Is the photon dispersion relation modified at linear order in $E/E_{\mathrm{P}}$?
In plain words
Some quantum gravity ideas make high-energy photons travel at slightly different speeds from low-energy ones. Gamma-ray bursts billions of light years away test this and already require any such linear effect to be weaker than Planck-scale estimates.
Precise statement
Parametrize photon propagation as v(E) = c [1 - s ((n+1)/2) (E/E_QG,n)^n] with $s = +1$ (subluminal) or $-1$ (superluminal). Measure or bound E_QG,1 and E_QG,2 for both signs, and determine whether any candidate UV completion predicts a nonzero linear term consistent with these bounds. An answer is a detection of an energy-dependent arrival delay, or a demonstration that a given completion forbids linear Lorentz violation.
What would settle it
Time-of-flight measurements of variable high-energy sources at cosmological distances with sensitivity beyond E_QG,1 = 10 E_P, together with predictions from specific completions.
Status in the literature
Unverified note: it names recent work and was partly written without a live literature search; it awaits a check by an editor.
LHAASO observations of GRB 221009A give, for subluminal propagation, E_QG,1 > 10 E_P and E_QG,2 > $6 \times 10^{-8}$ E_P at 95 percent confidence (2024); superluminal effects are bounded separately by the absence of photon decay.
Parent problems
- Special case of Which theory completes general relativity at the Planck scale? · open · from revision 1 The parent was revised since revision 1: it now states another question.
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