The above is all baloney as I've explained in another thread. For convenience I'll repost those comments here.
In a nutshell, lqg (I discuss strings below) must take the position (see
Black Hole Entropy from Loop Quantum Gravity. Note that I checked with rovelli that there has been no significant changes in the arguments as originally given in this paper) that the entropy S in hawking's famous formula S=(1/4)A refers only to black hole states that are causally connected to hole exteriors. But this stands in direct opposition to the near universal view – based on a preponderance of theoretical evidence - that S counts
all hole states. (see
On the nature of black hole entropy for a dissenting view, which however the author of this paper apparently no longer holds).
In other words, lqg is inconsistent with holography, which is regarded as perhaps the most profound insight into quantum gravity that the past thirty years of research has produced. Holography is the idea that physical information ultimately scales as area and not as volume. In the case of black holes, all of the apparently volume-extensive properties of material falling into a black hole reappear area-extensively on the event horizon. This is a very strange idea which we of course don't yet completely understand, but it's nonetheless regarded as perhaps the best clue we've got about what a correct quantum theory of gravity should be like.
Let me illustrate the above statements. As you probably know, LQG states are given in terms of lattices called spin-networks whose nodes represent quanta of volume and links represent quanta of area. It is thus obvious in LQG that only links can contribute to the black hole area-entropy relation, and equally obvious that the surface they puncture must be the event horizon. This trivially produces in the macroscopic limit the expected proportionality S ~ A between horizon area and entropy. There’s nothing deep about this result: It’s exactly what one would naively expect from this misleadingly intuitive point of view.
However, as I discussed above, the correct interpretation of S=(1/4)A is actually quite strange. It would be remarkable if a theory could take this very odd viewpoint and as a result produce the correct factor of 1/4. But this is precisely what string theory achieves!
In string theory we can explicitly construct black holes out of D-branes of various masses and charges. Then we can use the rules in string theory that tell us how to count the states of D-branes to calculate the number of black hole microstates associated with a given macrostate: We are counting all of a black hole’s states, not just some subset of them. Completely independent of this calculation we can compute the black hole entropy in terms of the masses and charges of the D-branes out of which the black hole was constructed. It’s then verified that in the macroscopic limit these two unrelated calculations agree precisely and yield the correct factor of 1/4. It’s kind of hard to believe that this sort of magic is just an accident and thus hard to take LQG seriously in light of this, which, relatively speaking, hardly anyone does, as I’ve stated many times.
From the above point of view the problem with LQG is that it’s not holographic: the nodes in spin-networks represent the kind of volume-extensive fundamental degrees of freedom that shouldn’t be involved in a correct fundamental theory of quantum gravity.
In fact, things are even worse for LQG. If LQG truly is a fundamental theory of gravity as claimed, deriving the black hole area-entropy relation shouldn’t require recourse to outside arguments. However, implicit in the above is that one has to justify the LQG point of view by using thermodynamical and statistical mechanical arguments, and not just to derive the proportionality, but the factor of a 1/4 as well, the latter presently appearing impossible to do: Spin-networks are absolutely fundamental in LQG and so simply don’t contain anymore information which would allow us to get the right answer.
Needless to say that none of this is a problem for strings.
So in summary LQG fails to pass the only reliable check of the correctness of a QG theory that we have while strings are completely successful.
Let me make one final remark about the string result. The statements that LQG people make to the effect that the kinds of black holes involved in the string calculation are unrealistic are wrong-headed. The string calculation has been performed successfully on both non—supersymmetric holes and four dimensional holes. There is thus every reason to expect - and we pretty much do - that it’s only a matter of time before the correct result will be produced in all cases. The same can never be expected of lqg period.
