  Special relativity has been tested at low energy with great accuracy, but
these results cannot be extrapolated to very high-energy phenomena: this new
domain of physics may actually provide the key to the, yet unsettled, question
of the ether and the absolute rest frame. Introducing a critical distance
scale, a, below 10E-25 cm (the wavelength scale of the highest-energy observed
cosmic rays) allows to consider models, compatible with standard tests of
special relativity, where a small violation of Lorentz symmetry (a can, for
instance, be the Planck length) leads to a deformed relativistic kinematics
(DRK) producing dramatic effects on the properties of very high-energy cosmic
rays. For instance, the Greisen-Zatsepin-Kuzmin (GZK) cutoff does no longer
apply and particles which are unstable at low energy (neutron, some hadronic
resonances like the Delta++, possibly several nuclei...) become stable at very
high energy. In these models, an absolute local rest frame exists (the vacuum
rest frame, VRF) and special relativity is a low-momentum limit. We discuss the
possible effects of Lorentz symmetry violation (LSV) on kinematics and
dynamics, as well as the cosmic-ray energy range (well below the energy scale
associated to the fundamental length) and experiments (on earth and from space)
where they could be detected.
