A question for the end of the talk: Does BI lead to The End of Time (Barbour) or Time Reborn (Smolin)?

He’ll set things up by telling us about classical varieties of BI, so…

3 views of Background Independence:

a. Diffeomorphism Invariance: Following Guilini and Rickles <M,D,B> where D are dynamical fields and B are background fields. We have general covariance if diffeomorphisms applied to both B and D take solutions to solutions. We have invariance if we can transform only the D fields and take solutions to solutions. So GR, with no B fields is both covariant and invariant under diffeomorphisms…

b. Absolute v. Dynamical objects: Anderson and Friedman. Absolute objects are those that are the same in every solution of the theory… standard Anderson line.

c. A matter of degree?: Following Gordon Belot – Backgrounf is a fixed stage on which the physics of the theory is set. We have clear cases of BI when we have fixed fields determining geometry. Need to define an abstract geometry – fully background dependent theories are then those that only realize one abstract geometry (so again, every solution has the same abstract geometry). In full BI, no two solutions have the same abstract geometry. Near background dependence – family of abstract geometries realized in the theory is finite dimensional. Near background independence – family of abstract geometries is infinite dimensional.  (Carlip QG in 2+1 dimensions is a case of near background dependent).

Oriti: isn’t the actual geometry here fixed as minkowski? Only topological degrees of freedom.