Relativistic speed
Relativistic speed refers to speed at which relativistic effects become significant to the desired accuracy of measurement of the phenomenon being observed. Relativistic effects are those discrepancies between values calculated by models considering and not considering relativity. Related words are velocity, rapidity, and celerity which is proper velocity. Speed is a scalar, being the magnitude of the velocity vector which in relativity is the four-velocity and in three-dimension Euclidean space a three-velocity. Speed is empirically measured as average speed, although current devices in common use can estimate speed over very small intervals and closely approximate instantaneous speed. Non-relativistic discrepancies include cosine error which occurs in speed detection devices when only one scalar component of the three-velocity is measured and the Doppler effect which may affect observations of wavelength and frequency.Relativistic effects are highly non-linear and for everyday purposes are insignificant because the Newtonian model closely approximates the relativity model. In special relativity the Lorentz factor is a measure of time dilation, length contraction and relativistic mass increase of a moving object.
Velocity-addition formula
where the speed of light is set to unity so that formula_69 and formula_70 agree. It this expression, formula_71 and formula_72 are velocities of two objects in any one given frame. The quantity formula_73 is the speed of one or the other object "relative" to the other object as seen "in the given frame". The expression is Lorentz invariant, i.e. independent of which frame is the given frame, but the quantity it calculates is "not". For instance, if the given frame is the rest frame of object one, then formula_74.