Quantum correction to classical gravitational interaction between two polarizable objects

TL;DR

This paper investigates the quantum correction to the classical gravitational interaction between two polarizable objects using linearized quantum gravity, revealing a potential that varies with distance as r^{-11} and r^{-10} in different regimes.

Contribution

It provides a quantum field-theoretic calculation of gravitational interaction corrections between polarizable objects, confirming previous results and demonstrating the robustness of linearized quantum gravity at low energies.

Findings

Interaction potential behaves like r^{-11} in the retarded regime.

Interaction potential behaves like r^{-10} in the near regime.

Results agree with previous approaches.

Abstract

When gravity is quantized, there inevitably exist quantum gravitational vacuum fluctuations which induce quadrupole moments in gravitationally polarizable objects and produce a quantum correction to the classical Newtonian interaction between them. Here, based upon linearized quantum gravity and the leading-order perturbation theory, we study, from a quantum field-theoretic prospect, this quantum correction between a pair of gravitationally polarizable objects treated as two-level harmonic oscillators. We find that the interaction potential behaves like $r^{-11}$ in the retarded regime and $r^{-10}$ in the near regime. Our result agrees with what was recently obtained in different approaches. Our study seems to indicate that linearized quantum gravity is robust in dealing with quantum gravitational effects at low energies.