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New entry critics of string theory to collect the references on controversies. I think they are often rambling and vague, not technically useful s the main references we want to collect under string theory and books in string theory. I have changed the sentence in string theory about mathematical definition of parts to somewhat more precise
But every now and then some aspect of string theory, some mathematical gadget or consequence found there is isolated and redefined independently and mathematically rigorously, retaining many features originally predicted.
The point is that most often one does not make rigorous the way some thing is defined via string theory, but one isolates an invariant of manifolds for example and defines a similar one via completely different foundations. The typical example is quantum cohomology which is defined in geometric terms and not in terms of field theory any more.
I have one disagreement with the entry: it says that topological quantum field theory has been discovered as part of string theory research, This is not true, TQFTs were found in 1977, 1978, 1980 articles of Albert Schwartz which had nothing to do with string theory. Only much later Atiyah’s formulation is influenced by string theory.
I have one disagreement with the entry: it says that topological quantum field theory has been discovered as part of string theory research, This is not true, TQFTs were found in 1977, 1978, 1980 articles of Albert Schwartz which had nothing to do with string theory. Only much later Atiyah formulation is influenced by string theory.
Hm, okay. I always thought that Witten’s “Jones polynomial”-article is the origin of the concept. Please add pointers to these historical references, then!
By the way, don’t you mean to have criticism instead of critics in the title?
Just wondering do we have a page “critics/criticism of category theory” or are you planning to create one?
Are there sound references about criticism of category theory worth recording ?
I do not mind that you add redirect or to change to a main title “criticism”, this variant just did not occur to me. I have chosen critics as more a list of main sources of critique (authors, articles) then as a page which would detail a particular reasoning in that vain. We better argue in nForum and then keep the link to those as to the other such discussions. Of course, for particular controversies of technical nature like phenomenology of string theory etc. we can envision separate pages with real content. I hope you agree.
Are there sound references about criticism of category theory worth recording ?
I’ll refrain from making an evident substitution in this sentence.
I think we should write a critique ourselves. While I see lots of people being critical, it always strikes me that an informed criticism is really missing.
I think we should write a critique ourselves.
Maybe. But there’s something a little bit strange about such a thing. As an analogy: would anyone feel moved to write a “criticism of partial differential equations”?
It seems to me that such criticism would mostly be sociological in nature; for example, one could maybe point to an overemphasis on categorical methods, or to the hubris of certain practitioners, their ignorance, their militance, or whatever. What would be some reasonable criticisms of the field considered simply as a body of results?
I think we should write a critique ourselves.
Maybe. But there’s something a little bit strange about such a thing. As an analogy: would anyone feel moved to write a “criticism of partial differential equations”? […] What would be some reasonable criticisms of the field considered simply as a body of results?
I think this is going directly to the heart of the matter: the “theory of partial differential equations” is a piece of mathematics. In mathematics you set up (in principle) whatever axioms you feel like and study their consequences. As long as you don’t make a logical error you get a body of results that is beyond criticism. The worst one will be able to say about it is that it is not interesting.
But for a theory in physics it’s a bit different. The criticism that I think Zoran is having in mind (judging from the keywords that he listed) is about string theory as a theory of physics. Many people have been criticising string theory as a theory of physics. A better analogy to have in mind is: the critique of Kelvin/Thomson’s vortex theory of atoms.
That was a physical theory that was studied as a piece of math, too. In fact, as recalled behind the above link, the development of knot theory was influenced by this “vortex theory”. Over a long period some physicist’s could hold the view that vortex theory is a viable model of the fundamental physics of atoms. Today we have to say: this physics theory is worthy of criticisms: because it does not match phenomenological reality (to be distinguished from “mathematical reality”). One also says: it is wrong. :-)Even if all the mathematical conclusions from its assumptions were right.
Much of string theory could well be like vortex theory in this respect, as far as we know. And people have been criticizing this at length. They fill books with suchj criticism.
Wasn’t Todd in #7 alluding to Urs’ proprosal of a critique of category theory in #6? His comparison with a criticism of partial differential equations suggests that no such thing is necessary, and Urs appears to support this in #8 by distinguishing the potential wrongness of a piece of physics with the mere potential failure to be interesting of a piece of mathematics. I’m confused then by #6.
There seems to me a perfectly legitimate and worthwhile activity of raising questions about ’the way mathematics is going’, which could include making arguments that certain programs are not as valuable as their exponents suggest. The Cafe has shown on a number of occasions however that, even within the fairly narrow umbrella of its clientele, offence is readily taken whenever such issues are raised. Even when it concerns the fairly objective question of whether someone’s research can be seen as a part of someone else’s larger program, we have seen discord.
I have rather low hopes then that much would be gained by our listing some criticisms of category theory. To be useful we’d need the advocates of those criticisms to participate, and a large smattering of that rarest of intellectual virtues - the pleasure in being shown to have incomplete or false opinions.
More generally, however, one should fear what can come into the vacuum left by an absence of discussion of the internal and external values of a discipline. Just look at this post by Tim Gowers if you dare.
@David thanks for the link to Tim Gowers blog. As you know Ronnie and I were passionate about the need for “discussion of the internal and external values of’ mathematics and tried to instill something of that in or students. (We were closed down… was there a link between those facts! … just joking!) The events in the EPSRC are very worrying. (and people in other countries should fight to try to make sure that similar things do not happen chez eux!)
David, I agree with you that questioning is needed and that true discussion is worthier than merely listing key bibliography (but you know criticism usually stems from the same points of view and has the same answers, and the cycle repšeats, so if we have wide and key literature this equips us with some care preventing from too much of repetition). But discussion if from our circle, should be at n-cafe and nForum and the proceedings there will be collected by linking from $n$Lab. Hardly enough consensus and stable digest can appear at this point in $n$Lab, so let $n$Lab for now have a mere bibliography, and let discussion goes to blogs and then we can see if at some point we havce a maturity to add a digest to $n$Lab too. What do you think ?
Is there much written criticism of category theory to be listed from within mathematics? I know people in the US have felt funders have not looked kindly upon them. But, if so, have these sentiments been expressed in print?
I can add some papers by philosophers whose accusations largely amount to the charge that category theory fails to act as a ’foundation’ in some sense they have of the term.
But, if so, have these sentiments been expressed in print?
I have seen some paper on the arxiv dedicated to this issue, but it did not look very intelligent and does not deserve my time to look after it again and leave a reference. But my response above was about criticism of string theory.
As far as criticism of category theory, however, it could make sense to absorb the discussion of criticism into a discussion of the social and other position of category theory in scientific community. For example, related to the fact that major category theory journals are not listed in databases like Thomson Reuters SCI, SCIE or Current Contents lists, and MathSciNet does not count citations in some of them either.Various discussions like the page about “General nonsense” semantics and history of category theory should be listed in such discussions as well, IMHO.
Is there much written criticism of category theory to be listed from within mathematics? I know people in the US have felt funders have not looked kindly upon them. But, if so, have these sentiments been expressed in print?
There was a famous incident in 1993, at the opening of a joint conference on Universal Algebra and Category Theory which, if I have understood it correctly, was held at Berkeley and was much commented on by category theorists who were there. I know of this only second-hand; Vaughan Pratt has made references to it in various places around the internet.
Apparently Bill Thurston, who was at the time director of MSRI, opened the ceremony with an address that had some derogatory comments about category theory. As best I can make out, the gist was the needless abstraction of category theory. I heard from one participant, I believe Alex Heller, that Thurston asked (in a rhetorical vein) whether there were any significant categories that were not concrete (sets with structure). In tellings with slight variations, Vaughan Pratt reported that the idea of an opposite of a category made Thurston feel dizzy (words to that effect). I even heard that Thurston made specific remarks to the effect that some agency, perhaps MSRI, would not be providing any funding for category theory – I think this was from Alex Heller again, who told me that up until then he had never considered himself a category theorist, but from then on would, out of a spirit of solidarity. (Of course he’s no longer around to ask. My conversation with AH took place in 1997.)
I am sure it wouldn’t be hard to find someone who was actually there – well, we know Pratt was there. Anyway, at least one luminary of mathematics has made very public (and to the category theorists present, fairly upsetting) criticisms regarding category theory.
Incidentally, Thurston was also very much opposing the call for need of work on rigorousness and foundational questions in the area connected to mathematical physics, as witnessed by his witty, very interesting and insightful, but quite exclusive discussion after Jaffe/Quinn article on theoretical and experimental mathematics in Bulletin which is mentioned at critics of string theory.
His main arguments as far as I recall from that reading in my student days, were that two experts when they talk about some subject can skip lots of things because they know quite well how to fill the blanks and that in the communication the essence is remarkably well communicated and mutually understood by experts from the main hints. I was furious as a student at the second part of the argument: I had no single math book (apart from school books and one book on “mathematics and game”) until age 17, being raised at a village; this was the time when I wasmost hungry at information and could not get it; I had to take bike to the neighboring town to do some reading on quantum mechanics from a library, as the scientific section of that library could not be read. Then I came to university and then to US and to a place which had no tradition in mathematical physics which I wanted to study. It had good math and good physics but not mathematical physics. There were no good textbooks of CFT at the time which I wanted to study (di Francesco’s book did not yet appear, when it did I absorbed first half of the book in 4 days of frenetic reading). On the other hand reading papers in this part of theoretical physics assumed lots of conventions, folklore facts, silent assumptions, jargon. And then Thurston comes and says all that is OK. OK for him and people at Princeton and Moscow maybe, but for mere mathematicians raised in a province that is hi brow elitism of privileged casta of pundits and insiders who laugh at the need to write complete, technically inductive articles. It is not true that everybody understands the hints, not everybody is from his seminar. This is my recollection from the student perspective. Thanks god, Di Francesco’s book got out few weeks before by Preliminary Examination so I could fill the gaps which frustrated me for few years while people like Thurston laughed at my need of filling the gaps. I felt strongly as a graduate student that outsiders are mocked by this attitude and not helped to bridge the gap. The references will be developed below (I made one but Vanilla has eaten it up, when I pressed edit of another entry in the thread, in NLab I could use back button but here it is gone).
Thurston article pdf
Arthur Jaffe, Frank Quinn, “Theoretical mathematics”: Toward a cultural synthesis of mathematics and theoretical physics , Bull. Amer. Math. Soc. (N.S.) 29 (1993), no. 1, 1–13; MR94h:00007,math.HO/9307227, doi
Michael Atiyah, Armand Borel, G. J. Chaitin, Daniel Friedan, James Glimm, Jeremy J. Gray, Morris W. Hirsch, Saunder MacLane, Benoit B. Mandelbrot, David Ruelle, Albert Schwarz, Karen Uhlenbeck, René Thom, Edward Witten, Christopher Zeeman, Responses to “Theoretical Mathematics: Toward a cultural synthesis of mathematics and theoretical physics”, by A. Jaffe and F. Quinn, Bull. Am. Math. Soc. 30:178-207, 1994, math.HO/9404229
Michael Atiyah, Reflections on geometry and physics, Surveys in differential geometry, Vol. II (Cambridge, MA, 1993), 1–6, Int. Press, Cambridge, MA, 1995.
William P. Thurston, On proof and progress in mathematics, Bull. Amer. Math. Soc. (N.S.) 30 (1994), no. 2, 161–177, MR94m:00006, doi, arxiv/math.HO
David Corfield at el. Wittgenstein and Thurston on understanding, nCafe
Somewhat later and with different scope, but related to this series, is also a long article
Vanilla has eaten it up,
May I also recommend to you the Lazarus add-on for this.
Wow, this is amazing. I will try as soon as I find time for testings.
i have added to the References-section at string theory a pointer to Matthias Blau’s Zürich-talk slides on string theory. This strikes me as a good and sober account of insights and open problems.
With reference to Toby’s comment 17, let me say that I had occasion to try Lazarus last night, and it worked great! What a godsend. Thanks so much for this advice, Toby.
You’re welcome! (I have found that it slows down slow computers, however.)
Special issue of Foundations of physics on superstring theory Forty Years of String Theory - Reflecting on the Foundations. The articles are free only this month.
A Critical Look at Strings (Carlo Rovelli) (pdf, 414 kB)
A Perspective on the Landscape Problem (Lee Smolin) (pdf, 684 kB)
On the Foundations of Superstring Theory (Gerard 't Hooft) (pdf, 285 kB)
Mirror Symmetry and Other Miracles in Superstring Theory (Dean Rickles) (pdf, 775 kB)
Theory Assessment and Final Theory Claim in String Theory (Richard Dawid) (pdf, 537 kB)
What We Don’t Know About Time (Vijay Balasubramanian) (pdf, 540 kB)
Is String Theory a Theory of Quantum Gravity? (Steven B. Giddings) (pdf, 802 kB)
The Gauge-String Duality and Heavy Ion Collisions (Steven S. Gubser) (pdf, 522 kB)
Evolving Notions of Geometry in String Theory (Emil J. Martinec) (pdf, 585 kB)
String Theory (Leonard Susskind) (pdf, 275 kB)
String and M-Theory: Answering the Critics (M.J. Duff) (pdf, 526 kB)
Thanks, Zoran!
Weird.
Weird.
Do you mean the whole idea of commissioning such articles by such authors is weird?
What I mean is that many of the contributions to that collection are weird. That it is hence a bit weird that this collection was bundled this way. I also find this thread here and the fact that/how this book is discussed/not discussed in this thread a bit weird.
What I mean is that many of the contributions to that collection are weird.
I agree. I posted the link in part to get your critic here (I find you too silent still); I see on the net that people take this book quite benevolently. Foundations of physics is a journal which has a tradition of doing things on the edge and risking sometimes presenting ideas without full foundations (maybe the journal should be called unfoundations :)). Since ’t Hooft took the editorship the articles got much more serious and the threshold of rigor rose more than significantly, but still the journal is largely open to speculative contributions.
I also find this thread here and the fact that/how this book is discussed/not discussed in this thread a bit weird.
Discussed ? What do you mean ?
I find you too silent still
Unfortunately I am once again a bit time pressured with preparing my seminar talk for tomorrow. Shouldn’t be replying here at all, if I knew what was good for me…
Since ’t Hooft took the editorship
His contrinution I’d also count as weird. Not in itself, but as a contribution to a volume “40 Years of String theory” it seems weird to include a speculation that is a few months old and so far supported mainly by the author himself (ingenious as it may turn out to be, maybe in the next 40 years).
The last contribution shows where things end when one drops scientific discourse alltogether and prolongs web fights into supposedly scientific volumes. The 5th has a similar feel to it, certainly not the style that one expects in a scientific book. The fourth also starts out this way, though then it gets a bit better. The first two were probably incorporated in order to show the will to counteract that tendency, but somehow to me it only seems to make things more like the usual blog comment chaos.
There is such a universe of things that have happened inside string theory in the last 40 years. If you only knew this book, you’d have no idea. Of course some of the contributions are reasonably nice, for instance Martinec’s. And I don’t know what the editors asked the authors to contribute. I am getting away with the feeling that the explicitly asked them in a way that led in the wrong direction.
Discussed ? What do you mean ?
I mean that if you open a thread “critics of string theory” and then post content to it, such as pointers to this book now, I am expecting some kind of discussion to go with it, some reflection.
In some post above I already tried to show you the analogy: it’s a bit like posting a thread “critics of category theory”. Not hard to find these either, you just need to throw out a random question to MO to catch some. But pure existence of these critics and their criticism does not seem to me to be worth recording much. If one started to do so, one should do so in the context of some discussion, such as to give readers some idea.
But never mind me much, I’ll go back to my seminar notes now. I maybe find many things
weird that others don’t (for instance voting behaviour on MO ;-). So, never mind me.
I mean that if you open a thread “critics of string theory” and then post content to it, such as pointers to this book now
Urs, this thread is not in Math, Physics and Philosophy category but in the Latest changes category. I have created a stub critics of string theory where one can put the critics links, in order to be able to reflect, crosslink and answer, as an $n$Lab’s support for future discussions. So my intention was purely constructive rather than conclusive. We still do not have phenomenology of string theory which should go along with it.
For Russian readers, stringworld.ru has among other resources, the list of main criticizers of string theory along with funny judgement on what the level of the critics is, they call that list “string clinic” – nonadequate web resources on string theory – with a point of view that most of the well known figures there, according to the site analysis, have some level of lack of expertise or somewhat irrational point of view.
I have created a stub critics of string theory
I know, that’s what I am talking about.
For Russian readers, stringworld.ru has among other resources, the list of main criticizers of string theory along with funny judgement on what the level of the critics is,
I don’t understand why you are trying to draw us into these swamps. Let’s discuss techncial aspects of string theory and write $n$Lab entries about it. Let’s have critical discussion of whatever needs to be critically discussed. But let’s keep the $n$Lab a place of scientific discourse and keep it free of those camp wars that lead nowhere and only corrupt good scientific practice.
Let me put it more constructively:
which “criticism of string theory” would you wish to discuss? Let’s discuss it and write a good $n$Lab page about it!
Urs, the entry says clearly “under construction”, nobody was drawing you there, I just posted a notice under latest changes. That means that things are NOT ready for any discussion, as it is early, very early (and the tempo of my learning is nowdays about order to two of magnitude slowlier than yours, unfortunately, most of my time per day I have no luxury of doing science, and when I do I am also far slowlier) in the process. For you, who is an expert in string theory, stringworld.ru might look as a swamp (though the site is inhabited by the people who think the same as you, and are very allergic to mainstream critics of string theory). I however find very clear arguments there why Woit is not relevant for discussion etc. Stringwolrd.ru has some technical resources, explanation of string theory which are very useful (just in Russian, plus many books and paper links in English, cf. this link). Those links to string theory books and papers and so on, are on the level which is much closer to what I can absorb. We face critics from Woit-kind-of camp at our workplaces every day. You can easily defend from such, but I can not. I need arguments. I need to look at why their arguments are wrong. Some of my collaborators wanted to push some loop quantum gravity into our focus as it was related to some mathematical structures which we discovered. Thanks to my posting some links here and your critics of those, I restrained from that and even my collaborators did. This was very useful to me.
Let’s discuss it and write a good nLab page about it!
I did propose to have a page phenomenology of string theory but I have no expertise to write it up.
From the point of view of the title: ’critics’ suggests a list of the people involved in the criticism; ’criticism’ sounds to be more the negative views of the subject, whilst ’critiques of string theory’ would involve also treatments that looked at both good and less good points of the subject. Perhaps the latter is the fairest title (and the easiest to write) as it allows for articles that are critical of some aspects of the subject without being totally negative. I do not know which is intended so do not put any one title forward above the others.
Even though I’m an outsider, I would be generally interested in having within the nLab a précis of Woit’s criticisms, and counter-criticisms that he is “not even wrong”. The only general thing I’ve retained from his book is sociological criticism, i.e., how string theory is a prevailing orthodoxy and how this is unhealthy in a situation where experimental evidence for string theory is hard or impossible to get, etc. Dyson says much the same thing, IIRC.
@Zoran: with “this swamp” I am not referring to that webpage you pointed to, but to the bickering discussion that revolves around people more than arguments. I don’t want to talk about critics of string theory anymore than I want to talk about critics of global warming. I want to talk about the arguments that are brought forward and the replies to them.
@Todd: in the same spirit, I feel hesitant to talk about “Woit’s criticism”. Hard to tell.
Let’s look at concrete content, instead. Semi-technical questions about the nature of string theory.
Given what you all say above, my impression is that what you really want is an FAQ!?!
Which questions (on the theory, not on people) would you like to see discussed in an FAQ on string theory?
Let me try to guess some of the questions that might be bothering you.
(I need to split the following over several comments, as the comment length restriction kicks in).
first sketches for a String theory FAQ
What is string theory?
(short answer: perturbative string theory is well-defined idea which is a natural variation of perturbative QFT, (namely…), and mostly this is the default meaning of string theory. A non-perturbative formulation however remains mysterious, even though there are various educated guesses. Sometimes the unknown non-perturbative formulation is referred to as a “theory” and lots of confusion arises.)
Does string theory make predictions? How? What if not? Is string theory testable?
(short answer: most every theory and model in physics has parameters and makes predictions only after sufficiently many parameters have been fixed by measuring them in experiment. For instance Newton’s theory of gravity says that the gravitational force of a point source is proportional to one over the square of the distance. This is the theory, the proportionality factor has to be fixed by experiment. In string theory it’s the same general principle, only that the theory is much richer. There are tons of models in string theory that make very detailed statements about the resulting physics. Moreover, many of these have good general agreement with presently observed data (just see at G2-MSSM for an example), so this is as in traditional model building. The remaining problem is the following, and this is not specific to string theory but faced by any theory that provides a UV-completion of the standard model: the problem is that after parameters have been fixed this way by finding a model that reproduces the standard model reasonably accurately, all the remaining properties of the model which are he predictions of the model tend to be at high energies (“Planck scale”) and hence not within reach of experiment in the foreseeable future. This is a very general aspect of present particle physics: while theoretically it is clear that the standard model must have a UV-completion by something, at presently available experimental energies that standard model works perfectly. While this is a general fact of particle physics and model building, not special to string theory, a sociological aspect of string theory is that in the 1980s many theoreticians started to believe and claim that string theory would be better than ordinary model building in that when fully understood it would admit only very few models, such that even the parameters measured in the standard model would be predicted by the theory+some mode basic parameters. More recently this hope has vanished, and much of what should be an absolute estimate of string theory is more a perception in the gradient of this hope. But one technical specialty of string theory over standard model building certainly exists in either case: what in the standard model are external parameters put into a QFT Lagrangian, in string theory models are all dynamical fields of the theory instead. The simple familiar example to compare this to is the cosmological constant in Einstein gravity: one can either consider it as an external parameter, a constant real number coefficient in front of the volume form summand of the Einstein-Hilbert Lagrangian, or else one can consider Einstein gravity coupled to a scalar field with some potential and consider those solutions to the equations of motion where this field is is almost constant to good approximation. Then the field itself serves as an effective cosmological constant. Hence the theory has one less external parameter, which has instead been replaced by a field. In string theory this happens with all parameters. There is no external choice of parameter, but there remains the choice of studying “solutions to the equations of motion” (which in string theory means: choices of 2d CFTs) which might model observed physics. That’s why in string theory instead of adjusting parameters one searches solutions. Since these are also called “vacua”, one searches vacua. The infamous term “landscape of string theory vacua” refers to attempts to understand the space of possibilities here more globally. But very little is actually known.) In summary: models in string theory make predictions just as any other model in physics does. Moreover, the situation is even slightly better in that in principle the choice of model in string theory is constrained by the theory. While the standard model is just written to paper, when one reproduces approximations to it in string theory one has to check that a host of consistency conditions are satisfied. Nevertheless, despite of this higher predictivity in principle, in practice it has not lead to much insight that would actually affect the standard model in practice.
continued from above…
Did string theory provide any insight that affected recent progress in experimental particle physics, such as the discsovery of the Higgs-boson like particle?
Yes. One curious aspect of string theory is that independently of its role as a source for models in particle physics, it provides connections in the space of all possible quantum field theories: lots of different quantum field theories (many of them highly unrealistic as phenomenology goes, but interesting for theoretical investigations) appear as different limits and special cases inside string theory, and their embedding into a single framework this way explains many unexpected relations between them. One of this has led to recent progress simply in computional tools of perturbation series. LHC physicists claimed that without the insight from string theory, the evaluation software used at the LHC ould not have been precise enough to see the Higgs in the data. Details on this are linked to at string theory results applied elsewhere. This is maybe the example most directly related to experimental physics, but there are varius other relations (“dualiteis”) between QFTs learned from or better understood with string theory. (Seiberg duality for instance, long list will go here…)
What if the answer to the above questions in No, or at least I don’t follow the arguments for why it should be Yes, is string theory then without any merit?
(…)
Urs, of course I’m asking about the arguments/criticisms put forward, not about e.g. Woit as a person. That should have been clear from #35. The FAQ you started looks very good by the way, but it will take me a while to read everything carefully.
I’ll ask Zoran instead: according to stringworld.ru, why is Woit [meaning the criticism coming from Woit] not relevant for discussion?
Hi Todd,
sure, what I mean is that I don’t want to discuss “Woit’s criticism”. I am not sure what his arguments really are and I don’t think that he is a particular source or authority pointing to which is helpful in this discussion.
I would like to ask you: from your reading (as I gather you have) his writings, what are the questions that you come away with thinking are to be raised? Let me know about concrete questions you have about string theory (motivated by reading Woit’s writing or not) and I will try to reply (or maybe somebody else chimes in and tries).
How about something about the way string theory sees gravity in terms of interacting massless spin 2 particles?
We could also have something on brane cosmology.
Or should these FAQ be more the kind of a question asked by someone suspicious of string theory?
Hi David,
sure, could you phrase actual questions? I suppose the first one is
I try to write something in reply a little later. Concerning brane cosmology: this seems to me to be a topic a bit tangential to what people are mainly concerned with here. Of course it won’t hurt to discuss that, too, but maybe I’ll regard that as having lower priority.
Meanwhile I have started to edit a bit at a new entry
Or should these FAQ be more the kind of a question asked by someone suspicious of string theory?
I think the nature of the person who asks the question should be irrelevant. The question itself counts.
You see, perturbative string theory is a well-defined mathematical object. We can discuss this as any mathematical object. It is not a topic in politics or religion, where suspicion and believes are important. I want the discussion to be a technical discussion as in any other entry on the $n$Lab. It is sad that somehow discussion about string theory in the public domain has this tradition of being so unscientific. I don’t want to have the $n$Lab infected by that. There is no need.
Urs, that’s fine what you said about Woit. If Zoran wants to reply, I’d still be interested.
As for questions: any I might raise could well be embarrassing (to me), but I’ll try. One general criticism I’ve heard is that string theory assumes a fixed spacetime background, whereas in general relativity, space-time is inherently dynamical (actually, what that means is something I’d like clarified as well: if not time, what parameter is the dynamical evolution along?). Anyway, how do string theorists see this conflict being resolved?
Related to this: from my readings, loop quantum gravity takes this dynamical aspect of spacetime seriously as part of the underlying theory. Are there compelling physical reasons that string theorists see that loop quantum gravity is not seriously worth pursuing? What are the relations between string theory and loop quantum gravity?
What does it mean to say that string theory depends on ’miracles’, such as anomaly cancellation, avoidance of divergences, etc.? Can’t we understand how they work?
Okay, that’s a great question! Here is a first go at an answer:
string theory FAQ - How/why does string theory depend on background fields?
As you see there, the key point is that perturbative string theory is perturbation theory and hence by design gives perturbations about a chosen point, just as a Taylor series does.
Concerning LQG: this approach is advertized as providing a non-perturbative quantizaiton of gravity. However, the construction it involves is unlike any construction that in physics goes by the word “quantization”.
The problem is that applying any standard prescription for non-perturbative quantization (e.g. geometric quantization or strict deformation quantization) to the Einstein-Hilbert action fails as there arise singularities in the expressions.
In approaxches such as string theory one regards the Einstein-Hilbert action as just an effective field theory which is not supposed to have a non-perturbative quantization. In LQG instead they simply change the rules for quantization drastically such as to define the problem away.
@David:
Good question. I’ll write a section on the “miracles” later.
In brief, the point is that in constructing a quantum field theory or similar, there are various steps that have what in math terminology are simply: obstructions. The term “anomaly” is just another term for “obstruciton”, essentially. For the process to work all these obstruction have to vanish.
If these obstructions do vanish but for non-trivial reasons, people tend to speak of “miracles”. You know how people are. They shouldn’t, but that’s what it feels like.
More later.
Urs, thanks for #46. It’s always very nice to hear from someone who really knows what he’s talking about and says things straight, instead of some Reader’s Digest version.
When I first clicked on the link, I was sent to the page in edit mode, and now it thinks I’m editing the page when I’m not. Maybe this will go away after half an hour.
Ah, I have fixed the link now
(I had posted the above while changing trains and had a bit of trouble with my WiFi-connection being carried away by the leaving train, the station’s connection not working and my cell-phone connection being shaky. It was a bit of trouble and it seems my latest edits didn’t even survive it…)
But, Todd, let me ask you: given what you said above I doubt that your biggest worry is the dependence on backgrounds. What’s your urgent question? Or else: if you look around in internet discussions, which questions strike you as particularly acute and to which ones would you like to see decent answers?
It seems to me very easy to think up questions,
“Does string theory tell us anything about the Big bang or Inflation?”
“What does supersymmetry add to string theory?”
“How can string theories have duals which appear to describe the universe in very different ways?”,
but maybe we should focus on the particularly acute ones.
I am sorry, I am in a rush today and can not answer some questions from Todd. Just to mention, yes, I meant mainly I guess criticism, I was a bit ignorant of English subtleties here. I agree with Urs that I did not mean to focus on people, but rather on arguments and schools of thought; this means that a minor critic may be more pertinent than a famous nut.
Does string theory tell us anything about the Big bang or Inflation?
No. Looking back at the answer to What is string theory? we have that the only thing really understood is perturbative string theory and quantum perturbation theory is clearly insufficient to discuss strongly coupled phenomena such as cosmological phenomena (as opposed to those tiny excitations studied in particle accelerators).
Maybe more precisely: given that perturbative string theory does describe classical gravitational backgrounds with small quantum flutuations about them, and given that this is all that traditonal cosmology considers, certainly all of traditional cosmology can sensibly be modeled in string theory. But perturbative string theory cannot say much about the long-expected strong quantum corrections to gravitational effects.
This hasn’t stopped people from making lots of speculations, and there is something like a “field” called “string cosmology” in that you find authors writing about this, giving talks and lectures about it. This is a bit like a soccer match with a pingong ball.
What would be needed here is an understanding of non-perturbative string theory.
On the other hand, in theories of supergravity such as string theory, there are some observables that are independent of the coupling constant (called “protected”), the BPS states. If one can compute such observables in perturbation theory and then has an idea of what these correspond to as the coupling constant is set to a finite value, then one can know the value of the corresponding obserbable in the non-perturbative theory without even known that non-perturbative theory. This is the mechanism by which perturbative string theory does make statements about black hole entropy, where black holes by their very nature are strongly coupled gravitational configurations. More on how this works is at black holes in string theory.
Since the singularity involved in back holes is a similar kind of singularity as that involved in the big bang one might think that some analogous method is useful in the latter case. But if so, it has not surfaced so far.
I was a bit ignorant of English subtleties here.
Ah!
Would you mind then renaming this thread here and the nLab entry into criticism of string theory ? That would make me happy!
But, Todd, let me ask you: given what you said above I doubt that your biggest worry is the dependence on backgrounds. What’s your urgent question?
Given what I said where? Back in #35 I said something about “Woit’s criticisms”, which was picking up from Zoran’s #33. But really, I don’t care if it’s Woit or some other “critic” – I simply mean I wouldn’t mind having a précis of general criticisms and responses to them. One of the main theoretical criticisms – about the only one I remember, to be honest – has to do with a fixed non-dynamical spacetime. (There are other criticisms of a sociological nature that I am happy to elide over, insofar as they might not fit well in the nLab. Similarly for the charge that string theory is experimentally largely untested and for the moment largely untestable.) I figured this might be a respectable sort of theoretical criticism, since I believe the point was also raised by Baez and Dolan in HDA0 (back in the day when John was thinking more about LQG).
Otherwise, I don’t really have an urgent question, and not sure how I gave you that impression. I was really just inquiring as a layman who would like generally to be better educated (and having an advantage of a good mathematical background, and slightly greater than lay understanding of physics). Picture me as calmly inquiring with good will written all over my face, but with no particular sense of urgency.
I agree with Urs that I did not mean to focus on people, but rather on arguments and schools of thought; this means that a minor critic may be more pertinent than a famous nut.
I am 90% sure I know what famous “nut” is being alluded to here, but I really wish not to name names (particularly if said nut occasionally reads the nLab or nForum, which I can’t rule out). With that in mind, I would still enjoy hearing from Zoran, whenever he feels like he has some time and inclination, but it might be wise to talk offline. The email I’m mostly using these days is topological tod musings ta gee mail tod com.
Hi Todd,
okay. The reason why I am trying to make you give me questions is that I can’t say what “Woit’s criticism” is. If I could, I would reply to it. But since you say you are interested in Woit’s criticism, I thought you could tell me what you extracted from it.
I had started to write a bit about
in the entry. Here is a bit more.
In both QFT as well as ST one “builds models” within the general theory and tests these, as far as their predictions are about available experiments. Loads of string theoretic models and non string-theoretic models have been excluded by LHC data in the last months, when the experiment ruled out more and more of the possible parameter space for one global spacetime supersmmetry somewhere at the EW scale. So all this was testable, has been tested and turned out to be wrong.
So model building in string theory is much as in QFT. When a model is ruled out, it does not necessarily mean that string theory is ruled out or that QFT is ruled out, but it means that the possibilities for adjusting the free parameters in the theory are being reduced.
To see that this is a common scientific process, it may help to look at some important historical examples. For instance shortly after Einstein proposed the theory of gravity now named after him, he proposed a cosmological model within that theory. Since he thought back then that the observable universe was static, he chose a free parameter of his theory, the cosmological constant, to take just such a value that the resulting equations of motion fitted his expectations. But just shortly afterwards it became clear that this is wrong, that instead the observable universe is expanding. Was Einstein’s theory wrong? No, his model within the theory was wrong. (He famously called it his “biggest blunder”, but it’s common for models to be ruled out. It’s fundametally a trial and error process, after all. ) The model was discarded and quickly a new model was “built”, the now standard FRW model, still within Einstein’s theory. That has nicely fitted all data since, with slight adjustments, and so we are fond of it.
This kind of model-building process happens within string theory, too. And the models are being tested, discarded or adjusted, tested again, etc.
Ironically, string theory model buidling is actually more constrained than plain QFT model building, due to the fact that at the heart of it there is no free parameter, since all parameters are instead fields of the theory, as mentioned before.. So ultimately it gives more, not less reasons to discard a model already on theoretical grounds. There are QFT models which cannot be realized in string theory, because the constraints on the parameters are stronger in string theory, because string theory is not just any old effective field theory that can be further adjusted as the energy scale is increased, but is already a UV-completion. It either makes sense at all energies, or not at all. (A practical problem here is that in computations usually lots of approximations are introduced which are not always guaraneteed to be viable. For instance nobody really has a good theoretical handle if all the points in the alleged landscape of string theory vacua really are solutions to the theory. They have all been checked to be so only in some approximation.)
An example of how string theory is more constrained in its model building than effective QFT keeps the community busy since 1998: then it was observed experimentally that the cosmological constant of the observable universe these days is small but positive. But accomodating a positive cosmological constant into string theoretic models is harder than negative cosmological constant. So this observation tested a large region of string model building and found it to be wrong. But as for the example of Einstein’s “biggest blunder” above, even with all these models ruled out, the theory is still not ruled out (maybe one day with more obserbations it will!) Instead, as in the historical example, the failure of the favorite models lead to new theoretical activity in understanding the theory and its remaining possible models. All this talk about “metastable vacua”, etc since in string theory originates in this experimental observation in 1998.
On the other hand, no other theoretical framework was equally tested by this observation. In all other existing theoretical frameworks you simply take a pen and change the sign of the cosmological constant by hand. The theory does not control it, it’s a free parameter. So I would say it is clear that string theory is actually more testable than other existing theoretical frameworks. Of course to appreciate what this means one has to pay attention to what it means to test a theory by testing all its parameter space of models, as illustarted by the Einstein “biggest blunder”-example.
Urs, I have both Woit’s and Smolin’s popular books contra string theory, and I could try to extract more arguments from them. Possibly something useful could come out of such an effort (particularly to see how a professional string theorist handles their charges). Dyson is another critic apparently (maybe due to some innate contrarian streak), and maybe I could see what he says as well.
All this energy you’re putting into this is much appreciated!
Todd, of course I know of the existence of these books and I know what you are referring to. Mainly they are saying that they find the behaviour of the high energy physics community weird and irrational and counterproductive. It’s indeed hard not to get that impression. Other people find the opinions of these authors weird and irrational and counterproductive. And there is good evidence for that, too. So an endless fight ensues, which, as we have seen above, is now fought even inside invited contributions to scientific volumes, which is a shame.
But if we concentrate on science and theories, forgetting all those weird people that we are and that are around us and that make noise around us. Imagine we are the only people on this planet, undisturbed by questions of funding, of prestige, of any worldly issues, just interested in studying platonic ideas and theories of physics. One of them is string theory. What do we think of it?
I think that once we get to this point, we see that string theory is quite a gem in the world of ideas. It’s not worse than many other ideas that enjoy high esteem. Indeed, I think it is much nicer.
Of course it may be wrong. Okay, so then it’s wrong. It may also be right.
But what would be really sad if the noise made around us makes us come to believe that this nifty item in the world of platonic ideas and theories is instead a silliness which is “not even wrong”. This would mean we’d given up logical thinking for the sake of effect.
Urs, I think we’re probably all on the same page here. I should repeat that I don’t give a damn about Woit or Smolin or whoever the criticisms come from. In other words, we are agreed not to worry about persons or personal weirdness. Let’s just make a list of the criticisms that are out there, see how forceful they are, and see how forcefully they can be handled or refuted. That’s all.
Would you mind then renaming this thread here and the nLab entry into criticism of string theory ? That would make me happy!
Of course I would not mind.
Okay, I have changed the entry title now to criticism of string theory.
(I cannot change the title of this nForum thread here, I think only you can do that, since you started it. But maybe it is good to not change it, as otherwise all the discussion at the beginning of this thread will look weird to newcomers, as the context has changed).
I have also edited the entry criticism of string theory a bit:
Gave it a lead-in paragraph to say what this is about.
Started to add brief comments on the references you listed there, such as to give the reader an orientation as to what it is we are pointing him/her to.
I removed the pointer to my post on supersymmetry. I don’t see what it has to do in this entry. But I’ll add a paragraph with much the content of that remark to string theory FAQ later.
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