  The propagation of TeV gamma rays can be strongly modified by B-field induced
conversion to axionlike particles (ALPs). We show that, at such high energies,
photon dispersion is dominated by background photons - the only example where
photon-photon dispersion is of practical relevance. We determine the refractive
index for all energies and find that, for fixed energy density, background
photons below the pair-production threshold dominate. The cosmic microwave
background alone provides an "effective photon mass" of (m_gamma)^2 = -(1.01
neV * E/TeV)^2 for E < 1000 TeV. The extragalactic background light is
subdominant, but local radiation fields in the galaxy or the source regions
provide significant contributions. Photon-photon dispersion is small enough to
leave typical scenarios of photon-ALP oscillations unscathed, but big enough to
worry about it case by case.
