Between quantum and classical gravity: Is there a mesoscopic spacetime?

TL;DR

This paper explores the possibility of a mesoscopic regime of spacetime between quantum and classical scales, arguing that such a regime either does not exist or only allows tiny corrections to physical fields, not geometry.

Contribution

It provides a theoretical argument against the existence of a mesoscopic spacetime regime that preserves the relativity principle, clarifying the nature of quantum-to-classical transition.

Findings

Either no mesoscopic regime exists, or corrections are limited to physical fields.

The relativity principle constrains the possible intermediate regimes.

Quantum gravitational effects on geometry are likely negligible at mesoscopic scales.

Abstract

Between the microscopic domain ruled by quantum gravity, and the macroscopic scales described by general relativity, there might be an intermediate, "mesoscopic" regime, where spacetime can still be approximately treated as a differentiable pseudo-Riemannian manifold, with small corrections of quantum gravitational origin. We argue that, unless one accepts to give up the relativity principle, either such a regime does not exist at all (hence, the quantum-to-classical transition is sharp), or the only mesoscopic, tiny corrections conceivable are on the behaviour of physical fields, rather than on the geometric structures.