A constraint on canonical quantum gravity?

Here I show that if the effects of quantum gravity are linearly proportional to the ratio of the photon energy to the characteristic scale energy of quantum gravity, then the polarization of photons with energies of about 0.1 MeV should be completely random, contrary to what is observed. I conclude that, should the polarization measurement be confirmed, quantum gravity effects act with a power that is greater than linearity, or that loop quantum gravity is not viable. Compared with previous methods and results (see ref. 2, for example), testing of the linear polarization of cosmic gamma-ray bursts may substantially extend the observational window on the theory of quantum gravity.