Theories with maximal acceleration

TL;DR

This paper explores the concept of maximal acceleration in physics, discussing its theoretical foundations, formulations, and potential implications for understanding minimal time scales and quantum gravity effects.

Contribution

It introduces four major formulations of kinematics with maximal acceleration and discusses their phenomenological implications.

Findings

Maximal acceleration relates to minimal time scales in physical systems.

Four formulations of kinematics with maximal acceleration are presented.

Potential phenomenological consequences are discussed for future research.

Abstract

Maximal accelerations are related to the existence of a minimal time for a given physical system. Such a minimal time can be either an intrinsic time scale of the system or connected to a quantum gravity induced ultraviolet cut off. In this paper we pedagogically introduce the four major formulations for kinematics accounting for a maximal acceleration. Some phenomenological repercussion are offered as hints for future investigations.