Rapidity

Summary

The rapidity of a velocity $v$ along a line is $\varphi = \operatorname{artanh}(v / c)$. It is the hyperbolic angle of a Lorentz transformation boost. In terms of rapidity, a boost looks like a rotation with hyperbolic functions in place of trigonometric ones. Rapidities of boosts in the same direction simply add, while velocities do not.