An alternative formulation of relativistic head-on collision problem

Abstract

In this work, complex quaternions have been used instead of four vectors to reformulate the relativistic elastic head-on collision problem. Even though four vectors are much more commonly used for this formulation, complex quaternionic formalism presented in this work provides a very useful and elegant representation. From the educational point of view, complex quaternionic representation has some advantages with its simpler and more expressive nature. Unfortunately, four vectors with four real components are not adequate to distinguish quantities that are of a different physical nature. On the other hand, because of having a very useful symbol i complex quaternions contribute to separate physical quantities explicitly. Thus, it can easily be seen how to relate independent results.