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We have used a stringy model of quantum space-time foam to suggest that the vacuum may exhibit a non-trivial refractive index depending linearly on gamma-ray energy: eta -1 ~ E_gamma/M_QG1, where M_QG1 is some mass scale typical of quantum gravity that may be ~ 10^18 GeV: see Phys.
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This range is also compatible with the weaker limits found previously by the Whipple Collaboration, who found no significant time-lag in emissions during a flare of AGN Mkn 421: S. D. Biller et al
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