The principle of relative locality

TL;DR

This paper introduces a framework where the fundamental invariant for physics is phase space, leading to a concept of relative locality where different observers perceive spacetime differently, but agree on local interactions.

Contribution

It develops a theory of relative locality based on deforming momentum space, linking its geometry to observable effects and extending the relativity principle beyond spacetime.

Findings

Interactions are local in local observer coordinates.

Momentum space geometry affects energy-momentum conservation laws.

Experimental signatures of momentum space deformations are discussed.

Abstract

We propose a deepening of the relativity principle according to which the invariant arena for non-quantum physics is a phase space rather than spacetime. Descriptions of particles propagating and interacting in spacetimes are constructed by observers, but different observers, separated from each other by translations, construct different spacetime projections from the invariant phase space. Nonetheless, all observers agree that interactions are local in the spacetime coordinates constructed by observers local to them. This framework, in which absolute locality is replaced by relative locality, results from deforming momentum space, just as the passage from absolute to relative simultaneity results from deforming the linear addition of velocities. Different aspects of momentum space geometry, such as its curvature, torsion and non-metricity, are reflected in different kinds of deformations of the energy-momentum conservation laws. These are in principle all measurable by appropriate experiments. We also discuss a natural set of physical hypotheses which singles out the cases of momentum space with a metric compatible connection and constant curvature.