Abstract

Assuming the speed of light to be constant, we showed in a recent work the existence of a generalized group of space and time transformations in which the Lorentz transformation is included. In the present work, starting from the hypothesis of the invariance of the sub-luminal momentum and applying these new transformations, we derive a new equation for the invariant momentum-velocity of particles which can be applied to sub-luminal or super-luminal particles. The kinetic energy shows a maximum at the speed of light, and falls at sub-luminal or super-luminal speeds. There is good agreement with the Newtonian and relativistic results for particle momentum and energy at sub-luminal velocities. We propose as an experimental method for the classification of a particle as sub-luminal, luminal, or super-luminal, the measurement of the ratio between its kinetic energy and momentum, which is independent of the mass of the particle.