistics-limited has an unusually clear improvement path, and the improvements are available to small telescopes. That makes this a program other people can join without building anything new.
Status
Living document, last revised 18 August 2026. Claims here about the state of the literature are drawn from the comparison table of the timing paper; see the evidence table for per-row verification status. Corrections are welcome and will be dated.
