On the notion of kinetic energy in a spacetime of maximal proper acceleration

Abstract

It is shown in this work that in spacetimes of maximal proper acceleration there are situations where a particle decelerates and simultaneously increases its kinetic energy. To illustrate the effect, a classical $1$-dimensional electric cavity-like scheme is discussed. The gain in kinetic energy by deceleration suggests an equivalence between velocity and acceleration from the energetic point of view. Such an equivalence is stated in a form resembling Born reciprocity principle but formulated in the framework of higher order jet spacetime geometry. We also show the existence in the theory of a dynamical superluminal sector for point particles with positive mass and characterized by superluminal speed and a proper acceleration larger than the maximal proper acceleration. Therefore, the speed of light and the maximal proper acceleration become only {\it separation conditions} at the classical level of the two dynamical sectors.