Energy-dependent speeds of light have been considered an observable signature
of quantum gravity effects. The two simplest dispersion relationships produce
either linear or quadratic corrections, in particle energy, to the photon
speed. The macroscopic limits of these theories -- how objects with small
energy per particle, but with large mass, behave -- are not fully understood.
We here briefly discuss some features of the macroscopic limit, that are
necessary for understanding how detectors and emitters interact with the
high-energy photons that probe spacetime.