[Moderator's Note: This thread was split off from a previous thread because of a change of topic.] It doesn't. Matter influences the curvature of spacetime locally; the curvature of spacetime propagates to distant locations; and the curvature of spacetime at those distant locations tells the matter there how to move. In a static or nearly static situation, the "propagation" part is not easily tested; but there are small effects that show it. One of them is the perihelion precession of the planets; that wouldn't be there if gravity were an "instantaneous" Newtonian force acting through empty space.