Introduction to Electrodynamics · Problem 12.19

Electrodynamics and Relativity — David J. Griffiths

Physics · rapidity

Problem

The parallel between rotations and Lorentz transformations is even more striking if we introduce the rapidity: θ≡tanh⁡−1(v/c).(12.34)\theta \equiv \tanh^{-1}(v/c). \tag{12.34} (a) Express the Lorentz transformation matrix Λ\Lambda (Eq. 12.24) in terms of θ\theta, and compare it to the rotation matrix (Eq. 1.29). (b) Express the Einstein velocity addition law in terms of rapidity.

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