Special Relativity and possible Lorentz violations consistently coexist   in Aristotle space-time
  Some studies interpret quantum measurement as being explicitly non local. Others assume the preferred frame hypothesis. Unfortunately, these two classes of studies conflict with Minkowski space-time geometry. On the contrary, in Aristotle space-time, Lorentz invariance, interpreted as a physical property applying to all phenomena actually satisfying this symmetry (as opposed to a geometrical constraint applying to an assumed pre-existing Minkowski space-time) consistently coexists with possible Lorentz violations. Moreover, as will be pointed out, the geometrical framework provided by Aristotle space-time is in fact necessary to derive the Lorentz transformations from physical hypotheses. 
B. Chaverondier