In the quantum-gravity literature there has been interest in the possibility
that quantum properties of spacetime might affect the energy/momentum
dispersion relation. The most used test theory for data analysis is based on a
modification of the laws of propagation proposed in astro-ph/9712103 [Nature
393,763], and the present best limit on the quantum-gravity scale was obtained
in gr-qc/9810044 [Phys.Rev.Lett.83,2108]. I derive an improved limit using
recent experimental information on absorption by the infrared diffuse
extragalactic background of γ-rays emitted by blazars. Foreseeable more
accurate determinations of the absorption levels could achieve Planck-scale
sensitivity. As a corollary I also show that, contrary to the recent claim of
astro-ph/0208507v3, the test theory here considered does not allow decays of
photons into electron-positron pairs, and I expose the limitations of
phenomenological proposals, such as the one reported in astro-ph/0212190, in
which one attempts to infer limits on the kinematic theory here considered
through the ad hoc introduction of a dynamical framework.Comment: Published version [New J.Phys. 6 (2004) 188]. Title changed. Several
changes made during the long editing period. Revised commentary on
Crab-nebula synchrotron-radiation analysis reflects differences between
astro-ph/0212190v1 and astro-ph/0309681 (astro-ph/0212190v1 made a strong
claim which was softened in astro-ph/0309681). Added cautionary Comments also
relevant for the analysis of the gamma-ray threshold, the cosmic-ray GZK
threshold and photon stabilit
