Possibility of the Speed of Sound Exceeding the Speed of Light in Ultradense Matter

We show that, in the classical physics of very dense matter, Lorentz invariance imposes no restriction on the speed of sound or on the ratio of pressure to energy density. Indeed, the simplest and most reasonable classical many-particle theory can manifest such apparently noncausal behavior whenever the calculated self-energy of a particle exceeds its observed (renormalized) rest energy. This comes about because ordinary mass renormalization subtracts out part of a particle's self-interaction energy without altering the interaction with other particles that contributes to pressure. Two types of models are exhibited which, at low densities, show normal behavior and, at high densities, become superluminal (speed of sound greater than speed of light in vacuum) and ultrabaric (pressure greater than energy density). One is a system of classical particles which, when stationary, repel each other by a short-range repulsive Yukawa interaction. Although the particles interact through ordinary retarded neutral vector fields, after mass renormalization there must always be a domain of sufficiently high densities where this matter becomes superluminal and ultrabaric. The second group of models is a class of classical Lorentz-invariant nonlinear field theories which, in the limit of low densities, reduces to a noninteracting Klein-Gordon field. If matter deep inside superdense stars could be ultrabaric, then the limiting gravitational red shift from the star's surface would be slightly under 2. This is perhaps suggestive of the observed clustering of quasar absorption-line red shifts at 1.95.