Yet, relational observables find wide application.
The solution to the clock problem is deparametrisation, which gives us a one-parameter family of gauge fixings, which serves as a nice system of clocks.
Example: longitudinal gauge for flat/homogenous spacetimes.
Dittrich discusses the “naive” solution of relational observables.
Spatial positions together with time co-ordinates are observables, as in:
“Position of particle at 5pm” is an observable.
But this is problematic:
a) In QG we do pre- or postdictions, seemingly incompatible
b) What are good clocks?
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.
Beyond Spacetime 