Geometries of Maximal Acceleration

TL;DR

This paper compares various geometric frameworks that impose an upper limit on particle acceleration, highlighting differences in their symmetry groups and implications for dynamical theories.

Contribution

It systematically analyzes and contrasts multiple geometric structures that set an upper acceleration bound, emphasizing their symmetry properties and impact on dynamics.

Findings

All structures imply an acceleration upper bound.

Different structures have distinct symmetry groups.

Implications for underlying dynamical theories vary.

Abstract

We discuss and compare several geometric structures which imply an upper bound to the acceleration of a particle measured in its rest system. While all of them have the same implications on the motion of a point particle, they differ in other important respects. In particular, they have different symmetry groups, which influence in a different way the search for an underlying dynamical theory.