Quantum-first gravity

TL;DR

This paper proposes a quantum-centric framework for gravity, emphasizing a novel Hilbert space structure that reproduces classical gravity and quantum field theory in appropriate limits, addressing localization and subsystem independence.

Contribution

It introduces a new Hilbert space structure based on inclusion maps for quantum gravity, challenging tensor product approaches and aiming to unify quantum mechanics with gravitational phenomena.

Findings

Hilbert space networks encode gravitational gauge invariance

Localization in quantum gravity may differ from traditional tensor factorization

Constraints from unitarity influence subsystem evolution

Abstract

This paper elaborates on an intrinsically quantum approach to gravity, which begins with a general framework for quantum mechanics and then seeks to identify additional mathematical structure on Hilbert space that is responsible for gravity and other phenomena. A key principle in this approach is that of correspondence: this structure should reproduce spacetime, general relativity, and quantum field theory in a limit of weak gravitational fields. A central question is that of "Einstein separability," and asks how to define mutually independent subsystems, e.g. through localization. Familiar definitions involving tensor products or operator subalgebras do not clearly accomplish this in gravity, as is seen in the correspondence limit. Instead, gravitational behavior, particularly gauge invariance, suggests a network of Hilbert subspaces related via inclusion maps, contrasting with other approaches based on tensor-factorized Hilbert spaces. Any such localization structure is also expected to place strong constraints on evolution, which are also supplemented by the constraint of unitarity.