What is String Theory?

This semester the KITP has been running a program asking What is String Theory?, which is winding up next week, and was promising to “arrive at a deeper answer to the question in the title.” It seems though that this effort has gone nowhere, with this report from the scene:

Went to a string theory conference with many of the top researchers in the field centered around tackling the question “what is string theory” and the consensus after the conference was that nobody knows lmao

For an answer to the question from someone with a lot more experience, I recently noticed that Lubos Motl is very active on Quora, giving thousands of sensible answers to a range of questions, especially having to do with Central Europe. He explains the relation of string theory and M-theory (disagreeing with Wikipedia), and defines string theory as

the name of the consistent theory of quantum gravity which covers all the vacua found in the context of critical string theory and M-theory.

I had trouble getting my head around the concept of an undefined theory known to be consistent when I first heard about it nearly 30 years ago, but it seems to still be a thing.

Posted in Uncategorized | 11 Comments

How I fell out of love with academia

Sabine Hossenfelder today posted a new video on youtube which everyone in theoretical physics should watch and think seriously about. She tells honestly in detail the story of her career and experiences in academia, explaining very clearly exactly what the problems are with the conventional system for funding research and for training postdocs.

After a string of postdocs requiring moving and living far from her husband, she decided she needed to move back to Germany and applied for a grant to fund her research (I believe for this project). This is how she describes the situation:

At this point I’d figured out what you need to put into a grant proposal to get the money. And that’s what I did. I applied for grants on research projects because it was a way to make money, not because I thought it would leave an impact in the history of science. It’s not that what I did was somehow wrong. It was, and still is, totally state of the art. I did what I said I’d do in the proposal, I did the calculation, I wrote the paper, I wrote my reports, and the reports were approved. Normal academic procedure.

But I knew it was bullshit just as most of the work in that area is currently bullshit and just as most of academic research that your taxes pay for is almost certainly bullshit. The real problem I had, I think, is that I was bad at lying to myself. Of course, I’d try to tell myself and anyone who was willing to listen that at least unofficially on the side I would do the research that I thought was worth my time but that I couldn’t get money for because it was too far off the mainstream. But that research never got done because I had to do the other stuff that I actually got paid for.

As that grant ended, she decided to try instead applying for grants to work on research that she found to be more promising and not bullshit, but those grant proposals were not successful. Since then, she has left the academic research system and concentrated on trying to make a career oriented around high-quality Youtube videos about scientific research.

It seems to me that Hossenfelder correctly analyzes the source of her difficulties: “The real problem I had, I think, is that I was bad at lying to myself.” Those more successful in the academic system sometimes criticize her as someone just not as talented as themselves at recognizing and doing good research work. But I see quite the opposite in her story. Many of those successfully pursuing a research career in this area differ from her in either not being smart enough to recognize bullshit, or not being honest enough to do anything about it when they do recognize bullshit.

Posted in Uncategorized | 33 Comments

A Report From Mochizuki

I don’t really have time to write seriously about this, and there’s a very good argument that this is a topic anyone with any sense should be ignoring, but I just can’t resist linking to the latest in the abc saga, the REPORT ON THE RECENT SERIES OF PREPRINTS BY K. JOSHI posted yesterday by Mochizuki.

To summarize the situation before yesterday, virtually all experts in this subject have long ago given up on the idea that Mochizuki’s IUT theory has any hope of proving the abc conjecture. Back in 2018, after a trip to Kyoto to discuss in depth with Mochizuki, Scholze and Stix wrote up a document explaining why the IUT proof strategy was flawed. Scholze later defended this argument in detail and as far as I know has not changed his mind. Taking a look at these two documents and at Mochizuki’s continually updated attempt to refute them, anyone who wants to try and decide for themselves can make up their own minds. All experts I’ve talked to agree that Scholze/Stix are making a credible argument, Mochizuki’s seriously lacks credibility.

The one hope for an IUT-based proof of abc has been the ongoing work of Kirti Joshi, who recently posted the last in a series of preprints purporting to give a proof of abc, starting off with “This paper completes (in Theorem 7.1.1) the remarkable proof of the abc-conjecture announced by Shinichi Mochizuki…”. My understanding is that Scholze and other experts are so far unconvinced by the new Joshi proof, although I don’t know of anyone who has gone through it carefully in detail. Given this situation, an IUT optimist might hope that the Joshi proof might work and vindicate IUT.

Mochizuki’s new report destroys any such hope, simultaneously taking a blow-torch to his own credibility. He starts off with

.. it is conspicuously obvious to any reader of these preprints who is equipped with a solid, rigorous understanding of the actual mathematical content of inter-universal Teichmüller theory that the author of this series of preprints is profoundly ignorant of the actual mathematical content of inter-universal Teichmüller theory, and, in particular, that this series of preprints does not contain, at least from the point of view of the mathematics surrounding inter-universal Teichmüller theory, any meaningful mathematical content whatsoever.

and it gets worse from there.

: A commenter points to a response from Joshi here.

Update: Scholze has a comment on MathOverflow indicating precisely where Joshi’s attempted proof runs into trouble.

Update: Mochizuki and those around him award themselves \$100,000 (this is the IUT Innovator Prize described here).

Posted in abc Conjecture | 47 Comments

David Tong: Lectures on the Standard Model

David Tong has produced a series of very high quality lectures on theoretical physics over the years, available at his website here. Recently a new set of lectures has appeared, on the topic of the Standard Model. Skimming through these, they look quite good, with explanations that are significantly more clear than found elsewhere.

Besides recommending these for their clarity, I can’t help pointing out that there is one place early on where the discussion is confusing, at exactly the same point as in most textbooks, and exactly at the point that I’ve been arguing that something interesting is going on. On page 7 of the notes we’re told

We can, however, find two mutually commuting $\mathfrak{su}(2)$ algebras sitting inside $\mathfrak{so}(1, 3)$.

but this is true only if you complexify these real Lie algebras. What’s really true is
$$\mathfrak{so}(1, 3)\otimes \mathbf C = (\mathfrak{su}(2)\otimes \mathbf C) + (\mathfrak{su}(2)\otimes \mathbf C)$$
Note that
$$\mathfrak{su}(2)\otimes \mathbf C=\mathfrak{sl}(2,\mathbf C)$$

Tong is aware of this, writing on page 8:

The Lie algebra $\mathfrak{so}(1, 3)$ does not contain two, mutually commuting copies of the real Lie algebra $\mathfrak{su}(2)$, but only after a suitable complexification. This means that certain complex linear combinations of the Lie algebra $su(2)\times su(2)$ are isomorphic to $so(1, 3)$. To highlight this, the relationship between the two is sometimes written as
$$\mathfrak{so}(1, 3) \equiv \mathfrak{su}(2) \times \mathfrak{su}(2)^*$$

This is a rather confusing formula. What it is trying to say is that the real Lie algebra $\mathfrak{so}(3,1)$ is the conjugation invariant subspace of its complexification
$$(\mathfrak{su}(2)\otimes \mathbf C) + (\mathfrak{su}(2)\otimes \mathbf C)$$
where the conjugation interchanges the two factors. Tong goes on to use this to identify conjugating an $\mathfrak{so}(3,1)$ representation with interchanging its properties as representations of the two $\mathfrak{su}(2)\otimes \mathbf C=\mathfrak{sl}(2,\mathbf C)$ factors.

For a very detailed explanation of the general story here, involving not just the Lorentz real form of the complexification of $\mathfrak{so}(3,1)$, but also the other (Euclidean and split signature) real forms, see chapter 10 of the notes here. My “spacetime is right-handed” proposal is that instead of identifying the physical Lorentz Lie algebra in the above manner as the “anti-diagonal” sub-algebra of the complexification, one should identify it instead with one of the two $\mathfrak{sl}(2,\mathbf C)$ factors (calling it the “right-handed” one). Conjugation on representations is then just the usual conjugation of representations of the right-handed $\mathfrak{sl}(2,\mathbf C)$ factor.

Posted in Euclidean Twistor Unification, Uncategorized | 13 Comments

Abel Prize to Michel Talagrand

I was very pleased to hear yesterday that this year’s Abel Prize has been awarded to Michel Talagrand. For more about Talagrand and his mathematics, see the Abel site, Quanta, NYT, Nature and elsewhere. Also, see lots of reactions on Twitter like this one.

Almost exactly ten years ago I got an email from someone whose name I didn’t recognize, expressing interest in the notes I had made available online which would turn into the book on quantum mechanics. He was reading the notes and had some comments which he included, saying he thought they were trivial but maybe I would want to take a look. Some of them were of the type “I don’t quite understand the argument on page X”. Figuring that I’d help out an earnest reader with a weak background by explaining the argument a bit better, I took a look at the argument on page X. After a while I realized that what I had written was nonsense, a very different argument was needed. “I don’t quite understand” was his way of politely telling me “you have this completely wrong.”

I soon ran into Yannis Karatzas and asked him if he knew anything about this “Michel Talagrand”. He told me “of course! He’s amazing, almost got a Fields Medal”. Over the next year or two I benefited tremendously from Michel continuing to read carefully through my notes and send me detailed comments. He was very much responsible for improving a lot the quality and accuracy of what I was writing. He had begun his own project of trying to understand quantum field theory by writing a book about it. The result is available as What Is a Quantum Field Theory?, which is a wonderful resource for anyone interested in a precise and accurate account of much of the basics of the subject. If you’ve seen Gerald Folland’s excellent Quantum Field Theory: A Tourist Guide for Mathematicians, you can think of Talagrand’s book as a much expanded version, giving the full story that Folland only sketched.

During many of my trips to Paris since that time I’ve gotten together with Michel and his wife Wansoo, and have also seen them here in New York. It has been a great pleasure to get to know Michel in person, he is a wonderful human being as well as a truly great mathematician.

Posted in Uncategorized | 7 Comments

20 Years of Not Even Wrong

The first entry on this blog was 20 years ago yesterday, first substantive one was 20 years ago tomorrow (first one that drew attacks on me as an incompetent was two days later). Back when I started this up, blogging was all the rage, and lots of other blogs about fundamental physics were starting around the same time. Almost all of these have gone dormant, with Sabine Hossenfelder’s Backreaction one notable exception. She and some others (like Sean Carroll) have largely moved to video, which seems to be the thing to do to communicate with as many people as possible. There are people who do “micro-blogging” on Twitter, with the descendant of Lubos Motl’s blog StringKing42069 on Twitter. I remain mystified why anyone thinks it’s a good idea to discuss complex issues of theoretical physics in the Twitter format, flooded with all sorts of random stupidity.

Looking back on what I was writing 20 years ago it seems to me to have held up well, and there is very little that I would change. The LHC experiments have told us that the Standard Model Higgs is there, and that supersymmetry is not, but these were always seen as the most likely results.

My point of view on things has changed since then, especially in recent years. When I started the blog I was 20 years past my Ph.D., in the middle of some sort of an odd career. Today I’m 66, 40 years past the Ph.D., much closer to the end of a career and a life than to a beginning. In 2004 I was looking at nearly twenty years of domination of fundamental theory by a speculative idea that to me had never looked promising and by then was clearly a failure. 20 years later this story has become highly disturbing. The refusal to admit failure and move on has to a large degree killed off the field as a serious science.

The technical difficulties involved in reaching higher energy scales at this point makes it all too likely that I’m not going to see any significant new data about what the world looks like above the TeV scale during my lifetime. Without experiment to keep it honest, fundamental theory has seriously gone off the rails in a way which looks to me irreparable. With the Standard Model so extremely successful and no hints from experiment about how to improve it, it’s now been about 50 years that this has been a subject in which it is very difficult to make progress. I’ve always been an admitted elitist: in the face of a really hard problem, only a very talented person trained as well as possible and surrounded by the right intellectual environment is likely to be able to get somewhere.

My background has been at the elite institutions that are supposed to be providing this kind of training and working environment. Harvard and Princeton gave me this sort of training in 1975-1984 and I think did a good job of it at the time, but from what I can tell things are now quite different. 40 years of training generations of students in a failed research program has taken its toll on the subject. I remember well what it was like to be an ambitious student at these places, determined to get as quickly as possible to the frontiers of knowledge, which in those times meant learning gauge field theory. These days it unfortunately means putting a lot of effort into reading Polchinski, and becoming expert in the technology of failed ideas.

One recent incident that destroyed my remaining hopes for the institutions I had always still had some faith in was the program discussed here, which made me physically ill. It made it completely clear that the leaders of this subject will never admit what has happened, no matter how bad it gets. Also having a lot of impact on me was the Wormhole Publicity Stunt, which showed that the problem is not just refusing to face up to the past, but willingness to sign onto an awful view of the future, as long as it brings in funding and can be sold as vindication of the past. Watching the director of the IAS explain that this was comparable to the 1919 experimental evidence for GR surely made more than a few of those in attendance at least queasy. This particular stunt may have jumped the shark, but what’s likely coming next looks no better (replace quantum computing with AI).

The strange thing is that while the wider world and the subject I care most about have been descending into an ever more depressing environment of tribalistic behavior and intellectual collapse, on a personal level things are going very well. In particular I’m ever more optimistic about some new ideas and enjoying trying to make progress with them, seeing several promising directions. Whatever years I have available to think about these things are looking like they should be intellectually rewarding ones. Locally, I’m looking forward to what the next twenty years will bring (if I make it through them…), while on a larger scale I’m dreading seeing what will happen.

Update: For a place with extensive comments about this blog posting, see Hacker News.

Posted in Uncategorized | 73 Comments

Spring Course Notes

This spring I’ve been teaching a course aimed at math graduate students, starting with quantum mechanics and trying to get to an explanation of the Standard Model by the end of the semester. Course notes for the first half of the course are available here, but still quite preliminary, in particular I need to do a lot of work on section 9.4 and add material to chapter 10. Hoping to get to this tomorrow.

There won’t be much progress on the notes for the next couple weeks. This coming week I’m hoping to spend some time trying to understand Peter Scholze’s IAS lectures, will go down to the IAS on Tuesday. On Thursday I’m heading out on a spring break vacation to the Arizona-Utah desert.

Perhaps a good way to think about these notes is that they’re both aimed more at mathematicians than physicists (although I hope accessible to many physicists) and also designed more to supplement than to replace the discussions in the standard physics texts. So, a lot of the standard material is not there, since it’s well-covered elsewhere, but there are a lot of topics covered that usually aren’t.

One unusual aspect of the notes is that I spend a lot of time trying to explain non-relativistic quantum field theory, since that seems to me to be a better starting point than immediately diving into the relativistic case. I’d be curious to know if anyone can point me to a good discussion of the path integral formalism for non-relativistic quantum field theory, which is something I haven’t found. This is one reason it’s taking a while to finish writing up my own version.

Also original here I think is a careful discussion of the real forms of spinors and twistors. This in some sense is background for the new ideas about “spacetime is right-handed” which I’ve been working on. Nothing in the notes now about the new ideas, but I hope the explanation of the conventional story in these notes is useful.

Posted in Uncategorized | 18 Comments

A New Approach to Modularity

I was assuming that Peter Scholze’s Emmy Noether lectures at the IAS would be the big news about advances in the Langlands program this coming week, but an anonymous correspondent just sent me this link. Tomorrow Andrew Wiles will be giving a talk in Oxford on “A New Approach to Modularity”, with abstract:

In the 1960’s Langlands proposed a generalisation of Class Field Theory. I will review this and describe a new approach using the trace formua as well as some analytic arguments reminiscent of those used in the classical case. In more concrete terms the problem is to prove general modularity theorems, and I will explain the progress I have made on this problem.

I’m curious to hear from anyone who knows what this is about or can report tomorrow after the talk. Wiles does have a certain track record of unveiling unexpected huge progress in a talk like this…

Update: Well, the talk should be over now. Sure someone who was there can let us know what happened?

Update: There’s a tweet with some photos.

: The first of Scholze’s talks is available at the IAS youtube channel.

Posted in Langlands | 4 Comments

Three Items

Kind of like the last posting, but this time you get two worthwhile items to make up for one that’s not.

  • Dan Garisto has a very good article here examining the present state of high energy experimental particle physics and phenomenology. He also summarizes current thoughts about the future. The CERN FCC-ee proposal is still in feasibility study mode, with the big problem its high cost. Numbers like \$15 – \$20 billion have shown up in press reports, and Garisto has “tens of billions”. The feasibility study is supposed to be finished late next year, and presumably a big part of it is people at CERN crunching numbers trying to figure out some plausible way this could work financially.
  • There’s a very good article at Quanta about efforts to put together version 3 of the very influential “Kirby List” of open problems in topology. For version 1, see here, version 2 here, and as far as I can tell, version 3 still not finished (but discussed here).
  • Brian Keating has a video asking “What would It take for String Theory to move beyond the realm of pure math, Into verifiable territory”? The answer obviously is a conventional substantive scientific prediction of anything. By describing the problem with string theory as being that it is now in “the realm of pure math”, I think Keating is missing the point. The problem with “string theory” is not that it’s pure math, but that it’s not a theory. “String theory” is now a 50 year old set of failed hopes and dreams that a theory might exist, see for instance Theorists Without a Theory. Every so often I try to figure out what people still pursuing this are up to, most recently today taking a quick look at KITP talks by Liam McAllister here and here.

    The problem shows up clearly at 10:23 of the first talk where he’s talking about his goal, which gives up on studying all or even representative string theory solutions and tries just to find any “valid solutions”. But what is a “valid solution”?

    And by valid solutions, we should say what equations are we trying to solve? And, it’s not the case that we can currently think about finding cosmological solutions of the exact theory in any non-perturbative sense.

    McAllister artfully avoids saying what everyone at the talk knows (after all, the talk is part of a program entitled “What is String Theory?”): you can’t look for solutions to the theory because there is no theory. More specifically, no “exact” theory, just a long list of possible theories that one hopes might be in some sense approximations to a real theory. He then goes on to specify the extremely complex approximate theory he wants to work in, chosen by the “look under the lamppost” method as something you could actually imagine calculating. Whenever I look at things of this kind I’m completely mystified why anyone thinks it make sense to embark on insanely complicated calculations like these with essentially zero credible scientific motivation. Somehow though, he has a whole group of people doing this. By the end of the second talk he’s giving his vision of the future, which features an old photo of a room of hundreds of men in suits and ties calculating with pencil, paper and slide rules.

    I was mystified twenty years ago why anyone thought this was a good idea, and the whole thing has just gotten stranger and stranger…

Posted in Uncategorized | 21 Comments

Two Items

If I’m going to point to something about string theory and say the same things as always about it, seems best to first start with the opposite, an item about something really worth reading.

  • This spring I’ve been teaching a graduate course aimed at getting to an explanation of the Standard Model aimed at mathematicians. The first few weeks have been about quantization and quantum mechanics, today I’m starting on quantum field theory, starting with developing the framework of non-relativistic QFT. While trying to figure out how best to pass from QM to QFT, I’ve kept coming across various aspects of this that I’ve always found confusing, never seen a good explanation of. Today I ran across a wonderful article by Thanu Padmanabhan, who I knew about just because of his very good introductory book on QFT, Quantum Field Theory: The why, what and how. The article is called “Obtaining the Non-relativistic Quantum Mechanics from Quantum Field Theory: Issues, Folklores and Facts” and subtitled “What happens to the anti-particles when you take the non-relativistic limit of QFT?” It contains a lot of very clear discussion of issues that come up when you try and think about the QM/QFT relationship, a sort of thing I haven’t seen anywhere else.

    Looking for more of Padmanabhan’s writings, I was sad to find out that he passed away in 2021 at a relatively young age, which is a great loss. For more about him, there’s a collection of essays by those who knew him available here.

  • For something I can’t recommend paying more attention to, New Scientist has an article labeled How to Test String Theory, which is mostly an interview with Joseph Conlon. Conlon’s goal is to make the case for string theory, in its original form as a unified theory with compactified extra dimensions. On the issue of testability there’s nothing new, just the usual unfalsifiable story that among all of the extra stuff (moduli fields, axions, extra dimension, extended structures) that appears in string theory and that string theorists have to go to great trouble to make non-observable, it’s in principle conceivable that somebody might observe one of these things someday. But, that’s not really what people mean when they ask for a test. For details of the sort of thing he’s talking about in the New Scientist article, see here.

    I strongly disagree with Conlon about some of what he’s saying, but the situation is very much like it has always been with many string theorists since way back to nearly forty years ago. We don’t disagree about the facts, it’s just that I’ve always looked at these facts and interpreted them as showing string theory unification ideas to be unpromising, whereas string theorists like Conlon somehow find reasons for optimism, or at least for believing there’s no better thing to do with their time. Last time I was in Oxford, Conlon invited me to lunch at his College and I enjoyed our conversation. I think we agreed on many topics, even about what is going on in string theory, but it looks like we’re always going to have diametrically opposed views on this particular question. For more from him, as far as popular books by string theorists go, his Why String Theory? book is about the best there is, see more about this here.

Update: A couple more.

  • Curt Jaimungal has a conversation with Lee Smolin.
  • Andy Strominger is giving talks on Celestial Holography at the KITP “What is String Theory?” program, first one is here. Lots of questions from the audience. One thing he makes clear is that this is not leading to a theory of quantum gravity. Stringking is back, his comments on this:

    KITP program on what is string theory such a joke this week. Strominger shilling his celestial vaporware.

Posted in This Week's Hype | 14 Comments