On the General Covariance in the Bohmian Quantum Gravity

TL;DR

This paper demonstrates that in Bohmian quantum gravity, Einstein's equations are modified by non-covariant quantum corrections at the individual level, but covariance is restored statistically.

Contribution

It reveals the breakdown of general covariance at the individual level in Bohmian quantum gravity and its restoration at the statistical level.

Findings

Quantum corrections to Einstein's equations are non-covariant.

General covariance breaks down at the individual level.

Covariance is restored when considering statistical ensembles.

Abstract

It is shown explicitly that in the framework of Bohmian quantum gravity, the equations of motion of the space-time metric are Einstein's equations plus some quantum corrections. It is observed that these corrections are not covariant. So that in the framework of Bohmian quantum gravity the general covariance principle breaks down at the individual level. This principle is restored at the statistical level.