Status of Relativity with observer-independent length and velocity scales

TL;DR

This paper updates the status of a modified relativity framework incorporating observer-independent length and velocity scales, exploring algebraic structures like kappa-Poincare' to support these new postulates.

Contribution

It proposes a consistent formulation of relativity with observer-independent scales and discusses the role of kappa-Poincare' algebra in realizing these ideas.

Findings

Consistent formulation of relativity with observer-independent length and velocity scales.

Extension of kappa-Poincare' algebra tools to support new relativity postulates.

Revised understanding of energy-momentum coproduct in this context.

Abstract

I have recently shown that it is possible to formulate the Relativity postulates in a way that does not lead to inconsistencies in the case of space-times whose structure is governed by observer-independent scales of both velocity and length. Here I give an update on the status of this proposal, including a brief review of some very recent developments. I also emphasize the role that one of the kappa-Poincare' Hopf algebras could play in the realization of a particular example of the new type of postulates. I show that the new ideas on Relativity require us to extend the set of tools provided by kappa-Poincare' and to revise our understanding of certain already available tools, such as the energy-momentum coproduct.