The Box-Problem in Deformed Special Relativity

TL;DR

This paper investigates how deformations in special relativity with energy-dependent light speed affect the concept of space-time events and derives bounds that challenge certain modifications at first order in energy over the Planck mass.

Contribution

It introduces a framework to analyze nonlocality in deformed special relativity and establishes constraints that exclude first-order modifications in the energy over Planck mass.

Findings

Strong bounds on deformations of special relativity.

First-order modifications in energy over Planck mass are ruled out.

Nonlocality must be compatible with particle interactions.

Abstract

We examine the transformation of particle trajectories in models with deformations of Special Relativity that have an energy-dependent and observer-independent speed of light. These transformations necessarily imply that the notion of what constitutes the same space-time event becomes dependent on the observer's inertial frame. To preserve observer-independence, the such arising nonlocality should not be in conflict with our knowledge of particle interactions. This requirement allows us to derive strong bounds on deformations of Special Relativity and rule out a modification to first order in energy over the Planck mass.