Modeling transverse relative locality

TL;DR

This paper explores transverse relative locality in relativistic theories, revealing its significance comparable to longitudinal effects and connecting it to phenomena like dual gravity lensing and potential spacetime noncommutativity.

Contribution

It extends the concept of relative locality to the transverse direction, demonstrating its importance and linking it to dual gravity lensing and noncommutative spacetime models.

Findings

Transverse relative locality is as significant as longitudinal relative locality.

Dual gravity lensing is a component of transverse relative locality.

Potential spacetime noncommutativity enhances transverse relative locality effects.

Abstract

We investigate some aspects of relativistic classical theories with "relative locality", in which pairs of events established to be coincident by nearby observers may be described as non-coincident by distant observers. While previous studies focused mainly on the case of longitudinal relative locality, where the effect occurs along the direction connecting the distant observer to the events, we here focus on transverse relative locality, in which instead the effect is found in a direction orthogonal to the one connecting the distant observer to the events. Our findings suggest that, at least for theories of free particles such as the one in arXiv:1006.2126, transverse relative locality is as significant as longitudinal relative locality both conceptually and quantitatively. And we observe that "dual gravity lensing", first discussed in arXiv:1103.5626, can be viewed as one of two components of transverse relative locality. We also speculate about a type of spacetime noncommutativity for which transverse relative locality could be particularly significant.