As I understand history, before general relativity Einstein tried(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# Elastic forces and relativity

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