Low Energy Description of Quantum Gravity and Complementarity

TL;DR

This paper proposes a low-energy quantum gravity framework that preserves locality, incorporates black hole complementarity, and distinguishes between low-energy physics and trans-Planckian effects using a relativistic observer-based approach.

Contribution

It introduces a novel observer-dependent description of gravity that clarifies the separation of low-energy and quantum gravitational effects, addressing the firewall problem.

Findings

Identifies the gravitational observer horizon as a cutoff surface.

Classifies Hilbert space elements by horizon properties.

Suggests complementarity persists due to trans-Planckian physics.

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.