A Linear Dispersion Bound from the 31 GeV Photon of GRB 090510

The short gamma-ray burst GRB 090510, at redshift 0.903, delivered a photon of about 31 GeV that arrived 0.829 s after the low-energy trigger. Treating that whole interval as an upper limit on any propagation delay, the linear vacuum-dispersion scale is bounded below at E_QG = 1.713e+19 GeV, which is 1.40 times the Planck energy; a dispersion scale at the Planck energy itself would have delayed the photon by only 1.163 s, and a scale at a tenth of the Planck energy by 11.63 s. The frame examined here states that photon speed in vacuum is independent of energy, so its prediction for this burst is a delay of exactly zero apart from source effects; the measurement is consistent with that statement and excludes a linear dispersion term at and below the scale quoted. The study is computed from published arrival data and stated cosmological assumptions; it is not a new measurement.