It seems that one can easily repost one of my articles from Wikipedia, so that even the links are preserved. Let's try.
In theoretical physics, loop quantum gravity is one speculative approach to quantum gravity, sometimes cited as a competitor theory to string theory. The loop quantum gravity page summarises the theory as it appears to those working in the field.
As a physical theory, loop quantum gravity has been subject to some heavy criticisms. Some objections to the ideas of loop quantum gravity are given here.
Too many assumptions
Loop quantum gravity makes too many assumptions about the behavior of geometry at very short distances. It assumes that the metric tensor is a good variable at all distance scales, and it is the only relevant variable. It even assumes that Einstein's equations are more or less exact in the Planckian regime.
The spacetime dimensionality (four) is another assumption that cannot be questioned, much like the field content. Each of these assumptions is challenged in a general enough theory of quantum gravity, for example all the models that emerge from string theory. These assumptions have neither theoretical nor experimental justification. Particular examples will be listed in a separate entry.
The most basic, underlying assumption is that the existence of a meaningful classical theory, of general relativity, implies that there must exist a "quantization" of this theory. This is commonly challenged. Many reasons are known why some classical theories do not have a quantum counterpart. Gauge anomalies are a prominent example. General relativity is usually taken to be another example, because its quantum version is not renormalizable. It is known, therefore, that a classical theory is not always a good starting point for a quantum theory. Theorists of loop quantum gravity work with the assumption that "quantization" can be done, and continue to study it even if their picture seems inconsistent.
Commentary from the renormalization group aspect
According to the logic of the renormalization group, the Einstein-Hilbert action is just an effective description at long distances; and it is guaranteed that it receives corrections at shorter distances. String theory even allows us to calculate these corrections in many cases.
There can be additional spatial dimensions; they have emerged in string theory and they are also naturally used in many other modern models of particle physics such as the Randall-Sundrum models. An infinite amount of new fields and variables associated with various objects (strings and branes) can appear, and indeed does appear according to string theory. Geometry underlying physics may become noncommutative, fuzzy, non-local, and so on. Loop quantum gravity ignores all these 20th and 21st century possibilities, and it insists on a 19th century image of the world which has become naive after the 20th century breakthroughs.
On one hand, loop quantum gravity prohibits many types of new physics that have become natural and likely in the recent era. On the other hand, it brings no order to the structure and values of the higher-derivative terms. Indeed, the infinitely many parameters that govern the effective action and make quantized general relativity non-renormalizable and unpredictive are simply replaced by an infinite number of parameters of the Hamiltonian constraint and/or the spin foam Feynman rules.
As a predictive theory
Loop quantum gravity is therefore not a predictive theory. Moreover, it does not offer any possibility to predict new particles, forces and phenomena at shorter distances: all these objects must be added to the theory by hand. Loop quantum gravity therefore also makes it impossible to explain any relations between the known physical objects and laws.
Loop quantum gravity is not a unifying theory. This is not just an aesthetic imperfection: it is impossible to find a regime in real physics of this Universe in which non-gravitational forces can be completely neglected, except for classical physics of neutral stars and galaxies that also ignores quantum mechanics. For example, the electromagnetic and strong force are rather strong even at the Planck scale, and the character of the black hole evaporation would change dramatically had the Nature omitted the other forces and particles. Also, the loop quantum gravity advocates often claim that the framework of loop quantum gravity regularizes all possible UV divergences of gravity as well as other fields coupled to it. That would be a real catastrophy because any quantum field theory - including all non-renormalizable theories with any fields and any interactions - could be coupled to loop quantum gravity and the results of the calculations could be equal to anything in the world. The predictive power would be exactly equal to zero, much like in the case of a generic non-renormalizable theory. There is absolutely no uniqueness found in the realistic models based on loop quantum gravity. The only universal predictions - such as the Lorentz symmetry breaking discussed below - seem to be more or less ruled out on experimental grounds.
Unlike string theory, loop quantum gravity has not offered any non-trivial self-consistency checks of its statements and it has had no impact on the world of mathematics. While string theory smells by God, loop quantum gravity smells by Man. It seems that the people are constructing it, instead of discovering it. There are no nice surprises in loop quantum gravity - the amount of consistency in the results never exceeds the amount of assumptions and input. For example, no answer has ever been calculated in two different ways so that the results would match. Whenever a really interesting question is asked - even if it is apparently a universal question, for example: "Can topology of space change?" - one can propose two versions of loop quantum gravity which lead to different answers.
There are many reasons to think that loop quantum gravity is internally inconsistent, or at least that it is inconsistent with the desired long-distance limit (which should be smooth space). Too many physical wisdoms seem to be violated. Unfortunately the loop quantum gravity advocates usually choose to ignore the problems. For example, the spin foam (path-integral) version of loop quantum gravity is believed to break unitarity. The usual reaction of the loop quantum gravity practitioners is the statement that unitarity follows from time-translation symmetry, and because this symmetry is broken (by a generic background) in GR, we do not have to require unitarity anymore. But this is a serious misunderstanding of the meaning and origin of unitarity. Unitarity is the requirement that the total probability of all alternatives (the squared length of a vector in the Hilbert space) must be conserved (well, it must always be 100%), and this requirement - or an equally strong generalization of it - must hold under any circumstances, in any physically meaningful theory, including the case of the curved, time-dependent spacetime. Incidentally, the time-translation symmetry is related, via Noether's theorem, to a time-independent, conserved Hamiltonian, which is a completely different thing than unitarity.
A similar type of "anything goes" approach seems to be applied to other no-go theorems in physics.
Gap to high-energy physics
Loop quantum gravity is isolated from particle physics. While extra fields must be added by hand, even this ad hoc procedure seems to be impossible in some cases. Scalar fields can't really work well within loop quantum gravity, and therefore this theory potentially contradicts the observed electroweak symmetry breaking; the violation of the CP symmetry, and other well-known and tested properties of particle physics.
Loop quantum gravity also may deny the importance of many methods and tools of particle physics - e.g. the perturbative techniques; the S-matrix, and so on. Loop quantum gravity therefore potentially disagrees with 99% of physics as we know it. Unfortunately, the isolation from particle physics follows from the basic opinions of loop quantum gravity practitioners and it seems very hard to imagine that a deeper theory can be created if the successful older theories, insights, and methods (and exciting newer ones) in the same or closely related fields are ignored.
Moreover, it has been recently argued that in every consistent theory of quantum gravity, gravitational force must be the weakest one (much like in the real world). More precisely, there must always exist objects whose repulsive force of any kind exceeds the attractive force of gravity. Loop quantum gravity, much like all other attempts to start with "pure quantum gravity", violates this insight maximally because it is an expansion around the point in which the other interactions are turned off. This point in the parameter space is inconsistent.
Smooth space as limiting case
Loop quantum gravity does not guarantee that smooth space as we know it will emerge as the correct approximation of the theory at long distances; there are in fact many reasons to be almost certain that the smooth space cannot emerge, and these problems of loop quantum gravity are analogous to other attempts to discretize gravity (e.g. putting gravity on lattice).
While string theory confirms general relativity or its extensions at long distances - where GR is tested - and modifies it at the shorter ones, loop quantum gravity does just the opposite. It claims that GR is formally exact at the Planck scale, but implies nothing about the correct behavior at long distances. It is reasonable to assume that the usual ultraviolet problems in quantum gravity are simply transmuted into infrared problems, except that the UV problems seem to be present in loop quantum gravity, too.
Clash with special relativity
Loop quantum gravity violates the rules of special relativity that must be valid for all local physical observations. Spin networks represent a new reincarnation of the 19th century idea of the luminiferous aether - environment whose entropy density is probably Planckian and that picks a priviliged reference frame. In other words, the very concept of a minimal distance (or area) is not compatible with the Lorentz contractions. The Lorentz invariance was the only real reason why Einstein had to find a new theory of gravity - Newton's gravitational laws were not compatible with his special relativity.
Despite claims about the background independence, loop quantum gravity does not respect even the special 1905 rules of Einstein; it is a non-relativistic theory. It conceptually belongs to the pre-1905 era and even if we imagine that loop quantum gravity has a realistic long-distance limit, loop quantum gravity has even less symmetries and nice properties than Newton's gravitational laws (which have an extra Galilean symmetry, and can also be written in a "background independent" way - and moreover, they allow us to calculate most of the observed gravitational effects well, unlike loop quantum gravity). It is a well-known fact that general relativity is called "general" because it has the same form for all observers including those undergoing a general accelerated motion - it is symmetric under all coordinate transformations - while "special" relativity is only symmetric under a subset of special (Lorentz and Poincare) transformations that interchange inertial observers. The symmetry under any coordinate transformation is only broken spontaneously in general relativity, by the vacuum expectation value of the metric tensor, not explicitly (by the physical laws), and the local physics of all backgrounds is invariant under the Lorentz transformations.
Loop quantum gravity proponents often and explicitly state that they think that general relativity does not have to respect the Lorentz symmetry in any way - which displays a misunderstanding of the symmetry structure of special and general relativity (the symmetries in general relativity extend those in special relativity), as well as of the overwhelming experimental support for the postulates of special relativity. Loop quantum gravity also depends on the background in a lot of other ways - for example, the Hamiltonian version of loop quantum gravity requires us to choose a pre-determined spacetime topology which cannot change.
One can imagine that the Lorentz invariance is restored by fine-tuning of an infinite number of parameters, but nothing is known about the question whether it is possible, how such a fine-tuning should be done, and what it would mean. Also, it has been speculated that special relativity in loop quantum gravity may be superseded by the so-called doubly special relativity, but doubly special relativity is even more problematic than loop quantum gravity itself. For example, its new Lorentz transformations are non-local (two observers will not agree whether the lion is caught inside the cage) and their action on an object depends on whether the object is described as elementary or composite.
Global justification of variables
The discrete area spectrum is not a consequence, but a questionable assumption of loop quantum gravity. The redefinition of the variables - the formulae to express the metric in terms of the Ashtekar variables (a gauge field) - is legitimate locally on the configuration space, but it is not justified globally because it imposes new periodicities and quantization laws that do not follow from the metric itself. The area quantization does not represent physics of quantum gravity but rather specific properties of this not-quite-legitimate field redefinition. One can construct infinitely many similar field redefinitions (sibblings of loop quantum gravity) that would lead to other quantization rules for other quantities. It is probably not consistent to require any of these new quantization rules - for instance, one can see that these choices inevitably break the Lorentz invariance which is clearly a bad thing.
Testability of the discrete area spectrum
The discrete area spectrum is not testable, not even in principle. Loop quantum gravity does not provide us with any "sticks" that could measure distances and areas with a sub-Planckian precision, and therefore a prediction about the exact sub-Planckian pattern of the spectrum is not verifiable. One would have to convert this spectrum into a statement about the scattering amplitudes.
Loop quantum gravity provides us with no tools to calculate the S-matrix, scattering cross sections, or any other truly physical observable. It is not surprising; if loop quantum gravity cannot predict the existence of space itself, it is even more difficult to decide whether it predicts the existence of gravitons and their interactions. The S-matrix is believed to be essentially the only gauge-invariant observable in quantum gravity, and any meaningful theory of quantum gravity should allow us to calculate it, at least in principle.
Loop quantum gravity does not really solve any UV problems. Quantized eigenvalues of geometry are not enough, and one can see UV singular and ambiguous terms in the volume operators and most other operators, especially the Hamiltonian constraint. Because the Hamiltonian defines all of dynamics, which contains most of the information about a physical theory, it is a serious object. The whole dynamics of loop quantum gravity is therefore at least as singular as it is in the usual perturbative treatment based on semiclassical physics.
We simply do have enough evidence that a pure theory of gravity, without any new degrees of freedom or new physics at the Planck scale, cannot be consistent at the quantum level, and loop quantum gravity advocates need to believe that the mathematical calculations leading to the infinite and inconsistent results (for example, the two-loop non-renormalizable terms in the effective action) must be incorrect, but they cannot say what is technically incorrect about them and how exactly is loop quantum gravity supposed to fix them. Moreover, the loop quantum gravity proponents seem to believe that the naive notion of "atoms of space" is the only way to fix the UV problems. String theory, which allows us to make real quantitative computations, proves that it is not the case and there are more natural ways to "smear out" the UV problems. In fact, a legitimate viewpoint implies that the discrete, sharp character of the metric tensor and other fields at very short distances makes the UV behavior worse, not better.
Moreover, as explained above, the "universal solution of the UV problems by discreteness of space" implies at least as serious loss of predictive power as in a generic non-renormalizable theory. Even if loop quantum gravity solved all the UV problems, it would mean that infinitely many coupling constants are undetermined - a situation analogous to a non-renormalizable theory.
Black hole entropy
Despite various claims, loop quantum gravity is not able to calculate the black hole entropy, unlike string theory. The fact that the entropy is proportional to the area does not follow from loop quantum gravity. It is rather an assumption of the calculation. The calculation assumes that the black hole interior can be neglected and the entropy comes from a new kind of dynamics attached to the surface area - there is no justification of this assumption. Not surprisingly, one is led to an area/entropy proportionality law. The only non-trivial check could be the coefficient, but it comes out incorrectly (see the Immirzi discrepancy).
The Immirzi discrepancy was believed to be proportional to the logarithm of two or three, and a speculative explanation in terms of quasinormal modes was proposed. However it only worked for one type of the black hole - a clear example of a numerical coincidence - and moreover it was realized in July 2004 that the original calculation of the Immirzi parameter was incorrect, and the correct value (described by Meissner) is not proportional to the logarithm of an integer. The value of the Immirzi parameter - even according to the optimists - remains unexplained. Another description of the situation goes as follows: Because the Immirzi parameter represents the renormalization of Newton's constant and there is no renormalization in a finite theory - and loop quantum gravity claims to be one - the Immirzi parameter should be equal to one which leads to a wrong value of the black hole entropy.
Nonseparable Hilbert space
While all useful quantum theories in physics are based on a separable Hilbert space, i.e. a Hilbert space with a countable basis, loop quantum gravity naturally leads to a non-separable Hilbert space, even after the states related by diffeomorphisms are identified. This space can be interpreted as a very large, uncountable set of superselection sectorsthat do not talk to each other and prevent physical observables from being changed continuously. All known procedures to derive a different, separable Hilbert space are physically unjustified. Equivalently, loop quantum gravity does not allow one to derive the conventional notion of continuity of space.
Loop quantum gravity has no tools and no solid foundations to answer other important questions of quantum gravity - the details of Hawking radiation; the information loss paradox; the existence of naked singularities in the full theory; the origin of holography and the AdS/CFT correspondence; mechanisms of appearance and disappearance of spacetime dimensions; the topology changing transitions (which are most likely forbidden in loop quantum gravity); the behavior of scattering at the Planck energy; physics of spacetime singularities; quantum corrections to geometry and Einstein's equations; the effect of the fluctuating metric tensor on locality, causality, CPT-symmetry, and the arrow of time; interpretation of quantum mechanics in non-geometric contexts including questions from quantum cosmology; the replacement for the S-matrix in de Sitter space and other causally subtle backgrounds; the interplay of gravity and other forces; the issues about T-duality and mirror symmetry.
Loop quantum gravity is criticised as a philosophical framework that wants us to believe that these questions should not be asked. As if general relativity is virtually a complete theory of everything (even though it apparently can't be) and all ideas in physics after 1915 can be ignored.
The criticisms of loop quantum gravity regarding other fields of physics are misguided. They often dislike perturbative expansions. While it is a great advantage to look for a framework that allows us to calculate more than the perturbative expansions, it should never be less powerful. In other words, any meaningful theory should be able to allow us to perform (at least) approximative, perturbative calculations (e.g. around a well-defined classical solution, such as flat space). Loop quantum gravity cannot do this, definitely a huge disadvantage, not an advantage as some have claimed. A good quantum theory of gravity should also allow us to calculate the S-matrix.
Loop quantum gravity's calls for "background independence" are misled. A first constraint for a correct physical theory is that it allows the (nearly) smooth space(time) - or the background - which we know to be necessary for all known physical phenomena in this Universe. If a theory does not admit such a smooth space, it can be called "background independent" or "background free", but it may be a useless theory and a physically incorrect theory.
It is a very different question whether a theory treats all possible shapes of spacetime on completely equal footing or whether all these solutions follow from a more fundamental starting point. However, it is not a priori clear on physical grounds whether it must be so (it can be just an aesthetic feature of a particular formulation of a theory, not the theory itself), and moreover, for a theory that does not predict many well-behaved backgrounds the question is meaningless altogether. Physics of string theory certainly does respect the basic rules of general relativity exactly - general covariance is seen as the decoupling of unphysical (pure gauge) modes of the graviton. This exact decoupling can be proved in string theory quite easily. It can also be seen in perturbative string theory that a condensation of gravitons is equivalent to a change of the background; therefore physics is independent of the background we start with, even if it is hard to see for the loop quantum gravity advocates.
Claims on non-principled approach
Loop quantum gravity is not science because every time a new calculation shows that some quantitative conjectures were incorrect, the loop quantum gravity advocates invent a non-quantitative, ad hoc explanation why it does not matter. Some borrow concepts from unrelated and fields, including noiseless information theory and philosophy, and some explanations why previous incorrect results should be kept are not easily credible.