Low Energy Description of Quantum Gravity and Complementarity

TL;DR

The paper develops a covariant, observer-centric framework for low-energy quantum gravity that preserves locality while incorporating non-global spacetime effects associated with complementarity. It introduces an observer horizon where the local acceleration reaches the cutoff $M_*$ to separate low-energy physics from trans-Planckian stringy physics and builds a covariant Hilbert space ${\mathcal H}_{\rm QG}$ decomposed as ${\mathcal H}_{\rm QG} = {\mathcal H} \oplus {\mathcal H}_{\rm sing}$ with horizon-based organization ${\mathcal H} = \bigoplus_{\partial{\cal M}} {\mathcal H}_{\partial{\cal M}}$, including a bulk/boundary split constrained by holographic bounds. By using observer-centric coordinates and a clock-based Schrödinger evolution, the framework explains how local bulk physics remains accessible while boundary degrees of freedom on horizons encode exterior regions under frame changes, addressing issues like firewalls through complementarity. The approach yields concrete prescriptions for when and where semi-classical spacetime ceases to exist (via $\lambda_{\rm obs}$, $\lambda_{\rm app}$, $\lambda_{\rm sing}$, and $\lambda_{\rm conj}$) and offers a unified picture in which horizon dynamics reconcile unitarity with the equivalence principle, albeit with caveats about state-dependence and the full theory above $M_*$. Overall, the work provides a structured path toward incorporating horizon and trans-Planckian physics into a consistent low-energy quantum gravity description, with detailed future work to connect to string theory and resolve remaining conceptual issues.

Abstract

We consider a framework in which low energy dynamics of quantum gravity is described preserving locality, and yet taking into account the effects that are not captured by the naive global spacetime picture, e.g. those associated with black hole complementarity. Our framework employs a "special relativistic" description of gravity; specifically, gravity is treated as a force measured by the observer tied to the coordinate system associated with a freely falling local Lorentz frame. We identify, in simple cases, regions of spacetime in which low energy local descriptions are applicable as viewed from the freely falling frame; in particular, we identify a surface called the gravitational observer horizon on which the local proper acceleration measured in the observer's coordinates becomes the cutoff (string) scale. This allows for separating between the "low-energy" local physics and "trans-Planckian" intrinsically quantum gravitational (stringy) physics, and allows for developing physical pictures of the origins of various effects. We explore the structure of the Hilbert space in which the proposed scheme is realized in a simple manner, and classify its elements according to certain horizons they possess. We also discuss implications of our framework on the firewall problem. We conjecture that the complementarity picture may persist due to properties of trans-Planckian physics.

Figures (1)

• Figure 1: A schematic depiction of the observer-centric coordinate system.