I've read a lot of arguments in support of LQG over string theory, mainly focusing on ST's lack of background independence. I'm also told that there are some pretty good arguments against LQG. What are some of these arguments? Have they been summarized somewhere?
It is about time you string lqg guys came out, reveal what you have, i guess it will not get to many hot under the collar, unless they have a good imagination.
These statements are highly frame dependent. For me, the biggest thing that string theory has going is the natural incorporation of gauge symmetries and chiral matter. We KNOW that gauge symmetries and chiral matter exist in our universe, and these mathematical structures occur all over the place in the edifice of string theory. Another thing we notice about our universe is that all of the matter lives in small representations of gauge groups---fermions are ALWAYS in the fundamental representation of the gauge group. In string theory, this is the typical state of affairs---that is, we don't have to work too hard to see everything we need to describe nature just fall out of the theory "for free". For example, suppose you want to build a theory based on open strings. You go through the quantization procedure and have a perfectly happy theory, with no gauge symmetries. But now, you talk to Joe Polchinsky about your theory, and tells you "Ah, there are things in your theory you MISSED, called d branes, that MUST be there." Once you include d-branes, you find that closed string MUST begin and end on them. Now you get creative, and you imagine taking stacks of dbranes (which are already in your theory) and intersecting various stacks at different angles. Suppose you take N dbranes and intersect them with M dbranes---if you study the different types of open strings that you can have, you find out that you have EXACTLY and SU(N)xSU(M) gauge theory, with matter in the fundamental representations of the gauge group. And all of this just by playing around with states that are already in your theory. This, to me, is the most remarkable thing about string theory---it tells you how to get quarks and leptons, and non-Abelian gauge groups. String theory is a more ambitious program than the other approaches to QG---they aren't trying to explain the standard model, they're ONLY trying to quantize gravity. In fact, all of the attempts to explain where the gauge groups actually COME from have failed. In string theory, this was done as early as the mid to late eighties. {irrelevant comment removed - Zz}
Hi Ben, Thanks for your comments. I have a couple of questions for you. I didn't understand the relevance of the statement because this is not true of, e.g., SU(5) or SO(10) grand unified theories. I don't understand what this says about string theory? I'm not sure about the gauge group problem, but I read about an idea in Lee Smolin's book about treating particles as braids in the spin-network. Does this idea hold much water?
Not LQG per se, but LQC's present stage seems somewhat background dependent (Section 5.1): http://relativity.livingreviews.org/Articles/lrr-2008-4/ Are the spectra of geometrical operators in Loop Quantum Gravity really discrete? Bianca Dittrich, Thomas Thiemann http://arxiv.org/abs/0708.1721 Infinite Degeneracy of States in Quantum Gravity Jonathan Hackett, Yidun Wan http://arxiv.org/abs/0811.2161
Ahh good. I should be more careful with what I say in the following :) I perhaps should have made a different statement, that all of the things we have observed so far live is representations smaller than the adjoint, but you would have pointed out to me the large higgs representations that are needed in GUTs in general. The statement is correct in the context of the standard model, but is not true in SU(5), where the fermions come in a 5* + 10, or SO(10) where the fermions live in the spinor rep. Of course, very few people believe in SU(5) anymore (the minimal SUSY models are firmly dead by dim 5 and dim 6 proton decay, see Pierce and Murayama, http://arxiv.org/abs/hep-ph/0108104), and evading the constraints with SO(10) gets a bit tight (see "SUSY GUTs under siege" by Dermisek, Mafi, and Raby). So what DOES this say about strings? First of all, when you get your hands dirty with string models, you find that it is difficult to get representations larger than the adjoint. In fact, I only know of one way to get large representations (i.e. bigger than adjoints) out of string theory. This is in a paper by Kieth Dienes here: http://arxiv.org/abs/hep-th/9604112. Conversely, I know of TONS of ways to get small representations out of string theory. "Small" here means "smaller than adjoint". So, the question again comes: what does this say for the SO(10) models that require higgses in the 45 + 120 + 210 + ... representations. I would say that the question isn't "what does this say about strings", but "what does this say about SUSY GUTs"? I don't know what the right answer is, but I have never seen a string model that gets something like the complicated SO(10) models that people build. (The Dienes paper only shows that it is possible, and I know one of his students is working on that.) My feeling is that these models don't have a good stringy embedding. (Please, don't take my word for it---I'd LOVE to see some realistic SO(10) models come out of string theory :) ) Of course, you can even construct models that don't NEED SO(10) or E6---we certainly have never seen SO(10) or E6. You can break E8 (or SO(32))directly to the standard model at the string scale and have a perfectly happy model. Or, you can view the unification of forces as an accident, and imagine that we live on intersecting stacks of 6 branes wrapped around various cycles of various Calabi Yau shapes. Or (...) Getting particle physics from string theory is a robust field, with many approaches. But from what I know, you are more or less limited to the smallest (adjoint or smaller) representations of whatever gauge group you have. Have you heard of a successful model? The absolute best attempt that I've seen predicts a fourth generation, which is pretty well eliminated by Z decays and astrophysical constraints. Of course, Nature could be weird like that, but I don't think so. There was a Connes' non-commutative geometry standard model a few years ago, but that was firmly ruled out earlier this year by CDF, when they killed a higgs at 160 GeV. (Of course, as a good model builder, Connes found a way to fix his model, but this is the same things that people deride string theorists for...) And, of course, there is the Lisi model which has nice cartoons, but probably can't describe Nature. If getting standard model looking things out of other QG (notice absence of L!!!) approaches were easy (as is the case in string theory), then someone would have done it. This means that it is probably hard, or not possible. "Hard" doesn't mean that it should be eliminated from the spectrum of possibilities, it just makes it more difficult to be optimistic about it being true. But either way, in my mind this is the main argument for string theory---not only is it a finite theory of quantum gravity, it contains non-Abelian gauge symmetries and chiral matter, and it even contains the right KIND of chiral matter (small reps).
The arguments against LQG are more technical than anything else. The weird nonseperable hilbert space really grates me more than anything else about the formalism. I don't mind lorentz breaking so long as you can convince me that its smaller than observation bounds, eg tiny etc etc. Still you have to realize even the best models on the market are extremely naive, the inclusion of matter (braids or whatever) is poorly developed and not taken seriously by phenomenologists. I hate to say it, but the immense majority of scientists are highly critical of the subject, despite all the popularizing on the internet and by a few silly books. What might be interesting about the program is if they are successful or not in the whole canonical quantization of gravity endeavour. For years that was a dead end, and the certain success they've had might be an indication that what they've worked on is at least valid in some limit or as a toy model. So interesting in its own right. Still the entire field is very, very far from being fleshed out. Its a bit like string theory or Regge Calculus was in the 70s, or nuclear physics in the 60s. Many calculations can still go wrong in principle and they don't really have a smoking gun yet to draw the best people in. Of course this can be said about most QG programs. For instance the much talked about noboundary proposal and euclidean path integral advocated by Hawkins et al is also greeted with extreme skepticism b/c of how naive it is.
No, just a specific model was rulled out. Forget about when he admited defeat on a blog,with a sad peom. He came up with a small modification, that I don't yet understand, about 3 months after later, that still fits all of STM, including lower mass higgs... As for LQG, expecting that something gravitational weird can be measurable, that cannot be aproximated by a more classical theory, is hopeless, pretty much like string theory. But unlike string theory, it does not even try to tackle the oter forces. Anywaym, that is a sad state of affairs for both fields.
As a side note to the motivation of this discussion, I'd like to ask if anybody would have strong arguments to claim that string theory, loop quantum gravity, and Connes' noncommutative geometry must be incompatible with each other. It might as well be, to me, that they are different approaches and ingredient to an unique solution.
Thats a little hard to say exactly without comparing specific LQG theories, with a particular NC model and string theory with a given vacua. I'd guess lorentz breaking/nonbreaking would be a big indicator. String theory doesn't really make sense without the inclusion of matter, theres really no wiggle room possible for decoupling the matter degrees of freedom from the gravitational ones so hard to make contact with the better understood LQG models. In a related fashion, many LQG versions seem to have Einstein-Hilbert to all order, which cannot at face value be compatible with ST unless theres a duality somewhere (but then the physical predictions don't necessarily match either) The NC models seem to have low energy matter relationships thats close to something like a nonsupersymmetric GUT and I guess that could be made close to st. but the high energy predictions looks completely different from what I've read.
For what it's worth, I suspect that Lee Smolin would argue they can't be different paths to the same solution because LQG is "background independent" where as ST is "background dependent". This conclusion seems based on the argument that a fixed background model can't be made to agree in general with a model lacking such a fixed background. I don't have the tools to judge wether this is correct, but it sounds convincing while reading his book.
This is all model building :) Correct me if I'm wrong, but the abstract of this paper makes a pretty specific prediction: http://arxiv.org/abs/hep-th/0610241. The timbre of the paper is certainly "This is a prediction of the model". So either there IS a prediction and it's wrong, or there never WAS a prediction. If it's the latter, the model is no better or worse than any of the other models that people build using SUSY or technicolor.
There is a specific testable prediction of a LQG model relating to the fine-scale structure of the vacuum. Fotini Markopoulou predicted years ago that we would see a frequency-dependent delay in the arrival-times of gamma rays from GRBs. Her idea was that the more energetic gamma rays would interact more frequently with the space through which they propagate, and would therefor be slowed more than EM of lower frequencies. Though she hung her observational hopes on GLAST, such an effect may already have been recorded by the MAGIC project. If such a frequency-dependent delay can be observed and confirmed multiple times, it would help to rule out source-based systematics. If the magnitude of the delays could also be shown to be proportional to the redshift of the source, things are going to get exciting.
There were some thoughts about 2005 in which LQG was a kind of limit of M-Theory just like superstrings. Sergei Gukou and Ashok Sen were guys that wondered about that. Some simple things made that conjecture invalide... But I guess some recent articles made that possible, I think. I will post a thread about that later.
I do not know if this is the best paper but it is the best i can find, nor do i pretend to even understand all of it, but it doe's seem to give a good overview. http://arxiv.org/abs/gr-qc/0501053 G. Amelino-Camelia, C. Lämmerzahl, A. Macias, H. Müller (Submitted on 17 Jan 2005) Abstract: We give an overview of ongoing searches for effects motivated by the study of the quantum-gravity problem. We describe in greater detail approaches which have not been covered in recent ``Quantum Gravity Phenomenology'' reviews. In particular, we outline a new framework for describing Lorentz invariance violation in the Maxwell sector. We also discuss the general strategy on the experimental side as well as on the theoretical side for a search for quantum gravity effects. The role of test theories, kinematical and dymamical, in this general context is emphasized. The present status of controlled laboratory experiments is described, and we also summarize some key results obtained on the basis of astrophysical observations.