Maximal-acceleration phase space relativity from Clifford algebras

TL;DR

This paper introduces a new physical model linking maximum speed and minimal length scales through Clifford algebras, proposing a maximal-acceleration relativity principle in phase space that aligns with previous theoretical predictions.

Contribution

It develops a Clifford algebra-based framework for maximal-acceleration relativity, offering a more physically consistent approach than kappa-deformed quantum groups.

Findings

Maximal proper acceleration is a = c^2/Λ, consistent with prior theories.

Clifford algebra approach provides a natural minimal scale in phase space.

Extended Scale Relativity with Clifford spaces is more physically appealing.

Abstract

We present a new physical model that links the maximum speed of light with the minimal Planck scale into a maximal-acceleration Relativity principle in the spacetime tangent bundle and in phase spaces (cotangent bundle). Crucial in order to establish this link is the use of Clifford algebras in phase spaces. The maximal proper-acceleration bound is a = c^2/ \Lambda in full agreement with the old predictions of Caianiello, the Finslerian geometry point of view of Brandt and more recent results in the literature. We present the reasons why an Extended Scale Relativity based on Clifford spaces is physically more appealing than those based on kappa-deformed Poincare algebras and the inhomogeneous quantum groups operating in quantum Minkowski spacetimes. The main reason being that the Planck scale should not be taken as a deformation parameter to construct quantum algebras but should exist already as the minimum scale in Clifford spaces.