# Non-diff theories of dynamical spacetime

1. Mar 30, 2012

### julian

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?

Last edited: Mar 30, 2012
2. Mar 30, 2012

### atyy

Well, basically you have to say what you mean by "active diff". Some people define "active diff" = "no prior geometry" in which case it is not possible by definition.

3. Mar 30, 2012

### julian

By active diff I mean taking all the physical fields that are localised over the blank spacetime manifold and dragging them around however you like.

4. Mar 30, 2012

### atyy

Sure, even SR is invariant under active diff by that definition.

5. Mar 30, 2012

### julian

Sorry I meant to say if you drag all DYNAMAICAL fields. In SR the geometry is fixed by the prior given non-dynamical Minkowski metric, the dynamical field might be the Maxwell field for example but deforming that anyway you like will not end in a new solution...

Last edited: Mar 30, 2012