Not Even Wrong

When I was young, I recall that a standard assignment when restarting school was an essay on “what I did on my summer vacation”. Now that I’m back in the office after a vacation, here’s a version of that, covering the physics/math aspects:

• In Paris I visited the Palais de la Découverte, the science museum in the heart of the city. This was the site of some of my earliest memories of getting interested in science, back in the late 1960s. I started out by visiting the physics section, some of which looked like it hadn’t changed much since those days. One addition was a video screen with some seating nearby. It was running Particle Fever, and surely someone trying to annoy me had timed things so that I got there just as the part promoting SUSY finished, and the part featuring Nima Arkani-Hamed promoting the multiverse got underway.

  Besides revisiting my youth, this made me wonder what the effect of trying to impress the young with glitzy pseudo-science will turn out to be. Will it turn off youngsters looking for something intellectually serious? What would my 12 year old self have made of this?

  I soon made my way though to a big LHC exhibit, which cheered me up immediately. This was quite well-done, giving a good idea of what a machine like the LHC really is and what the scientists working there are doing. I quite enjoyed the last part of the exhibit, a recreation of typical grimy offices at CERN that people work in. I’d like to think that I’d have appreciated that, with its unspoken message that these are people who care not about appearances but just about the fascinating work they are doing.

• Now that scientific bookstores are gone in New York, checking out the ones in Paris is a high-priority when visiting there. This time I bought a few books in French, one of which was a new biography of Grothendieck, by Georges Bringuier. I’ve read widely among the many sources emphasizing Grothendieck’s mathematics, this is one that instead focuses on his life, including quite a bit about the years after he left the IHES in 1969. This is an amazing story, and there’s much in the book that I didn’t know, especially about Grothendieck’s mystical views.

  The last years of his life he was a hermit, just about completely isolated and perhaps paranoid, but still supposedly writing (the biography explains his view that one shouldn’t read mathematics, but write it). Perhaps someday we’ll find out what he was writing about, for some information about this, see here. While in the earlier part of his career Grothendieck wanted nothing to do with physics, associating it with the Bomb, evidently at the end he had physics books in his home rather than mathematics ones.

  One person Grothendieck was in communication with in the early 1990s was Robert Thomason, see a letter available here. Thomason died in Paris in 1995, his notebooks have just become available at this site.

• Another book I found in Paris was from a few years back, about the “unification of mathematics” by Parrochia, Micali and Anglès. The topics are Clifford algebras, abstract algebraic geometry (a la Grothendieck), and the Langlands program, wrapped up in an argument that these provide a unified framework for mathematics. The point of view is the very French one emphasizing the “philosophy” of a subject, and much of the argument is that philosophers of science should be paying close attention to the “Langlands philosophy” and its significance as a unifying set of ideas. They also argue that physics should fit naturally into this sort of unification, an idea I’m very fond of, but they don’t seem to be very aware of the actual connections between physics and the Langlands story (they refer only to the classification of branes by twisted K-theory).

Heading out soon for summer vacation travels, this time to Ireland and France, back in about two weeks. While away comments will be shut off.

My vacation will spare readers commentary on the rest of the Strings 2015 talks, which at some point will appear here. It seems that the conference included the usual publicity campaign for string theory, with Ashoke Sen continuing to demonstrate a sense of humor by telling the press that

In string theory, we are essentially following in the same steps

as the 50 year story of the Higgs mechanism, the Standard Model and the discovery of the Higgs particle. It does put modern HEP research in perspective once one realizes that its greatest success (the Standard Model) and greatest failure (string theory unification) are essentially the same…

Some of the talks at Strings 2015 have now appeared online, and one of them I found quite fascinating, Witten’s Anomalies Revisited. Some of his motivation comes from string perturbation theory and M-theory, but the questions he addresses are fundamental, deep questions about quantum field theory (and not just any quantum field theory, but exactly the sort of qft that appears in the SM, spinors chirally-coupled to gauge-fields/metrics).

The fundamental issue is that these are theories where the path integral does not determine the phase of the partition function. Part of story here is the well-known story of anomalies, perturbative and global. One interesting point Witten makes is that vanishing of these anomalies is not sufficient to be able to consistently choose the phase of the partition function, and he gives a conjecture for a necessary condition that is stronger than anomaly cancellation.

The standard story of QFT textbooks is that once a Lagrangian is chosen, the corresponding QFT is well-defined. But quantization really is a lot more subtle than that, and the anomaly phenomenon is just one indication of the problem. In earlier parts of my career I spent a lot of time thinking about anomalies; the connections to some of the deepest mathematics around (K-theory, index theory and much more) are truly remarkable. In recent years I’ve been thinking about other things, but Witten’s talk is a strong encouragement to go back and revisit the anomaly story (some of his best work has “revisited” in the title…)

In particular, Witten emphasizes a particular case I’d never paid much attention to: the 3d massless Majorana fermion. One would think that this is among the simplest quantum field theories around, but Witten explains how this is an example of a theory with a potential inconsistency (no way to consistently choose the sign of the partition function), even when the anomaly vanishes. This theory also appears in a hot topic in condensed matter physics, the theory of topological superconductors. One reference Witten gives to related work is to this recent paper (there’s a typo in his reference, should be 1406.7329 not 1407.7329).

Witten ends with:

I hope I have at least succeeded today in giving an overview of the tools that are needed to study the subtle fermion integrals that frequently arise in string/M-theory. A detailed analysis of a specific problem would really require a different lecture. Write-ups of some of the problems I’ve mentioned – and some similar ones – will appear soon.

I look forward to those write-ups, with the theories he’s talking about of a lot more interest than just their role in string/M-theory calculations.

Another conference that starts today is the Convergence conference at the Perimeter Institute. The concept is explained by Neil Turok here. His point of view is one I’m very much in sympathy with:

Turok explains that the “large bandwagon” of the last 30 years has not found experimental support. The bandwagon in question is the Standard Model of particle physics established in the 1970s, which, he says, people have been elaborating ever since. “Grand unified theories, supersymmetry, string theory, M-theory, multiverse theory,” he lists. “Each is not particularly radical, but is becoming ever more complex and arbitrary.”

To illustrate the lack of experimental support for these ideas, Turok describes how many people were hoping string theory would represent a radical development; but since string theory – as currently interpreted – leads to the multiverse, Turok describes it as the “least predictive theory ever”.

Indeed, experimental support has not been found for other extensions of the Standard Model either. “We have discovered the Higgs and nothing else,” says Turok, “yet the vast majority of theorists had been confidently predicting WIMPS (weakly interacting massive particles) and supersymmetric particles…Theorists are walking around in a bit of a stunned silence.” He adds that it could turn out to be right that all sorts of other particles are needed along with the Higgs – but that thought seems to be misguided.

“My view is that this has been a kind of catastrophe – we’ve lost our way,” he says. “What we need are ideas as simple and radical as in the start of the 20th century with quantum mechanics.”

So what might these ideas look like? Turok explains how observations have shown that the universe is simpler than we ever expected – in contrast to our theories, which are becoming ever more complex.

It’s great to see this, very encouraging to think that a more reality-based point of view on fundamental physical theory may finally be emerging. My only criticism is that the program doesn’t seem to include any mathematics or mathematicians (except perhaps in the context of history and Emmy Noether). If you have a structure you don’t understand, which is unusually simple, with surprising explanatory power, you might want to ask mathematicians about it…

The schedule is here, there’s a blog here.

Update: You can follow a lot of what is going on at this conference on Twitter, here. For example, I was glad to hear about this comment from Dimopoulos

There is no difference that we know right now … between the story of divine intervention and the multiverse.

It’s great to see a conference on fundamental physics where the multiverse is coming in for some appropriate skepticism.

Update: One thing to say about the multiverse, it does provide an excuse for an endless number of popular articles mulling it over. Just today, there’s Caleb Scharf and George Johnson.

Ordered from the more to less serious…

• On the geometric Langlands front, there’s video posted today of this talk by Dennis Gaitsgory. Michael Harris has already commented here about the local geometric Langlands conjecture in terms of 2-categories that Gaitsgory discusses. Today’s arXiv listings have a new paper on geometric Langlands by Witten, which begins with his version of a formulation relating the categorical point of view and quantum field theory.
  I wrote recently here about a talk by Jacob Lurie that alluded to an explanation of this categorical equivalence for the simplest case of G invertible complex numbers (rather than the case of G a general semi-simple Lie group that Gaitsgory and Witten are discussing). I’m still far from being enlightened concerning that simplest case, but have learned a lot from Alexander Polishchuk’s Abelian varieties, theta functions and the Fourier transform which I take as treating the global versions of this equivalence.
• Witten has been busy, with yesterday’s arXiv listings including a 429 page paper with Gaiotto and Moore (does anyone know of a longer hep-th paper that’s not a review article?). There’s also a companion shorter summary paper. The motivation here is again a categorical picture expressed in terms of quantum field theory models, but for more insight you’ll need to find someone more expert than me on this topic.
• Strings 2015 will be held in Bangalore in a couple weeks. Talks titles are now available, so you can see what the hot topics in the “string theory” community are. Of Gaiotto, Moore and Witten, only Witten will be speaking. Perhaps his talk on An Overview of Worldsheet and Brane Anomalies will shed some light on the 429 page paper.
• On the Mochizuki/abc front, hopes rest on a planned workshop at Oxford this December. Fesenko has circulated a letter about the workshop, which gives suggestions about how to approach the subject.
• Via Chandan Dalawat’s Google+ page I found out about this autobiographical piece by Misha Gromov. One thing it made clear to me is why I couldn’t get anything out of the couple times I’ve heard him lecture.
  

  Being trivial is our most dreaded pitfall: you say stupid things, not original things, outrageously wrong things – all will be forgotten when the dust settles down. But if you pompously call a+b=c “Theorem” in your paper, you will be forever remembered as “this a+b guy”, no matter you prove bloody good theorems afterwords…
  I was introduced to the idea on September 1st 1960 at the then Leningrad University when our analysis professor Boris Mikhailovich Makarov said to me after our first calculus class – he expressed this in somewhat metaphorical terms – that I should’ve kept my mouth shut unless I had something non-trivial to say.
  Further encouraged by my teachers and fellow students, I tried to follow his advice and, apparently, have succeeded – I hear nothing disrespectful about my mouth for the last 10-20 years. Strangely, this does not make me feel a lot happier.
  “Trivial” is relative. Anything grasped as long as two minutes ago seems trivial to a working mathematician.

  Another thought this raises is that I’ve just spent the last 3 years of my life writing something trivial…

• I really like Jordan Ellenberg’s suggestion of Cold Topics Workshops.
• Mathematics makes it into the Guardian with an article about mathematical modeling.
• With the LHC inactive, some LHC physicists have had to spend their time studying plots (trigger warning, and NSFW).

Update: One more, far more serious than anything above. Sabine Hossenfelder brings up an important and rarely discussed topic here.

Every so often I’ve taken a look at something about theoretical physics on Reddit, generally ending up not spending much time there. One reason was that I realize I’m already spending more of my life than is healthy arguing with people about string theory and the like, so better to avoid a new venue for that. The temptation to respond is strong when one sees someone mischaracterizing one’s opinions, but I’ve generally been able to resist temptation at that site.

Today I happened to come across a really wonderful discussion there though, and wanted to draw attention to it, even though it’s from a year ago. It’s entitled A View from an Ex-String Theorist and consists of a long piece by someone who has recently left string theory, as well as some answers to questions asked by others. If you want to understand what string theory looks like these days to good theorists who are working on it, read what “No_More_Strings” has to say.

No_More_Strings explains very well the difficult job situation in the field, and the effects this has. With a lot of very smart people and almost no jobs, postdocs are in no position to take the time to try and learn something new that isn’t a “hot topic”, or try and work on an unpopular idea that might take years to go anywhere. This is a huge part of the story of why this field is in trouble, and the situation seems to have just gotten worse since I wrote about it in my book over 10 years ago.

The suggestion that “string theorists” should stop calling what they do “string theory” is an excellent one. No_More_Strings explains how smart people in the field are not working on string unification, but have moved on to different things with little relation to quantized strings. Giving up the name would be a good first step to allowing people to think of what they are doing in a less narrow way. If you didn’t have to start every grant application by explaining that you’re motivated by “our best hope for a theory of everything”, you might find it easier to work on something quite different, with no relation at all to quantized strings.

I can’t quite resist correcting a couple things mentioning me. No, I don’t think string theorists are stupid. No, I don’t think that Witten “singlehandedly destroyed the study of “real” physics” (the last one isn’t the fault of No_More_Strings).