Special relativity as classical kinematics of a particle with the upper bound on its speed. Part II. The general Lorentz transforrmation and the generalized velocity composition theorem

Abstract: The kinematics of a particle with the upper bound on the particle's speed (a modification of classical kinematics where such a restriction is absent) has been developed in [arXiv:1204.5740]. It was based solely on classical mechanics without employing any concepts , associated with the time dilatation or/and length contraction. It yielded the 1-D Lorentz transformation (LT), free of inconsistencies (inherent in the canonical derivation and interpretations of the LT). Here we apply the same approach to derive the LT for the 3-dimensional motion of a particle and the attendant law of velocity composition. As a result, the infinite set of four-parameter transformations is obtained. The requirement of linearity of these transformations selects out of this set the two-parameter subset . The values of the remaining two parameters ,dictated by physics of the motion, is explicitly determined , yielding the canonical form of the 3-dimensional LT. The generalized law of velocity composition and the attendant invariant ( not postulated apriori) of the motion are derived, As in the one-dimensional case, present derivation, as a whole, does not have any need in introducing the concepts of the time dilatation and length contraction, and is based on the classical concepts of time and space.