Baez and Schroer

John Baez’s latest This Week’s Finds is out. As in other recent issues, he starts with some of the most fantastic astronomical pictures around. He also links to his recent non-technical talk Fundamental Physics: Where We Stand Today, which also has fantastic pictures. In the talk he describes how, since the 80s, “many physicists feel stuck”, and “continue to make predictions but they are usually wrong or not yet testable. This has led to a feeling of malaise. Why are they failing?” He partially answers this question with

But when their theories made incorrect or untestable predictions, many theorists failed to rethink their position. It is difficult to publicly retract bold claims. Instead, they focus more and more attention on the mathematical elegance of their theories… some becoming mathematicians in disguise. (There are worse fates).

Someone who was at the talk reports that afterwards Carlo Rovelli asked Baez “whether what he had just presented didn’t imply that the theoretical physics of the last 25 years was ‘junk'”, and that Baez “replied after some hesitation ‘You said it'”.

A physicist who has been concerned for quite a while about the sociological changes in how particle theory is done and the ever more critical situation that the field finds itself in is theorist Bert Schroer. His specialty is in the area of algebraic approaches to QFT, especially conformally invariant ones. More than a decade ago he was writing review articles on QFT well-worth reading that included warnings about what has been going on. For some examples, see his Reminiscences about Many Pitfalls and Some Successes of QFT Within the Last Three Decades and Motivations and Physical Aims of Algebraic QFT.

Schroer has just posted three new articles on the arXiv. One of these is entitled String theory and the crisis in particle physics and is well worth reading if you have any interest in the ongoing controversy over string theory. Schroer has many interesting points to make on the subject, and one of his main concerns is that a great deal of knowledge developed about QFT during the last century may be effectively lost as the training of young theorists focuses on string theory. This article has already drawn Lubos Motl’s trademark rant accusing anyone skeptical about string theory of being an incompetent crackpot.

The second of his new articles is called Physicists in times of war and begins with comments on the Iraq war and Schroer’s profound disappointment at the refusal of Witten and others to join him in a public campaign against the war before it began. The second part of the article tells the story of Pascual Jordan, one of the founders of quantum mechanics who joined the Nazi party. Schroer’s politics are diametrically opposite to those of Jordan, but he is highly sympathetic to Jordan’s scientific point of view, from the earliest years of quantum mechanics, that it is necessary to think about quantum systems in a way which doesn’t depend on starting with a classical Lagrangian and “quantizing”.

The last of Schroer’s new articles should appear on hep-th tonight and is entitled Positivity and Integrability. It tells some of the history of the QFT group at the Free University in Berlin and has a lot of interesting things to say about reflection positivity and the Euclidean approach to quantum field theory.

Update: I haven’t heard anything at all back from the arXiv about the trackback issue, but just noticed that trackbacks to the two recent Schroer articles mentioned here have appeared. The ways of the arXiv are highly mysterious….

Update: Baez has a clarification here of his response to Rovelli.

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30 Responses to Baez and Schroer

  1. Robert says:

    Peter forgot to mention that in the first paper Schroer advocates an approach that dumps all geometric parts from our treatment of quantum physics as it is inherently classical. Not quite in line with Peter’s favourite alternative direction.

  2. woit says:


    Schroer definitely favors an algebraic, non-geometric approach to QFT, while I’m starting from a very geometric direction. However, one of the basic lessons of mathematics is that to understand a mathematical structure at the deepest level you often need to simultaneously use algebraic and geometric insights, and understand how they are related. I still think the geometric starting point is most promising, but over the years I’ve become more and more aware of how important it is to also think about these questions from a more abstract, algebraic point of view (have you heard me go on about K-theory and representation theory?).

  3. DMS says:

    Well, Bert is wrong in lumping all American physicists on the Iraq war; see for instance

    Nobel laureates oppose war against Iraq

    29 January 2003

    Forty-one American Nobel laureates have signed a declaration opposing war with Iraq. The declaration was organised by Walter Kohn, a theoretical physicist at the University of California at Santa Barbara, and former adviser to the Defense Advanced Research Projects Agency at the Pentagon. The signatories include 19 winners of the physics prize.

    The declaration reads:

    “The undersigned oppose a preventive war against Iraq without broad international support. Military operations against Iraq may indeed lead to a relatively swift victory in the short term. But war is characterized by surprise, human loss and unintended consequences. Even with a victory, we believe that the medical, economic, environmental, moral, spiritual, political and legal consequences of an American preventive attack on Iraq would undermine, not protect, US security and standing in the world.”

    The signatories include Norman Ramsey, who worked on the Manhattan Project, and Charles Townes, a former research director of the Institute for Defense Analyses at the Pentagon. Townes was also chairman of a federal panel that studied nuclear warheads.

    Kohn expects more laureates to sign this week but the current list of signatures is:


    Philip W Anderson, Hans A Bethe, Nicolaas Bloembergen, Owen Chamberlain, Leon N Cooper, James W Cronin, Val L Fitch, Sheldon L Glashow, Leon M Lederman, Arno A Penzias, Martin L Perl, William D Phillips, Norman F Ramsey, Robert Schrieffer, Jack Steinberger, Joseph H Taylor Jr., Charles H Townes , Daniel C Tsui, Robert W Wilson

  4. A.J. says:

    Two comments:

    1) I was the last person to edit the wikipedia paragraph that Schroer quotes as “string-theoretical adulation in its purest form”, and I completely disagree with his characterization of the writing. The paragraph is hardly the praise he makes it out to be. Frankly, I saw dwelling at length on the variety of things the “M” might stand for as a way of correcting a common misconception on wikipedia, namely that anyone has much of a clue what M-theory actually might be.


  5. A.J. says:

    2) … Schroer’s been banging on now for some time about the conceptual superiority of the algebraic approach to QFT. I think it’s about time that he included in one of his polemicals an explanation of how renormalization theory fits into the AQFT conceptual framework. The techniques of effective field theory are essential to anyone who actually does computations or makes connections to experiment, and it’s difficult, to say the least, to take seriously a proposed framework which seems basically to ignore and/or dismiss these tools.

  6. Peter Shor says:

    What I found astonishing is the idea that young string theorist are not learning a lot of quantum field theory. How can you possibly hope to generalize QFT when you don’t completely understand it?

  7. Igor J. says:

    RE: DMS – Nobel laureates oppose war against Iraq

    As I read the declaration, it does not seem to me as a categoric oposition against the Iraqi war, but rather they point out that this war is not in US interest… Eg. see the excerpts:
    “…oppose a preventive war against Iraq without broad international support. ”
    “…Even with a victory, we believe that …”
    Which I would read as: “If the world is with us and we have a quick and politically correct victory, we have no problem with the war….”.

    I believe that Schroer was looking for some strict refusal of the war (or any war in general), this would be clearly not enough for him…
    [[If you read the article it is clear that he basically does not understand how any physicist could support any war at all etc…]]
    Igor J.

  8. woit says:


    I think Schroer’s point is that quantum field theory remains a poorly understood subject, about which we still have a lot to learn; no one completely understands it. Certain parts of it are well-understood, are in standard textbooks, etc. Most string theorists know those, and also know quite a bit about the more advanced parts of the subject that are relevant to string theory. But there is a lot about quantum field theory that isn’t relevant to string theory, and it is knowledge about those parts of the subject that I think Schroer fears may get lost.

  9. Who says:

    Update: I haven’t heard anything at all back from the arXiv about the trackback issue, but just noticed that trackbacks to the two recent Schroer articles mentioned here have appeared…

    one trackback being to NEW


  10. Chris Oakley says:

    I could be that Schroer’s attitude toward String theory and string theorists was not helped by Lubos’s reviews of two AQFT books on Amazon, here and here, especially as these are the same (negative) review pasted in two places. Having said that I think that Lubie is right to point out that a lot of people seem to have worked on Axiomatic/Constructive/Algebraic QFT for a long time and yet still cannot calculate cross sections or decay rates.

  11. Chris W. says:

    Wouldn’t it be fair to say that at some point the effort to understand quantum field theory becomes inseparable from the effort to formulate a quantum theory of gravity, or at the very least, how quantum field theory should be understood in the presence of gravity? It seems to me that this has always been implicit in the understanding that gravitation is not just another physical field, notwithstanding the many formal connections that can be made between the mathematical structure of general relativity and gauge theories. More precisely, it is—to use Julian Barbour’s term—the frame within which all physical processes happen.

    The study of quantum field theory in curved spacetime seems to reinforce this conclusion. Note that in physics/0603112 Schroer discusses (on page 27) a recent paper of Stefan Hollands and Robert Wald, Quantum Field Theory Is Not Merely Quantum Mechanics Applied to Low Energy Effective Degrees of Freedom.

  12. Arun says:

    Since Schroer skewers Motl at a rather personal level, I think Motl’s ire is understandable.

  13. Who says:

    Since Schroer skewers Motl at a rather personal level, I think Motl’s ire is understandable.


    Spooner-rhymes are hard to forget

    Gehe nicht zu Motl’s Tristan
    schau Dir nicht dieses Trottels Mist an,
    schaff dir lieber ’nen viertel Most an
    und trink dir mit diesem Mittel Trost an

    several people have tried to translate but they did not provide
    a simple literal translation—just to give the meaning of the words. I will try:

    don’t go to Motl’s Tristan
    do not consider this idiot’s manure
    rather get yourself a glass of apple wine
    and drink comfort by this means.

    Trottel = imbecile
    Mist = manure
    Most = hard cider, new wine
    Trost = comfort, consolation
    anschauen = contemplate, consider

  14. Haelfix says:

    AQFT is something people need to work on, but at this point its really of mathematical interest moreso than physical interest. This could and probably will change eventually but I just don’t see many young physicists staking their tenure trying to reproduce cross sections that people have known for 30 years. As such its really the domain of tenured proffessors as its a very difficult problem with absolutely no guarentee of quick results.

    If something really new and exciting came out of the field, people will jump on the bandwagon, but until that time its similar to working on the measurement problem, read probably career suicide

  15. Thomas Larsson says:

    What struck me in Schroer’s article was his comment on AdS/CFT on p 14. Apparently he claims that it cannot be correct because the number of degrees of freedom on the two sides do not match. Does anyone know more about this?

    Of course I strongly disagree with Schroer’s statement (on p 26) that loop groups do not admit higher-dimensional counterparts. Both the Kassel algebra (multi-dimensional affine) and the Larsson-Rao-Moody algebra (multi-dimensional Virasoro) have been around for many years, and their beautiful representation theory is now being converted to physics (hep-th/0504020). There are of course errors and omissions at this stage (the worst errors are being weeded out, however), but progress has been surprisingly rapid. The most important conceptual conclusion is that the observer must be integrated seemlessly with the formalism, something which in a sense was anticipated by Rovelli’s relational QM.

    Schroer’s ignorance about this development shows that I must increase my M-arketing efforts.

  16. Chris Oakley says:


    I’m not arguing with your translation, but in being literal you have foregone the sublime rhyme of “Motl” (as mispronounced by anglo-saxons) and “bottle”.


    You are not quite right there. There are active AQFT groups in Hamburg, Zurich and Basel and probably at other European universities as well. Working on this is not quite professional suicide. Suicidal tendencies are more likely as a result of trying to keep up with their research output, which, like Superstrings, gets more detached from reality year on year. I am not sure that they are really interested in calculating cross sections anyway – if you want proof, have a look at the correspondence I had with a referee (who presumably belonged to the AQFT camp) on my web site from 1986/1987.

  17. ObsessiveMathsFreak says:

    Another humanities style paper in arXiv. How many of these are there?

  18. Sam says:

    Woohoo! AdS/CFT is wrong? The one development in string theory that Peter had to grudgingly admit was worthwhile. Now that Schroer has demolished AdS/CFT, we can truly say that string theory is a failure!

  19. woit says:

    Thomas and Sam,

    Schroer doesn’t say “AdS/CFT is wrong”. My reading is that he is just pointing out the obvious fact that it isn’t a precise relationship between two standard QFTs, but a relationship between a standard QFT (4d N=4 supersymmetric YM), and a 5d theory which is not a standard QFT (although you get a QFT, supergravity, in the low energy limit).

    I don’t think any of the positive things I’ve had to say about AdS/CFT are said grudgingly. But I do think it’s important to remember that what is going on with AdS/CFT is still poorly understood. Lacking a non-perturbative definition of one side of the correspondence, one can’t even precisely say what the conjecture is. There’s something very interesting going on here, and a lot is known, but a lot isn’t.

  20. Aaron Bergman says:

    Schroer is probably referring to Rehren’s work relating an AQFT on AdS space to an AQFT on Minkowski space in one fewer dimension and Arnsdorf and Smolin’s follow-up hep-th/0106073. There were discussions of it on spr at the time. My recollection of the upshot is that the AQFT’s produced by Rehren’s procedure have aren’t physically useful (bizarro thermodynamics, for example.) It’s not particularly clear what this relation has to do with Maldacena’s duality between a QFT in four dimensions and quantum gravity in five dimensions (well, ten dimensions really).

  21. urs says:

    Maybe the applications of AQFT most relevant to interesting applications in physics concern AQFT of 2-dimensional conformal field theory.

    For instance Antony Wassermann’s discussion (math.OA/9806031) of representations of loop groups and the fusion of these reps (hence relevant to WZW models) is based on methods borrowed from AQFT.

    Furthermore, representations of AQFT operator algebras are known to be one source of modular tensor categories from which 3D TFTS and 2D CFTs are constructed (

  22. Benjamin says:

    “but he [Schroer] is highly sympathetic to Jordan’s scientific point of view, from the earliest years of quantum mechanics, that it is necessary to think about quantum systems in a way which doesn’t depend on starting with a classical Lagrangian and “quantizing”.

    As a mere engineer interested in physics, please indulge a naive comment. I was delighted to read this, since I have also been puzzled by what seems to me like ‘blind adherence to formal recipes’ in quantum theory, such as simply assuming commutation relations among operators instead of deriving them from observation.

    So in superstrings, as I understand it, they assume an open or closed string, instead of a traditional point particle, associate position and momentum operators with this so-called ‘string’ (I mean, is it really like a little piece of spaghetti?), and then simply assume commutation relations ‘by analogy’ with point particles. But since the idea of a string is so different from a point particle, why blindly follow the same formal procedure and assume (hope?) that it works? Obviously, I’m missing a great deal, probably almost everything. But it does seem somewhat like a case of robotic imitation of a formal procedure that somehow worked in a different context.

    In a similar vein, one could criticize formal procedures in ‘orthodox’ quantum theory, as the quoted authors do, even if the agreement with experiment is good. I like to be able to picture what is going on, just as Maxwell’s ‘abstract’ equations correspond to Faraday’s ‘lines of force’. Just because a formal recipe produces valid predictions of data doesn’t impress me so much per se. One could consider it jerry-rigged to do so. One could say that the formal procedures are ‘parroting’ reality, without really shedding light. I guess this line of thought is either too stupid or too philosophical for real physicists…

  23. Bert Schroer says:

    Some remarks about the various comments on my 3 papers of yesterday and today are in order.
    Having lived in Brazil for the last 4 years, my flux of information is very incomplete. Concerning the Iraq war, my main source of information comes from sites of international newspapers, but I am detached from the sociology of US physics departments. It seems that I had the bad look to encourage Ed Witten in an email to start an anti-war campaign and I interpreted his negative answer in a too sweeping way. Actually I am sharing an office with Walter Baltensperger who is a good friend of Walter Kohn, but unfortunately he never told me about Kohn’s anti-war activities. Baltensperger is basically apolitical and he is presently trying to get a documentary about “the Power of the Sun” (with Walter Kohn the main presenter) adapted to Portuguese to be afterwards distributed to schools in Brazil.
    Concerning my string theory…essay I think that one should use a polemic style in physics only in situations of utmost emergency. Polemics, if it is good, sometimes has the power of opening frozen minds and leads to a scientific light bulb moment, but it is of course totally useless with people who allowed fundamentalism to take over. A perfect example of scientific polemics at its best is Res Josts’s article in Helvetica Physica Acta 36, (1963) 77. This was written at the hight of the S-matrix bootstrap fashion and I think it did something to clear the air. The situation is much harder now, and if my efford is in vain it is probably not only because it lacks the elegance and coherence of Jost.
    By the way the limerick which I remembered from my student times (maybe because it is as far as limerinks go the most perfect I ever run across, I think it is a delightful jewish flavor) was not meant personally against Lubos Motl. I just looked at his site and got the impression that he also did not misunderstand my intentions (although scientifically we are in different boats). Looking at his photo it remined me of how my former FU (younger) colleague Hagen Kleinert looked like when I met him the first time in Boulder (Colerado) where he was enthusiastically preaching the virtues of infinite component fields. When we are young we all go through a Sturm and Drang period. I also experienced this in connection with physics&differential geometry and this has a lot to do with my present more critical view and the differences in opinion with Peter Woit on this matter. Since this is quite interesting and needs some more time, I would like to come back to this (I have an appointment right now) soon.
    That there is nothing as a gauge principle is the conclusion of algebraic field theorist for a long time. I became aware of this in connection with different ways present certain 2-dim. models. Recently I run into an interesting observation from Wigner’s representation point of view (see the recent paper with Jens Mund and Jakob Yngvason).
    No I did not say that the Maldecena conjecture is wrong, I only pointed out that there is a mathematical theorem which says that if you want a supersymmetric gauge theory on the conformal side (that’s what most people want) than the AdS side cannot be a QFT for which you can write down a Lagrangian (algebraic QFT envisages a vast territory beyond the Lagrangian setting with which many string theorists unfortunately identify QFT). The best mathematically controllable illustration can be given in terms of so called generalized free fields which have to many degrees of freedom for a lagrangian formulation (I think a good reference is a paper of Duetsch and Rehren which should be easy to find). I am not saying anything which is not (at least implicitly) already in the literature but which may have been lost in thausands of publications on the subject. My statement was somewhat provocative since I proposed to use the Maldacena statement as a vehicle to get some intrinsic understanding of what string theory is. I think without an intrinsic understanding of string theory you cannot hope to prove the conjecture.

  24. Peter Shor says:

    Peter (Woit) says:

    “But there is a lot about quantum field theory that isn’t relevant to string theory, and it is knowledge about those parts of the subject that I think Schroer fears may get lost.”

    This still boggles my mind. In my experience of mathematics, it has become quite clear that anything mathematical has a chance of being useful for anything else. So I don’t how see can string theorists say that any part of quantum field theory is irrelevant to string theory, especially when the paths that they currently think are relevant to string theory appear to be leading into a vast swampland. Is this arrogance or just a fad mentality?

  25. woit says:


    Some parts of QFT really are quite important to string theory, others don’t seem to have much to do with it. While there is plenty of arrogance and fad mentality among string theorists, they certainly have tried all sorts of things to get string theory to work, including using many ideas from QFT. But I don’t think that there is some idea about QFT out there which will fix the problems of string theory. What’s remarkable about string theorists and their descent into the swampland is not so much that they’re not willing to try new ideas from QFT to fix string theory, but that they’re unwilling to abandon the idea that the answer to the problem is a string theory.

  26. Arun says:

    Is the superstring an extended object or not?
    Bert Schroer writes:

    It was already mentioned before that whereas it is true that the extension of the classical Nambu-Goto string (whose canonically quantized version is the “mother” of the string-theoretic reformulation of Veneziano’s dual model) is really a relativistic spacetime string, this is not the case for its canonically quantized counterparts.

    The only intrinsic notion of a quantum relativistic localization is that obtained by translating this object into other positions and checking whether its commutator with the original object is nonvanishing once the second would be string shape enters the causal influence region of the first. This test was made (even by string theorists) and the result was negative [7][8]; the commutator is just that of two pointlike objects localized at the center of mass points of the imagined strings.

  27. Aaron Bergman says:

    Quantum field theory means different things to different people, for what it’s worth. At the risk of generalizing too much, it’s a widespread opinion that the axiomatic approach to quantum field theory hasn’t been particularly fruitful. Most don’t look at it as ignoring “part of quantum field theory” so much as ignoring an approach that is not viewed as useful.

    Dr. Schroer obviously disagrees.

  28. Juan R. says:

    Benjamin said,

    “So in superstrings, as I understand it, they assume an open or closed string, instead of a traditional point particle […]”

    There exists many misconception around string “theory” hype. I carefully recommend to anyone does not believe even a 10% is said in popular treatises about string “theory”.

    The objects called strings play a fundamental role in an asymptotic regime of the branescan. However, once outside the asymptotic regime, one finds a sea of new objects called p-branes, with p taking values from 0 to 9. The 2-branes are usually identified with the traditional superstrings.

    There is a joke claiming that now string theory is not about strings!

    The history of the subject is full of historical twists. One of more interesting I know is that after of decades “explaining” us how “stupid” the pointlike particles of the standard model were and why a concept of extended objects (the strings) was “cool”, we have finalized that string theory is not fundamental and we need some thing new called “M-theory” by now.

    The (M)atrix version of M-theory (only known at my best current knowledge) is based in D0-branes as fundamental entities. The D0-branes are pointlike particles… The strings are considered derived objects in the new approach.

    Therefore, in some sense, stringers are returning to the “old” (but effective) quantum field theory of pointlike particles but they do not say in that way of course 🙂

    Juan R.

    Center for CANONICAL |SCIENCE)

  29. Thomas Love says:

    Schroer listed some legitimate complaints against string theory. Since no one knows what the M stands for (Mystery, Membrane, Mistake), in the future, let’s refer to M-Theory by its initials. M-T as in empty.

  30. Dumb Biologist says:

    Holy cow! I completely missed the note about the trackbacks! Mysterious indeed. It strikes me as a bit of an anticlimactic resolution to what looks to have been a rather painful and/or irritating episode for all involved, this sudden and silent reversal.

    I sincerely hope the end result is not just a reasonable acknowledgement of your bona fides, Dr. Woit, but refinement of arXiv policies that allows everyone, including the moderators, to avoid future headaches.

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