Ad 1). What are observables?
In QG, it is difficult to answer this question, and hence quantisation presents a challenge.
This is the perennial “Problem of time”, due to diffeomorphism symmetry. If this is taken to be a gauge symmetry, then time translations are also gauge, and hence unphysical.
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?”
The title: “Prospects in (canonical) Quantum Gravity”
The lecture theatre is steadily getting into an excited state about the upcoming talk…
Discussion.
Audience: Can you say a bit more about fine-tuning?
Daniel: The technique has been applied to a very simple model. We haven’t yet considered more complex models.
Audience: Question about the Bunch-Davies vacuum. Can you use other vacuum states?
Daniel: Yes, but that doesn’t change the fundamental question: How do you break the initial symmetry?
The quantity of interest (that is zero without CSL, but non-zero with CSL) is a result of a random walk on the complex plane… One can now calculate this quantity and compare it with the CMB data, and this, it turns out, let’s us calculate CSL predictions (like the collapse rate parameter).
In the SCG Einstein equation, the zero mode is responsible for the inflationary expansion, and the non-zero modes are responsible for the emergence of structure.
At the early stages of inflation, the scalar field’s vacuum state is homogeneous and isotropic (the Bunch-Davies vacuum). Now apply to this, the CSL theory (a particular dynamical collapse theory). The random collapses that result are then responsible for the emergence of structure out of initial homogeneity/isotropy.
Dynamical collapse theories, recall, unify Penrose’s U and R processes.
Daniel’s approach: Adapt this to situations involving quantum fields and gravitation, within a semi-classical framework. During inflation, gravity is classical, but matter is quantum.
Audience: So the deepest level should be ordinary QM?
Daniel: It should just be quantum, but whether it’s ordinary QM is unclear.
To address this, Daniel suggests a step back: We need to identify a physical process that can explain the emergence of the seeds of cosmic structure.
Proposal: Add to the inflationary paradigm some spontaneous dynamical collapse of the state function.
But: If one considers a slightly different theoretical quantity, the resulting prediction is not confirmed by observation.
Beyond Spacetime 