Final Draft Version

I finally have finished a draft version of the book that I’ve been working on for the past four years or so. This version will remain freely available on my website here. The plan is to get professional illustrations done and have the book published by Springer, presumably appearing in print sometime next year. By now it’s too late for any significant changes, but comments, especially corrections and typos, are welcome.

At this point I’m very happy with how the book has turned out, since I think it provides a valuable point of view on the relation between quantum mechanics and mathematics, and contains significant amounts of material not well-explained elsewhere. I’m simultaneously rather unhappy with it, very much aware of a long list of ways in which it could be improved. Any of these though would require putting more time into the project, and right now I’m thoroughly sick of it, desperately wanting to think about other things. So, this is pretty much it.

I’ve learned a huge amount by writing this, and I hope to apply some of this in work on several different new projects. As I work on these, perhaps I’ll do some more writing that would partially take the form of new chapters extending what’s in the book. We’ll see…

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A New 30 GeV Particle?

Last night a preprint appeared on the arXiv, with a re-analysis of old 1992-5 LEP data, looking at the dimuon spectrum for b-tagged (identified as involving a b-quark) events. An excess around 30 GeV was found, which would indicate a possible new particle around that energy. The author quotes various significance numbers for the bump, with look-elsewhere effect included, of 2.4 to 2.9 sigma.

Thinking a bit about the look-elsewhere effect here, something very funny is going on. To properly compute the look-elsewhere effect, one really should know how many other channels the author looked at and found nothing, but there’s no mention of looking at other channels. Why did this particular physicist decide to go and reanalyze LEP data, looking only at the b-tagged dimuon spectrum (and it seems he’s doing this by himself)? It’s hard to understand why anyone would do this, unless perhaps they had heard that one of the LHC experiments might be seeing something in the b-tagged dimuon spectrum, say, around 30 GeV.

We’ll likely find out more about this story soon. If the LHC experiments haven’t been looking closely at this particular channel, they will do so now. 30 GeV is low enough that I don’t see why you would need the Run 2 13 TeV data, this should be in the older Run 1 data.

I should make the obvious remark though: this is an extraordinary claim, and the evidence for a new particle is very far from the extraordinary level. So, at a high confidence level, the probability is that there’s nothing there.

For much more about this, Tommaso Dorigo and Matt Strassler have just put out blog postings.

Update: Tommaso has an update with more about this: the author was not a member of ALEPH and that collboration does not support this but thinks this is bogus. It appears that the signal is spurious, with the muons coming from semileptonic b decays, not a new particle. Still a mystery: why was this physicist looking at this old data for one very specific signal?

Posted in Experimental HEP News | 20 Comments

Math Items

A few mathematics items:

• David Ben-Zvi’s overview talk about Representation Theory as Gauge Theory given last month at the Clay conference in Oxford that I attended is now available online, as slides and video. Other talks from the conference are here.
• My fantasy that I might try and understand arithmetic algebraic geometry by reading Tate’s collected papers keeps getting delayed as the AMS puts off publication (now scheduled for January 18 of next year). While the books are not available, at least Milne’s review is.
• A couple weeks ago there was a Beyond Endoscopy conference at the IAS, at the same time I gather functioning as an 80th birthday celebration for Langlands. There’s a write-up by Langlands of his talk here. I think it can be described as the current Langlands take on “Geometric Langlands”.
• No recent news I’m aware of concerning Mochizuki and the the abc conjecture, but Inference magazine has just published a long article by Ivan Fesenko giving his take on “Inter-universal Teichmuller Theory”.
• The Breakthrough Prize symposium this year is scheduled for December 5 at UCSF, so I guess that means the prizes will likely be announced and awards ceremony held December 4, if things go like in recent years. I have no idea who will get the $3 million math prize since it’s a relatively new prize and there is a whole world of accomplished mathematicians who would make good candidates. One can be pretty sure though who won’t get it, arguably the most accomplished young mathematician around, Peter Scholze (since he turned down the junior version last year). I have a modest proposal for whoever is awarded the prize: if you’re financially pretty well set already, how about doing the math community a huge favor? Donate the money to your university to endow a faculty position, then use the influence and moral high ground this will buy you to try and convince the Breakthrough Prize people to make this a policy. In the future, the winner gets a$3 million check made out to their institution to endow a position in their name. Then they could even try again with Scholze and perhaps get him to accept.

At the same time, there will also be a \$3 million physics award. For a while these things were going pretty uniformly to string theorists, then they turned around and started giving them to experimentalists. I have no idea what they’ll do this year.

Posted in Langlands, Uncategorized | 23 Comments

YITP at 50

The past couple days the YITP at Stony Brook has been celebrating its 50th birthday. It was started back in 1966 by C. N. Yang and has been an active center for theoretical physics ever since. The ITP at Stony Brook was as some point renamed in honor of Yang, now it’s officially the “C. N. Yang Institute for Theoretical Physics”. I was a postdoc there in 1984-87, when it was just the ITP, and Yang was still the director. I had been hoping to go out to Stony Brook for at least one day of the event, but unfortunately other things have kept me here in New York.

Luckily, with today’s technology one can watch the talks online (see here) and follow what happened at the conference. I’ve watched a few of the talks, and they give a good survey of the kind of work that has been going on at the institute over the last 50 years. One aspect that isn’t emphasized in the talks (although there’s a little bit in Fred Goldhaber’s talk) is that the institute is in the same building as the mathematics department with, at least back in my day, some physicists and some mathematicians even having offices nearby on the same floor. Being able to talk to and learn from some great mathematicians (soon after Yang, in 1968 Jim Simons came to Stony Brook and brought together a world-class mathematics department) was a big influence on me during my postdoc years. These days, with the Simons Center for Geometry and Physics, Stony Brook is one of the great centers of mathematical physics.

The last talk of the event was a public talk by Ashoke Sen on What is String Theory? (slides here), one which made me think that maybe it wasn’t a bad thing that I hadn’t made it out to Stony Brook, since I might have been there for this. Sen’s talk was a depressing compilation of ancient hype and misleading claims about string theory, with the standard multiverse excuse for why it predicts nothing at all about particle physics.

My time at the ITP coincided with the early years of this kind of string theory hype, which got started in late 1984, about the time I got there. By my last year there (exactly 30 years ago, 1986-87), everyone in the physics community had already been subjected to a couple years of this kind of thing, so much so that Ginsparg and Glashow had published in spring 1986 their Desperately Seeking Superstrings article, noting that

…years of intense effort by dozens of the best and the brightest have yielded not one verifiable prediction, nor should any soon be expected.

They worried that

Contemplation of superstrings may evolve into an activity as remote from conventional particle physics as particle physics is from chemistry, to be conducted at schools of divinity by future equivalents of medieval theologians.

which many at the time thought was kind of harsh, but in retrospect looks quite prescient. I doubt that even they thought that anyone in the physics community would sit still 30 years later to listen to a talk like Sen’s.

My own attitude at the time was that superstring theory was just one in a sequence of fads that had gotten the attention of particle theorists, with one to two years the usual decay time for such things. So by 86-87, I figured this one was now past its sell-by date and would soon be on the way out. How wrong I was.

Posted in Uncategorized | 38 Comments

Retraction at Annals of Physics

Retraction Watch reports that Annals of Physics has removed a recently published article by Joy Christian, replacing it by a publisher’s note that just says:

“This article was erroneously included in this issue. We apologize for any inconvenience this may cause.”

The paper is available on the arXiv here. Christian’s affiliation in the abstract is listed as “Oxford”. This refers to the Einstein Centre for Local-Realistic Physics which is not at Oxford University, but at a location in the town that I think I unknowingly walked past on my way to go punting last week. The only person involved with the centre who lists an academic affiliation is Dr. Jay R. Yablon (MIT), who appears to be a patent attorney in Schenectady.

This story brings back memories of the Bogdanov affair of 2002, one aspect of which was the publication by the Bogdanovs in Annals of Physics of a paper that, as far as I could tell, made little sense. That paper was never removed or retracted. The editor-in-chief when the Bogdanov paper was accepted was Roman Jackiw. Frank Wilczek took over from him and said at the time that he was hoping to improve the journal’s standards. The current editor-in-chief is my Columbia colleague Brian Greene.

Comments are off since I would rather not host a discussion involving the merits of this paper. I haven’t tried to seriously read it, and don’t want to spend time doing so. In the Bogdanov case I spent (wasted…) a lot of time reading their papers, so felt comfortable discussing them, not about to do the same in this case.

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Back

Now back from traveling, regular blogging will resume. Here are a few items:

• I was going to write something yesterday, explaining that this year’s physics Nobel would surely go to the LIGO trio who have gotten every other major physics prize this year. Luckily I was too lazy to do that yesterday, since this morning’s news is that it instead went to Haldane, Kosterlitz and Thouless, work going way back to the early 1970s. When I was doing my thesis work trying to figure out how to find a lattice version of topological invariants of gauge fields, I started out looking at the case of the 2d XY model which they had studied, where the topology is much simpler.

Congratulations to them, probably next year for the LIGO guys…

• My colleague Daniel Litt has started up a really nice blog.
• Some sort of time warp back to the days of pre-LHC hype of the last decade seems to have occurred while I was in Germany, leading to lots of media stories like this one.
• In Heidelberg among the people I met were Dirk Huylebrouck, who reminded me that there’s lots of great material in the Mathematical Intelligencer, including his “Mathematical Tourist” column, and Barry Cipra, one of the authors of the AMS’s What’s Happening series.
• John Baez is involved with a new project, funded by DARPA, that he describes here.
• Last week there was a conference in Madrid devoted to the question Is SUSY Alive and Well?. Of the talks I looked at, the only one with a sensible answer to the question was that of Alessandro Strumia.
Update: A commenter points to this very interesting survey of the participants.
• In case you haven’t heard what’s going on in Leicester, Tim Gowers explains here.
• I was very sorry to hear of the passing last Saturday of Joseph Birman, a theorist at CCNY, and husband of my colleague Joan Birman. Some information about one aspect of Joe’s work is here, perhaps more about other aspects will appear soon.
Posted in Uncategorized | 20 Comments

Still Not Even Wrong

A while back Tushna Commissariat of Physics World came to talk with me at Columbia, partly to discuss the topic of “Not Even Wrong, ten years later”, and that has now been turned into a podcast available as Still Not Even Wrong.

I’ve now forgotten what I said then, but presumably I still agree with it. This coming week I’m traveling and won’t have much time to deal with the blog, so comments from me may be few and far between.

Update
: There’s an appreciative blog post about this here from ZapperZ.

Posted in Not Even Wrong: The Book | 11 Comments

Heidelberg Laureate Forum

This week I’m in Heidelberg, attending the Heidelberg Laureate Forum, where I’ll be writing some blog posts for their website (which should appear here). You can follow talks on their website, either in real-time as streaming video, or by watching a talk video later on.

This event brings together mathematicians and computer scientists. More specifically winners of the Fields Medal, Abel Prize, ACM Turing award and Nevanlinna Prize come to give talks and interact with a large group of young researchers (and various hangers-on such as myself).

Update: I wrote blog entries for the HLF about Faltings, Ngo, Wiles, Atiyah and Voevodsky. Now on my way to London, will spend the next week in England, mostly in Oxford.

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This Week’s Hype

Quanta Magazine has over the past couple years been establishing a well-deserved reputation as the smartest and best science journalism around. At the opposite extreme, over many years of interacting with science journalists, the most embarrassingly incompetent one I’ve run across has been KC Cole, so I was surprised today to see that Quanta has published a piece by her.

Back in 2006 she wrote a review for the LA Times, basically explaining that Lee Smolin and I shouldn’t be listened to because we were incompetent embittered failures who didn’t understand the beauties of string theory. When I contacted her and the LA Times to complain that her review had completely misrepresented what I wrote in my book about neutrino physics, she wrote back to explain to me that I didn’t know what I was talking about, whereas she was an expert on neutrino physics. Her other main evidence for my ignorance was this:

As for Woit’s claim that string theory has “absolutely zero connection with experiment,” experiments already planned for a new European particle accelerator will look for the existence of extra dimensions and extra families of particles — both predicted by string theory. In fact, many statements about string theory in these books are plain wrong.

The topic of her new article is The Strange Second Life of String Theory, which makes the claims that string theory has failed as a theory of quantum gravity (which will be news to a lot of string theorists), but that “it has blossomed into one of the most useful sets of tools in science.”

The article has all sorts of interesting quotes from experts about the state of string theory these days, mostly indicating that people have given up on it and are trying to figure out how to move on. For instance:

David Gross: “After a certain point in the early ’90s, people gave up on trying to connect to the real world,” Gross said. “The last 20 years have really been a great extension of theoretical tools, but very little progress on understanding what’s actually out there.”

Robbert Dijkgraaf: “But now we have this big mess.” “Things have gotten almost postmodern.”

“Nobody knows whether to say they’re a string theorist anymore,” said Chris Beem, a mathematical physicist at the University of Oxford. “It’s become very confusing.”

At last year’s big annual string theory meeting, the Stanford University string theorist Eva Silverstein was amused to find she was one of the few giving a talk “on string theory proper,” she said.

Juan Maldacena jokingly defines “string theory” as “Solid Theoretical Research in Natural Geometric Structures.”

Like many of his colleagues, [David] Simmons-Duffin says he’s a string theorist mostly in the sense that it’s become an umbrella term for anyone doing fundamental physics in underdeveloped corners. He’s currently focusing on a physical system that’s described by a conformal field theory but has nothing to do with strings.

I’m amused to hear that according to Maldacena and Simmons-Duffin, it appears that I’m a string theorist. One thing Cole gets right is that most theorists are now working on questions about quantum field theories. Sean Carroll objects to this:

It’s the kind of work that makes people such as Sean Carroll, a theoretical physicist at the California Institute of Technology, wonder if the field has strayed too far from its early ambitions — to find, if not a “theory of everything,” at least a theory of quantum gravity. “Answering deep questions about quantum gravity has not really happened,” he said. “They have all these hammers and they go looking for nails.” That’s fine, he said, even acknowledging that generations might be needed to develop a new theory of quantum gravity. “But it isn’t fine if you forget that, ultimately, your goal is describing the real world.”

It’s a question he has asked his friends. Why are they investigating detailed quantum field theories? “What’s the aspiration?” he asks. Their answers are logical, he says, but steps removed from developing a true description of our universe.

Instead, he’s looking for a way to “find gravity inside quantum mechanics.” A paper he recently wrote with colleagues claims to take steps toward just that. It does not involve string theory.

Cole tells us that

Like many a maturing beauty, string theory has gotten rich in relationships, complicated, hard to handle and widely influential. Its tentacles have reached so deeply into so many areas in theoretical physics, it’s become almost unrecognizable, even to string theorists.

According to her, string theory has made “essential contributions to cosmology” (this likely is news to cosmologists), especially by revealing the multiverse, which is now “taken for granted by a large number of physicists”, one of whom you might think is David Gross, since she writes:

Inflationary models get tangled in string theory in multiple ways, not least of which is the multiverse — the idea that ours is one of a perhaps infinite number of universes, each created by the same mechanism that begat our own. Between string theory and cosmology, the idea of an infinite landscape of possible universes became not just acceptable, but even taken for granted by a large number of physicists. The selection effect, Silverstein said, would be one quite natural explanation for why our world is the way it is: In a very different universe, we wouldn’t be here to tell the story.

This effect could be one answer to a big problem string theory was supposed to solve. As Gross put it: “What picks out this particular theory” — the Standard Model — from the “plethora of infinite possibilities?”

Silverstein thinks the selection effect is actually a good argument for string theory. The infinite landscape of possible universes can be directly linked to “the rich structure that we find in string theory,” she said — the innumerable ways that string theory’s multidimensional space-time can be folded in upon itself.

The piece ends with a different genre of hype:

Arkani-Hamed believes we are in the most exciting epoch of physics since quantum mechanics appeared in the 1920s.

I actually spent much of the day down in Princeton at the IAS, attending some of the talks at the Natifest in honor of Nati Seiberg’s 60th birthday. Lots of different ideas were discussed by the speakers, with essentially no mention of string theory. A serious journalist who talked to all the people Cole did would likely have noticed the obvious and framed the same material quite differently: string theory hasn’t worked out and theorists have moved on to other things, with the center of gravity of the subject now the deeper study of quantum field theory.

Update: I took a look again at the KC Cole review of my book, the second page of it is here. It was even more dishonest and unethical than I remember. She takes my

superstring theory has had absolutely zero connection with experiment,

and turns it into

Woit’s claim that string theory has “absolutely zero connection with experiment,”

Note how pulling a phrase out of sentence, you get to do fun stuff like change the tense of the sentence.

On the neutrino issue, Cole writes:

To say, as Woit does, that fundamental mysteries about neutrinos are being ignored will come as news to the dozens of physicists who’ve been working on these problems for years.

This is based on the fact that on page 93 of the US edition I write, after giving a description of the things the standard model leaves unexplained, including a parameter count that ignores neutrino masses:

One complication that has been ignored so far involves neutrinos.

and then go on to explain about the experimental evidence for neutrino masses. The “ignored so far” obviously means “ignored so far in this chapter”, not “fundamental mysteries about neutrinos are being ignored” by physicists.

When I contacted her to complain about this, her response was that there was nothing wrong with what she had done, and that, unlike me, she was an expert on neutrino physics.

The Quanta article has lots of her characteristic “quotes”, words or phrases pulled out of context. I’ll bet that lots of those misrepresent what the person being quoted actually said. I’d urge the Quanta editors to re-fact check this piece, asking for full quotes, in context.

Posted in This Week's Hype | 25 Comments

Fashion, Faith, and Fantasy

Roger Penrose’s Fashion, Faith and Fantasy in the New Physics of the Universe is finally being published this week. This is a bit of a landmark event, since the book has a long history, going back to a series of lectures that he delivered in 2003 at the university and IAS. At one point I remember watching videos of these lectures hosted by Princeton here, but these no longer seem to be available.

In giving these lectures, Penrose was walking into the lion’s den, bringing a forceful critique of string theory to the academic institution where it is most popular. Congratulations to Princeton University Press for publishing this despite it challenging the hegemonic viewpoint at Princeton (I had less luck with them: when my British publisher sent them my book for consideration way back when, they hired Lubos Motl to write an evaluation of it…).

Besides a mathematical appendix, the book is divided up into four parts:

• Fashion: This is the section that deals with string theory, and Penrose’s central objection is to the use of extra spatial dimensions as a crucial part of the theory. When trying to use string theory as a unified theory, an assumption is made that one can take four space-time dimensions very large, and the rest very small, decoupling the large and small dimensions. Penrose argues that there is no reason to believe one can consistently do this, that there should be couplings between these degrees of freedom that cannot be ignored, leading to instability of the theory, rather than a stable ground state with large dimensions.

The problem is that one doesn’t actually have a non-perturbative string theory in which one could properly study this issue. There’s no consistent theory, so Penrose can’t rigorously prove there’s a problem of this kind. He faces the generic problem of arguing not with a well-defined theory, but with people’s speculative hopes of what kind of theory might exist. I agree with him though that the extra dimensions are a deadly problem for the theory. Even if you accept the most optimistic hopes that Penrose’s and other problems will go away, you are still going to be left with the landscape problem. Everything known about conjecturally stable states with 4 large dimensions indicates an infinite complexity of such conjectural things, capable of giving you any physics you want, leaving the theory able to predict nothing and empty of explanatory power.

• Faith: In this section Penrose addresses the measurement problem of quantum mechanics, pointing out correctly that our standard story about quantum mechanics introduces an “ontological shift”, indicating that something more is going on than a well-understood consistent framework. He favors the idea that perhaps the introduction of gravity into the usual framework could resolve this problem, backing this up with a dimensional analysis argument that a relevant effect could come from gravity, while being too small to be observable so far.

Here I think he does an excellent job of explaining the usual story and why there’s a problem, but personally I’ve never been convinced that this problem requires new physical laws, non-linearities, or the introduction of gravitational effects. To me the “ontological shift” has always seemed due to the standard story being not a full theory of what happens in a real measurement process, but being a phenomenological approximation of what happens, with approximation needed to get a tractable description. As people build and study more complicated and larger fully quantum systems, the inadequacies of the standard story about “measurement” I think will become clearer, and we’ll get a better understanding of how classical behavior emerges from quantum laws, with no need to change those laws.

• Fantasy: Here Penrose describes in detail some basic problems in the theory of cosmology, and how they are supposedly resolved by the theory of inflation. He explains that characterizing this as “fantasy” is not meant to be purely critical, that “fantasizing” about the moment of the big bang is what theorists do in the absence of compelling evidence, and that he just has other fantasies he thinks worthwhile.

I don’t think I can do justice here to the depth and complexities of his arguments in this section. This is a topic involving subtle questions about the behavior of general relativity where Penrose is one of our deepest thinkers and greatest experts. While acknowledging some of the achievements of inflationary theory, part of his critique is related to that of Paul Steinhardt and others, showing that the theory doesn’t accomplish what it sets out to do, with the exponential expansion not providing a way to get observed homogeneity from arbitrary initial conditions. At the same time there is a lot more there, and this section seems to me that it should be required reading for anyone trying to make sense of fantasies of the description of the big bang itself.

• A new physics for the universe?: In a final section, Penrose describes some of his more positive ideas addressing the problems pointed out in the earlier sections. This begins with a wonderful summary of the theory of twistors, and I strongly suspect that he’s right that this very different way of thinking about space-time geometry will ultimately be part of any successful integration of our understanding of quantization and geometry. That this geometry is very specific to four space-time dimensions provides yet another reason for skepticism about the fashion of theories with more spatial dimensions.

I’m less convinced by his speculation about quantum state reduction, and by what he refers to as his “Conformal Crazy Cosmology”, although the emphasis on conformal invariance may very well be a correct one.

In a final “Personal Coda” he explains that he sees himself not as a “maverick”, but as rather embodying an “inner conservatism”, somewhat allergic to the appeals of fashion. In particular:

So when I heard that string theory – to which I had been distinctly attracted, partly because of its early use of Riemann surfaces – had moved itself in the direction of requiring all those extra spatial dimensions, I was horrified, and far from being tempted by the romantic attractions of a higher-dimensional universe. I found it impossible to believe that nature would have rejected all those beautiful connections with Lorentzian 4-space – and I still do.

A wonderful aspect of the book are Penrose’s many and detailed graphical illustrations, which have been made available separately by Princeton here. At their website you can also read the Preface, and an interview. Unfortunately I’ll be in Germany next week, missing Penrose’s book tour events here in New York, at the American Museum of Natural History and MoMath.

The range of non-crackpot speculative ideas about fundamental physics that normally get much attention is unfortunately quite narrow. In this environment Penrose is a breath of fresh air, providing here a different point of view on several topics, backed by serious and detailed argument. In some ways this is a popular book, but in others it is something else, deserving the attention of experts in the subject. I can’t recommend it too highly to anyone with a serious interest in fundamental questions about physics.

Update: A somewhat different version of this review is up at MAA Reviews.

Posted in Book Reviews | 34 Comments