In the electromagnetism of loop quantum gravity , two helicities of a photon have different phase velocities and group velocities , termed as “ vacuum birefringence ” . Two novel phenomenons , “ peak doubling ” and “ de-polarization ” , are expected to appear for a linearly polarized light from astrophysical sources . We show that the criteria to observe these two phenomenons are the same . Further , from recently observed \gamma -ray polarization from Cygnus X-1 , we obtain an upper limit \sim 8.7 \times 10 ^ { -12 } for Lorentz-violating parameter \chi , which is the most firm constraint from well-known systems . We also suggest to analyze possible existence of “ peak doubling ” through Fermi LAT GRBs .