  If textbook Lorentz invariance is actually a property of the equations
describing a sector of the excitations of vacuum above some critical distance
scale, several sectors of matter with different critical speeds in vacuum can
coexist and an absolute rest frame (the vacuum rest frame) may exist without
contradicting the apparent Lorentz invariance felt by "ordinary" particles
(particles with critical speed in vacuum equal to $c$, the speed of light).
Sectorial Lorentz invariance, reflected by the fact that all particles of a
given dynamical sector have the same critical speed in vacuum, will then be an
expression of a fundamental sectorial symmetry (e.g. preonic grand unification
or extended supersymmetry) protecting a parameter of the equations of motion.
Furthermore, the sectorial Lorentz symmetry may be only a low-energy limit, in
the same way as the relation $\omega $ (frequency) = $c_s$ (speed of sound) $k$
(wave vector) holds for low-energy phonons in a crystal. In this context,
phenomena such as the absence of Greisen-Zatsepin-Kuzmin cutoff for protons and
nuclei and the stability of unstable particles (e.g. neutron, several
nuclei...) at very high energy are basic properties of a wide class of
noncausal models where local Lorentz invariance is broken introducing a
fundamental length. Observable phenomena are expected at very short wavelength
scales, even if Lorentz symmetry violation remains invisible to standard
low-energy tests. We present a detailed discussion of the implications of
Lorentz symmetry violation for very high-energy nuclear physics.
