Observing Shape in Spacetime

TL;DR

This paper introduces the concept of 'Shape Observers' as conformal reference frames in spacetime, establishing a holographic duality that links boundary conformal structures to bulk physics in maximally symmetric spacetimes.

Contribution

It proposes a new notion of conformal reference frames called 'Shape Observers' and provides a precise dictionary relating them to traditional inertial frames, advancing the understanding of holographic dualities in gravity.

Findings

Shape Observers are defined on asymptotic boundaries and relate to bulk physics.

A precise dictionary between conformal and inertial reference frames is established.

The approach offers a classical holographic correspondence applicable to complex spacetimes.

Abstract

The notion of "reference frame" is a central theoretical construct for interpreting the physical implications of spacetime diffeomorphism invariance in General Relativity. However, the alternative formulation of classical General Relativity known as Shape Dynamics suggest that a subset of spacetime diffeomorphisms - namely hypersurface deformations - are, in a certain sense, dual to spatial conformal (or Weyl) invariance. Moreover, holographic gauge/gravity dualities suggest that bulk spacetime diffeomorphism invariance can be replaced by the properties of boundary CFTs. How can these new frameworks be compatible with the traditional notion of reference frame so fundamental to our interpretation of General Relativity? In this paper, we address this question by investigating the classical case of maximally symmetric spacetimes with a positive cosmological constant. We find that it is possible to define a notion of "Shape Observer" that represents a conformal reference frame that is dual to the notion of inertial reference frame in spacetime. We then provide a precise dictionary relating the two notions. These Shape Observers are holographic in the sense that they are defined on the asymptotic conformal boundaries of spacetime but know about bulk physics. This leads to a first principles derivation of an exact classical holographic correspondence that can easily be generalized to more complicated situations and may lead to insights regarding the interpretation of the conformal invariance manifest in Shape Dynamics.