Improved limit on quantum-spacetime modifications of Lorentz symmetry from observations of gamma-ray blazars

In the recent quantum-gravity literature there has been strong interest in the possibility that quantum properties of spacetime might affect the laws of particle propagation. The most used test theory for data analysis is based on a quantum-gravity-scale modification of the laws of propagation proposed in astro-ph/9712103 [Amelino-Camelia et al, Nature 393 (1998) 763], and the present best limit on the quantum-gravity scale was obtained in gr-qc/9810044 [Biller et al, Phys.Rev.Lett. 83 (1999) 2108]. I find an improved limit by using recent experimental information on the way in which gamma-rays emitted by blazars are absorbed by the far infrared diffuse extragalactic background. There are still some sizeable experimental uncertainties in the analysis of this absorption, but even factoring in these uncertainties (adopting the conservative analysis of the experimental situation described in astro-ph/0102226 [Stecker and Glashow, Astropart.Phys. 16 (2001) 97]) I find a limit on the quantum-gravity scale which is improved by a factor 100, and is just a factor 3 below the Planck scale. As a corollary I show that, contrary to the recent claim of astro-ph/0208507 [Stecker, Lectures at Chalonge International School 2002], the test theory here considered does not allow decays of photons into electron-positron pairs, and therefore the limit obtained in astro-ph/0208507 does not hold.