Relative motion in euclidean space and time

Abstract

This is an expository paper of a new approach to the special theory of relativity. Rewriting Lorentz Transformation equations in differential form, the basic equations of unrestricted motion are formulated in the euclidean 4-space-time, showing that such a formulation is posible, with the advantage of cancellation of all paradoxes and giving a clear physcal picture of the space and time, as well as the meaning of the relativistic transformation in the free space. Starting with the principle of momentum conservation, the dynamics of the free particle is also considered and, by following the proposed new line of attack, quite unusual results are derived, such as the volume of the Universe or the mass (and energy) invariance principle.