Bulk Observers in Non-Factorizable Geometries

TL;DR

This paper investigates how effective distances are perceived in five-dimensional non-factorizable geometries, revealing that long geodesics with different transverse shifts appear identical to bulk observers, impacting the interpretation of measurements.

Contribution

It introduces a consistent way to define effective distances in non-factorizable geometries, accounting for transverse shifts and observer resolution.

Findings

Long geodesics with transverse shifts have nearly identical lengths.

Effective distances depend on the observer's resolution and position.

Provides a framework for interpreting measurements in non-factorizable geometries.

Abstract

We consider five dimensional non-factorizable geometries where the transverse dimension is bounded and the remaining (parallel) dimensions are not. We study the construction of effective theories at distances much longer than the transverse size. An observer unable to resolve the transverse direction can only measure distances along the parallel dimensions, but the non-factorizable geometry makes the length of a curve along the parallel dimension sensitive to where on the transverse direction the curve lies. We show that long geodesics that differ in their endpoints only by shifts along the transverse direction all have the same length to within the observer's resolution. We argue that this is the correct notion of distance in the effective theory for a bulk observer. This allows us to present a consistent interpretation of what is measured by observers that live either on a brane or in the bulk.