Problem

The parallel between rotations and Lorentz transformations is even more striking if we i...

The parallel between rotations and Lorentz transformations is even more striking if we introduce the rapidity:

(a) Express the Lorentz transformation matrix Λ (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. 11 For one thing, it ranges from −∞ to +∞, instead of −c to +c. More significantly, rapidities add, whereas velocities do not.

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

Equation 12.24