# Dittrich: Prospects in (Canonical) Quantum Gravity

2013-09-28 09:06:18: The lecture theatre is steadily getting into an excited state about the upcoming talk…

2013-09-28 09:12:55: The title: “Prospects in (canonical) Quantum Gravity”

2013-09-28 09:18:27: And we’re off. Dittrich begins with some deep questions:

“What is observable?

What is vaccum?”

What is nothing?How can we now that there is something?”

2013-09-28 09:40:42: More difficult example (due to Dittrich & Tambornino): Two-point function of scalar field relative to (four) clock scalars.

${\phi(\Psi), \phi(\Psi + \epsilon)} = G(\Psi, \Psi + \epsilon) \left ( 1 + \frac{Energy(\phi)}{Energy(\Psi)} \right )$

where G is the Green’s function on fixed background.

The resolution limit for degrees of freedom depends on the energy of clocks: the higher the energy, the higher the resolution.

There is general amusement at the proposal for “fashionable” clocks: Just change clocks whenever necessary!

2013-09-28 09:55:27: ad 2). What is vacuum?

It surely isn’t a simple object. Maybe one of the following?

– lowest-energy state

– invariant under symmetries of the background space-time

– encode the geometry of Minkowski space

– cyclic state which generates the Fock space.

In LQG, we have a kinematical vacuum. (Simple: it’s a box!)

In all seriousness: It’s a peculiar state. In LQG, it’s maximally squeezed state, in the sense that all spatial geometry operators have zero expectation value on it, and zero fluctuations! It’s a state of no spatial geometry. Truly nothing!

As in non-gravitational quantum theory, we can build a highly excited state from the vacuum by applying loads of ‘creation operators’, based on graphs.

The LQG representation of the kinematical observable algebra is unique! I.e., it is

– cyclic

– irreducible, and it

– carries a representation of spatial diffeos.

2013-09-28 09:59:24: We can embed a discrete state into a contiuum theory and describe those states as equivalence classes of states in that theory.

Cylindrical consistency ensures that the result of a computation (e.g. an inner product, an expectation value) does not depend on which representative one chooses. This gives us a contiuum theory!

Huggett: where does the cylinder come in? Artefact from QFT!

How do we embed? embeddings should be determined by the dynamics of the theory; and fine- and coarse graining should play a role!

2013-09-28 10:01:53: How do we get a vacuum of a statistical system? Dittrich has the answer.

More boxes. Lots more boxes!

2013-09-28 10:03:19: Now moving from 1+1D to 2D!

2013-09-28 10:12:12: We can apply all this to spin foams / spin nets!

The key question is this. Is there a phase which leads to smooth space times?

Some promising results! Dittrich & collaborators have found fix points from which one could extract different systems of embedding maps. Those would correspond to different (non-) realisations of ’emergence of space-time).

Task for the future: Expand the theory around this vacuum!

Coming back to the initial question: What is (quantum) space-time? Dittrich suggests the time scales for constructing an answer are ~2500ys. Challenge accepted!

2013-09-28 10:19:29: Bianca Dittrich takes questions from Butterfield and Pitts.