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Tom gave an honest assessment just now in another thread of the real situation with LQG which in effect includes the several roads from there to cosmology (eg. Agullo, Alesci, Barrau, Engle, Vidotto, Wilson-Ewing and others).
He made a very good point which is that the problems are not different for cosmology, which after all is not formulated the same way it was back in 2005! It is increasingly formulated as a reduced version of the main theory, or embedded in the the main theory, and for that matter in formulations that are not even isotropic.
So, as Tom pointed out, is is good to look at the problems not separately but together.
So I want to comment on what he said in that post:
I think the main issue here, not mentioned by name, is the boundary formalism which comes up when one wants a general covariant quantum field theory underlying GR that is amenable to statistical mechanics/thermodynamics.
That is, if you want the theory to be general covariant then it does not make sense to ask for "transition amplitudes" between "initial" and "final" states. Instead one wants a theory that gives boundary amplitudes.
In the next few posts I'll try to explain (because it isn't immediately clear) how this addresses the question Tom raised. I think it is a good way to look at the focus where the most crucial development of LQG could be expected to occur in the next couple of years. As usual, I could be wrong
He made a very good point which is that the problems are not different for cosmology, which after all is not formulated the same way it was back in 2005! It is increasingly formulated as a reduced version of the main theory, or embedded in the the main theory, and for that matter in formulations that are not even isotropic.
So, as Tom pointed out, is is good to look at the problems not separately but together.
So I want to comment on what he said in that post:
tom.stoer said:...
...But to be honest, this distinction is of minor importance.
What bothers me more is that time-gauge is an essential ingredient for full LQG as well. Afaik other approaches avoiding time-gauge and applying the full Dirac program to all d.o.f. has never succeeded...
So it might be that full LQG suffers from the same problems as LQC in time-gauge, but in addition is insolvable w/o time gauge. That would kill the theory.
...
From my perspective the situation is as follows:
- kinematics is well understood, some proofs (LOST) do exist, the arena is clear
- physical applications are on their way, tools are available
- the main open issues have been identified, the conceptual problems are known
... I see two major issues:
- consistent, anomaly-free quantization
- role of the cosmological constant
I think the main issue here, not mentioned by name, is the boundary formalism which comes up when one wants a general covariant quantum field theory underlying GR that is amenable to statistical mechanics/thermodynamics.
That is, if you want the theory to be general covariant then it does not make sense to ask for "transition amplitudes" between "initial" and "final" states. Instead one wants a theory that gives boundary amplitudes.
In the next few posts I'll try to explain (because it isn't immediately clear) how this addresses the question Tom raised. I think it is a good way to look at the focus where the most crucial development of LQG could be expected to occur in the next couple of years. As usual, I could be wrong