arXiv:hep-th/0207113v6 30 Mar 2008 Magueijo-Smolin Transformation as a Consequence of a Speci?c De?nition of Mass,Velocity, and the Upper limit on Energy Alex Granik ? Abstract We consider an alternative approach to double special-relativistic the- ories. The point of departure is notκ-deformed algebra (or even group- theoretical considerations) but rather 3 physical postulates de?ning parti- cle’s velocity, mass, and the upper bound on its energy in terms of the re- spective classical quantities. For a speci?c de?nition of particle’s velocity we obtain Magueijo-Smolin (MS) version of the double special-relativistic theory. It is shown that this version follows from theκ-Poincare algebra by the appropriate choice of on the shell mass , such that it isalways less or equal Planck’s mass. Theκ-deformed Hamiltonian is found which invalidates the recent arguments about unphysical predictions of the MS transformation. A recent research (.[1],[2],[3],[4],[5],[6],[7]) on the so-called double special rel- ativity not only reexamined its relation toκ-deformed kinematics, but in one speci?c example [4] also subjected to criticism physical predictions of one of these theoretical constructs [7]. It should be mentioned that as early as in 1994, with collaborators [8] demonstrated that there exist an in?nite set of transformations reducing the κ-deformed Casimir in Majid-Ruegg
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