On of the (self-admitted) flaws in Newton's conception of gravity is that it's in terms of forces (or potentials) that act across large distances; it's part of

On of the (self-admitted) flaws in Newton's conception of gravity is that it's in terms of forces (or potentials) that act across large distances; it's part of his "hypotheses non fingo". One of the philosophically more pleasing things about GR is that it is local. But, of course, Newton's conception is a small-mass / low-velocity limit, so how can that be? GR says that the effect of stress/energy at a place x changes the metric at that place. But the metric is something made of derivatives, so the space in some small neighborhood (this is the local part) nearby gets deformed. That deformation is itself a form of stress, and so places in the neighborhood of x effect places THEIR neighborhoods and so on. So there's nothing built-in that's long-distance. Big long-distance effects are built up out of everybody talking to their immediate neighbors.