Abstract

Presented at XXV International Colloquium on Group Theoretical Methods in Physics, Mexico, August 2004. Following Minkowski in 1908, we consider the relative velocity to be the Minkowski space-like vector. We show that the Lorentz boost entails the relative velocity to be ternary: ternary relative velocity is a velocity of a body with respect to interior observer as seen by a preferred exterior observer. The Lorentz boost imply non-associative addition of ternary relative Einsteinian velocities. Within Einstein's special relativity theory, each preferred observer (aether, fixed stars, etc), determine the unique relative velocity among each pair of massive bodies. The special relativity founded on axiom that each pair of reference systems must be related by the Lorentz isometry, needs the preferred reference system in order to have the unique Einstenian relative velocity among each pair of massive bodies. This choice-dependence of relative velocity violate the Relativity Principle that all reference systems must be equivalent.