It is one of the axioms of special relativity that the photon has no rest frame; light travels at speed c when measured in any inertial frame of reference. As a corollary, it is often said that if one were in a photon's rest frame, infinite time-dilation and length-contraction would make the universe appear (from a photon's perspective) to be unchanging, with zero length in its direction of motion. In other words a measurement would not be possible in the reference frame of a photon, because there would be no time or space in which one could conduct it.
My question is: how does this accord with the fact that parallel-moving photons can interact with each other via loop diagrams[*]? Photons can therefore be used to perform measurements in the photon's rest frame. I suppose an answer may be "the act of measurement changes the photons momentum vector and therefore its co-moving frame is non-inertial" however this can be said of any measurement.
[*] Or can they? I can't find an explicit amplitude to check this (for, say, the photon-photon "box" diagram), however as far as I can tell from the Euler-Heisenberg Lagrangian nonlinear effects should be present for parallel photons.