I ordinarily keep a short list on my desk of things I’ve seen recently that I’d like to write about here. The last few days this list has gotten way too long, so I’ll try and deal with it by putting as many of these topics as I can in this posting.
The June/July issue of the AMS Notices is out, with many things worth reading. The two long articles are one by Ken Ono about Ramanujan and one by Arthur Jaffe telling the story of the founding of the Clay Mathematics Institute and the million dollar prizes associated with seven mathematical problems. There’s also a book review of Roger Penrose’s The Road to Reality, news about the proposed US FY 2007 budget for mathematical sciences research, and an account of a public talk by Michael Atiyah, who evidently closed by explaining some of his very speculative ideas about how to modify quantum mechanics, then said:
This is for young people. Go away and explore it. If it works, don’t forget I suggested it. If it doesn’t, don’t hold me responsible.
The June issue of Physics Today is also out. In its news pages it reports that Robert Laughlin is out as the president of the Korea Advanced Institute of Science and Technology (KAIST), and will return to Stanford in July “where he plans to teach, research, and write ‘anything that brings income.'” The report gives conflicting reasons for why things didn’t work out for him at KAIST, but notes that “90% of KAIST professors gave him a vote of no-confidence and nearly all deans and department chairs quit their administrative posts to protest his continuing in the job.”
There’s an extremely positive review of Leonard Susskind’s The Cosmic Landscape by Paul Langacker, which ends:
The Cosmic Landscape is a fascinating introduction to the new great debate, which will most likely be argued with passion in the years to come and may once again greatly alter our perception of the universe and humanity’s place in it.
Why any particle theorist would want to encourage other physicists outside their field to read this book and give them the idea that it represents something theorists think highly of is very unclear to me.
Finally there’s an article by Jim Gates entitled Is string theory phenomenologically viable? Gates aligns himself with the currently popular idea that string theory doesn’t give a unique description of physics:
The belief in a unique vacuum is, to me, a Ptolemaic view – akin to that ancient belief in a unique place for Earth. As I wrote in 1989, a Copernican view, in which our universe is only one of an infinity of possibilities, is my preference, but there were very few Copernicans in the 1980s.
He seems to promote the idea that one should not use 10d critical string theory and thus extra dimensions, but instead look for 4d string theories, and that perhaps the problem is the lack of a “completely successful construction of covariant string theory.” For more about this point of view, see Warren Siegel’s website.
There are quite a few idiosyncratic things about Gates’s article, including the fact that he refers to non-abelian gauge degrees of freedom as “Kenmer angles”, after Nicholas Kemmer (not Kenmer) who was involved in the discovery of isospin.
Some of his comments about string theory are surprising and I don’t know what to make of them. He claims that “some aspects of string theory seem relevant to quantum information theory”, and the one supposed observational test of string theory he discusses is one I hadn’t heard of before and am skeptical about (observing string-theory-predicted higher curvature terms in Einstein’s equations through gravitational wave birefringence). His discussion of supersymmetry seems to assume that observation of superpartners is unlikely, since for reasons he doesn’t explain he expects their mass to be from 1 to 30 Tev. Finally, he worries that people will not investigate things like covariant string field theory since we are about to enter an “era that promises an explosion of data”. I certainly hope he’s right about the forthcoming availability of large amounts of interesting new data.
The Harvard Crimson has an interesting article about Ken Wilson.
John Baez is getting ever closer to having a blog in its modern form, now he has a diary.
Read about the tough summer life of theoretical physicists in Paul Cook’s report from Cargese (which reminded me of when I went there as a grad student), and JoAnne Hewett’s report from Hawaii (which reminded me of a very pleasant vacation I spent on the Big Island).
Science magazine has an article about progress on increasing luminosity at the Tevatron, hopes for getting enough events there to see the Higgs before the LHC, and the debate that is beginning about whether to run the machine in 2009.
Slides are available from the Fermilab User’s Meeting.
There’s a news story out from China (and picked up by Slashdot) about the new paper by Huai-Dong Cao and Xi-Ping Zhu soon to appear in the Asian Journal of Mathematics. This paper is more than 300 pages and is supposed to contain a proof of the Poincare conjecture and the full geometrization conjecture, filling in an outline of a proof due to Perelman, who used methods developed by my Columbia colleague Richard Hamilton. Other groups have also been working on this in recent years including my other Columbia colleague John Morgan together with Gang Tian; for another example, see the notes on Perelman’s papers recently put on the arXiv by Bruce Kleiner and John Lott. Cao and Zhu have evidently been explaining their proof in a seminar at Harvard run by Yau during the past academic year, and Yau will talk about this at Strings 2006 in Beijing later this month. When the paper appears it will be interesting to see what some of the other experts in the field think of it and whether there’s a consensus that the proof of Poincare and geometrization is finally in completely rigorous form.
Update: According to a blog entry from the Guardian, “Perelman seems to be active in string theory.”
Why shouldn’t Langacker give Susskind’s book a favorable review? They might be friends (I do not know). The next to last paragraph states
“Many scientists are strongly opposed to the multiverse-landscape paradigm. Some objections are technical. For example, are there really 10^500 vacua, or does the multiverse really exist? Others are that the ideas are not testable and not really science, or that they might seduce researchers into giving up the traditional goal of finding a unique and elegant explanation for the observed laws of Nature. Sussking makes no attempt to give an impartial overview — after all, he is advocating his own ideas. However, he does offer a reasonable survey of the objections and his own responses to them.”
That’s a fairly balanced review statement. Langacker doesn’t try to whitewash the fact that many people disagree with the ideas in the book. It’s a reasonable review.
I think the review of “The Road to Reality” in the Notices is very well balanced. I would be curious to know what Peter and commenters think.
If Cao and Zhu’s proof is right , what percent of contribution does their work occupy to the Poincare Conjecture? They will share the prize provided by the Clay Math Inst? An amateur
Dear Prof. Woit:
I’m a science reporter of Southern Weekly, a very influential newspaper which circulates around China. Currently the Chinese media are highly praising the paper pubished by Profs. Huaidong Cai and Xiping Zhu. I’m wondering that if I can quote your blog words in my story, and could you say something more:
1. What’s your comment on the work of Cao-Zhu, and other groups like Morgan-Tian, Kleiner-Lott?
2. Some people thought that Prof. Shing-Tung Yau is making a hype:
(http://mathforum.org/kb/message.jspa?messageID=4767368&tstart=0)
(http://mathforum.org/kb/message.jspa?messageID=4768229&tstart=0)
Do you agree with them or not?
3. Cloud said:
“If Cao and Zhu’s proof is right, what percent of contribution does their work occupy to the Poincare Conjecture? Will they share the prize provided by the Clay Math Inst? ”
That’s also what I want to know.
Best regards,
Hujun Li
——————————
Beijing bureau of Southern Weekly
705, Tower B, COFCO, 8 Jiannei Ave.
Beijing, 100005 China
Phone: 86-10-8511-8726
Fax: 86-10-8511-8725
Email: li_hujun AT hotmail.com
Url: http://www.southcn.com/weekend
Science column:
http://tech.sina.com.cn/focus/lihujun
Hujun Li,
It should be made clear that I am not an expert in this area of mathematics, and this blog entry is just quoting other widely available sources. I don’t think you should quote it, you should contact people who are experts. Of the people I have talked to about this, as far as I know they haven’t even seen the Cao-Zhu manuscript, and thus have no basis yet for an opinion.
Physics Today is uncritical of speculation so its not surprising they publish nonsense. A decade ago (apr 96) they published Witten’s claim “String theory has the remarkable property of predicting gravity.” Still no string prediction a decade on.
I did a little research, and it turns out Witten’s prediction of gravity has indeed been confirmed in experiments by physicists I. Newton and G. Galilei. I don’t know about you, but I think a Nobel is in order.
http://www.wanyidun.com/blog_r2u/?p=65
Can anybody explain to me what is the physical meaning of a theory with several vacua (Gates) in view of the fact that the application of the cluster factorization means that (without loss of physical generality) one can decompose the theory into a direct sum of components where each component has a unique vacuum? This is a mathematical theorem and probably its derivation can be found in Streater-Wightman (presently not available to me).
Be careful, I am presently not saying that Gates is wrong, there may be a misunderstanding on my part.
Prof. Schroer,
can you please comment on the paper of Grigore&Scharf “Against Supersymmetry” ?
Thank you.
Since I presently don’t have the time to read the article, and I do not want to comment on just the basis of the abstract, I asked Dan Grigore to address this question on this weblog.
I did not see the Cao-Zhu paper listed in the math arXiv. Why would it not be there?
I did see three Grisha Perelman Ricci-flow papers at math.DG/0307245, math.DG/0303109, and math.DG/0211159 , so it seems to me that precedent would be to put the paper on the math arXiv.
Tony Smith
http://www.valdostamuseum.org/hamsmith/
PS – I did not see on either the physics arXiv or the math arXiv any paper by Grisha Perelman that looked like a superstring paper, although some, such as Martin Rocek, have spoken about connections between Ricci flow and string theory, and I think that Perelman may have discussed such things. However, to me that does not mean that Perelman is an advocate of string theory, just that he is open to discussion about possible applications of his Ricci flow ideas to ANYTHING, even string theory.
Further, I did not see anything in the Guardian blog but an unsupported assertion.
The Cao-Zhu work was not put on the arXiv. As far as I know, many of the relevant experts have still not even seen a copy.
Saying Perelman is active in string theory is a complete joke, which is why I quoted it. In his work he uses the kind of flow equation that also appear in renormalization group flows for sigma models, which I guess to string theorists makes him “active in string theory”. I wonder where the Guardian writer got that nonsense.
Cao and Zhu’s full paper has not even shown up in the Journal yet. I guess by far only Shing-tong Yau and some Harvard mathematicians have read it. It seems that Yau is convinced.
I’m glad someone is attempting to present a complete unified presentation of a proof of the Poincaré conjecture. It would be a shame if this very important conjecture is finally declared proved, but left scattered to the winds in bits and pieces in various papers published in many different places.
I find it very odd that
1. The paper will appear next month in Asian J of Math, but has not appeared on the arXiv,
2. The result was announced in a press conference, rather than at a regular math meeting (or by simply posting the paper on the arXiv), and
3. In the abstract, the authors declare that their work is “a crowning achievement”. I thought they should let the readers say that.
Since the authors of yesterdays “Against Supersymmetry” (Grigore&Scharf) did not yet react to my email, I feel that I should make some preliminary comments with respect to their obviously consequence-bearing statement. The title should be understood in the sense: the old suspicions about the incompatibility beetween supersymmetry and gauge theory finally passes to a No-Go theorem.
With their opening statement against the use of functional integrals for the calculation of physically relevant (renormalizable) results they run into my open doors; functional integrals are basically for incantation and baptization of QFT, but not for calculating renormalized results (they only have a metaphorical existence for unrenormalized correlation functions and are incorrect for renormalized correlations of strictly renormalizable theories). Functional integrals totally ignore the singular (distributional) nature of quantum fields and the people who worship them are usually those who believe that the ultraviolet problems are the real limitations of QFT, whereas in reality (Epstein-Glaser) the physical problem is to find finite-parametric islands (stable under a finite-parametric renormalization group) in the “universal” QFT which is a formal construct with infinitely many couplings (shared between Petermann-Stueckelberg and Wilson).
Atiyah belonged to the strongest venerators of functional integrals within the mathematical community and it is interesting to notice that he found other mathematical arguments which cast doubts on the depth and utility of supersymmetry (the starting point of participation in this particular blog section).
I still did not find the time to read the article (but I know the authors as very competent, although not exactly representing AQFT as one participant here was claiming), and I still hope that they will enter this blog and explain themselves what they have done.
Prof. Schroer,
thank you for your comment.
So the LHC has a real chance to falsify the causal AQFT approach?
Well it is not the causal approach which is under discussion, but only what the authors call the minimally supersymmetric extended standard model. Other extensions are not investigated but of course their paper is an invitation to do this (including to themselves I suppose).
Perelman is not just a Ricci flow person. When he first appeared on the scene, he established his reputation in Riemannian geometry and its generalizations. He then disappeared for about 7 years (yes, just like Wiles). When he re-emerged, he started sending emails to Ricci flow experts, asking technical questions. To quote one reaction, “uh-oh”. He’s written three papers on how to use the Ricci flow to prove Thurston’s conjecture. The rumors are that he has moved on and is now working on the Navier-Stokes equation.
MathPhys, the abstract says “crowning achievement of the Hamilton-Perelman theory of Ricci flow”. This is not odd (no self-praise or theory-hype or whatever), it is true.
MathPhys:
The full sentence in their abastract is “This proof should be considered as the crowning achievement of the Hamilton-Perelman theory of Ricci flow”. I think that “a crowning achievement”should be understood in its context.
“I find it very odd that
1. The paper will appear next month in Asian J of Math, but has not appeared on the arXiv,
2. The result was announced in a press conference, rather than at a regular math meeting (or by simply posting the paper on the arXiv),”
Something similar happened when Andrew Wiles informed the world about his initial (flawed) proof. Mathematicians don’t seem to use arxiv as much, ulinke theoretical physicists, a shame.
If Yau is wrong, it will be embarassing to him, so I don’t think he is doing it lightly.
Wiles is far from being a computer/internet oriented man, and his proof was “announced” in a series of talks at the Newton Institute. It’s still quite a different story.
No one thinks that the Cao-Zhu work is wrong. Everyone believes Perelman to be right, so it’s a safe bet on Yau’s part.
Yidun,
“This proof should be considered as the crowning achievement of the Hamilton-Perelman theory of Ricci flow”.
Still sounds like something that a referee or a reader, rather than an author should say.
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Regarding Laughlin’s departure from KAIST, see the apparently well-informed comments on this post at The Marmot’s Hole.
Chris W,
I read the post at The Marmot’s Hole of Laughlin and KAIST. Very interesting. Very funny too. Almost a script of a funny movie on how third world countries (and I think S Korea is one) manage science.
One of my readers has predicted that Prof. Bert Schroer would endorse the crackpot paper “Against Supersymmetry” and he or she was completely right. The paper is completely absurd because supersymmetric gauge theories are a subset of ordinary gauge theories with a properly chosen spectrum and adjusted interactions, after all, so an anomaly of this kind would affect all gauge theories, not just supersymmetric ones.
What the authors have probably (it’s hard to decode it in their very unusual formalism and terminology) found is that – in ordinary language – one can’t work without the FP ghosts at one-loop level. Their “anomaly” is proportional to two copies of the structure constants, which looks like two cubic vertices in a diagram with a FP ghost loop. If they learned a basic class of quantum field theory, this would have been explained in the second semester. If they did their exercise correctly, they can easily cancel the anomaly by adding fermionic scalar fields in the adjoint representation, the ghosts, and their auxiliary superpartners if needed.
Even at the level of social sciences, a statement that there is a universal anomaly killing supersymmetric theories is a proof of crackpotism. 3,000 very smart people have written 20,000 papers that go well beyond naive checks that these two authors have attempted to do correctly but failed. Moreover, these theories follow from string theory, belong to the powerful web of dualities that imposes all required consistency criteria, and they have been recently studied at a much higher level of rigor in string theory as field-theoretical duals of particular gravitational backgrounds of string theory.
Prof. Bert Schroer has no idea about quantum field theory.
Lobos,
if anybody ever claims you understand QFT you may give him a thorough spenking. It seems that the stringy alimentation you already received in Prague has damaged your brain beyond repair.
Dear Prof. Schroer,
if you can’t learn quantum field theory – indeed, you could not have passed my course QFT II in the spring because this was a standard part of the material written in the syllabus – you could at least try to struggle and learn my name.
My name is Luboš.
All the best to you and all the crackpots here
Luboš
Lubos,
I wrote papers on supersymmetry. Does that make me very smart?
Anyway, I must agree with Lubos on this one, and I’m willing to bet good money that there is no problem, and that the paper (which I haven’t read) contains a basic mistake.
Maybe it’s a mistake along the lines that Lubos anticipated, or maybe something even more banal.
There is no doubt that susy gauge theories are perfectly well behaved, and the more supersymmetric, the better behaved.
Incidentally, there was a little ‘scare’ along the same lines around 1984 (when Lubos was still in diapers) when ‘tHooft and a PhD student (van Damme) claimed that susy gauge theories have an anomaly at 2 loop level, and therefore unrenormalizable. They were wrong. Van Damme made a computational mistake.
Dear MathPhys,
does it make one smart? It may depend on the content of the paper. But more generally, the answer is probably Yes. One needs to be above a certain lower threshold of IQ to be able to write at least a slightly meaningful paper about supersymmetry, and all the data I have indicate that your knowledge and intelligence in the context of gauge theory probably exceeds those of Prof. Schroer.
All the best
Lubos
I told you that I have not red the paper (I am still on the road) and that I know both authors as very competent and careful colleagues. Since I was asked on this weblog to say something and since my attempts to get the authors directly involved failed up to now, I tried to at least understand what they are claiming. Nothing to get emotional about. This is what a weblog is for, isn´t it. The previous statement about the physical aspects of supersymmetry which I made in connection with a remark attributed to Atiyah I of course stand by, but they fall short of what these two authors are claiming.
Lubos,
These were some of the silliest and most trivial papers I’ve ever written. It’s too easy.
You see, I know supersymmetry well enough to believe that, while perfectly consistent, susy is the most obvious stumbling block in the development of theoretical high energy physics today.
There is something very wrong with the idea of sypersymmetrizing everything until you can compute something, then break the supersymmetry by hand and push everything you don’t want all the way up till you can’t see them (only to find that you recover the problems that made you supersymmetrize in the first place).
It is just too easy, and too contrived at the same time. And it doesn’t work.
MathPhys,
it was just this issue of breaking of supersymmetry which I commented on earlier. It is precisely at this point where SUSY outs itself as being eerily different from any other symmetry under the sun.
Dear Prof. Schroer,
Sir Atiyah has co-authored at least one famous paper in which four-dimensional supersymmetric non-Abelian gauge theories play an important role:
http://arxiv.org/abs/hep-th/0107177
Well, yes, one can probably guess which of the two authors wrote most of these physics-related sections of that paper. The complexity and the mathematical depth of this Atiyah-Witten paper exceeds the complexity and depth of the paper by Grigore and Scharf by two orders of magnitude or more.
But Sir Atiyah is a mathematician who does not have to understand supersymmetric gauge theories well and he would never be foolish enough to make far-reaching statements about topics that he does not understand, unlike you.
You may find Grigore and Scharf to be “careful” and “competent” colleagues, according to your standards, but according to the usual standards, they are something very different because the one-loop structure of gauge theories – and all possible anomalies and non-anomalies that might occur at one-loop level – is a standard material in every modern textbook of quantum field theory and no careful and competent physicist would ever publish a paper making far-reaching statements about these topics before he understands their standard presentation in the textbook.
This can’t really be compared with the two-loop paper by van Damme et al. in 1984 because one-loop level is something much more elementary, and moreover 22 years have ended since the van Damme et al. paper.
But certain people just think that they can make important discoveries while ignoring virtually all insights that have been made in the last 50 years, checked, re-checked, experimentally verified, and summarized in quantum field theory textbooks. And this is the context in which I just find the word “crackpot” appropriate.
All the best
Lubos
Dear Prof Schroer,
Yes, I get your point.
Incidentally, are you permanently based in Rio now? Do you like the working conditions there?
It is worthwhile to remember that wayback there were serious problems to find regularizations which maintain gauge invariance and supersymmetry simultaneously. Not knowing whether these problems have been resolved meanwhile, I find it reasonable to take from AQFT the idea of an approach which avoids regulators and cutoffs altogether and to base perturbation theory on ideas which take care of the distributional aspects of fields throughout the calculation (e.g. the Epstein-Glaser approach). What confuses Lubos so much is that the authors prefer this setting in order to stay on the safe side.
Lubos,
For some very odd reason, British knights are called by their first name, rather than surname, after ‘Sir’. So, one says ‘Sir Michael’ and ‘Sir Roger’, and not ‘Sir Atiyah’ or ‘Sir Penrose’.
On the other hand, following ‘Lord’, one uses a chosen name, but the origins of that would be too difficult to explain (Martin Rees is Lord Ludlow).
When in doubt, just call him ‘Professor Atiyah’. He wouldn’t mind.
Prof Schroer,
There is no problem regularizing supersymmetric gauge theories. Olivier Piguet can tell you all about that.
Yes I live in Rio where I have an apartment, but I am presently in Sao Paulo. I retired from the FU-Berlin and the working conditions, apart from a 2 by 3 m desk corner in an office I share with another pensionist Prof. Walter Baltensperger (look up his name in physics/ he has some interesting ideas about the origin of the tropical flora and fauna in earlier geological epochs of siberia) I am creating my own working conditions.
They obviously don’t stay on the safe side if they can “derive” so completely ludicrous “results”. Prof. Schroer is profoundly confused which insights in physics are robust and which are not. As far as I can say, the Epstein-Glaser approach is exactly as flawed as everything else that Prof. Schroer has ever attempted to sell. It contradicts the genuine renormalization group behavior of all the operators and interactions.
Epstein & Glaser also have roughly 100 citations per 33 years. Prof. Schroer must believe that there has been some world-wide conspiracy that makes this important (?) paper look 30 times less important than papers that most experts find really important.
Whether or not one uses a regularization that preserves both gauge symmetry and supersymmetry simultaneously is irrelevant. Even in the case of ordinary gauge theory itself, one can use regulators that don’t manifestly preserve supersymmetry. It just means that gauge-invariance-violating counterterms can be generated and must be canceled, as additional renormalization conditions (masslessness of the photon in QED, for example). But once they are canceled, the results are equivalent to manifestly gauge-invariance regularizations such as dim. reg.
Analogously, we may use dim. reg. for SUSY gauge theories which preserves the gauge symmetry. Supersymmetry is then also preserved as long as the couplings are renormalized so that the supersymmetric relations between them are preserved at every order, which is easily seen to be possible in the full quantum theory if it is possible in the classical theory. If you just define Feynman diagrams in superspace, things become more or less manifest.
It may be difficult to put SUSY on the lattice – less difficult with the help of deconstruction – but it is straightforward to preserve SUSY by renormalization at the loop level.
“that don’t manifestly preserve supersymmetry.” in the previous comment should have been “that don’t manifestly preserve gauge symmetry”.
Mathphys,
are you sure that Olivier Piguet does not use the regularization-free algebraic approach? (his work with Sorella is often called “algebraic renormalization”.)
Lubos, you are in a weblog about particle physics and not in a bookmaker´s shop.
“Lubos, you are in a weblog about particle physics and not in a bookmaker´s shop.”
It certainly does not look so. My feeling is just the opposite.
If you want to see how a particular physics blog looks like, see e.g.
http://www.google.com/search?hl=en&q=particle+physics+blogger
particular -> particle
Piguet uses a ‘modern’ version of BHPZ. Yes, they call it ‘regularization free’, but I’m not so sure that that’s a fair name. There is a lot of debate about that that I don’t wish to get involved in. There was also work by I Jack and D R T Jones (disproving van Damme and ‘t Hooft), where they obtain the same results as Piguet et al, but using a version of dimensional regularization that somehow preserves supersymmetry.
The message is that one can subtract the infinities, while retaining susy and gauge invariance. I’m sure these issues were settled more than 20 years ago.