Vidotto distinguishes two senses of discreteness in LQG: a real physical discreteness that follows just from the existence of a minimum length scale, and the discreteness that comes with starting from spin networks, graphs etc.

Judging from the discussion paper (here) and the slides, Vidotto’s talk will argue that in LQG, the ancient dispute between substantivalists and relationalists gets resolved by being dissolved: space(time) is a real quantum field, but quantum theory is inherently relational, and moreover the classical gravitational field (= spacetime) emerges from a discrete, i.e. atomistic, basis.  Her talk will represent a Rovellian philosophy and approach to quantum gravity.

Butterfield: question on spin foam cosmology, about relaxing the various approximations and about obtaining more genaral anisotropic geometries. Vidotto: one can indeed generalize the class of states used, and use them to study anisotropic situations. A more difficult question is the dynamical one, i.e. relaxing the approximation to the dynamics that are used. But results are encouraging.

Conclusions: highlight two main open issues. One: dynamical – what physical processes lead to decoherence in this context. Two: conceptual – do spin foams resolve the problem of time?

Application of general idea to the setting of “spin foam cosmology”, where results are available about obtaining semi-classicality in the spin foam setting. Lots of unsettled questions but interesting results to consider. Brief summary of framework and of approximations used.

Can write down formaly the decoherence functional in terms of the sum over 2-complexes, which is however very difficult to control. Still, one can at least identify which properties such functional should satisfy.

Comment by Dittrich: these observables are not diffeo-invariant, however. Indeed, an interesting issue, says the speaker.