Three-line derivation of the Thomas precession Available to Purchase

Recently,¹ a half-page derivation of the Thomas precession effect² has been presented (see also all the references in Ref. 1 for the history and prehistory of the problem). In this short note, we provide a much simpler, three-line derivation of that effect which, to our knowledge, is the simplest in the literature.

Consider Bob B moving relative to Alice's frame A with a relativistic velocity v, as shown in Fig. 1. If Bob's velocity changes by an infinitesimal value $dv′$ relative to his initial reference frame B, Alice will observe his new velocity to be some $v+dv$⁠. The new Bob's frame $B′$ is now rotated relative to Alice's frame by a Thomas–Wigner angle $dΩ$⁠. In the non-relativistic theory, we have $dv′=dv$ and the rotation is absent. Therefore, the Thomas–Wigner...