Rapidity

Common card · No. 415970

In special relativity, the classical concept of velocity is converted to rapidity to accommodate the limit determined by the speed of light. Velocities must be combined by Einstein's velocity-addition formula. For low speeds, rapidity and velocity are almost exactly proportional but, for higher velocities, rapidity takes a larger value, with the rapidity of light being infinite. 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. Using the inverse hyperbolic function artanh, the rapidity w corresponding to velocity v is: w = artanh ⁡ ( v c ) {\displaystyle w=\operatorname {artanh} \left({\frac {v}{c}}\right)} where c is the speed of light. Instead of w, some authors use...

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