We look for the properties of empty space-time proceeding from the general relativity principle. An infinite number of the so-called covariant ether theories (CETs) has been found, which, like the special relativity theory (SRT), satisfy all known experimental facts in the physics of empty space-time. In this connection a new approach to the problem of experimental testing of SRT is discussed. In particular, we show that covariant ether theories predict a dependence of Thomas-Wigner angle on an absolute velocity of a reference frame of observation. Hence, a measurement of this dependence is capable to distinguish SRT and CETs. It has been shown that the Lorentz ether theory is one of CETs, corresponding to the admissible Galilean transformations in physical space-time. Hence, we conclude that SRT and Lorentz ether theory can be distinguished experimentally, at least in principle. A crucial experiments, based on the Moessbauer effect, has been proposed.