Large quantum gravity effects: Unexpected limitations of the classical theory

TL;DR

This paper demonstrates that quantum fluctuations in 3D gravity coupled to matter are significant unless photon parameters are extremely constrained, revealing limitations of classical gravity at quantum scales.

Contribution

It provides an exact solution for axi-symmetric 3D gravity with matter, showing quantum effects impose fundamental limits on classical descriptions.

Findings

Quantum fluctuations are large unless N(ħGω)^2 << 1.

Single Planckian photon causes significant metric uncertainties.

Results extend to certain 4D gravitational wave sectors.

Abstract

3-dimensional gravity coupled to Maxwell (or Klein-Gordon) fields is exactly soluble under the assumption of axi-symmetry. The solution is used to probe several quantum gravity issues. In particular, it is shown that the quantum fluctuations in the geometry are large unless the number and frequency of photons satisfy the inequality $\N(\hbar G\omega)^2 << 1$. Thus, even when there is a single photon of Planckian frequency, the quantum uncertainties in the metric are significant. Results hold also for a sector of the 4-dimensional theory (consisting of Einstein Rosen gravitational waves).