  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.
