Failures of LQG
Dear nonunitary,
I sort of misunderstood who you are, but it is probably polite to answer anyone who is interested in physics. Based on your text, I guess that you've read Three Roads to Quantum Gravity by Smolin or something like that, right, and you want to learn how real physics looks like, don't you? You might find my answers helpful, especially because it seems obvious that there are many things that I can teach you about LQG - I've worked on it and studied it, one could say "in detail".
You have probably a very, very long way to go if you want to learn something about quantum gravity, but you should not be scared because of this long way in front of you.
First: continuity of space. Well, yes, various LQG people are saying various things, but the more important thing is the truth. The fact is that the variables to describe gravity are chosen in such a way that the areas are quantized. One needs about 5 minutes to understand why the area quantization is a direct consequence of the choice of the variables. For example, see the 10-page paper
http://arxiv.org/abs/gr-qc/9806079
The presentation could be written on 3 pages, too, if one used the mathematical language that most up-to-date theoretical physicists know, and these 3 pages would essentially contain everything about LQG that is at least a little bit interesting. If you chose a different gauge theory parameterization of the metric, you could not obtain the usual area quantization known in LQG. In this sense, the area quantization is put in, because it determines the way how you should translate the metric into the language of gauge fields.
Different parameterizations lead to different results. There are thousands of other ways to discretize non-renormalizable theories such as gravity, and all of them lead to a similar type of problems. The special feature of LQG is that it assumes the metric to be a good variable at the Planck scale, which we just know to be naive. In my opinion, this characteristic feature of LQG is more of a disadvantage than an advantage.
One of the most far-reaching insights in particle physics of the 1970s is the concept of Renormalization Group (RG) that implies that field theories and their degrees of freedom are associated with a scale, and the necessary description varies with the scale. In fact, we can derive how the equations of gravity are affected by the change of the scale, and in the case of gravity, we know how this force looks at astronomical scales, and therefore we know that it must look different at short distance scales. The UV divergent structure of GR proves that Einstein's equations are missing new physics and new degrees of freedom at short distances - new physics that is necessary to reconcile gravity with quantum mechanics.
LQG assumes that Einstein's equations are essentially correct exactly in the regime where we know they must be wrong, and because physics at different scales is guaranteed to be different, physics of LQG at long distances can't agree with Einstein's equations i.e. with the observations.
Concerning non-uniqueness of LQG: there are hundreds of different unrelated versions of it once we want to include matter and not just gravity - and gravity without matter is really useless. There are many ways how people try to add gauge fields and fermions; none of them can really reproduce quantum field theory, and a really unsolvable problem seems to be adding the scalar fields (i.e. the Higgs scalar that is more or less necessary for electroweak symmetry breaking) to the LQG framework.
LQG has not even proved that the "canonical formalism" is equivalent to the path-integral-like formalism - i.e. the spinfoams - and there are good reasons to be afraid that they can't be really equivalent. All of these things are random and mostly unrelated ideas - whose intersection is made of the wrong prejudices about the Planck scale geometry - and there does not seem to be a working theory behind them.
There is an extremely strong evidence (almost a proof) - based on the Renormalization Group - that smooth space can't emerge from LQG. There is comparably strong evidence that LQG can't be compatible with special relativity - even most LQG practitioners admit that, and some of them even want to transmute this obvious flaw into a virtue. I don't know what you meant by your comparison with M-theory: M-theory certainly has no problems to get smooth space, gravity and essentially all other required particles and forces at long distances. What is the point of this confusing comparison?
Concerning your sentence "This claim is based in your prejudices that a theory that does not look like string theory is wrong", let me tell you something, and let us hope that it won't make you too frustrated. That claim of mine - that the tens of the *assumptions* of LQG have been proved incorrect - was not really based on prejudices but rather thousands of insights that people have accumulated in thousands of papers about field theory, particle physics, and its gravitational extension (string theory) during the last 30 years, and it is not too likely that all these insights are incorrect.
Concerning the Immirzi parameter. The Immirzi parameter is a multiplicative constant that measures how wrong prediction of the black hole entropy - based on a very unconvincing and heuristic treatment of LQG - predicts unless one tries to cheat. If one tries to cheat, he can argue that this discrepancy does not really matter and things can be "renormalized". Unfortunately all attempts to calculate the "renormalization" of Newton's constant - the Immirzi parameter - have failed so far, and the research direction based on quasinormal modes is the newest example of this fact.
There is nothing surprising or non-trivial about the LQG calculation of the entropy of the horizons. The fact that the result is proportional to the area was calculated by Hawking, not LQG, and it was inserted as input to the heuristic argument based on LQG. When one assumes that the entropy comes from objects spread over the horizon (and he or she simply cuts the interior of the black hole by hand, without explaining why is it allowed), it is not surprising that the entropy will turn out to be proportional to the area. However, the proportionality factor - the only non-trivial number that might have been calculated - is wrong.
Well, you say that it is "not clear whether LQG should predict anything about them". Well, a theory of gravity must predict everything about the gravitational equation. It might be questionable whether a theory XY is able to calculate AB, but one thing is clear: LQG is not able to predict the QN modes, it is also not able to predict the existence of gravitons, Newton's force, the quantitative black hole thermodynamical properties - simply nothing that we usually call "gravitational phenomena". The reason is simple: it is a discrete system that is formally related to geometry, but its physics has nothing to do with geometry.
Concerning LQG, experiments and black hole entropy - the answer to your question is no. My point was only to demonstrate that the claimed "successes" of LQG are just parodies about real physics and that LQG has no reasonable prediction whatsoever that the future experiments might test. You may be sad about it, you might cry, but it is the last thing that you can do about this fact.
I hope that you will find this text helpful, and that you will kindly forgive me that I won't reply to your personal attacks or comments "you are wrong" that are not supported by any argument. At any rate, it is sort of amazing how the "popular science" can often differ from real science. There are so many people who are interested in telepathy; ESP; LQG and so forth - even though these fields are considered to be "most likely incorrect" by most of the scientists (especially in the case of the ESP phenomena). There are no new jobs for the LQG people in the USA. I sort of wonder where does the idea that LQG is something that can be compared to string theory come from?
Sincerely Yours
Luboš
