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It's a truism that in science it is at least as important to state the reasons why a theory or idea might be wrong, as to state the reasons why it is might be correct. For example, early renormalization methods made experimental predictions that were very accurate, but the inventor's famously worried for decades about the conceptual problems of divergences; and many of their papers/articles/books on the subject include a long discussion about how acutely worried they were that their method for handling divergences was deeply flawed somehow.

My intention with this post is not to engage any user in a debate about whether string theory is true or not. I think anyone who takes string theory seriously should be happy to acknowledge as clearly as possible all the potential theoretical issues/problems with the theory.

Therefore I would like to ask, what are the major theoretical problems which would lead a reasonable person to be worried that string theory is not an accurate theory? I am excluding the fact that string theory has made no (major) predictions that have been confirmed, I am only interested in conceptual and theoretical ideas which might discredit the theory.

Please keep all answers to one issue per post.

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Have you looked at Peter Woit's "Not even wrong" blog? –  Sean Tilson Dec 13 '10 at 5:50
    
@Sean: I haven't read Woit's blog in awhile, but I used to read it everyday. @kall43: It's hard for me to answer your question, I am trying to be a broad and general as possible in my formulation; so basically if there is anything at all that bothers you about string theory, but not that it has never made a prediction that was confirmed, then it's acceptable for an answer in my opinion. –  Matt Dec 14 '10 at 4:25
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I think you may be missing a bunch of interesting answers because of the phrasing of your question. Based on your analogy, you may be interested in the ways string theory is incomplete, and the various ideas people have on how to remedy that. None of this necessarily leads you to suspect there is something wrong (as in the QFT analogy), just that something is still missing. –  user566 Jan 25 '11 at 16:03
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7 Answers 7

I don't know any reason to suspect string theory may be incorrect, but the closest analogy to renormalisation infinities is the fact that we only know string theory as a perturbation series from a fixed background, plus a collection of non-perturbative dualities that relate different versions. By rights there should be a better formulation from which all the perturbative string theories can be derived directly. M-theory is a name sometimes used in this connection but we still don't know what it is.

Even if string theory were not a theory of physics there would be good reason from the mathematics to think that such a formulation exists because otherwise all the relationships between the different string theories would be just creepy coincidences. There really has to be some underlying framework that explains them.

I think this is comparable in some ways with the original view of renormalisation which made people question the original perturbative formulations of quantum field theories. Once non-perturbative formulations such as lattice gauge theory emerged they were able to understand renormalisation as a scaling behaviour related to critical points in the theory and things were better understood.

String theory has other problems such as the need to understand how a vacuum can be selected that explains low energy particle physics and the cosmological constant. We also need to understand better what happens to spacetime in string theory at Planckian energies. These problems are often highlighted because they are the reason why string theory cannot yet make any testable predictions, but I don't think they can be resolved properly until the underlying principles of the theory are known. So that is the key issue to resolve first.

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Philip wrote: "Once non-perturbative formulations such as lattice gauge theory emerged they were able to understand renormalisation as a scaling behaviour related to critical points in the theory and things were better understood." What critical points are you talking about? Is the lattice step has physical meaning? I thought it could be made as small as you liked, similarly to arbitrariness of the cutoff L in the before-lattice analytical calculations. –  Vladimir Kalitvianski Jan 25 '11 at 16:51
    
In this case the critical point is in the limit where lattice spacing goes to zero. –  Philip Gibbs Jan 26 '11 at 7:35
    
So there is no better understanding but better illusion of understanding. –  Vladimir Kalitvianski Jan 26 '11 at 9:36
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There are two sides to this coin. String/M theory is more than a theory, it is more in a way a framework of theories. It is a vast territory, at least from a mathematical perspective. A lot of it is not likely correct, or should we say does not manifest itself in anything physical. On the other hand there appears to be universality to some stringy structure, where it is appearing in condensed matter physics. Some stringy or AdS structure is making an appearance in heavy ion physics. So the other side of the coin is that stringy/M structures are too rich for the whole thing to be completely false.

When looking at string physics it is probably best to hold more to basic physical ideas, such as how Susskind approaches things, and to remain close to mathematics which has some foundational aspect to it. Highly rococo mathematics that deviates from “basics,” and theory which is increasingly complex might be held up to greater suspicion. Where the dividing line lies here is a bit hard to define.

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Rococo mathematics! There's a great and lively working of words. :) –  WetSavannaAnimal aka Rod Vance Jul 16 '13 at 11:08
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This question is a little confusing. There are really no reasons to "suspect it may be wrong" (and there are surely many reasons to suspect it may be right!) in the sense you're probably thinking of. It seems you're more likely asking the very different question: "what things would we like string theory to do, but do not know how to do in it."

In that case, of course, the list is very long because we would like to do everything with it!

More concisely, the obvious point is that we'd like to be able to explicitly construct a model in string theory which reduces, at low energy, to the Standard Model plus classical gravity, and we do not know how to do this.

One could potentially wonder, as in the case of the old Kaluza-Klein theories, whether there is an obstruction to getting the correct structure. In Kaluza-Klein, everything looks promising until you (or, Ed Witten) prove that while the theory does permit the correct gauge groups, it does not permit the correct representations (you don't get chiral theories).

However, in this case, we know that we can get both the right groups and representations out. As far as I know, there are no good reasons to suspect that any particular property of the Standard Model is not allowed in string theory. In fact, many models very similar to the Standard Model can be constructed, so in a sense, we can qualitatively get the right kinds of answers.

We also have things like the AdS/CFT correspondence, which allows us to explicitly construct stringy duals of some ordinary field theories, so string theory is at least as right as those field theories are!

So I would say there are no theoretical reasons to expect string theory to be "incorrect" in any reasonable way, and there are only marginally good ones to suspect that it could be unable to give us the Standard Model.

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Wow, I'm so happy that all of a sudden lots of people are answering this old post. Since I seem to have confused you Jeremy, let me just explain that I am a hardcore disbeliever in string theory, and have been for about five years. I don't really want to get into a debate in this thread, because I promised not to in the OP, but basically my intention behind the question was to compile a list of problems with string theory, without offering any of my own ideas/opinions. Actually I think this thread can have a lot of value for the folks who like string theory, as well as those who dont. –  Matt Jan 27 '11 at 7:54
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If I understand what you're looking for correctly:

One issue is that string theory predicts the number of spacetime dimensions to be 10 (or 11 in M-theory), larger than the 4 we observe. Of course, it's possible to explain that away by postulating that 6 (or 7) of the dimensions form a compact manifold with characteristic scale much smaller than we are able to detect, but as far as I know, nobody knows whether that's a realistic configuration. The predictions of the theory would depend on the particular topology of the compact manifold, and it's not clear whether there is any choice of topology that makes the theory correspond to reality.

And even if there is, it'd still be an open question why nature has "chosen" that particular topology, out of all the possibilities.

N.B. I haven't studied this in full detail so perhaps I've gotten some of the details wrong, in which case hopefully someone more knowledgeable will correct me.

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Can I ask an additional question to this: is it true that the conclusion of " exactly 11 dimentions" comes from non-divergence of certain quantity, while this quantity is just a term in perturbation theory? –  Kostya Dec 13 '10 at 6:31
    
@Kostya It's been a while since I've looked at string theory, but if I remember correctly, the restriction on the dimensionality of spacetime comes from a computation of the Poisson Brackets of the classical constaints of the theory. Unless the dimensionality of spacetime is a certain number (that is different for different string theories-10 for superstrings, 11 for M-theory, 26 for bosonic strings), then the Poisson brackets of a subset of the constraints will be equal to something nonzero, meaning that the constraints can't be solved and the theory is inconsistent. But its been a while. –  Jerry Schirmer Dec 13 '10 at 20:41
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Vafa and Brandenberger argued that spacetime will not expand unless wrapped strings are able to combine and annihilate (lest their energy grow with the size of the universe) -- two-dimensional worldsheets will only meet generically in no more than four dimensions. This is a mostly heuristic argument, I guess, but one which tries to address the observed dimensionality of large spacetime dimensions. As for the total number of dimensions, this is a kind of technical point in string theory. The number 10 comes from preserving Lorentz invariance, in one derivation. (M-theory adds the 11th.) –  Eric Zaslow Dec 14 '10 at 3:01
    
11=7+4 appears in traditional compactification, because the antisymmetric tensor $A_{pqr}$ from 11D SUGRA allows for this kind of solutions, Freund-Robin. It only fails to be "realistic" because the 4D part happens to be anti-deSitter. –  arivero Jan 24 '11 at 19:23
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Contrary to D=11 Kaluza Klein theory, where you have a few small groups as SO(8) or SU(3)xSU(2)xS(2), in string theory you can produce very huge gauge groups down from E8xE8 or from SO(32), or even perhaps more complicated structures down from M-theory. This is suspicious but it could be more a a wrong interpretation that an incorrect theory. After all, there are some limiting procedures going to D=11 supergravity -and its multiplets-, which has a more adequate size.

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I think that QFT and the string theory have the following flaw in common: they treat perturbatively coupling the things coupled permanently. This is a conceptual flaw that not always can be "repaired".

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OK, let us consider one electron and the quantized electromagnetic field. They are permanently coupled. When you push the real electron, you excite the photon oscillators. This means the electron is a part of these oscillators and vice versa. This is not implemented as such in QED. In QED we have a free electron and free oscillators as the initial approximation. Then we couple them perturbatively. In the first Born approximation you can push the electron and have no radiation at all (elastic processes). Meanwhile the (soft) radiation is a process with unity probability - it happens always. –  Vladimir Kalitvianski Jan 24 '11 at 16:13
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You obtain IR divergences and have to sum up the soft diagrams to all orders to get a physical (inclusive) cross section. Before summing up the solution is wrong (a truncated series is wrong). It means you started from "too distant", non physical initial approximation if you need the whole sum (=exact solution) to be able to compare with experiments. See here: docs.google.com/… –  Vladimir Kalitvianski Jan 24 '11 at 16:18
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Seeing so many downvotes, I wonder if anybody can give any reasonable objection to my argument? Can anybody treat the electron and proton coupling in Hydrogen atom perturbatively? No? Why do you think you can treat quarks perturbatively? Do you think you know what quarks are? No? Do you know what strings are then? –  Vladimir Kalitvianski Jan 24 '11 at 22:21
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Dear downvoters, tell me where I am wrong, please. I would like to learn. –  Vladimir Kalitvianski Jan 31 '11 at 16:23
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I didn't downvote but a probable downvote reason I see is that not all of string theory is petrubative. - And, the answer is not detailed at all. . –  Dimensio1n0 Jul 16 '13 at 9:46
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beacuse it is not falsaifiable and this is the biggest problem of this theory ,

It is like saying 'God create the universe' you can not prove me neither wrong or right :) however i can give no proofs of my sentence.

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This is incorrect. String theory provides vaaaaarious predictions,; s-matrix, scattering amplitudes, , extra dimensions, caisimir energy, supersymmetric particles, GR, QFT, etc. The above is intended as an explanation for my downvote. –  Dimensio1n0 Jul 16 '13 at 9:49
    
@Dimension10 I think this is a good downvote explanation comment nobody can object too ... ;-) –  Dilaton Jul 16 '13 at 13:49
    
'predictions' are not physics i can predict GOD from miracles or from the Turin's Shroud, we in physics need facts this is not faith :) –  Jose Javier Garcia Jul 16 '13 at 15:17
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@JoseJavierGarcia: Predictions that can be tested. –  Dimensio1n0 Jul 21 '13 at 14:03
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In future please reply to a user by using "@username", as I have done here as an example. Else, they won't be notified. For example, to reply to me, "@Dimension10", etc. –  Dimensio1n0 Jul 21 '13 at 14:03
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