Perhaps it's interesting to connect to the discussion of "internal view" perspective from the other thread. After all, the core problem in these two threads are related, and more or less the same.In Lubos Motl's view, string field theory is not background independent: http://motls.blogspot.com/2008/10/observables-in-quantum-gravity.html
Also has interesting comments about the emergence of space and time, btw.
Lubos writes in the first two paragraph in an obvious way, what may not be so obvious in the context of consideration (the future understanding of foundations of physics):
"The goal of every quantum-mechanical theory is to predict the probabilities that particular physical quantities - "observables" - will take one value or another value after some evolution of the system, assuming certain initial conditions."
"Mathematics of quantum mechanics makes it inevitable that observables have to be identified with linear operators on the Hilbert space of allowed states."
This is rushing too fast. One of the key issues at least from my point of view, is that we should ask for a "physical inside basis". Then the concept of a continuum probability immediatly appears somewhat ambigous. The notion of a defined probability, implies the notion of a uniqued microstructure, or probability space.
Usually one considers the information needed to specify a distribution, in a distribution space. But one rarely considers the information needed to speficy the distribution space itself.
What is, from the inside point of view, the meaning of probability of a future event?
Does the repetitive, frequentist interpretation really make sense here? If not, it suggest that we do not understand the proper physical meaning of this "probability".
This is really basic stuff, and seemingly may have little to do with discussing spacetime, but the fact it's basic, and even part of our very reasoning, makes it even more remarkable and dangerous to not question it. This particular point, wasn't mentioned by Dreyer, but i think doing so, would take the vision of the ideas yet one step further. That is, the ultimate consequence of the "inside view" is a deep sort of "inside logic", and this is where I want to start.
One can not just talk about "the probability" unless the full process of acquisition, processing and computing the LIMIT, is made, as it's acknowledge tht this is not mathematical computations made in a parallell universe with infinitely fast computers and infinite memory; the "inside vision" constrains this to be physical processes!
(This is a further comment on the Dreyer's work, but put in this context. I think the more all questions can connect to a common issue for discussion, the more interesting new angles might emerge out of the discussion)