Quantum gravity: a quantum-first approach

TL;DR

This paper proposes a quantum-first framework for gravity, emphasizing a Hilbert space structure compatible with general relativity and quantum theory, and addressing the challenge of defining independent subsystems in quantum gravity.

Contribution

It introduces a novel quantum-first approach that avoids traditional quantization, focusing on a suitable Hilbert space structure and addressing Einstein separability.

Findings

Networked Hilbert space structure for gravity

Compatibility with general relativity and quantum field theory

Insights into subsystem independence in quantum gravity

Abstract

A "quantum-first" approach to gravity is described, where rather than quantizing general relativity, one seeks to formulate the physics of gravity within a quantum-mechanical framework with suitably general postulates. Important guides are the need for appropriate mathematical structure on Hilbert space, and correspondence with general relativity and quantum field theory in weak-gravity situations. A basic physical question is that of "Einstein separability:" how to define mutually independent subsystems, e.g. through localization. Standard answers via tensor products or operator algebras conflict with properties of gravity, as is seen in the correspondence limit; this connects with discussions of "soft hair." Instead, gravitational behavior suggests a networked Hilbert space structure. This structure plus unitarity provide important clues towards a quantum formulation of gravity.