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**I can do the same in LQG. **
- Of course you can.
Then what did you say I can not do in QG again? I thought your point was somehow that this amounted to unacceptable gaugefixing?
Yes when I say gaugeindependent in a fully constrained system that means frozen. Dittrichs observables are frozen observables on frozen states.
We started out talking about locality in Quantum mechanical systems without a background structure. So now you agree that in LQG I can play the same old relational space time scalar game.
This is of course one of the predecessors for (or a special case of) Rovellis game. You use a nongauginvariant quantity (the Rici scalar field) and relate it's value to another quantity that is nongaugeinvariant too in such a way that you get a gauge invariant quantity (Dittrich basically replays that game in the new language in her second paper on Observqbles in GR, and to my knowledge that is the first time the space time scalar game has actually been translated into real Dirac observables). Of course that's not the whole story since this does not reflect how we do real GR predictions. This is a chief concern, to make conceptionally clear how the actual predictions we make can be formulated in a background independent formalism.
*Matter information can be GENERICALLY retrieved from metric invariants.*
Are you talking about Kuchar's constructions now? Could you expand on this a bit?
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What are you actually saying I can not do in LQG?
You made very general points about what is impossible in Quantum Gravity. I point out that in LQG I can do these things so I provide a counterexample to your initial claims of incompatibility, no?
Now you are saying that we don't have a good Quantum algebra, that the quantization of GR has only partially succeeded so far. Well I would have to agree since Thiemann says the same thing as well. But what has that to do with your initial claims that background independence and locality are incompatible in Quantum mechanics?
"So, it is quite obvious that you can abstractly look for gauge invariant statements." So if I can do that, and these have a local interpretation in an appropriate sense of the word local (as you seem to agree for spacetime scalars for example which Dittrich treats with the same methods), then there is no fundamental conceptional incompatibility between Background independence, locality and QM, right?
So then there is no reason to conclude that background independence as suggested by GR is a red herring Quantum mechanically.
- Of course you can.
Then what did you say I can not do in QG again? I thought your point was somehow that this amounted to unacceptable gaugefixing?
Yes when I say gaugeindependent in a fully constrained system that means frozen. Dittrichs observables are frozen observables on frozen states.
We started out talking about locality in Quantum mechanical systems without a background structure. So now you agree that in LQG I can play the same old relational space time scalar game.
This is of course one of the predecessors for (or a special case of) Rovellis game. You use a nongauginvariant quantity (the Rici scalar field) and relate it's value to another quantity that is nongaugeinvariant too in such a way that you get a gauge invariant quantity (Dittrich basically replays that game in the new language in her second paper on Observqbles in GR, and to my knowledge that is the first time the space time scalar game has actually been translated into real Dirac observables). Of course that's not the whole story since this does not reflect how we do real GR predictions. This is a chief concern, to make conceptionally clear how the actual predictions we make can be formulated in a background independent formalism.
*Matter information can be GENERICALLY retrieved from metric invariants.*
Are you talking about Kuchar's constructions now? Could you expand on this a bit?
---
What are you actually saying I can not do in LQG?
You made very general points about what is impossible in Quantum Gravity. I point out that in LQG I can do these things so I provide a counterexample to your initial claims of incompatibility, no?
Now you are saying that we don't have a good Quantum algebra, that the quantization of GR has only partially succeeded so far. Well I would have to agree since Thiemann says the same thing as well. But what has that to do with your initial claims that background independence and locality are incompatible in Quantum mechanics?
"So, it is quite obvious that you can abstractly look for gauge invariant statements." So if I can do that, and these have a local interpretation in an appropriate sense of the word local (as you seem to agree for spacetime scalars for example which Dittrich treats with the same methods), then there is no fundamental conceptional incompatibility between Background independence, locality and QM, right?
So then there is no reason to conclude that background independence as suggested by GR is a red herring Quantum mechanically.
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You simply seem to forget that these objections require answers (the critics are usually not stupid you know). The key issue in these presumed ``background independent´´ approaches is LOCALITY. The ``solutions´´ presented by the LQG community are well known for a few decades and do no not contribute really to our understanding. They merely replace the locality problem for the question why God placed his pin into the enormous landscape of possibilities in order to generate our universe (by the way, this does not mean yet that the locality problem is solved - the right dynamics still has to decide about that.). Moreover, locality or not, there are plenty of ambiguities left in LQG - the quantization of the Hamiltonian constraint seems to be plagued by that already. BTW, that is exactly the reason why I boldly state that locality has not been solved: I do not like pseudo solutions.