2014/05/09 by Alex Granik, Granik, Alex
Physics and Astronomy · #Advanced Mathematical Theories and Applications #Experimental and Theoretical Physics Studies #FOS: Physical sciences #General Physics (physics.gen-ph) #Quantum Mechanics and Applications #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.1407.6626
openalex publication_date 2014/05/09 · openalex created_date 2022/09/12 · openalex updated_date 2026/07/28
The kinematics of a particle with the upper bound on the particle's speed (a\nmodification of classical kinematics where such a restriction is absent) has\nbeen developed in [arXiv:1204.5740]. It was based solely on classical mechanics\nwithout employing any concepts , associated with the time dilatation or/and\nlength contraction. It yielded the 1-D Lorentz transformation (LT), free of\ninconsistencies (inherent in the canonical derivation and interpretations of\nthe LT). Here we apply the same approach to derive the LT for the 3-dimensional\nmotion of a particle and the attendant law of velocity composition. As a\nresult, the infinite set of four-parameter transformations is obtained. The\nrequirement of linearity of these transformations selects out of this set the\ntwo-parameter subset . The values of the remaining two parameters ,dictated by\nphysics of the motion, is explicitly determined , yielding the canonical form\nof the 3-dimensional LT. The generalized law of velocity composition and the\nattendant invariant ( not postulated apriori) of the motion are derived, As in\nthe one-dimensional case, present derivation, as a whole, does not have any\nneed in introducing the concepts of the time dilatation and length contraction,\nand is based on the classical concepts of time and space.\n