Gauge dependence of effective gravitational field.II. Point-like measuring device

TL;DR

This paper demonstrates that the effective gravitational field measured by a point-like device depends on gauge choice, challenging the assumption of gauge independence in classical point-particle equations of motion.

Contribution

It provides a detailed analysis showing gauge dependence of the effective gravitational potential for point-like particles, countering previous conjectures of gauge invariance.

Findings

Effective gravitational potential depends on Feynman gauge parameter.

Gauge dependence persists in the one-loop effective action.

Challenges the belief in gauge invariance of classical equations of motion.

Abstract

The role of the measurement process in resolving the gauge ambiguity of the effective gravitational potential is reexamined. The motion of a classical point-like particle in the field of an arbitrary linear source, and in the field of another point-like particle is investigated. It is shown that in both cases the value of the gravitational field read off from the one-loop effective action of the testing particle depends on the Feynman weighting parameter. The found dependence is essential in that it persists in the expression for the gravitational potential. This result disproves the general conjecture about gauge independence of the effective equations of motion of classical point-like particles.