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julian

Gold Member

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Is it possible to formulate a dynamical theory of spacetime geometry that isn't invariant under active diffeomorphisms? Or does requiring no invariance under active diffeomorphisms restore of gravity as a force?

If yes, then it makes it difficult to disentangle the issue of active diffeomorphisms from the idea that gravity is dynamical spacetime and allows people to believe the shift in perspective in going from SR to GR is solely to do with geometry being dynamical with matter determining the geomety over which it moves, in doing so dismissing the incredible fact that you can take the grav+matter fields and drag them over the spacetime manifold however you like with the new configuration being physically equivalent to the original one (i.e. active diffeomorphisms)?

Is invariance under active diffeomorphisms down to dynamical geometry + coordinate invariance? Is this why some people dismiss active diffeomorphisms as being coordinate transformations viewed differently?...despite the fact that there is a fundamental differnce between them?

If yes, then it makes it difficult to disentangle the issue of active diffeomorphisms from the idea that gravity is dynamical spacetime and allows people to believe the shift in perspective in going from SR to GR is solely to do with geometry being dynamical with matter determining the geomety over which it moves, in doing so dismissing the incredible fact that you can take the grav+matter fields and drag them over the spacetime manifold however you like with the new configuration being physically equivalent to the original one (i.e. active diffeomorphisms)?

Is invariance under active diffeomorphisms down to dynamical geometry + coordinate invariance? Is this why some people dismiss active diffeomorphisms as being coordinate transformations viewed differently?...despite the fact that there is a fundamental differnce between them?

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