Macroscopic Objects in Theories with Energy-dependent Speeds of Light
  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. 
Simon DeDeo, Chanda Prescod-Weinstein