Principle of Equivalence at Planck scales, QG in locally inertial frames and the zero-point-length of spacetime

TL;DR

This paper explores how the Principle of Equivalence influences quantum gravitational effects near the Planck scale, demonstrating its role in ensuring consistency between quantum geometry and matter field propagators.

Contribution

It reveals that the Principle of Equivalence at sub-Planck scales ensures the consistency of quantum corrections from geometry and matter fields, highlighting its subtle role in quantum gravity.

Findings

Zero-point-length modifies matter propagators at mesoscopic scales.

Consistency between geometric and matter corrections is maintained by the Principle of Equivalence.

Quantum geometry effects are compatible with matter field self-gravity corrections.

Abstract

Principle of Equivalence makes effects of classical gravity vanish in local inertial frames. What role does the Principle of Equivalence play as regards quantum gravitational effects in the local inertial frames? I address this question here from a specific perspective. At mesoscopic scales close to, but somewhat larger than, Planck length one could describe quantum spacetime and matter in terms of an effective geometry. The key feature of such an effective quantum geometry is the existence of a zero-point-length. When we proceed from quantum geometry to quantum matter, the zero-point-length will introduce corrections in the propagator for matter fields in a specific manner. On the other hand, one cannot ignore the self-gravity of matter fields at the mesoscopic scales and this will also modify the form of the propagator. Consistency demands that, these two modifications - coming from two different directions - are the same. I show that this non-trivial demand is actually satisfied. Surprisingly, the Principle of Equivalence, operating at sub-Planck scales, ensures this consistency in a subtle manner.