Volume 18: Pages 286-299, 2005

Discrete Momentum Mechanics and Faster‐than‐Light Transition

Munir H. K. Al‐Hashimi

Institute of Theoretical Physics, Bern University, Sidlerstrasse 5, Bern 3012 Switzerland

In this work a new mechanics will be studied that is based on the hypothesis that the change in linear momentum of a particle happens as discrete pulses. By using this hypothesis and by considering Newton's relation between energy and momentum, and the law of mass and energy conservation as a priori, one can derive the Einstein dispersion relation as a zero approximation without using Lorentz transformations. Other terms will be derived as corrections to this relation. It will be shown that the effect of the corrections will be smaller and smaller with the increase of momentum. The work will offer an explanation of why the velocity of light seems to be constant regardless of the velocity of the source, and under which condition this will change. Also a prediction is made that faster‐than‐light transition could happen theoretically under certain conditions, and a nonzero mass photon can exist in nature. The work is purely classical in the sense that it doesn 't involve any uncertainty relations.

Keywords: discrete momentum, discrete linear momentum, discrete linear momentum mechanics, Einstein dispersion relation, Einstein energy‐momentum relation, special relativity, faster‐than‐light transition, photon's rest mass, kinetic mass‐velocity relation, correction to Einstein's relation, photons of very low energy, alternative to relativity

Received: January 22, 2004; Published online: December 15, 2008