Space-time Transformations in Ether Theories

By assuming the validity of the principle of inertia and the existence of a privileged frame, the transformation laws (TL) between inertial frames are investigated in ether theories. For onedimensional space the TL's are fixed up to two undetermined functions of absolute velocity, Δ (v) and E(v). If the principle of relativity is finally assumed, these functions acquire their well known Lorentzian expressions ΔL and EL. It is concluded that special relativity theory is "unstable", in the sense that any shift, however small, of Δ away from ΔL and/or of E away from EL leads to an ether theory. In Earth-based experiments one can expect deviations from c of the two-way and one-way velocity of light of the order of 10-12 and 10 -9 respectively