The composition of two non-collinear Lorentz boosts results in a Lorentz transformation that is not a pure boost but a composition of a boost and a spatial rotation known as the Wigner rotation.1 As a consequence, a reference frame attached to a body moving on a curvilinear trajectory undergoes a rotational precession that was first discovered by Thomas.2 In the vast majority of textbooks, this phenomenon is either omitted or described with very sophisticated mathematical tools, such as gyrogroups, associative-commutative groupoids, or holonomy groups.3,4 Simpler derivations have also been presented, but they are usually less general; for example, some only apply when the second boost is perpendicular to the first.5 Here, we present a half-page derivation of the general Thomas precession formula using only basic vector operations. Our approach is short and clear and leads to physical intuition for the essence of this relativistic effect.
Let...
