Abstract
By “causality of matter” one means its property not to admitsuperluminal excitations, i.e. excitations that propagate faster than the vacuum speed of lightc. In discussing the propagation of small excitations, one has to distinguish betweenphase velocities ω j /k, (1≦j≦g=number of dispersion branches),group velocities dω j /dk, a front velocityv f : =\(\mathop {\max }\limits_j \mathop {\lim }\limits_{k \to \infty } \left( {{{\omega _j } \mathord{\left/ {\vphantom {{\omega _j } k}} \right. \kern-\nulldelimiterspace} k}} \right)\) and the propagation speedv q :=(dp/dϱ)1/2 of isotropic quasistatic (small) perturbations. We discuss some of their properties. In particular, the (maximal) speedv s of small signals is not smaller thanv f , and equalsv f whenever the dispersion branches ω j (k) behave reasonably at infinity of the complexk-plane. In essence stronger conditions guaranteev q <v f (in which casev q ≧c would imply superluminal behaviour).
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Communicated by R. Geroch
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Krotscheck, E., Kundt, W. Causality criteria. Commun.Math. Phys. 60, 171–180 (1978). https://doi.org/10.1007/BF01609447
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DOI: https://doi.org/10.1007/BF01609447