Talk:Objections to the theory of loop quantum gravity

Hello Gentlemen! What about keeping these two pages (loop quantum gravity, loop gravity) as separate? LQG - which is obviously the more frequent name - could be dedicated purely to the viewpoints of those who happily work on LQG, while LG could collect more observations of others. The pages would refer to each other, much like they do now, and the POV labels could be removed. --Lumidek 12:25, 17 Sep 2004 (UTC)

Well, that is not the orthodox way of doing things. I think, in the end, there should probably be one page, not 'prosecution' and 'defence'. However, I won't insist on anything like that right now. Charles Matthews 16:03, 17 Sep 2004 (UTC)

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Wow. I've never before seen an article with almost no explanation of what the article's about, and then has 17 paragraphs arguing against what the article's about. POV? I think so. [[User:Mike Storm|Mike∞Storm]] 20:28, 11 Sep 2004 (UTC)

What loop gravity tries to be about is explained on the page loop quantum gravity. Yes, this is a POV, and the label POV may be OK. However, I think that it is more important whether it is true. I think it is. --Lumidek 20:44, 11 Sep 2004 (UTC)

It is never OK for an article to be POV. Yes, it does matter that it's true, but it is just as important that you present multiple viewpoints. [[User:Mike Storm|Mike∞Storm]] 22:00, 11 Sep 2004 (UTC)

Point 14 will certainly have to be edited in a very tough way (if it is to survive). That is, the other points are mostly about physics, and could be phrased in some better way as discussions within theoretical physics. A general attack on the standards of an academic subfield - well, on the face of it, that leads to all sorts of problems.

Charles Matthews 13:06, 12 Sep 2004 (UTC)

OK, here it is:

• most loop quantum gravity advocates are not good physicists, and they try to avoid learning anything from particle physics and other fields even though it is clearly necessary for a proper understanding of many questions in quantum gravity. They believe that a very narrow-minded understanding of reality that they propose - and that has not made any real progress for decades - is everything we need. They are making incorrect mental links between different concepts and they are unable to learn better. For example, it is often said by loop quantum gravity proponents that unitarity is no longer necessary because it only follows from time-translation symmetry. Well, the right answer is that unitarity is equivalent to the conservation of the total probability - something that must hold in any context in which basic rules of logic hold - while time-translation symmetry is equivalent to the existence of a conserved (time-independent) Hamiltonian, because of Noether's theorem, which is an entirely different issue.

*choke*... whoever had the nerve to say that people like Ashtekar are not good physicists, quite plainly do not have a clue about general relativity. They also may have no clue about algebraic quantum field theory. — Miguel 10:26, 2004 Nov 22 (UTC)

The first three sentences are pure polemic.

Charles Matthews 10:44, 13 Sep 2004 (UTC)

That is the most POV paragraph that I have ever seen. [[User:Mike Storm|Mike∞Storm]] 02:04, 14 Sep 2004 (UTC)

I've done some further work on POV here. There are now headings, so editing individual sections into more of a WP style should be relatively easy.

On the general issues: no reason why criticisms of a physical theory should not be part of WP. Whether this needs a page of its own will be resolved over time.

Charles Matthews 08:22, 14 Sep 2004 (UTC)

I have no problem with objections to loop quantum gravity, but one of my main questions is: Why was this page created at all? Wouldn't a better name have been "Objections to Loop Quantum Gravity"? And then, it still should be merged with the main Loop quantum gravity article. [[User:Mike Storm|Mike∞Storm]] 00:11, 17 Sep 2004 (UTC)

I don't mind so much whether (or not) this is eventually moved back into the LQG page. There is interesting material here, as well as some that is over the top. I hope it will be tweaked/massaged into a more normal style for Wikipedia. It might be rather provocative to move it back right now.

Charles Matthews 09:03, 17 Sep 2004 (UTC)

Loop quantum gravity versus string theory

Guys, I'm completely dumb in the subject but I feel the article is simply too big. May be we should move most of it to something like Loop quantum gravity versus string theory? And let's decide upon quantum gravity and loop quantum gravity articles -- they should be something like merged with this article. Having three articles with much similar content is really strange. I believe with can do it in a bloodless way.

Disagree, having looked around. Loop quantum gravity at 42K is already longer than WP likes. It has various articles hanging off it, and I've done the work required to make this another of those. Further, quantum gravity is not something that should be merged into an article on a particular theory: it should be a top-level article setting the general scene. So in a sense I'm coming closer to what User:Lumidek suggested, just because this seems to be generating a great deal of interesting writing. Still needs work, of course. Charles Matthews 11:26, 10 Oct 2004 (UTC)

NPOV

While this is a brilliant essay, it is still not a NPOV encyclopedic article. If I really have to point out specific sentences, let's start with: While string theory smells by God, loop quantum gravity smells by Man. --Pjacobi 15:22, 10 Oct 2004 (UTC)

Hi Pjacobi, thanks for your words. I understand that the article is far from perfect, and the poetic words "smells by Man" can be reinterpreted using more boring and less irritating terms (and substantiated by additional evidence). Is not the number of such objections against the article finite and fixable? I would be also happy if someone kept on improving the language because I am not a native speaker. By the way, I also find it obvious that this article also contains the topic "loop quantum gravity vs. string theory" although it is more focused on the problems of loop quantum gravity, and therefore it is not neutral from this viewpoint. Nevertheless, these questions should not be repeated at 10 different pages of Wikipedia. I think. It does not make sense to combine very different approaches after each sentence because they are not really compatible. It may be better to separate the criticism from the "constructive" work on LQG - and let them say all this stuff that is considered nonsense by many other physicists. Also, the article loop quantum gravity should probably refer to these "objections" in a more visible way, and both of them should lose the POV labels.--Lumidek 19:43, 10 Oct 2004 (UTC)

Oh, I realise it lacks NPOV. I keep working on it, and I think it can be turned into a good WP article in time. Charles Matthews 15:25, 10 Oct 2004 (UTC)

I applaud your work on editing the articles, I only commented on a temporary removal of the NPOV label. And of course, both articles are guilty, I can offer this sentence from Loop quantum gravity Being closely related to topological quantum field theory and group representation theory, LQG is mostly established at the level of rigour of mathematical physics, as opposed to string theory, which is established at the level of rigour of physics. --Pjacobi 16:22, 10 Oct 2004 (UTC)

OK - but being good mathematics and wrong isn't an advantage - look at some parts of economics. My attitude is to try to do surgery, without killing the patient. I hadn't realised that the LQG article had become so long. It seems that too much technical detail has been added there, and will have to be moved to a secondary article. So there will be a group of around five articles on loop gravity; and there is then some chance that smaller problems with the POV can be seen.

As for 'nonsense' - I'm a mathematician by training, and we are always amazed at the proportion of nonsense tolerated in physics. Niels Bohr - now that was nonsense. Anyway an advantage of the Wikipedia approach is we can just add 'this is not generally accepted'. Charles Matthews 20:08, 10 Oct 2004 (UTC)

What was nonsense? lysdexia 00:13, 17 Oct 2004 (UTC)

• • Lysdexia, what you did looks like a piece of good work, thanks! Before I looked into a dictionary, it was hard to believe that the words privileged, sibling, etc. were misspelled - but they really were! ;-) OK, let me sadly say that the comments about "smelling by God/Man" have been sacrificed peacefully. ;-) --Lumidek 01:01, 17 Oct 2004 (UTC)

Paragraph from Quantum Gravity

Hi, I've just removed a large section on String theorists' critisicm of LQG from Quantum gravity. While the text from there was generally worser than this text, it contained an introductory paragraph that I feel is very useful:

Lubos Motl is a string theorist who is highly critical of loop quantum gravity. On sci.physics.research/What's wrong with loop quantum gravity, Lubos debated Steve Carlip and John Baez, and offered the following criticisms of loop quantum gravity.

because it clearly indicates whose are the view expressed and where one can continue debates (because Wikipedia is of another purpose). I suggest that we insert it here. 193.124.225.253 16:21, 13 Oct 2004 (UTC)

The page history shows that too, for those who know Lubos = Lumidek (no secret). Can I make the point that the objective I have, in working on this page, is to remove the direct connection with the original polemic, while leaving what is an interesting discussion on fundamental physics? If I didn't think that could be done, I'd be wasting time here. So no attribution on the page, I think.

Charles Matthews 16:36, 13 Oct 2004 (UTC)

Specific requests needed to remove the POV tag?

I would like to encourage you to write your general comments about the changes required for this article to become a neutral point of view. It seems plausible that the main objections explained above have already been solved. What else do you want for the POV label to disappear? Incidentally, I removed the same label from the loop quantum gravity main article already. Thanks for your feedback, Lubos --Lumidek 18:52, 22 Nov 2004 (UTC)

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.

No, loop quantum gravity is an attempt at performing caninical quantization of some Lagrangian leading to Einstein's equations. If is not a metric theory, but a theory of a connection. Whether there is a metric description at all length scales and whether corrections to the Einstein equations will result from the classical limit is an open question.

Loop quantum gravity also wants to be a theory of quantum gravity. Even for you, it is an "open question" whether there is a metric description at all length scales, but as you agree as well, loop quantum gravity assumes that there is and just wants to quantize it. Others believe that it's an illegitimate and overly constraining assumption (it does not hold in string theory, for example) - and you seem to agree that it is at least an open question whether it is a good assumption or not - so I don't exactly understand what's your problem.--Lumidek 00:16, 23 Nov 2004 (UTC)

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.

You've got to be kidding! There is no experimental evidence whatsoever for any spacetime dimensionality other that 3+1. Loop quantization is a general framework for nonperturbative quantization of background-independent gauge theories. As such, it accommodates any spacetime dimensionality and field content. It works for TQFTs in any dimension.

No, we are not kidding. Your assumption that there are no new degrees of freedom - for example, no Kaluza-Klein tower of particles etc. - is, using today's perspective, an extremely constraining and sort of unlikely assumption. You should at least know that this assumption of pure 3+1 dimensions and nothing else at all is false in all 10^{300} models arising from string theory - or what's the estimate of the landscape people. It's just wrong in all of string theory, as described in 10,000+ papers. It's not just string theory - a large portion of beyond-the-standard-model phenomenology deals with extra dimensions of some type, and even those that don't deal with them usually don't claim that the 3+1-dimensional approximation is exact. There is no experimental evidence of extra dimensions, but there is an overwhelming theoretical evidence that a consistent theory of quantum gravity requires more than 4 dimensions at the fundamental level. What you say is a completely personal POV that certainly does not belong to the page of objections against your theory - simply because it is EXACTLY this strange opinion of yours that is believed to be silly by the majority of the theoretical high-energy community. --Lumidek 00:16, 23 Nov 2004 (UTC)

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.

I repeat: LQG is an attempt at performing canonical quantization of well-known Lagrangians for classical general relativity. LQG shows that, despite overwhelming evidence from perturbative quantum field theory, it may just not be true that general relativity cannot be quantized. LQG is, though, NOT a quantum field theory in the standard sense. Neither is string theory, by the way, it is a 2D conformal field theory where spacetime coordinates are fields. Its quantum theory is not renormalizable actually means that the perturbative quantum field theory of general relativity is not renotmalizable. LQG is not a perturbative quantum field theory.

You repeat exactly the things that are being criticized on this page, and that are being criticized by mainstream high energy theorists. It's just stupid to be quantizing a random Lagrangian in a random method if we have other ways to see that it does not lead to a consistent quantum theory. Your comments about being a quantum theory are extremely confused. String theory definitely is a standard quantum theory that satisfies the postulates of quantum mechanics. Your statements perturbative vs. non-perturbative are also ridiculous for most physicists, and they are also criticized in this article. The probability that non-perturbative physics can make an inconsistent 4D theory consistent is infinitesimal, and there is no evidence whatsoever that this may happen. You must admit that you have no idea how to extract consistent perturbative expansions from your formalism - and non-perturbative consistency is an even BIGGER constraint than perturbative consistency, and one can't reasonably expect the former without the latter. Let me summarize. You repeat exactly all these stupidities that are being criticized in this article. I can prove to you that it is a general opinion that your answers to these questions are viewed as ridiculous by mainstream physicists. Because it seems that there is no actual complaint that would suggest that this page describes the criticisms of LQG inaccurately, I will remove the POV label. --Lumidek 00:16, 23 Nov 2004 (UTC)

Have it your way. — Miguel 00:28, 2004 Nov 23 (UTC)

—Miguel 19:10, 2004 Nov 22 (UTC)

Right to reply

Well, maybe this page will need to evolve further. I anticipate that there may be some replies to objections written here in the future. Charles Matthews 07:18, 23 Nov 2004 (UTC)

Controversial tag

Dear Tweet Tweet, could you please be a little bit more specific and say something about this actual page, instead of just putting bombastically sounding labels here? --Lumidek 02:11, 29 Nov 2004 (UTC)

For one thing, it is true the factual accuracy of this article is questionable AND this topic IS controversial. And if you look at the corrections I have made to the article, aren't they reasonable? Tweet Tweet 02:40, 29 Nov 2004 (UTC)

"rv "Tweet Tweet" who converted this very specific web page into meaningless and very confused flamewar"

My corrections are not meaningless or very confused. Tweet Tweet 02:49, 29 Nov 2004 (UTC)

"You may have misunderstood the meaning of the page "Objections to loop quantum gravity". It is not meant to be another page propagating the beliefs of loop quantum gravity - see the main page loop quantum gravity which is exactly dedicated to this goal. The page "Objections" is meant to summarize the problems that other physicists see on LQG. All the philosophical positions that you've tried to put, in a very disorganized fashion, directly to the page "Objections" only show one thing - that the objections apply to you as well. But these objections are real. Most of your questions have very simple - and often rigorously known - answers." (Lumidek)

I'm agnostic about both LQG and string theory. I'm simply pointing out that the objections on this page are not all that reasonable. And why should there be a page full of mostly unfounded attacks on LQG and we're not supposed to answer these objections? And as for other physicists, it appears Lubos Motl is the only person with these objections. I also don't see what you are referring to about my philosophical objections since I'm not aware of discussing philosophy in my corrections. And if you claim my "questions" have very simple and rigorously known answers, can you list them here for all of us to inspect? Tweet Tweet 02:54, 29 Nov 2004 (UTC)

Too many assumptions

OBJECTION 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.

True, but even the quantized Fermi interaction gives good results below the electroweak scale even though it is nonrenormalizable and so does QED even though it only holds up to the electroweak scale. At any rate, even if the exact Einstein's equations turn out to be approximate, it's still a reasonable starting point to study the simpler model where it is exact first and then and only then consider corrections later.

The spacetime dimensionality (four) is another assumption that is not 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.

And as of 2004, there is no evidence that there are more than 4 dimensions. This isn't to say there aren't. But it also means we can't be sure there are.

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.

There are, however, nonrenormalizable QFTs which hold at all scales. They're simply not perturbative, that's all.

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. (Apprarently physically inconsistent, that is, not theoretically inconsistent)

Commentary from the renormalization group aspect

OBJECTION 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.

Assuming, of course, string theory is the right theory. And also, much of the more physical calculations in string theory are not truly theoretical but phenemological.

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.

19th century??? 20th century??? 21st century??? BOTH string theory and LQG (as well as Euclidean quantum gravity, twistor theory, etc are ALL late 20th century theories)

As a predictive theory

OBJECTION Loop quantum gravity is not a predictive theory. 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.

String theory is not a predictive theory. Its phenemological models do not follow directly from theory alone but are put in by hand.

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.

It's possible to include other fields and connections in LQG. LQG people are simply following the policy of studying simpler models before studying more complicated models. This is a common procedure in physics, like neglecting air resistance and friction unrealistically, solving the hydrogen atom by only considering the Coulomb potential and thus coming up with a model where excited hydrogen atoms don't decay, etc. etc. etc. Experimentalists are probably the people who are most aware of how common unrealistic simplifications are.

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 catastrophe 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.

If you look at the renormalization group flow, nonrenormalizable terms are irrelevant and since the Plank scale is so high up, nonrenormalizable terms would simply vanish effectively.

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.

Self-consistency

OBJECTION 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. 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 (really?) 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.

Unitarity does NOT follow from time translation symmetry. The conservation of energy does, but not unitarity. At any rate, Hawking showed that if matter collapses into a collapsing black hole and ends at the singularity and the black hole is later allowed to completely radiate away and disappear, pure states would get converted into mixed states. Sure, this is a violation of unitarity, but it's NOT a violation of the "conservation of probability". The trace (or if you prefer, the norm) of a mixed state is the same as the trace of a pure state. They're both 1.

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

OBJECTION 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.

And there are electroweak models where there is no scalar Higgs field, but instead, we have technicolor condensates or maybe the top sector. Also, it certainly isn't out of question for the Higgs field, if it exists, to be an effective field at some higher scale.

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.

And what's wrong with nonperturbative techniques? Perturbative theory only diverges asymptotically and overlooks many nonperturbative effects. Also, the S-matrix assumes a flat Minkowski space background, which is hardly realistic for gravity.

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.

Galileo came up with a better theory by ignoring the ("successful") older model of Aristotle. Relativity ignored the ("successful") Newtonian mechanics. So did quantum mechanics.

Nipping the revert war in the bud

Tweet Tweet, please do not get into a revert war with Lumidek. It is better to leave this page in its current pitiful state. — Miguel 03:59, 2004 Nov 29 (UTC)

Disputation approach

I am now trying to separate each section into a clearly-labelled OBJECTION, and brief REPLY. It is clearly not adequate for 'replies', which of course should be allowed here, to be written into the OBJECTION section. I'm asking for co-operation in keeping to this format (like a medieval disputation), since it seems unlikely that the differences can be resolved.

Please, no mass reverts, and edit section by section until we get the sections into readable statements.

Charles Matthews 11:42, 29 Nov 2004 (UTC)

Back to the {{merge}}label?

The recent editing re-instates my belief, that LQP and OtttoLQP must be merged, otherwise each faction tends to believe they "own" "their" article. On other topics, POV splits of articles aren't tolerated and I don't know why LQP should be different. The project which has one article per POV is called WikInfo. --Pjacobi 17:24, 29 Nov 2004 (UTC)

Heavens, it gets worse: After OBJECTION and REPLY, we've got CLARIFICATION. The Wikipedia is not the place to battle out scientific research, see also Wikipedia:No original research. --Pjacobi 18:07, 29 Nov 2004 (UTC)

User:Pjacobi is correct to argue that best WP practice would be a merge. The issue of length is, for me, the main obstacle to that. If the large cut made (generously) by User:Miguel leaves a shorter QCG article that still covers the substantive points, then I think we can maybe make progress here.

Charles Matthews 18:46, 29 Nov 2004 (UTC)

This isn't vandalism!!!!!!!!!!!!!

Lumidek has been writing everywhere that I'm vandalizing this page, which is not what I'm doing. I'm trying to reply to his objections. Tweet Tweet 23:57, 29 Nov 2004 (UTC)

Please try to keep all edits in appropriate places, brief, and in encyclopedic style. It is rather clear that this whole page is in need of a thorough edit.

Charles Matthews 09:48, 1 Dec 2004 (UTC)

Well, I have edited this down, to more like a FAQ style. It is still too long! Forgive me if I have cut out anything vital. Charles Matthews 11:38, 1 Dec 2004 (UTC)

what is this stuff about non-separable Hilbert spaces?

Hey, I'm a little confused about this talk about the Hilbert spaces being non-separable in LQG. Isn't it true that all Hilbert spaces have countable bases, which follows from the Axiom of Choice? Is there some reason why LQGers would not require the AC to hold in their model? -Lethe | Talk

No, that's not true: you can take l² on an uncountable set X, for example. I don't know how serious a point this is, though. It is anyway about technical considerations in mathematics, rather than the physical arguments. If the article at representations of diffeomorphism groups were better developed, perhaps the point belongs there.

Charles Matthews 09:06, 3 Dec 2004 (UTC)

Oh, I realize that this is purely a technical consideration, not a physical one. Still, if one thought that uncountable bases could be ruled out by the AC, that would make any physical arguments suggesting their necessity suspect. Right? But, you're right, the AC has an equivalent form that says that any vector space has a basis, no mention of whether this basis is countable. I think my addled brain inserted that erroneous bit. And I'm slapping my forehead now; l²(X) is certainly a Hilbert space I have seen before, and it obviously has uncountable basis (if X is uncountable). Oops. So thanks. -Lethe | Talk

Hello! Charles's right - non-separable Hilbert spaces are not prohibited by the axiom of choice. Whether or not a space is separable depends on the continuity & normalizibility conditions you choose. For example, consider all "wavefunctions" that are linear combinations of sqrt(delta(x-x0)) localized at different points x0. You can easily see that this has no countable basis. As you see, in mathematics, the non-separable Hilbert spaces are completely pathological, and sort of unimportant. In physics, their existence is a catastrophe. This is what you get if you follow the LQG rules directly. The LQG people argue that they may be allowed to truncate the Hilbert space to some separable Hilbert space, but no "inevitable" derivation of it exists yet. --Lumidek 12:38, 3 Dec 2004 (UTC)

Thanks for the explanation Luboš, but I'm a little confused by your example. Firstly, I could say the same thing about linear combinations of just delta functions delta(x-x_0) without square roots: there are uncountably many of those, but that's OK, because they aren't really in the Hilbert space, since they have infinite norm, right?

Well, this is why I talk about the square roots of delta function, which are - by construction - normalizable. You can call the basis vectors of my Hilbert space differently, if you don't like "sqrt(delta(y))", but I believe that this notation is self-explanatory. I really don't understand what you mean by "I could say the same thing about (something different), because the basic properties are different than in your example and your conclusion won't hold in mine". It sounds like a totally confused, self-contradicting sentence. It's very important that I defined the Hilbert space exactly the way I did, and if you just randomly erase the words from my sentence and introduce havoc to my statements, you won't get anything meaningful. My Hilbert space contains objects like 7.sqrt(delta(x-13))+8.sqrt(delta(x-15)). The norm of this state is 7^2+8^2 and it is finite. The states in your space of "discrete combinations of delta functions" are not normalizable, which is why your example is not a Hilbert space at all. By construction, I am not considering any smeared functions, unlike your "refined" example that would lead to the standard L2 Hilbert space. This is the whole point of my example, and it is necessary for the Hilbert space, as defined exactly by me, to be non-separable. My Hilbert space, by construction, does not contain any smooth functions, and you need the uncountable basis of sqrt(delta(x-a)) for all values of a to generate the space. The loop quantum gravity Hilbert space is analogous to this example, and it is non-separable, too. Is it clearer now? --Lumidek 22:20, 11 Dec 2004 (UTC)

OK, yeah, it's clearer now. I was initially unsure about what sense to make of the square root of a delta function, and that's why I tried to replace it with something else. But if I guess this is just a vector of unit norm, indexed by a real number, and I shouldn't worry about what it means to integrate it with other functions, because they're not in your Hilbert space. Thanks -Lethe | Talk 01:35, Dec 12, 2004 (UTC)

I'm not sure which Hilbert space Lumidek is refering to, but the Dirac delta distribution isn't an element of L²(R).

Luboš isn't talking about L²(R); that Hilbert space is separable, and the one Luboš gave is not -Lethe | Talk 01:43, Dec 12, 2004 (UTC)

Well, it did occur to me Lumidek might have been talking about L²(A) where A is the set of reals with the discrete topology and a measure such that the measure of a finite subset is its number of elements and the measure of an infinite subset is infinite

the measure you mention is called the counting measure, and I don't think the integral cares about the topology, only about the measure? So actually, I think that L²(R) with the counting measure is just l²(R). And actually, I think the Hilbert space Luboš made is the same space, as youo suspected, now that I've figured out what that space is. -Lethe | Talk 04:50, Dec 13, 2004 (UTC)

but in that case, what is the distribution notation δ(x) doing here? Also, I'm not aware of what the square root of the Dirac delta distribution is, if there is even such a thing. Of course, he could have been refering to another Hilbert space besides L²(R) or L²(A). Tweet Tweet 03:46, 13 Dec 2004 (UTC)

Of course, that's why I also was confused about his space. Just what is the square root of the dirac delta? If it's the thing I suggested before, that's not a linear functional, and so isn't dual to any distribution (I don't think). But now I see that you have to understand it simply as an object with the following properties:

$\int {\sqrt {\delta (x-a)}}{\sqrt {\delta (x-b)}}dx=0,a\neq b$

$\int {\sqrt {\delta (x-a)}}{\sqrt {\delta (x-a)}}dx]=\int \delta (x-a)dx=1$

from which it seems clear to me that this is just l²(R) with a funny looking basis. -Lethe | Talk 04:50, Dec 13, 2004 (UTC)

Of course, people weren't talking about Hilbert spaces, I think, before von Neumann came along but worked instead with an unspecified bra-ket vector space as developed by Dirac in his transformational theory. Dirac's bra space and it dual ket space contained Dirac delta distributions and plane waves and it's not so clear the shift to Hilbert spaces was really such a good move after all. Tweet Tweet 00:17, 12 Dec 2004 (UTC)

Rigged Hilbert spaces - need I say more? Charles Matthews

We can change to a basis which is smeared by some reapidly decreasing function, and this basis will have to be countable, right? Why could not the same thing apply to your example? Also, I don't know how to define the square root of a delta function, I guess it's this ${\sqrt {\delta }}:f\mapsto {\sqrt {f(0)}}$? Two more questions (if you don't mind, Luboš?): somehow I've heard that the dimension of the Hilbert space depends on the volume of phase space of the classical theory. Is the problem here that the volume of the diffeomorphism group is too big? Or does this question simply not make any sense (because diffeomorphism group is noncompact). Also, what's so bad about a nonseparable Hilbert spaces in physics? Won't it just lead to observables with a continuum of matrix elements? -Lethe | Talk 21:52, Dec 11, 2004 (UTC)

That's about six questions, by my count, and in a sort of cross-threaded way. Look, some of this is not very relevant, but so-called 'huge spaces' do turn up in the mathematics of the diffeomorphism group (Raoul Bott pointed this out decades ago). All you need to cause a technical problem would be something like a topological group that genuinely had uncountably many connected components. You can get these things in some kinds of foliation theory, and the LQG issue is something like a knot theory analogue (as far as I can see). If you ever want to integrate, you have to pray that the integrand vanishes on all but a countable number, or you have a serious problem of sense. Charles Matthews 22:58, 11 Dec 2004 (UTC)

Look at [1] - Rovelli et al. (in March 2004) try to propose a heuristic argument why some separable Hilbert space may exist in LQG - but they also admit, in the first sentence, that the standard construction leads to a non-separable Hilbert space. --Lumidek 12:42, 3 Dec 2004 (UTC)

Well, the position in the mathematics might be, that a non-separable Hilbert space H is used to make the formulation more convenient (and that was all). These things are not so strange from the point of view of Banach algebras, I guess. They might be useful in some traditional area like almost periodic functions, through the idea of Bohr compactification which starts by making a topological group into a discrete group. Charles Matthews 12:46, 3 Dec 2004 (UTC)

I can't read that recent reference, but[2] is an older comment on the same issue, also by Rovelli. Well, I'm not sure that the technicalities there really 'grip' the issue. Usually some care means that the abstract spectral theory stays the same. Charles Matthews 12:54, 3 Dec 2004 (UTC)

S-matrix

"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."

Do you have any reference for this claim of yours? Tweet Tweet 23:55, 19 Dec 2004 (UTC)

This is a sort of well-known lore. Every week, there is a paper that talks about these issues. For example, 10 minutes ago (today), a new preprint by Raphael Bousso appeared [3] - it's called Cosmology and S-matrix. It says that the S-matrix is the observable that we know how makes sense, and he tries to make some sense of it in nontrivial cosmological backgrounds, with mixed results. See also basic textbooks, e.g. page 97 of Polchinski volume I. These statements about the S-matrix are especially meant to express the fact that the local Green's functions of metric are not gauge-invariant, and quantum gravity is only well-defined on-shell. One could define some very non-covariant complicated gauge-invariant observables, but no doubt, they would be even much harder to calculate than the S-matrix. --Lumidek 01:12, 20 Dec 2004 (UTC)

Duplicates

Pjacobi identified these two very similar pages. Because this copy is not only disordered, but various people - not me - added many labels like "totally disputed", "POV", "deserves your attention" etc., I think it is generally agreed that this page is the "wrong" copy that should be redirected to the "correct" copy. --Lumidek 19:08, 28 Dec 2004 (UTC)

Sorry, this is the page which correctly got the mentioned meta tags, was edited by several contributors and complies with policy. Lumidek tried to setup a "private" copy at Problems with loop quantum gravity, which is of course against policy, even assuming it may be most brilliant. --

You misunderstood it completely, Pjacobi. Well, both of these pages were started as my pages, and it is the page "Objections..." that has become a "private" copy of Tweet Tweet. The current page "Problems with..." contains the new material, including the grammar improvements of all the other co-authors. The current text on this page "Objections to the theory of LQG" is a private project of Tweet Tweet who attempted to write "replies", but he never finished it, and therefore his confused replies are only attached to one half of the points raised in the articles. If you don't to allow personal copies of the pages, it's fine - but the personal one is "Ohjections to the theory", while the "Problems..." is the standard, community-owned wikipage that has been brought close to a perfect page. The "problems..." is the real page that has been linked and read for quite some time, and found no problems with the other Wikipedians. This "Objections..." became the personal, isolated web page which no one except for Tweet Tweet - and Charles Matthews who is trying to improve his formatting - visits. --Lumidek 19:28, 28 Dec 2004 (UTC)

But creating a new copy doesn't solve anything. What will you do, when another users starts editing "Problems..."? Also, this is the original as testified by the version history. Cut'n'pasting other users edits to the other copy is strictly speaking a violation of GNU FDL.

This may all sound formal, but it nevertheless applies.

Pjacobi 19:44, 2004 Dec 28 (UTC)

Of course that moving the copy solved absolutely everything, until you appeared. Everyone was satisfied, including Tweet Tweet. It's you who created all these pseudoproblems, Pjacobi. Speaking about violation of "GNU FDL" sounds not only formal, but really disgusting. It's easy to understand why they argued that this GNU stuff is a cancer - it's a very dangerous type of cancer especially if it is used by bad people. Is not the status of these edits GNU GFDL anyway? I am absolutely sure that I am legally allowed to copy and paste this mostly my text anywhere I want. --Lumidek 03:44, 29 Dec 2004 (UTC)

A brief summary of the "improvements" of Tweet Tweet

Sorry, Tweet Tweet, but it is neither helpful nor possible to argue with you simply because you don't seem to understand some very basic concepts in physics. The discussions would be completely infinite if we adopted this game. I just reject to pretend that the discussion with you is serious. It will be much easier for me to leave the LQG pages on Wikipedia so that they really become a place for crackpots' exhibitions. Why do I say these things about your "improvements"? For example, there is my explanation why you can't trust Einstein's equations at the Planck scale and beyond. Every particle physicist knows it - it's a completely quantitative fact. You reply "it's still reasonable to study a simpler model [Einstein's equations] at the Planck scale first". I see no other explanation than that you simply misunderstand this basic point - that it's, to say the least, extremely difficult to justify a non-renormalizable theory as a starting point. Then you continue with the existence of some QFTs that exist at all scales - but they have absolutely nothing to do with LQG. Then you criticize some statements for "having bias towards string theory being the right approach". Well, this "bias" is usually called "knowledge". Of course that the arguments that show why string theory answers XY correctly and LQG does not will be "biased". You misunderstood the "predictivity" section altogether - you just don't seem to understand what it means that a nonrenormalizable theory has infinitely many adjustable parameters, and why it means that predictivity is lost. Instead, you repeat your cliche "we study simpler models first". The problem is not that you study simpler models (and you misspell the name of Planck); the problem is that you study wrong and inconsistent models. Concerning the renormalization group argument - which has absolutely no direct link to string theory - you again say that I am biased towards string theory (?), but you can't discuss this question (Randall-Sundrum) because it is not understood in LQG. So why do you reply if you have absolutely nothing to say? Then you fortunately agree with the non-equivalence of unitarity and time-translation symmetry but you also try to argue that it's OK to lose unitarity - and you argue with the information loss in the black holes. First, virtually no one - not even Hawking (see the news from the summer 2004) - believes today that the information is lost. Second, the loss of information in the black holes would be completely innocent compared to the complete destruction of unitarity that you get from the spin foams. You also comment on the gap separating LQG and particle physics - your answer is that particle physics is like "Aristotle" and it's OK to ignore it, much like "Galileo" did. Are you serious that high-energy physics - the standard model, QED, QCD, weak interactions - is like Aristotle's philosophy for you? If you were a student at Harvard, we would simply fail you (or not accept you in the first place)+ if you were saying all these stupidities. But at Wikipedia, you feel to be a peer, right? You also criticize perturbation theory - which is arguably the most successful calculational technique in the whole of science. The S-matrix, the true observable of QFT and Quantum Gravity, is another target of your misunderstandings, and you say incorrect things that it only works in the Minkowski space. Half of the points are not addressed at all. The quality of your comments is disastrous, and I reject to consider you an equal partner in forming these pages. --Lumidek 03:35, 29 Dec 2004 (UTC)

I know GR is nonrenormalizable if expanded about a flat space background.

It is nonrenormalizable if expanded around any background.

I agree we don't know if LQG provides an approximately flat spacetime at large scales, but at the Plank scale, it provides a UV cutoff. I agree the Einstein-Hilbert action might not be the right one at the Plank scale.

Note that several lines below, you call Plank a "typo" - nevertheless, here you spell Planck incorrectly twice again. Is not it sufficient evidence that you are not saying the truth if you call it a "typo"? LQG does not provide any geometric cutoff in any known sense because there is no indication that something like geometry should emerge. You are pretending the you use the word "cutoff" in the standard sense, which is obviously impossible for LQG. Consequently, the statement about the cutoff makes no real sense. Making some eigenvalues discrete does not guarantee that you will remove UV problems - and actually in LQG we know that you don't remove them. This is discussed in a separate section of the article.

I'm just saying if we study the simpler Einstein-Hilbert action first, we might have a greater idea on how to proceed with more complicated actions.

Einstein-Hilbert action IS already complicated. It is complicated enough so that it is nonrenormalizable and completely useless to understand any physics at the Planck scale or above. Concerning your "might have a greater idea" - if you expected that you would have a greater idea, why is it that no such an idea has emerged in LQG for 20 years at least?

Besides, much of the results in LQG, which are kinematical, are not based upon the action,

These are not results, but defining assumptions of LQG, as explained in another section. And having no dynamics is a pretty serious problem, is not it? Physics IS dynamics, and if you don't have dynamics, you don't have physics. The kinematics is wrong anyway because it is based on incorrect assumptions about the discrete character of various observables.

but simply diffeomorphism covariance and Spin(3,1) gauge symmetry (which admittedly is broken to SU(2)), and as such, is likely to still hold. Although I have to admit because there are gauge constraints in the Hamiltonian approach, changing the action by adding higher order terms might change the Gaussian constraint in the Ashtekar variables, but that can be taken care of (this has been done in papers including other nongravitational fields).

Wooden earphones. What are you trying to do here? Surely not finding a meaningful predictive physical theory.

But if the Lagrangian contains second derivative or third derivative terms, we would have to modify the Hamiltonian approach greatly by adding more variables and so the results on spin networks would almost certainly not carry over (I admit this much. Satisfied?) and we might have to consider spin hypergraphs.

You clearly imagine that physics is some mathematical masturbation with random Hamiltonians into which you add random terms. But this is only physics done by ignorants. Real physics is based on many powerful principles, facts, theorems, and complementary methods. They're powerful enough to see that whole classes of mathematical masturbation cannot lead to anything physically relevant. You're not the only one who can write down a third derivative of some random observable - but that's not physics yet.

And yes, I do realize gravity could simply be an effective field theory, an emergent concept and diffeomorphism covariance and SU(2) gauge symmetry might be none other than emergent low energy approximate symmetries which become

There is no meaningful SU(2) gauge symmetry arising in physics of physical (non-topological) four-dimensional gravity. This is just your misconception based on a wrong field redefinition.

more exact at lower and lower energy scales and so, quantizing it on the Plank scale might not be a good idea. That's why I'm agnostic on LQG just as I'm agnostic about string theory. But that doesn't mean people mustn't study it, since it MIGHT possibly be an exact symmetry at all scales.

"Planck" again misspelled. One can say anything with the word "MIGHT" if you follow the same standards. There MIGHT exist a perpetuum mobile after all, right? In science, we must study things that are reasonable, not things that can be pronounced with the word "MIGHT". The SU(2) symmetry is meaningless in 4D gravity not only at high scales, it is also meaningless at low scales. The only true thing about this SU(2) gauge field is that 3x3 = 9, which is both the number of components of a spatial section of an SU(2) gauge field, as well as the number of components of a spatial 3-bein. But the physical meaning of these two things is different and a map between them is physically wrong, much like the map between any two different random sets of 9 degrees of freedom.

And yes, I do know about the renormalization group. If there are no new physics which alters the picture below the Planck scale, it means there could be many nonrenormalizable terms we could add at the Plank scale which would only show up as very tiny corrections (possibly undetectable, but we mustn't overlook the ingenuity of experimentalists) at low energy corrections.

"Planck" once again. Your comments "we could add something" show that you don't understand what the problem of these theories, in respect to the renormalization group, is at all. Read at least the newest paper of Lee Smolin, the first paragraph at least. You will see that he understands it much better. One would need to fine-tune infinitely many terms at the high energy scale to get a meaningful effective theory at low energies. A generic theory of your type simply won't run to a flat-space limit - the Hausdorff dimension itself won't be 3+1 - and a theory with infinitely many undetermined terms is physically useless.

I assume this is what you mean by nonpredictivity. But this nonpredictivity happens at the Planck scale and not at low energy scales where we can still use nonrenormalizable effective field theories.

But effective field theories is something very different from loop quantum gravity. Loop quantum gravity has been argued to be a theory of quantum gravity that exactly tells you what happens at the Planck scale. I am explaining you that this is inconsistent. Exactly all these typical features of LQG with spin networks, area eigenvalues and all this stuff is simply wrong because a correct theory that would have a low-energy smooth space limit would have to be supplemented with an infinite number of corrections of all types that would totally alter the "predictions" of LQG. At any rate, LQG cannot give you any new insights about physics as long as these insights are compatible at least with the existence of a Universe that looks 3+1-dimensional.

When you mentioned zero predictive power, I assumed you meant at lower energy scales, unless you were thinking of a Planck scale experiment.

If I talk about zero predictive power, I talk about predictive power and not about some energy scales. LQG has zero predictive power for any experiments. At long distances it does not exist and classical GR - and its quantization as an effective field theory - is the only thing we have if you want to avoid string theory. At short distances, the physics of LQG is nonpredictive as well because the naive rules of LQG would have to be supplemented with infinitely many unknown corrections that guarantee the existence of a long distance limit. With infinitely many modifications, no prediction of LQG may survive.

But that's only in a theory where we allow for arbitrary coefficients for higher order terms. Nonrenormalizable theories with a UV cutoff are predictive in principal

"in principle", not "principal"

once we specify what the nonrenormalizable terms are at the UV scale. I guess what you were trying to say is we can't predict what these nonrenormalizable terms are, and so, there isn't any reason to set them to zero as in standard LQG (but we can always modify LQG to include higher order terms while still keeping diffeomorphism covariance and SU(2) gauge symmetry),

Great that you got one of the points. Maybe.

but that isn't the same thing as stating any particular LQG model can't make predictions in principle. With a UV cutoff, nonrenormalizable theories aren't inconsistent.

Obviously we use the word "principle" in very different meanings. Yes, in principle there exists a theory that can give us right, meaningful, and new predictions about quantum gravity, and in principle you can obtain this theory by making infinitely many modifications of LQG - and the "higher-order terms" are clearly not enough. The theory that you obtain after infinitely many modifications like that is called String theory.

I wasn't the person who wrote you were biased towards string theory. That was Charles Matthews. What I wrote was some of your objections, like extra dimensions, T-dualities and mirror dualities, AdS/CFT presuppose string theory.

It may have been written by Charles Matthews, but it does not change anything about the fact that this comment is silly.

Plank was a typo.

I've given 7 pieces of evidence that you're lying here. You simply don't know how to spell Planck.

I did not say the Randall-Sundrum model is necessarily wrong. I just wrote extra dimensions is irrelevant to LQG and the only reason I mentioned extra dimensions is irrelevant was because you mentioned the failure of LQG to include extra dimensions as an objection.

I wrote an objection that LQG assumes that there is no new physics - like the extra dimensions - and the world is as naive as it seems to someone who observes it with the naivity of 18th century physics. It's just a failed attempt to picture the world as being "exactly what we see with our eyes", and I emphasize that this is how physics has not been working at least for 100 years.

In fact, I explicitly wrote extra dimension MIGHT be true, although it might equally well be false. "can't discuss the question because it is not understood" was not what I wrote. I didn't not write "can't understand". I wrote "irrelevant". If really necessary (but is it?), we can study 5 dimensional LQG with an orbifold instead of a manifold as a background.

You clearly don't have a control over the things that you write. You wrote, under the only paragraph that mentions the Randall-Sundrum models, the following:

REPLY The argument has a bias in favour of string theory being the theory with the right viewpoint, and towards radical solutions. The more physical calculations in string theory might be less truly theoretical than phenomenological. The geometry underlying LQG is not well understood, so it is not really possible to discuss its geometry at length.

The loss of unitarity for spin foams MIGHT be removed with a proper functional measure, but I'm not sure about that.

Well, once again, yes. If you make infinitely many corrections and improvements to loop quantum graviry, you can obtain a unitary gravitational S-matrix, and it's called string theory. But what's important is that the LQG starting point will be useless at the end.

I NEVER claimed particle physics is like "Aristotle". You misunderstood me once again! I never claimed anything about ignoring QED, QCD, weak interactions, the Standard Model, etc, which are very sucessful theories.

Could you then explain what you meant by Aristotle? I enumerated many properties of the Standard Model - violation of CP; electroweak symmetry breaking; S-matrix calculations from the Standard Model - that LQG seems incompatible with, or at least LQG has nothing to say about them whatsoever, and you replied:

REPLY Galileo came up with a better theory by ignoring the ("successful") older model of Aristotle. What's wrong with nonperturbative techniques? Perturbative theory diverges asymptotically and overlooks many nonperturbative effects. The S-matrix assumes a flat Minkowski space background, which is hardly realistic for gravity. In the absence of predictions for low energy phenomenology presently, some objections can be treated as moot. Besides, low energy QCD (as opposed to the high energy asymptotic freedom) is a meaningful theory for which perturbative calculations simply don't work.

How else should I interpret it than that you want to ignore the "successful" (not sure why the question marks) older model of particle physics - which is a model of Aristotle in your example??

My point wasn't a criticism of perturbation theory (which fails to predict nonperturbative effects), but to point out your claim that a nonperturbative theory is necessarily wrong is unjustified. Tweet Tweet 04:51, 29 Dec 2004 (UTC)

You are using the adjective "nonperturbative" incorrectly. Nonperturbative effect is something that is invisible in perturbation theory - like a monopole or an instanton. Nonperturbative approach to a question is an approach that is not based on Taylor expansions around an understood theory (usually a free theory). But these worlds don't change anything about the fact that if one does not have a working prescription to calculate physical observables, such as the S-matrix, then he has neither perturbative nor nonperturbative definition of a physical theory.

I don't understand this. When I edited Objections, you were upset, but when I didn't reply to every single one of your objections, you are also upset. I don't know EVERYTHING about LQG, some, like a "nonprincipled approach", I don't know how to reply to, and I agree there are problems in showing that a smooth space can emerge at large distances, although there is the Kodama state. Tweet Tweet 05:21, 29 Dec 2004 (UTC)

The reason why I am upset is that your replies are stupidities, and of course the ideal number of sections that you should have edited should have been proportional to your understanding of high-energy physics, i.e. it should have been zero. I only mention your inability to comment on all the topics to emphasize - for those who have not noticed yet - that your knowledge is certainly incomplete, to say the least.

from VfD

On 21 Jan 2005, this page was nominated for deletion. See Wikipedia:Votes for deletion/Objections to the theory of loop quantum gravity for a record of the debate.