Parisi-Sourlas-like dimensional reduction of quantum gravity in the presence of observers

One of the key sources of incompatibility between general relativity and quantum mechanics is non-renormalizability of perturbative quantum gravity in $3+1$ spacetime dimensions. Here, we show that in the presence of disorder induced by random networks of observers measuring covariant quantities such as scalar curvature $(3+1)$-dimensional quantum gravity exhibits an effective dimensional reduction analogous to the Parisi-Sourlas reduction observed for quantum field theories in random external fields. After averaging over associated disorder, the upper critical dimension of perturbative quantum gravity is lifted from $D_{\rm cr}=1+1$ to $D_{\rm cr}=3+1$ dimensions, effectively making the 4-dimensional theory renormalizable and controllable at all scales.