[alicewong]

Theories based on local symmetries (ie gauge theories) are more general than theories based on global symmetries (eg special relativity). An example is to consider scale symmetry. General relativity is already covariant to global scale transformations, but requires an additional connection field to make it covariant to conformal transformations (local scale transformations). The Weyl conformal tensor (as the name indicates) is a conformal tensor. The Ricci tensor however is not a conformal tensor in general relativity. According to my interpretation of reality, conformal symmetry must be a symmetry of the laws of physics. However, I find this difficult to reconcile with the scale-dependence of quantum theory. One way around this is to introduce a "quantum field" that breaks the scale symmetry. This implies a small-scale structure to reality that I would prefer to be unnecessary. The multiverse might be a solution by going beyond individual spacetimes towards relationships between them. It is specifically the non-gravitational relationship between energy-momentum and spacetime that is the essence of quantum theory (classical general relativity is the gravitational relationship between energy-momentum and spacetime, and this is mathematically independent).

I wish I had your handle on things KJW. It really is a struggle for me. PS I added a bit to my original post to give you an idea where I was coming from. :-))