# Quantum Reference Frames at the Boundary of Spacetime

## TL;DR

This paper explores how boundary modes in gravity coupled to matter serve as quantum reference frames, linking bulk and boundary states through a multi-fingered Schrödinger equation in a perturbative setting.

## Contribution

It introduces a framework for understanding boundary modes as quantum reference frames in gravity, deriving constraints that relate bulk and boundary quantum states.

## Key findings

- Identifies matter, Coulomb, and boundary modes as reference frames.
- Derives a multi-fingered Schrödinger equation for relational evolution.
- Establishes constraints linking bulk and boundary quantum states.

## Abstract

An analysis is given of the local phase space of gravity coupled to matter to second order in perturbation theory. Working in local regions with boundaries at finite distance, we identify matter, Coulomb, and additional boundary modes. The boundary modes take the role of reference frames for both diffeomorphisms and internal Lorentz rotations. Passing to the quantum level, we identify the constraints that link the bulk and boundary modes. The constraints take the form of a multi-fingered Schr\"odinger equation, which determines the relational evolution of the quantum states in the bulk with respect to the quantum reference fields at the boundary.