Modified gravity and the origin of inertia

TL;DR

This paper investigates how modified gravity theories, which violate Birkhoff's theorem, can explain inertia as a force arising from distant matter, predicting deviations from Newton's law at low accelerations that are experimentally testable.

Contribution

It demonstrates that in certain modified gravity theories, inertia emerges from the influence of distant matter, leading to testable deviations from Newtonian physics at low accelerations.

Findings

Inertia can be derived as a force proportional to mass and acceleration.

Deviations from Newton's law occur at very low accelerations.

Predictions are applicable to gravity theories with Yukawa-like weak field forces.

Abstract

Modified gravity theory is known to violate Birkhoff's theorem. We explore a key consequence of this violation, the effect of distant matter in the Universe on the motion of test particles. We find that when a particle is accelerated, a force is experienced that is proportional to the particle's mass and acceleration and acts in the direction opposite to that of the acceleration. We identify this force with inertia. At very low accelerations, our inertial law deviates slightly from that of Newton, yielding a testable prediction that may be verified with relatively simple experiments. Our conclusions apply to all gravity theories that reduce to a Yukawa-like force in the weak field approximation.