A generalization in the complex plane of the composition law of non-parallel velocities in special relativity

摘要

We present a generalization in the complex plane of the Einstein composition law for non-parallel velocities and show that a number of results that are quite difficult to obtain through the usual methods can be found easily using this law and elementary operations with complex numbers. Our first examples (Wigner's angle, Thomas precession, aberration of light) are given in two-dimensional space, while in the final part we also present a generalization of that law in three-dimensional space.