Maguejo-Smolin Transformation as a Consequence of a Specific Definition of Mass, Velocity, and the Upper limit on Energy

Abstract

We consider an alternative approach to non-linear special-relativistic theories. The point of departure is not $\kappa$-deformed algebra (or even group-theoretical considerations) but rather 3 physical postulates defining particle's velocity, mass, and the upper bound on its energy in terms of the respective classical quantities. For a specific definition of particle's velocity we obtain Magueijo-Smolin (MS) version of the double special-relativistic theory. It is shown that this version follows from the $\kappa$-Poincare algebra by the appropriate choice of on the shell mass, such that it is always less or equal Planck's mass. The $\kappa$-deformed Hamiltonian is found which invalidates some arguments about unphysical predictions of the MS transformation.