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We analyze the timing of photons observed by the MAGIC telescope during aflare of the active galactic nucleus Mkn 501 for a possible correlation withenergy, as suggested by some models of quantum gravity (QG), which predict avacuum refractive index \simeq 1 + (E/M_{QGn})^n, n = 1,2. Parametrizing thedelay between gamma-rays of different energies as \Delta t =\pm\tau_l E or\Delta t =\pm\tau_q E^2, we find \tau_l=(0.030\pm0.012) s/GeV at the 2.5-sigmalevel, and \tau_q=(3.71\pm2.57)x10^{-6} s/GeV^2, respectively. We use theseresults to establish lower limits M_{QG1} > 0.21x10^{18} GeV and M_{QG2} >0.26x10^{11} GeV at the 95% C.L. Monte Carlo studies confirm the MAGICsensitivity to propagation effects at these levels. Thermal plasma effects inthe source are negligible, but we cannot exclude the importance of some othersource effect.

Probing quantum gravity using photons from a flare of the active galactic nucleus Markarian 501 observed by the MAGIC telescope