Thomasrotation: a Lorentz matrix approach

Abstract

The composition of two pure Lorentz transformations (boosts)parametrized by non-parallel velocities is equivalent to a boostcombined with a pure spatial rotation - the Thomas rotation.Thirty years elapsed from Thomas's 1926 calculation for theprecessional application until an explicit result for theThomas rotation angle appropriate to two finite boostvelocities appeared in the literature. Over the years there havebeen a number of papers that have produced results by variousmethods for the Thomas rotation angle but none by directLorentz matrix methods. This paper repairs that deficiency bypresentation of an explicit Lorentz matrix proof of sufficientconciseness to show that the much-vaunted complexity of thedirect approach has been considerably overstated. Thedemonstration fills a gap at a fundamental level in thedevelopment of the basics of special relativity.