Relativistic limits of observable velocities

Relativistic transformations proposed in [A. Einstein, Zur Elektrodynamik der bewegter Körper. Ann. der Physik, 17 (1905) 891 921] are based on the speed V of a signal transmitting the information and on the relative speed v of a frame .k/ moving with respect to a still frame .K/, which velocities are considered as given constants. These transformations reflect the links that exist between motions and processes observed in one system from another, and with this theory some experimental effects (aberration, Doppler effect, pressure of light) were explained, and some other effects were predicted, and then confirmed experimentally. However, there is no need to postulate relative velocity v as a known constant since, using the original Einsteinʹs model of time synchronization and appropriate signals with known speed of propagation V, the relative velocity v of a moving frame (spacecrafts, asteroids, particles in accelerators) can be measured. In this paper, the observation method, reverse to that of Einstein, is presented, and the limit of observable relative velocities is found which is 30% less than the speed of a signal used for the observation. For example, if a radar or rays of light are used for the observation, then relative velocities jvj < V D 300 000 km=s can theoretically be considered, but only the velocities jvj < 2􀀀0:5V D 0:7071V D 212 132 km=s can be directly measured in still frame .K/ with a radar or rays of light. The method is applicable also to variable relative velocities v.t/ 6D const, which opens the possibility for relativistic feedback control of processes in a frame moving arbitrarily with respect to a still frame.