Quantum causality constraints on kappa-Minkowski space-time

TL;DR

This paper develops a notion of causality in 1+1-dimensional $ppa$-Minkowski space-time using Lorentzian noncommutative geometry, revealing quantum constraints on causal relations akin to a generalized speed limit.

Contribution

It introduces a new causality concept in $ppa$-Minkowski space-time within Lorentzian noncommutative geometry, addressing the challenge of defining causality with noncommutative time.

Findings

Causality can be defined in $ppa$-Minkowski space-time.

A quantum speed limit constrains causal relations.

The framework extends traditional causality concepts to noncommutative geometry.

Abstract

The $\kappa$-Minkoswki space-time provides a quantum noncommutative-deformation of the usual Minkowski space-time. However, a notion of causality is difficult to be defined in such a space with noncommutative time. In this paper, we define a notion of causality on a (1+1)-dimensional $\kappa$-Minkoswki space-time using the more general framework of Lorentzian noncommutative geometry. We show that this notion allows specific causal relations, but limited by a general constraint which is a quantum generalization of the traditional speed of light limit.