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.
Versions
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BibTeX
@misc{torrome2026notion,
title = {{On the notion of kinetic energy in a spacetime of maximal proper acceleration}},
author = {Ricardo Gallego Torromé},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12510},
eprint = {2610.12510},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12510},
}
RIS
TY - UNPB
TI - On the notion of kinetic energy in a spacetime of maximal proper acceleration
AU - Ricardo Gallego Torromé
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.12510
UR - https://arxiv.org/abs/2610.12510
AB - 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.
ER -