In consistent histories, for gauge theories, can the projection operators used in the chains be not gauge invariant?
In quantum gravity, for a projection operator to be gauge invariant means it has to be diffeomorphism invariant. There are no localized diffeomorphism invariant operators, not even localized in time. No localized observables.
So, what are the permissible chains in quantum gravity? Do they have to be delocalized, or localized on the boundaries of spacetime?
Are space and time illusions, as Andrew Strominger claimed? A Cosmic Hologram projecting out the illusion that is spacetime from the future boundary of time?