The parallel between rotations and Lorentz transformations is even more striking if we introduce the rapidity: θ = tanh–1 (v/c).

(a) Express the Lorentz transformation matrix A (Eq. 12.24) in terms of θ, and compare it to the rotation matrix (Eq. 1.29). In some respects rapidity is a more natural way to describe motion than velocity.

(b) Express the Einstein velocity addition law in terms of rapidity.