A possible birefringence effect that arises in quantum gravity leads to a
frequency-dependent rotation of the polarization angle of linearly polarized
emission from distant sources. Here we use the UV/optical polarization data of
the afterglows of GRB 020813 and GRB 021004 to constrain this effect. We find
an upper limit on the Gambini & Pulin birefringence parameter ∣η∣<2×10−7. This limit is of 3 orders better than the previous limits
from observations of AGNs and of the Crab pulsar. Much stronger limits may be
obtained by the future observation of polarization of the prompt γ-rays.Comment: typos correcte