As I understand history, before general relativity Einstein tried and failed to find a Lorenz invariant description of gravitational forces that would reduce suitably to Newtonian gravity in appropriate cases (in retrospect it seems obvious why such a description cannot exist). How do elastic forces work relativistically? I am quite sure that there does not exist a Lorenz invariant force that reduces to F = -kx to a first approximation. This question is not particularly important since elastic forces are not fundamental, but it seems to me it would be a cute pure math exercise to find a reasonably elegent tensor equation that would reduce in the limit to F = -kx for small k, x, and m. So what would the analogue of the Einstein tensor be if a fundamental force had a Newtonian limit of F = -kx and that had been Einstein's pressing concern rather than gravity? Perhaps this question is more fiction than physics, but I think there might exist an elegant mathematical answer. Any thoughts?