• /Archive 1 - up to May 2004

The development of a quantum field theory of a force invariably results in infinite (and therefore useless) answers. Physicists have developed mathematical techniques (renormalization) to eliminate these infinities which work for the electromagnetic, strong nuclear and weak nuclear forces, but not gravity.

The most obvious ways of combining the two (such as treating gravity as simply another particle field) run quickly into what is known as the renormalization problem. Gravity particles would attract each other and if you add together all of the interactions you end up with many infinite results which can not easily be cancelled out. This is in contrast with quantum electrodynamics where the interactions do result in some infinite results, but those are few enough in number to be removable via renormalization.

Thus the development of a quantum theory of gravity must come about by different means than were used for the other forces.

In LQG, the fabric of spacetime is a foamy network of interacting loops mathematically described by spin networks. These loops are about 10^-35 meters in size, called the Planck scale. The loops knot together forming edges, surfaces, and vertices, much as do soap bubbles joined together. In other words, spacetime itself is quantized. Any attempt to divide a loop would, if successful, cause it to divide into two loops each with the original size. In LQG, spin networks represent the quantum states of the geometry of relative spacetime. Looked at another way, Einstein's theory of general relativity is (as Einstein predicted) a classical approximation of a quantized geometry.

in my opinion this section is relevant to the subsection "space atoms", and "space atoms" is a relevant implication of LQG, but if you disagree miguel, and you decide to remove it, i'll respect your decision and won't reverse it.

n LQG, the fabric of spacetime is a foamy network of interacting loops mathematically described by spin networks. These loops are about 10-35 meters in size, called the Planck scale. The loops knot together forming edges, surfaces, and vertices, much as do soap bubbles joined together. In other words, spacetime itself is quantized. Any attempt to divide a loop would, if successful, cause it to divide into two loops each with the original size. In LQG, spin networks represent the quantum states of the geometry of relative spacetime. Looked at another way, Einstein's theory of general relativity is (as Einstein predicted) a classical approximation of a quantized geometry.

I have replaced the following

In order to account for the structure of space and time at the Planck scale, LQG breaks Lorentz invariance and posits that certain well known effects of special relativity such as length contraction and time dilation cannot occur below the threshold of the Planck scale. It also predicts that the speed of photon propagation in vacuum may be dependent on the photon's wavelength, and not constant as demanded by special relativity (where it is denoted by c). It is not clear whether an approximate Lorentz invariance can be recovered in LQG at long distances and whether LQG can explain the plethora of successful experimental tests of special theory of relativity. LQG proposes a privileged reference frame associated with the spin foam, and therefore it is natural to expect that it may suffer from the usual problems of the old-fashioned theories of luminiferous aether.

by an entirely new account. Comments are welcome! At the very least, the readability of the section needs to be improved. — Miguel 21:21, 25 Jul 2004 (UTC)

1. The introduction. "String theory claims to be a theory of everything". First, string theory is not "claiming" anything: it is *people* who might make such claims. Second, is there any citation for a leading figure in string theory actually saying or writing "String theory is a theory of everything"? I don't think anyone has seriously believed this since 1985 or so. The sentence could be rephrased as follows: "while LQG is intended to be only a quantum theory of gravity, string theory can accomodate many other phenomena including matter and gauge (vector) particles; this fact has led to attempts to model not only gravity but also elementary particle theory with strings.

The sentence about "mutually exclusive/incompatible models" with "6,7, or 22 extra dimensions" is somewhat misleading, because since about 1995, it is known that different types of superstring theory are interrelated through dualities, so that what were previously apparently "mutually exclusive" solutions are now seen as different points in a single parameter space or space of vacua. For example it is thought that there is a smooth transition from IIA strings in 10D to 11D supergravity. So, it would be more correct to say that at most one point in the (apparently very large) space of possible vacua could describe our patch of the Universe.

Most obviously, the reason why there are so many more strings papers is the fact that they *do* have matter and gauge particles, so there are many more opportunities to compare models with data. The number of particle theory papers *without* strings is similarly large. If you don't concern yourself with particle physics, then obviously you have a lot less to write about.

IMHO, there are too many mentions to String Theory in this article. There was an old version where I wrote something to the effect that "no attempt will be made to describe String theory in more detail here since it wouldn't be possible to do it justice" and left it at that. This page is slowly morphing into a debate of the relative merits of String Theory and LQG as theories of quantum gravity, which belongs neither in string theory nor here, but under quantum gravity.

Yes, I quite agree. I will continue to edit, reminding myself not to mention string theory unless necessary.

I think your criticism is well-places and I encourage you to act on this criticism by editing the article yourself. There are a lot of argumentative statements in the article that really get in the way of presenting LQG and, as you point out, cause internal consistency problems.

Miguel 02:38, 10 Jul 2004 (UTC)

2. SR/Lorentz invariance. I don't understand the sentence "effects of special relativity such as length contraction and time dilation cannot occur below the threshold of the Planck scale". Surely this is just the reverse of what people have been proposing (doubly-special relativity) - roughly that SR is exact in the low-energy limit but that transformations and dispersion relations become affected at energies near the Planck scale. Also, the statement "the speed of light, c, may be variable" is very confused. The value of c, the invariant speed of relativity, is defined exactly in SI units and cannot change. But, the actual speed of photon propagation may be frequency-dependent: in which case, it is inappropriate to denote it by the symbol "c". Rather than "the speed of light" I would use some other phrase such as "the speed of photon propagation".

3. Quantum cosmology. I agree with some previous commenter that any statement about "the Platonic ideal of absolute truths" is out of place and irrelevant in an article about a theory of physics. Also, so far as it makes sense, the discussion in the first paragraph is not directly related to LQG but could apply to almost any theory of quantum cosmology.

As for the cosmological constant, much of the discussion is quite erroneous. The observations which suggest nonzero Lambda are of *supernovae* (not galaxies) and include both brightness (magnitude) and cosmological redshift. The sentence "Some physicists have put forward the thesis that a positive cosmological constant is incompatible with supersymmetry, which, if true, would represent a problem for string theory and M-theory (...)" is pointless, since this thesis is simply wrong. What is the reference for this? String theorists (e.g. the Kachru group) are routinely discussing solutions with softly-broken supersymmetry which have positive cosmological constant. There is no incompatibility at all. (Exact supersymmetry, to be sure, is not compatible, but it has been known for decades that exact supersymmetry does not describe the world.)

4. Black holes. The discussion here seems to contradict the claim in the introduction that LQG has a higher level of mathematical rigour than strings. To truncate the interior region away and use an uncalculable free parameter does not seem to be a rigorous procedure, it seems rather arbitrary. Perhaps the meaning was that the rigour goes into the setting-up of the theory, but not into the derivation of its physical consequences? Also, while it is interesting that the radiation spectrum has fine structure, I don't think this can be called "potentially an improvement" without some reason. Why is a spectrum with fine structure an "improvement"?

In the same way that the fine structure of the Hydrogen atom is an improvement over the Balmer series and not a way to argue that Pauli's theory of electron spin must be wrong. You just can't use an empirically untested semiclassical result as a benchmark for a purported nonperturbative quantization. Miguel 02:38, 10 Jul 2004 (UTC)

I'm still puzzled. Do you mean improvement in the 'technical' sense of a more accurate calculation within a given theory, e.g. the scalar potential "improved" with radiative corrections?

5. Quantum field theory. It should be mentioned that string theory also addresses the "ultraviolet catastrophe" (a.k.a. problem of divergences). String theory allows the calculation of graviton scattering to one-loop, which is finite, and in principle to arbitrary loop order, although this presents considerable technical difficulty.

6. Graviton. Similar remarks apply here. While of course it does not have a real background-independent formulation, string theory has a graviton.

7. Theory of Everything. TOE is not a theory, as yet, since no-one knows if such a thing exists. Best to say "hoped-for theory" or similar. Is string theory "intended" to be a unified TOE? As far as I know it was invented as a theory of the strong interactions. Does string theory "have the capacity" to describe all matter and interactions? No-one knows, and I don't know of any leading string theorist who makes precisely such "grandiose" claims. Reference please?

There is a common error in stating that the electromagnetic and weak forces "become indistinguishable" at the electroweak breaking scale. Not so, they just get mixed up into two other *distinguishable* gauge groups SU(2)xU(1). The statement "unification can no longer be expected from low-energy phenomenology" is extremely dubious. It depends very much on the details, for example threshold corrections. Unified models exist that still work perfectly well, although they are increasingly tightly constrained. The sentence implies that unification is ruled out by data, which is not true. Unification is not just a matter of philosophy, it is a matter of physics, since it implies constraints and predictions, and the more constraints and predictions, the better the theory (ceteris paribus).

8. Experimental tests. In fact, people such as Kostelecky have done work on spontaneous breaking of Lorentz symmetry in string theory. Hence it is incorrect to say that 'string theory predicts exact Lorentz symmetry at all scales'. To be sure, spontaneous violation of Lorentz symmetry would be an unexpected result, but it would not precipitate a crisis.

9. Sociology and politics. I'm not sure what this section, which consists mainly of opinion and gossip, is doing in an encyclopedia. It seems to have a (completely unwarranted) assumption that LQG and string theory should have "equal rights" and thus any inequality ("imbalance"!) between them is remarkable and worthy of discussion. Since LQG deals with only quantum gravity, whereas strings deal with both gravity and particle physics, I don't see any reason why they should be treated equally. (Besides which, there is the great difference in the number of things that can be calculated in each theory.) The apparent complaint that string theory funding is not fungible into LQG funding is particularly bizarre. If a department has a professor who is expert in string theory, they are hardly going to accept a grad student to study LQG (or vice versa). The remark "it is psychologically difficult for anyone to accept he or she may have dedicated their graduate studies and academic careers on the wrong theory" is tangential and (at present) irrelevant, since we have no idea what is "the wrong theory".

I don't know why the fact that Motl and Baez and Carlip used to argue on s.p.r. (etc.) is important enough to mention here. --Tdent 15:39, 9 Jul 2004 (UTC)

This may be due to many factors: the greater range of physical application of string theory, its close connection with many areas of advanced mathematics which flourished in the 1990's, and the existence of very many different solutions or vacua of string theory (related to the existence of extra dimensions beyond the observed 3 of space and 1 of time, which have to be "hidden" by compactification somewhat as in Kaluza-Klein theory) without a conclusive principle to choose which solution describes our Universe.

Feel free to move it back, but does the fact that one theory has more activity than the other really need explaining rathen than just stating? Miguel 03:11, 10 Jul 2004 (UTC)

OK. I only wrote that because the previous version had a supposed explanation at this point - which only mentioned the vacuum selection problem and nothing else.

String theory not only is connected to flourishing branches of mathematics, but it is responsible for some of that flourishing and actually spawned some of those branches of mathematics. Miguel 03:11, 10 Jul 2004 (UTC)

Sure, but this doesn't explain why strings themselves remained popular - mathematicians have little influence in funding/directing physics.

Another removed bit:

while string theory is typically established at the level of rigour of theoretical physics

which really is gratuitous ST-bashing. I left it in the article that LQG is established at the level of rigour of mathematical physics because LQG practitioners take pride in actually having quantized a constrained, non-linear gauge field theory from scratch using rigorous existence theorems for all the objects involved. A mathematical physicist is really a breed of mathematician, and most theoretical physicists really couldn't care about that level of rigour, which brings them back bad memories of things like axiomatic quantum field theory. In fact, the original spin network papers of Rovelli and Smolin was very physicsy, and were then polished into actual mathematical theorems by the likes of Ashtekar, Baez, Krasnov and Thiemann. Miguel 03:24, 10 Jul 2004 (UTC)

OK. As you said, the article is not for a comparison of string theory with LQG.

--Tdent 18:27, 11 Jul 2004 (UTC)

I assume something is missing here, which the contributors of the article may find self evident: I read, that there is a string community and a loop community. And the Differences between LQG and string/M-theory may come from the fact, that String theory and LQG are the products of different communities. Namely String theory emerged from the particle physics community.

O.K. now the $1M question which isn't addressed: Where and in which community did LQG emerge?

Or can all this community-talk be moved that a sub-article?

Pjacobi 17:21, 11 Jul 2004 (UTC)

I don't think LQG can be ascribed to any one community, unline string theory which has both feet firmly grounded in high-energy physics. LQG comes of the intersection of general relativity, axiomatic quantum field theory, and high-energy physics, and I think for a while people in LQG didn't fit in any community and had a hard time finding jobs while string theory was accepted as mainstream theoretical high-energy physics.

The article shows that LQG is based on Dirac's work on quantization of constrained systems, Einstein-Cartan theory, lattice gauge theory, axiomatic quantum field theory, and topological quantum field theory. All actually very mathematical and farther removed from experiment than the originators of string theory (theorists working on quark confinement in the 1970's). The philosophical influence of MTW's Gravitation and of Wheeler in general is immense.

String theory has its roots in the attempts to understand quark confinement in the 1970's. Lattice gauge theory is a theory with phase transitions and in one of the phases it has string-like excitations. This was one of the motivations for Polyakov's first string lagrangiann models. 't Hooft's work on the large-N limit of SU(N) theories also showed that to leading order in 1/N the theory is described by planar (actuall, spherical) diagrams composed of closed strings. Then people realized that the spectrum of string theory necessarily contained the graviton, and string theory became the leading candidate for a unified theory of all interactions. Finally it was realized that extra dimensions and/or supersymmetry were necessary for mathematical consistency, and made the perturbative theory much better behaved than could be expected in light of past experience with QFT. So, in terms of community, string theory originated from high-energy physics, and Weinberg's book an gravitation is written from this perspective.

Philosophically, the HEP community viewed gravity as just another interaction to be quantized, mediated by the graviton. For example, if you look at Feynman's lectures on gravity you'll see that he takes this approach, and (at the classical level) he shows that starting with a massless spin-2 particle minimally coupled to the traceless symmetric part of stress-energy one has to add correction terms for consistency until one gets the full-blown Einstein-Hilbert action, that the background metric one started with becomes physically unobservable and that the graviton gauge freedom corresponds to general covariance. This is very much like what string theory says: start with a background metric, quantoze a string on it, obtain the graviton, and then let "graviton condensation" change the background metric.

The interesting thing is that lattice gauge theory and Wilson loops techniques are at the core of both strings and loops. But in high-energy physics lattice theories are seen as computational techniques, not fundamental models. This is totally unlike statistical mechanics, and is one of the reasons that the renormalization group looks so different seen from high-energy physics and from condensed-matter physics.

I can't really do sociology, but I can do history a little better, so rather that talk about communities I prefer to look at the history of the development of theories and try to draw conclusions from there.

I would move the community talk elsewhere, but I don't know where. Maybe to quantum gravity?. Also, do we have a page about "the sociology and politics of science"? If we can come up with a cogent analysis of this which does not descend into partisan bickering and name-calling as on USENET the quantum gravity communities could be a case study of scientific communities. But I think a lot of it has to do with people who dislike string theory and want to argue that LQG isn't more popular because of politics and sociology. I think I can see that subtext in the current state of the article, and I don't like it because it gives LQG a bunch of points on the crackpot index.

Miguel 20:07, 11 Jul 2004 (UTC)

The article is rather long (42k) and it contains sections, which don't give core information but are meta to the topic. Also the extensive lists in Research in LQG and related areas detract from the core message. IMHO, and believe I don't want to start editing the page, the lists should go to Research in LQG and LQG and the sociology and politics of science, Differences between LQG and string/M-theory, and Philosophy around LQG should go to LQG in context (not that brilliant a title). Pjacobi 22:09, 24 Jul 2004 (UTC)

I agree. I have recently broken up the absurdly long "implications" section, and most of the subsections need to be rewritten because the emphasis of the sections they are in is different (and for quality). Some of the early sections of the article are in a mature state, and already contain links to "main articles". They might be summarized (maybe one sentence per paragraph) and the current text moved to the main article. I would like to wait until some of the later sections reach a more mature form before moving them elsewhere. Miguel 16:12, 25 Jul 2004 (UTC)

But now you are outsourcing the core the other articles and keeping all the fluff here. If you take this to the extreme, the article will look like some weirdo pseudo-science. Just my 0.02 Euro on this. Pjacobi 16:42, 25 Jul 2004 (UTC)

I agree with you, but I don't have time to do all the rewriting that I think is necessary. The "fluff" can't be moved out either, IMHO most of it needs to be rewritten. I'll revert to the longer paragraphs if you prefer, and leave it to others to reduce the length. Miguel 20:38, 25 Jul 2004 (UTC)

Here's the deal: I have become the de-facto maintainer of the article and I don't particularly like that. It encourages feelings of ownership that are contrary to the wiki spirit. Anyway, I have my hands full just reacting to people's criticism of the article. I had in mind a complete rewrite and I started from the beginning. The sections up to Loop Quantization are the result of that effort. Admittedly, that is just about 1/3 of the article so far, but at least that means the first 14k of the article are ok. I don't think it's right to move stuff around until it has been massaged into its final form. I also agree a lot of the content does not belong here, but I haven't decided where it should be, or how I'd like to see it rephrased. But, if you think stuff should be moved around, be bold in updating pages. Miguel 20:46, 25 Jul 2004 (UTC)

I added the POV label because the current version of the article contains too many things that are believed to be incorrect by most theoretical and particle physicists. For example:

• The main successes of loop quantum gravity are: a nonperturbative quantization of 3-space geometry, with quantized area and volume operators; a calculation of the entropy of physical black holes; and a proof by example that it is not necessary to have a theory of everything in order to have a candidate for a quantum theory of gravity. Many of the core results in LQG are established at the level of rigour of mathematical physics.

The quantization of the area operators' eigenvalues is not a result, it is a defining assumption of the theory. The metric tensor degrees of freedom are rewritten using the gauge field. This map is fine locally, but it is not faithful globally exactly because it imposes new periodicites and quantization rules on the degrees of freedom. They are seen as the area quantization rules. This area quantization has nothing to do with quantum gravity - it is a trivial consequence of the particular not-quite-legitimate change of variables.

Also, it is not generally accepted that LQG has been able to calculate the black hole entropy, and a growing amount of recent evidence seems to indicate that it is not the case. Also, it is generally believed that a quantum theory of only gravity cannot be consistent, and loop quantum gravity has not proved the opposite. (Well, no one can prove it because it is not true, but I admit that this sentence is a POV.) The comment about the "level of rigour" sounds very arrogant. It would be more appropriate to say that many LQG proponents like to pretend that they are very rigorous, but they do not care whether their models have anything to do with physics and whether they respect at least the most basic principles of physics.

Similar criticism applies to most of the other sections, and I believe that the reader has the right to learn what theoretical physicists think about this speculative approach to quantum gravity.

20:55, 11 Sep 2004 User:Lumidek

Attribution added Pjacobi 20:59, 11 Sep 2004 (UTC)

"lumidek:, there have been requests to merge your essay "loop gravity" with this article, would you prefer to

1- leave it as it is, do not merge the two articles, but keep them seperate 2- merge them, with your criticisms at the end, possibly after "recent research directions" as one long continuous section 3- intersperse and interdigitate the two artciles?

for (2) or (3) would you prefer to do this, or would you want a volunteer to do this?

05:33, 20 Sep 2004 64.63.220.226

Attribution added.

Folks, is it that difficult, to put the four tilde signs at the end of your post?

Pjacobi 06:26, 20 Sep 2004 (UTC)