Causal loop in the theory of relative locality

TL;DR

This paper investigates how the concept of relative locality, a Planck-scale modification of special relativity, can lead to causal loops, potentially violating causality even in minimal deformations of the Poincaré group.

Contribution

It demonstrates the existence of causal loops within the framework of relative locality, highlighting potential causality violations at the Planck scale.

Findings

Causal loops can arise in relative locality models.

Even weak deformations of the Poincaré group can violate causality.

The study provides a general construction of on-shell loop processes.

Abstract

We find that relative locality, a recently proposed Planck-scale deformation of special relativity, suffers from the existence of causal loops. A simple and general construction of such on-shell loop processes is studied. We then show that even in one of the weakest deformations of the Poincar\'e group in relative locality, causality can be violated.