Phase and signal velocities of waves in dissipative media. Special relativistic theory

The signal and phase velocities (and their frequency dependence) for all possible plane waves in a relativistic gas (of molecules or photons) with dissipation have been determined from the linearized relativistic 13-moment theory. For each direction in 3-space, and for each frequency, one transverse and two longitudinal waves were found. (In addition, some waves are associated with the mass flow and have the mass flow speed.) Of the longitudinal waves, the fast one is a pressure (sound) wave. It is accompanied by a slow longitudinal thermal dissipation wave and a transverse viscous dissipation wave. The pressure wave has a velocity larger than the Laplace adiabatic speed of sound, while the two dissipation waves have a velocity less than the Laplace speed. All the speeds have been expressed explicitly in terms of quantities associated with the state of equilibrium which existed before passage of the wave. It has also been shown that in the ultrarelativistic limit (extremely high temperatures) all signal speeds remain less than the speed of light in vacuo.The major part of this article was presented at the Seminar on Natural Philosophy at The Johns Hopkins University, Baltimore, on November 24, 1971.