Gamma rays run on time

Although absorption and refraction of radiation appear together in physical phenomena, this is not the case for γ rays travelling cosmic distances, that are absorbed but not refracted by the scarce matter and radiation.

We show that the real and imaginary parts of the refraction index are indeed commensurable, as they are related by dispersion relations, but when turning to physical observables, the (finite) optical depth is way larger than the (infinitesimal) time delay of the gamma rays relative to gravitational radiation.

The numerically large factor solving the apparent contradiction is Eγ/H0 arising from basic wave properties (Bouguer-Beer-Lambert law) and the standard cosmological model, respectively. In consequence, no delay of the γ-ray propagation affects multimessenger astronomy.

We particularly predict no such delay between gravitational waves and γ photons from binary mergers such as GW170817, save for that induced at the source, nor from more energetic events at cosmic distances.