Dual redshift on Planck-scale-curved momentum spaces

TL;DR

This paper explores how Planck-scale curvature in momentum space affects particle travel times, revealing a dual redshift effect analogous to spacetime redshift, and introduces the concept of relative momentum-space locality within quantum gravity research.

Contribution

It demonstrates that Planck-scale corrections to travel times can be understood as dual redshift due to momentum-space curvature, linking it to known spacetime redshift phenomena and expanding the understanding of relative locality.

Findings

Planck-scale corrections are described as dual redshift.

Identifies relative momentum-space locality as analogous to spacetime locality.

Suggests relevance to Born's duality in quantum gravity.

Abstract

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. In turn we can identify the novel notion of "relative momentum-space locality" as a known but under-appreciated feature associated to ordinary redshift produced by spacetime curvature, and this can be described in complete analogy with the relative spacetime locality that became of interest in the recent quantum-gravity literature. We also briefly comment on how these findings may be relevant for an approach to the quantum-gravity problem proposed by Max Born in 1938 and centered on Born duality.