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.
Comoving and proper distances
If one divides a change in proper distance by the interval of cosmological time where the change was measured (or takes the derivative of proper distance with respect to cosmological time) and calls this a "velocity", then the resulting "velocities" of galaxies or quasars can be above the speed of light, "c". This apparent superluminal expansion is not in conflict with special or general relativity, and is a consequence of the particular definitions used in physical cosmology. Even light itself does not have a "velocity" of "c" in this sense; the total velocity of any object can be expressed as the sum formula_15 where formula_16 is the recession velocity due to the expansion of the universe (the velocity given by Hubble's law) and formula_17 is the "peculiar velocity" measured by local observers (with formula_18 and formula_19, the dots indicating a first derivative), so for light formula_17 is equal to "c" (−"c" if the light is emitted towards our position at the origin and +"c" if emitted away from us) but the total velocity formula_21 is generally different from "c". Even in special relativity the coordinate speed of light is only guaranteed to be "c" in an inertial frame; in a non-inertial frame the coordinate speed may be different from "c". In general relativity no coordinate system on a large region of curved spacetime is "inertial", but in the local neighborhood of any point in curved spacetime we can define a "local inertial frame" in which the local speed of light is "c" and in which massive objects such as stars and galaxies always have a local speed smaller than "c". The cosmological definitions used to define the velocities of distant objects are coordinate-dependent – there is no general coordinate-independent definition of velocity between distant objects in general relativity. The issue of how best to describe and popularize the apparent superluminal expansion of the universe has caused a minor amount of controversy. One viewpoint is presented in Davis and Lineweaver, 2004.