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There are two issues of locality. Entangled states and background independence. These are conceptionally different and it would help if you would stop throwing them together. **
In order to speak about an entangled state within the context of *background independent* quantum gravity, you have to be able to identify the local degrees of freedom (hence you need a background independent notion of locality) - something which is a priori given in background dependent QFT. In LQG you can only speak about superposition of rigged spin network states since you cannot identify the local degrees of freedom. If you throw in matter, let's say point particles, then these objects will quickly diffuse on the spin networks (as is known by QM), so how can you speak about local geometry when a single particle is smeared out over the distance of half a meter - say ? In that case you must be playing around with projection operators of the type : ``particle is on a vertex with such intertwiner, so many ingoing and outgoing edges and such spin labels´´ or ``This is the geometry, where is the particle?´´. But where is the OBSERVER ??
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One is the observer within the QM system, wavefunction of the universe style. Nobody knows how to do this (except perhaps for Hartle). It's a well known problem, and not specific to QG. **
I did not claim it was specific to QG, I said QG makes the question more urgent. By the way, I always have seen THAT problem as the main one to be solved, we observers form part of the universe and cannot be separated from it. This has to be a dynamical result and not an assumption.
**However if we declare a part of the system to be the observer we have a working interpretation relative to that observer Everett style. No classical boundary information needed. (morally that's how Rovelli get's a propagator, notice that the classical boundary conditions drop out, there is a quantum mechanical state to which the question is relative, a semiclassical one, a superposition of many spinnetworks, but a real quantum mechanical state)**
But one problem is to show that this is consistent within a real dynamical framework (!) - that is you need to adress the issue of decoherence properly. Here Rovelli just argues that *background dependent* QM *practice* has thought us it is like that; sweeping lots of the difficulties from the table like that.
**Classical GR, no matter. What are the local observables? If I construct them via Dittrich it is crucial to realize that Kinematical information (before implementing the diffeoinvariance) supplies the notion of locality. **
Like I said, that is a gauge dependent construction. But it does not need to be like that at all you know : most classical relativists would argue that observers actually are nothing but matter flows themselves. Observables are diffeomorphism invariants which you can construct from matter and the metric. The spirit of Einsteins theory is that everything is dynamical included observation itself - of course this is one of the clashes between GR and QM which are not just solved by some local gauge fixing.
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Without that, talking purely about the 4-geometries allowed by Einsteins equations and not about metrics we don't have a notion of locality and the question becomes meaningless.**
? The 4 - geometries allowed by Einsteins equations ARE the metrics.
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The notion of locality obtained by going kinematical refers to the possibility of auxiliary systems with the same kinematics being coupled to the background independent theory relative to which we ask local questions. Test particles.**
Well first of all, you cannot violate ``background independence´´ classically. Second, when you pick out a gauge, it needs to be dynamically determined and this goes at the cost of adding Lagrange multipliers in your action principle. This is actually something Karel Kuchar has written a lot about in his papers on the problems of quantisation in the Gaussian gauge.
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Your spinfoam objection has a precise analogue in classical GR and is resolved by Rovellis/Dittrichs work. There is nothing specifically Quantum mechanical about your objection. **
Of course there is something specifically quantum mechanical about my objections unless you separate the observer from an isolated subsystem of the universe (an option which I mentioned already). By the way when you pick out isolated subsystems that is tantamount putting on ``classical boundary conditions´´ - you have to be of bad will if you do not want to understand that.
** Freidel has constructed 2+1 background independent QFTs with testparticles. If I have a testparticle on a superposition of spin networks that is a sollution to the Hamiltonian constraint I can of course ask local questions with respect to it's location on the spin network. Just like I use testparticles in classical theory relative to which I can ask about the local state of the geometry (which I can't sensibly if I *only* work with the allowed geometries)**
I have heard about this: apart from the salient feature that there is no gravitation in 2+1 dimensions (the theory is just topological), it of course fairly obvious that you can ask local questions about the state of the geometry - like the ones I mentioned in the beginning. The particle, being in more geometries at once of course, and at the same time in more places at once in the same spin network. Of course, you can choose some time T which you call evolution, a parameter which you treat *classically* I presume (time should *also* be a quantum observable, no ?) and ask for the expectation value of the volume the particle is occupying or even a specific probability about the local geometry itself. It is just that for one realistic particle of dimensions of 10^{-18} meters you will have an immense number of states to consider.
**Is Quantum mechanics nonlocal? Not really. It leads to no nonlocal effects at least. That's one of the points of Rovellis relational QM which makes good sense if taken as an epistemology of QM rather then an interpretation.**
I am not going to nag about terminology here: Rovelli just does not address the issue of self consistency (of his relational QM) AFAIK by appealing to an argument that *experience* shows that it works consistently.
Look f-s, we clearly have different views here, when I speak about QG, I mean wave function of the universe, a unification between the observed and the observer. That is something LQG has stopped adressing, instead it took the more pragmatic road which is clear from the ideas behind relational QM (I am wondering when Rovelli is going to write a paper about consciousness and zombies).
Bedtime now.
Cheers,
Careful
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It seems extremely unlikely that perfect entanglement exists so on long distances any such line of thinking is saved by the very low measurement rates (which is actually a prediction in SED and therefore far from conspirational). But let's not discuss this now. 
The point is if that the background field is believed to act by pushing the electron towards this particular orbit, then by what phenomenon would an electron manage to maintain any other sort of orbital?
I was rather referring to point individuation, as that would be an example how you get "kinematical" background (i.e. manifold itself, of diff class rather) from dynamics (Einstein Eq's). I KNOW that such schemes are difficult, but no difficulty is too big to save the holy realism a la 19th century physics