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.
Speed of light
According to special relativity, the energy of an object with rest mass "m" and speed "v" is given by , where "γ" is the Lorentz factor defined above. When "v" is zero, "γ" is equal to one, giving rise to the famous formula for mass–energy equivalence. The "γ" factor approaches infinity as "v" approaches "c", and it would take an infinite amount of energy to accelerate an object with mass to the speed of light. The speed of light is the upper limit for the speeds of objects with positive rest mass, and individual photons cannot travel faster than the speed of light. This is experimentally established in many tests of relativistic energy and momentum.
More generally, it is normally impossible for information or energy to travel faster than "c". One argument for this follows from the counter-intuitive implication of special relativity known as the relativity of simultaneity. If the spatial distance between two events A and B is greater than the time interval between them multiplied by "c" then there are frames of reference in which A precedes B, others in which B precedes A, and others in which they are simultaneous. As a result, if something were travelling faster than "c" relative to an inertial frame of reference, it would be travelling backwards in time relative to another frame, and causality would be violated. In such a frame of reference, an "effect" could be observed before its "cause". Such a violation of causality has never been recorded, and would lead to paradoxes such as the tachyonic antitelephone.