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
In the literature the quantity formula_110 as well as formula_73 are both referred to as the relative velocity. In some cases (statistical physics and dark matter literature), formula_110 is referred to as the "Møller velocity", in which case formula_73 means relative velocity. The true relative velocity is at any rate formula_95. The discrepancy between formula_95 and formula_73 is relevant though in most cases velocities are collinear. At LHC the crossing angle is small, around 300 rad, but at
the old Intersecting Storage Ring at CERN, it was about 18.