On the notion of kinetic energy in a space–time 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 one-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 the Born reciprocity principle but formulated in the framework of higher order jet space–time 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 separation conditions at the classical level of the two dynamical sectors.