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In fact, it was by demanding a local version of special relativity that Einstein got the equations for the metric field that are the core of general relativity! And it is by demanding local versions of rotations in property spaces that C.N. Yang and Robert Mills found the equations that bear their name and govern the weak and strong fluids. Yang and Mills built on the work of Herman Weyl, who showed that Maxwell's equations for the electromagnetic fluid can be derived in that way.
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