Dual redshift on Planck-scale-curved momentum spaces

Understand

Several approaches to the investigation of the quantum-gravity problem have provided "theoretical evidence" of a role for the Planck scale in characterizing the geometry of momentum space.

• One of the main obstructions for a full exploitation of this scenario is the understanding of the role of the Planck-scale-curved geometry of momentum space in the correlations between emission and detection times, the "travel times" for a particle to go from a given emitter to a given detector.
• These travel times appear to receive Planck-scale corrections for which no standard interpretation is applicable, and the associated implications for spacetime locality gave rise to the notion of "relative locality" which is still in the early stages of investigation.
• We here show that these Planck-scale corrections to travel times can be described as "dual redshift" (or "lateshift"): they are manifestations of momentum-space curvature of the same type already known for ordinary redshift produced by spacetime curvature.