In relativity, rapidity is an alternative to speed as a measure of rate of motion. On parallel velocities (say, in one-dimensional space) 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.
Using the inverse hyperbolic function artanh, the rapidity w corresponding to velocity v is w = artanh(v / c). For low speeds, w is approximately v / c. The speed of light c being finite, any velocity v is constrained to the interval −c < v < c and...