rapidityrəˈpɪd ɪ ti; ˈræp ɪd nɪs
rapidity (n)
English Definitions:
celerity, quickness, rapidity, rapidness, speediness (noun)
a rate that is rapid
rapidity (Noun)
speed, swiftness; the condition of being rapid
rapidity (Noun)
A measure of velocity relative to the speed of light
rapidity (Noun)
A measure of the velocity of a particle in a beam relative to the beam#s axis
Rapidity
In relativity, rapidity is an alternative to speed as a measure of motion. On parallel velocities rapidities are simply additive, unlike speeds at relativistic velocities. For low speeds, rapidity and speed are proportional, but for high speeds, rapidity takes a larger value. The rapidity of light is infinite. The rapidity concept is not widely used; speed has the advantage of more direct measurability.
Using the inverse hyperbolic function tanh−1, the rapidity φ corresponding to velocity v is φ = tanh−1. For low speeds, φ is approximately v/c. The speed of light c being finite, any velocity v is constrained to the interval -c
Rapidity
In relativity, rapidity is commonly used as a measure for relativistic velocity. Mathematically, rapidity can be defined as the hyperbolic angle that differentiates two frames of reference in relative motion, each frame being associated with distance and time coordinates. For one-dimensional motion, rapidities are additive whereas velocities must be combined by Einstein's velocity-addition formula. For low speeds, rapidity and velocity are proportional but, for higher velocities, rapidity takes a larger value, with the rapidity of light being infinite. Using the inverse hyperbolic function artanh, the rapidity w corresponding to velocity v is w = artanh(v / c) where c is the velocity of light. For low speeds, w is approximately v / c. Since in relativity any velocity v is constrained to the interval −c < v < c the ratio v / c satisfies −1 < v / c < 1. The inverse hyperbolic tangent has the unit interval (−1, 1) for its domain and the whole real line for its image; that is, the interval −c < v < c maps onto −∞ < w < ∞.
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