  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. We show that, in this
context, phenomena such as the absence of Greisen-Zatsepin-Kuzmin cutoff and
the stability of unstable particles at very high energy are basic properties of
a wide class of noncausal models where local Lorentz invariance is broken
introducing a fundamental length. Then, observable phenomena are produced at
the wavelength scale of the highest-energy cosmic rays or even below this
energy, but Lorentz symmetry violation remains invisible to standard low-energy
tests. We discuss possible theoretical, phenomenological, experimental and
cosmological implications of this new approach to matter and space-time, as
well as prospects for future developments.
