Trying to keep track of everything happening in the Langlands program area of mathematics is somewhat of a losing battle, as new ideas and results keep appearing faster than anyone could be expected to follow. Here are various items:

- Dennis Gaitsgory was here at Columbia yesterday (at Yale the day before). I don’t think either lecture was recorded. Attending his lecture here was quite helpful for me in getting an overview of the results recently proved by him and collaborators and announced as a general proof of the unramified geometric Langlands conjecture. For details, see the papers here, which add up in length to nearly 1000 pages.
For a popular discussion, see this article at Quanta.

To put things in a wider context, one might want to take a look at the “What is not done in this paper?” section of the last paper of the five giving the proof. It gives a list of what is still not understood:

Geometric Langlands with Iwahori ramification.

Quantum geometric Langlands.

Local geometric Langlands with wild ramification.

Global geometric Langlands with wild ramification.

Restricted geometric Langlands for ℓ-adic sheaves (for curves in positive characteristic).

Geometric Langlands for Fargues-Fontaine curves.Only the last of these touches on the original number field case of Langlands, which is a much larger subject than geometric Langlands.

- Highly recommended for a general audience are the Curt Jaimungal – Edward Frenkel videos about the Langlands story. The first is here, the second has just appeared here, and there’s a third part in the works. One scary thing about all this is that Frenkel and collaborators are working on an elaboration of geometric Langlands in another direction (“analytic geometric Langlands”), which is yet again something different than what’s in the thousand-page paper.
- Here at Columbia, Avi Zeff is working his way through the Scholze proposal for a version of real local Langlands as geometric Langlands on the twistor P
^{1}, using newly developed techniques involving analytic stacks developed by Clausen and Scholze. This is an archimedean version of the Fargues-Scholze work on local Langlands at non-archimedean primes which uses ideas of geometric Langlands, but on the Fargues-Fontaine curve. Together these provide a geometric Langlands version of the local number field Langlands program, with no corresponding geometric global picture yet known. - Keeping up with all of this looks daunting. To make things worse, Scholze just keeps coming up with new ideas that cover wider and wider ground. This semester in Bonn, he’s running a seminar on Berkovich Motives, and Motivic Geometrization of Local Langlands, promising two new papers (“Berkovich motives” and “Geometrization of local Langlands, motivically”), in preparation.
As a sideline, he’s been working on the “Habiro ring” of a number field, finding there power series that came up in the study of complex Chern-Simons theory and the volume conjecture. According to Scholze:

My hope was always that this q-deformation of de Rham cohomology should form a bridge between the period rings of p-adic Hodge theory and the period rings of complex Hodge theory. The power series of Garoufalidis–Zagier do have miraculous properties both p-adically and over the complex numbers, seemingly related to the expected geometry in both cases (the Fargues–Fontaine curve, resp. the twistor-P

^{1}), and one goal in this course is to understand better what’s going on. - Finally, if you want to keep up with the latest, Ahkil Matthew has a Youtube channel of videos of talks run out of Chicago.

I heard this morning that Richard Hamilton passed away yesterday. He was a renowned figure in geometric analysis, and a faculty member here at Columbia since 1998. In terms of mortality, the last year or two at the Columbia math department have been grim ones, as we’ve lost five senior faculty at relatively young ages: Igor Krichever at age 72, Henry Pinkham at age 74, Lars Nielsen at age 70, Walter Neumann just last week at age 78, and now Hamilton at age 81.

Richard wrote a short autobiographical piece about himself at the time he was awarded the Shaw Prize in 2011, available here. There’s an interview conducted by his Columbia colleague John Morgan here. Just a couple months ago, Richard was award the Basic Science Lifetime award in Mathematics. You can watch his lecture given in Beijing at the time here.

Richard is best known for his work on the Ricci flow (see for instance this textbook). This was the basis for a program to prove the Poincare conjecture using methods of geometric analysis, a program that was brought to fruition by Grigori Perelman. When Perelman came to lecture at Columbia on this, I was sitting next to Richard at the back. He was paying close attention and afterwards told me that Perelman’s new ideas were impressive. He kept his distance though from the Perelman outline of a proof, trying to find instead a route to a proof using his own methods rather than Perelman’s Alexandrov space techniques. As far as I know though, this wasn’t ever successful and the Perelman outline was ultimately turned into a detailed and rigorously checked proof.

I often got the chance to talk to him over the years, sometimes at the daily math department tea, sometimes because he needed help since he had again spilled coffee and destroyed yet another laptop. This was always an entertaining experience, whether he was talking about mathematics, the joys of chasing women and spending time at his place in Hawaii, or politics (more right-wing than the median academic, but very anti-Trump). He enthusiastically enjoyed mathematics and life in general.

Richard shared with my four other colleagues that have recently passed away a truly generous outlook on life and other people, very much the opposite of some negative stereotypes of academics as narrow and competitive, hostile to their colleagues and institution. I’ll miss him, as I miss the others we have recently lost.

]]>Quanta magazine has just put out an impressive package of material under the title The Unraveling of Space-Time. Much of it is promoting the “Space-time is doomed” point of view that influential theorists have been pushing for decades now. A few quick comments about the articles:

- String theory is barely even mentioned.
- There is one article giving voice to an opposing point of view, that spacetime may not be doomed, an interview with Latham Boyle.
- The big problem with the supposedly now conventional view that spacetime needs to be replaced by something more fundamental that is completely different is of course: “replaced with what?”. A lot of attention is given to two general ideas. One is “holography”, the other Arkani-Hamed’s amplitudes program. But these are now very old ideas that show no signs of working as hoped.
Thirty years ago Lenny Susskind was writing about The World as a Hologram, and the idea wasn’t new then and seems to be going nowhere now. It was 17 years ago that Arkani-Hamed started re-orienting his research around the hope that new ways to compute scattering amplitudes would show new foundations for fundamental physics that would replace spacetime. Years of research since then by hundreds of theorists pursuing this have led to lots of new techniques for computing amplitudes (twistors, the amplituhedron, the associahedron, now surfaceology), but none of this shows any signs of given the hoped for new foundations that would replace spacetime.

Instead of saying any more about this, it seems a good idea to try and lay out a very different point of view which I think has a lot more evidence for it. This point of view starts by noting that our current best fundamental theory has been absurdly successful. There are questions it doesn’t answer so we’d like to do better, but the idea that this is going to happen by throwing the whole thing out and looking for something completely different seems to me completely implausible.

One lesson of the development of our best fundamental theory is that the new ideas that went into it were much the same ideas that mathematicians had been discovering as they worked at things from an independent direction. Our currently fundamental classical notion of spacetime is based on Riemannian geometry, which mathematicians first discovered decades before physicists found out the significance for physics of this geometry. If the new idea is that the idea of a “space” needs to be replaced by something deeper, mathematicians have by now a long history of investigating more and more sophisticated ways of thinking about what a “space” is. That theorists are on the road to a better replacement for “space” would be more plausible if they were going down one of the directions mathematicians have found fruitful, but I don’t see that happening at all.

To get more specific, the basic mathematical constructions that go into the Standard Model (connections, curvature, spinors, the Dirac operator, quantization) involve some of the deepest and most powerful concepts in modern mathematics. Progress should more likely come from a deeper understanding of these than from throwing them all out and starting with crude arguments about holograms, tensor networks, or some such.

To get very specific, we should be looking not at the geometry of arbitrary dimensions, but at the four dimensions that have worked so well, thinking of them in terms of the spinor geometry which is both more fundamental mathematically, and at the center of our successful theory of the world (all matter particles are described by spinors). One should take the success of the formalism of connections and curvature on principal bundles at describing fundamental forces as indicating that this is the right set of fundamental variables for describing the gravitational force. Taking spin into account, the right language for describing four-dimensional geometry is the principal bundle of spin-frames with its spin-connection and vierbein dynamical variables (one should probably think of vectors as the tensor product of more fundamental spinor variables).

What I’m suggesting here isn’t a new point of view, it has motivated a lot of work in the past (e.g. Ashtekar variables). I’m hoping that some new ideas I’m looking into about the relation between the theory in Euclidean and Minkowski signature will help overcome previous roadblocks. Whether this will work as I hope is to be seen, but I think it’s a much more plausible vision than that of any of the doomers.

]]>Today’s Washington Post has an opinion piece from Brian Greene, running under the demonstrably false title Decades later, string theory continues its march towards Einstein’s dream.

In the piece, the argument of string theory critics is given as:

Critics argue that the situation is untenable, noting, “If you can’t test a theory, it’s not scientific.” Adherents counter, “String theory is a work in progress; it’s simply too early to pass judgment.” The critics retort, “Forty years is too early?” To which the adherents respond, “We’re developing what could be the most profound physical theory of all time — you can’t seriously cross your arms, tap your foot and suggest that time’s up.”

The problem with the results of forty years of research into string theory is not that progress has been too slow but that it has been dramatically negative. To see this, one can just compare the text of chapter 9 of Greene’s 1999 *The Elegant Universe*, which has an extensive discussion of prospects for testing string theory by finding superpartners, fractionally charged particles, or cosmic strings. Twenty-five years later, the results of experimental searches are in: no cosmic strings, no fractionally charged particles, and most definitively no evidence of superpartners of any kind from the LHC.

The other sorts of predictions advertised in that chapter are based on the idea that string theorists would better understand the theory and be able to make testable predictions about neutrino masses, proton decay, axions or new long range forces, the nature of dark matter, and the value of the cosmological constant. Instead of progress towards any of these, things have gone in the opposite direction: all evidence from better understanding of string theory is that it either naturally predicts things in violent disagreement with experiment (wrong dimension of space time, huge number of new long-range forces, …) or predicts nothing at all. 25 years later, Greene now goes with the latter:

The challenge for string theory is that it has yet to produce

anydefinitive, testable predictions.

The article goes on to make a different case for string theory:

… string theory continues to captivate seasoned researchers and aspiring students alike because of the remarkable progress that has been made in developing its mathematical framework. This progress has yielded provocative insights into long-standing mysteries and introduced radically new ways of describing physical reality.

For instance, string theory has provided unmatched insights into the surface of black holes, unraveling puzzles that have consumed some of the greatest minds, including Stephen Hawking. It has offered a novel, though controversial, explanation for the observed speedup of the universe’s expansion, proposing that our universe might be just one of many within a larger reality than conventional science ever imagined.

The problem here is that these supposed advances aren’t from advances in string theory. If you follow the link above that justifies “string theory has provided unmatched insights into the surface of black holes”, you’ll find the text:

Most physicists have long assumed it would; that was the upshot of string theory, their leading candidate for a unified theory of nature. But the new calculations, though inspired by string theory, stand on their own, with nary a string in sight. Information gets out through the workings of gravity itself — just ordinary gravity with a single layer of quantum effects.

The string theory “explanation” for the value of the CC is just the “anthropic” explanation, which besides not really being a scientific explanation, has nothing to do with string theory.

The piece ends with something highly speculative and ill-defined (ER=EPR) that has nothing to do with string theory:

Roughly, it’s as if particles are tiny black holes, and the entanglement between two of them is nothing but a connecting wormhole.

If this realization holds up, we will need to shift our thinking about the unification of physics. We have long sought to bring general relativity and quantum mechanics together through a shotgun wedding, fusing the mathematics of the large and the small to yield a formalism that embraces both. But the duality between Einstein’s two 1935 papers would suggest that quantum mechanics and general relativity are already deeply connected — no need for them to marry — so our challenge will be to fully grasp their intrinsic relationship.

Which would mean that Einstein, without realizing it, may have had the key to unification nearly a century ago.

Where string theory research is after 40 years is not on a continuing march forward towards “Einstein’s dream”, but in a state of intellectual collapse with no prospects of any connection to the real world, just more hype about vague hopes for something different, something for which there is no actual theory.

]]>A few weeks ago I recorded a podcast with Robinson Erhardt, which has now appeared as String Theory and the Crisis in Physics. We mainly talk about the current situation of string theory in physics and the history of how things have gotten to this point, topics familiar to readers of this blog.

Some other items:

- A Frequently Asked Question from students is for a good place to learn about the geometry used in gauge theory, i.e. the theory of connections and curvature for principal and vector bundles. Applied to the case of the frame bundle, this also gives a way of understanding the geometry of general relativity. One reference I’m aware of is
*Gauge Fields, Knots and Gravity*, by John Baez and Javier P. Muniain, but I’d love to hear other suggestions. These could be more mathematical, but in a form physicists have a fighting chance at reading, or more from the physics point of view. - For new material from mathematicians lecturing about quantum field theory, see Pavel Etingof’s course notes, and Graeme Segal’s four lectures at the ICMS (available in this youtube playlist).
- If you want to understand the mindset of the young string theory true believer these days, stringking42069 is back.
- There’s something called “Plectics Laboratories” which has been hosting mainly historical talks from leading physicists and mathematicians. For past talks, see their youtube channel. For a series upcoming September 23-27, see here.
- The IAS is hosting an ongoing Workshop on Quantum Information and Physics. One topic is prospects for future wormhole publicity stunts based on quantum computer calculations, see here. At the end of the talk, Maldacena raises the publicity stunt question (he calls it a “philosophical question”) of whether you can get away with claiming that you have created a black hole when you do a quantum computer simulation of one of the models he discussed.
- Ananyo Bhattacharya at Nautilus has an article on the role of physics in creating new math. While there is a lot there to point to, recent years have not seen the same kind of breakthroughs Witten and Atiyah were involved in during the 1980s and 90s. I’m hoping for some progress the other way, that new ideas from mathematics will somehow help fundamental theoretical physics out of its doldrums.

I recently did another podcast with Curt Jaimungal, on the topic of unification, which is now available here. As part of this I prepared some slides, which are available here.

The main goal of the slides is to explain the failure of the general paradigm of unification that we have now lived with for 50 years, which involves adding a large number of extra degrees of freedom to the Standard Model. All examples of this paradigm fail due to two factors:

- The lack of any experimental evidence for these new degrees of freedom.
- Whatever you get from new symmetries carried by the extra degrees of freedom is lost by the fact that you have to introduce new ad hoc structure to explain why you don’t see them.

There’s also a bit about the new ideas I’ve been working on, but that’s a separate topic. Over the summer I’ve been making some progress on this, still in the middle of trying to understand exactly what is going on and write it up in a readable way. I’ll try and write one or more blog entries giving some more details of this in the near future.

]]>Ted Jacobson has put on the arXiv a transcription of a 1947 Feynman letter about his efforts to better understand the Dirac equation, in order to find a path integral formulation of it. The letter also contains some fascinating comments by Feynman about mathematics and its relation to “understanding”. In particular I like this one:

the terrifying power of math. to make us say things which we don’t understand but are true.

In some other places in the text he elaborates:

The power of mathematics is terrifying – and too many physicists finding they have the correct equations without understanding them have been so terrified they give up trying to understand them. I want to go back & try to understand them. What do I mean by understanding? Nothing deep or accurate — just to be able to see some of the qualitative consequences of the equations by some method other than solving them in detail.

The Dirac equation is something wondrous and mystifying. If one tries, like Feynman, to find a simple understanding of it in conventional geometric terms, one is doomed to failure. It is expressing something about not the conventional geometry of vectors, but the deeper and much more poorly understood geometry of spinors.

In terms of Feynman’s goal of finding a path integral formulation, the best answer to this problem I know of is the supersymmetric path integral. For one place to read about this, see David Tong’s notes, in particular section 3.3.1. In this paper, Atiyah gives a closely related interpretation of the Dirac operator in terms of an integral over the loop space of a manifold, using a formal argument in terms of differential forms on the loop space. I don’t think either of these though are what Feynman was looking for.

In any case, what one really cares about is not a single-particle theory, but the quantum field theory of fields satisfying the Dirac equation. Here there’s a standard apparatus of how to calculate given in every quantum field theory textbook. These standard calculations involving Dirac gamma-matrices fit well with Feynman’s “physicists finding they have the correct equations without understanding them have been so terrified they give up trying to understand them”.

]]>Brian Greene’s The Elegant Universe is being reissued today, in a 25th anniversary edition. It’s the same text as the original, with the addition of a 5 page preface and a 36 page epilogue.

The initial excitement among some theorists in late 1984 and 1985 that string theory would provide a successful unified theory had died down by the early 1990s, as it had become clear that this was not working out. This didn’t stop the theory from continuing to be sold to the public in hype-heavy books such as Michio Kaku’s 1995 Hyperspace. Interest in string theory among theorists was revived in the mid-nineties by the advent of branes/dualities/M-theory. The publication of the *The Elegant Universe* in 1999 brought to the public the same hyped story about unification, together with the news of the new “M-theory”. The book was wildly successful, selling something like 2 million copies worldwide. A 3-hour PBS special based on the book reached an even larger audience.

From the beginning in 1984 I was dubious about string theory unification, and by the late 1990s could not understand why this was dominating physics departments and popular science outlets, with no acknowledgement of the serious problems and failures of the theory. From talking privately to physicists, it became clear that the field of particle theory had for quite a while become disturbingly tribal. There was a string theory tribe, seeing itself as embattled and fighting less intelligent other tribes for scarce resources. Those within the tribe wouldn’t say anything publicly critical of the theory, since that would not only hurt their own interests, but possibly get them kicked out of the tribe. Those outside the tribe also were very leery of saying anything, partly because they felt they lacked the expertise to do so, partly because they feared retribution from powerful figures in the string theory tribe.

At some point I decided that someone should do something about this, and if no one else was going to say anything, maybe I needed to be the one to do so. My unusual position in a math department pretty well insulated me from the pressures that kept others quiet. I’ve told the story of the article I wrote starting at the end of 2000 here. It was put on the arXiv in early 2021 and ultimately published in American Scientist. Looking at it again after all these years, I think the argument made there stands up extremely well. While there was no direct reference to the Greene and Kaku books, there was:

String theorists often attempt to make an aesthetic argument, a claim that the theory is strikingly “elegant” or “beautiful”. Since there is no well-deﬁned theory, it’s hard to know what to make of these claims, and one is reminded of another quote from Pauli. Annoyed by Heisenberg’s claims that modulo some details he had a wonderful uniﬁed theory (he didn’t), Pauli sent his friends a postcard containing a blank rectangle and the text “This is to show the world I can paint like Titian. Only technical details are missing.” Since no one knows what “M-theory” is, its beauty is that of Pauli’s painting. Even if a consistent M-theory can be found, it may very well be a theory of great complexity and ugliness.

The subject of string theory and the state of fundamental physics was complicated and interesting enough that I thought it deserved a book length treatment, which I started writing in 2002 (the story of that is here). The book I wrote was not a direct response to T*he Elegant Universe*, but was an alternative take on the history and current state of the subject, trying to provide a different and more fact-based point of view.

During this time, Kaku came out with his own M-theory book, Parallel Worlds, published in 2004. Also in 2004, Greene published a follow-up to T*he Elegant Universe*, entitled *The Fabric of the Cosmos*, which was the basis several years later of a four-hour Nova special.

Over the last twenty-years there’s been no let up, with Kaku’s latest The God Equation, yet another hype-filled rehash of the usual string theory material. Greene regularly uses his World Science Foundation to do more string theory promotion, most recently putting out “The State of String Theory”, where we learn the subject deserves an A+++.

In recent years I’ve often heard from string theorists who feel that their research is getting a bad name because of the nature of the Greene/Kaku material. They see this hype as something that happened long ago, back before they got into the subject, so ask why they should be held accountable for it. When asked why they won’t do anything about the ongoing hype problem, it becomes clear that string theory tribalism is still a potent force.

Turning to the new material in this new edition of the book, much of it is the usual over-the-top hype, although often in a rather defensive mode:

the past twenty-five years have been such an astonishingly productive period that exploring progress fully could easily fill an entire book on its own… The fact is, the past twenty-five years have been jam-packed with discoveries in which string theorists have scaled towering problems and dug deeply into long-standing mysteries… the decades of rich development in string theory carried out by some of the most creative, skeptical and discerning minds on the planet is the most readily apparent measure of the field’s vitality. Scientists vote with their most precious commodity — their time. By that measure, and correspondingly, the measure of vibrant new ideas that have opened stunning vistas of discovery, string theory continues to be a source of inspiration, insight, and rapid progress.

While some scientists have left the field

others, indeed so many others that string theory has been berated by for attracting too many of the highest-caliber scientists, have found that the pace of new theoretical discoveries and novel physical insights is so rapid and thrilling that they are propelled onward with vigor and excitement.

The epilogue mostly deals with three topics. The first is the failure to find SUSY at the LHC, which Greene explains is perfectly compatible with string theory, and that, even before the LHC turned on:

there were theorists at that time who emphasized that string theory seems to favor superheavy superpartners, far too massive for the Large Hadron Collider or even any remotely realistic next-generations colliders to produce.

He acknowledges that at the present time string theory predicts nothing at all about anything, that even if we had a Planck scale collider:

We would still need to understand the theory with greater depth to make detailed comparisons between calculations and data, but in that imagined setting experiment would guide theorizing much as it has across a significant stretch of the history of physics.

The second topic is the string theory landscape and the anthropic multiverse “prediction” of the CC, with about ten pages devoted to explaining that

the dark energy has its measured value because if its value had been significantly different, we would not be here to measure it.

The final topic, taking up twelve pages, is AdS/CFT. The conclusion is that:

We now have powerful evidence that — shockingly — string theory and quantum field theory are actually different languages for expressing one and the same physics. In consequence, the experimental luster of quantum field theory casts a newfound experimental glow on string theory.

No more “what is M-theory?”, instead we’re told that the question “What is the fundamental principle underlying string theory?” gets answered by:

the new lesson seems to be that quantum mechanics already has gravity imprinted into its deep structure. The power of string theory is that its vibrating filiaments allows us to more easily see this connection.

The last section is “A Final Assessment.” No A+++, but:

In the arena of unification, both in terms of showing that gravity and quantum mechanics can be united as well as demonstrating that such a union can embrace non-gravitational forces and matter particles too, I give string theory an A. String theory surmounts the difficult mathematical hurdles that afflicted earlier work on unification and so, at least on paper, establishes that we have a framework in which the dream of unification can be realized.

In the arena of experimental or observational confirmation, I give string theory an incomplete.

One thing I was looking for in the new material was Greene’s response to the detailed criticisms of string theory that have been made by me and others such as Lee Smolin and Sabine Hossenfelder over the last 25 years. It’s there, and here it is, in full:

There is a small but vocal group of string theory detractors who, with a straight face, say things like “A long time ago you string theorists promised to have the fundamental laws of quantum gravity all wrapped up, so why aren’t you done?” or “You string theorists are now going in directions you never expected,” to which I respond, in reverse order “Well, yes, the excitement of searching into the unknown is to discover new directions” and “You must be kidding.”

As one of the “small but vocal group” I’ll just point out that this is an absurd and highly offensive straw-man argument. The arguments in quotation marks are not ones being made by string theory detractors, and the fact that he makes up this nonsense and refuses to engage with the real arguments speaks volumes.

**Note**: after tomorrow I’ll be on a short vacation for a while in San Francisco and dealing with blog comments might take longer than usual.

Two more items:

- I can’t recommend strongly enough that you watch the new Curt Jaimungal podcast with Edward Frenkel. The nominal topic is the recent proof of the geometric Langlands conjecture, but this is introductory material, with geometric Langlands and the proof to be covered in a part 2 of the conversation.
Before getting into the story of the Langlands program at a very introductory level, Frenkel covers a wide range of topics about unification in math and physics and the difference between these two subjects. While there’s a lot about mathematics, Frenkel also gives the most lucid explanation I’ve ever heard of exactly what string theory is, what its relation to mathematics is, and what its problems are as a theory of the real world. He has been intimately involved for a long time in research in this field, playing a major role in the geometric Langlands program and working together with both Langlands and Witten.

- Nordita this month is hosting a program on quantum gravity, aimed at covering a diversity of approaches. Videos of the talks are appearing here. The program includes an unusually large number of panel discussions about the state of the subject. One of these is a discussion of the Status of the string paradigm which has the unusual feature that two string theory skeptics (Damiano Anselmi and Neil Turok, who have worked on string theory) have been allowed to participate in the six member panel.
The response to the failures over the last forty years seems to be that current researchers should not be held accountable for ways in which the string theory paradigm of the past has not worked out. Things are fine now that they have moved on to the Swampland program, have realized that progress on string theory will have a 500 year time-scale, and know that string theory is better than the Standard Model since it has a finite or countable number of ground states.

Starting to write a longer, more technical posting, but for now, a few quick links:

- The film
*Particle Fever*(for more about this, see here) may get made into a musical. With a little luck they’ll skip the nonsense about the multiverse that blemished the film. - Tommaso Dorigo performs an experiment that the airline industry probably doesn’t want publicized.
- My big problem with discussions of climate change has always been that I’m not able to evaluate the science myself, so when told to “Trust the Science”, I get queasy, all too aware that in some parts of science I can evaluate, “Trust the Science” is a really bad idea. Luckily, there is someone with a track record I can trust, Sabine Hossenfelder, who has a new video about trusting scientists and climate change. She has carefully looked into this, and explains her conclusions: here you can trust the science, the problem is very real.
If you want to argue about climate change though, you’re going to have to find some place else.

Lawrence Krauss has just put up a long interview with Lenny Susskind. I was listening to it while doing something else, found myself shocked when the discussion got to the current state of string theory to find that I mostly agreed with what Susskind has to say. Here’s some of it (around 1:23):

I can tell you with absolute certainty String theory is not the theory of the real world, I can tell you that 100%…. My strong feelings are exactly that String theory is definitely not the theory of the real world.

Here he’s referring to “String theory” (with a capital S) as the superstring theory which has a known definition, at least perturbatively. He goes on to explain that he thinks it possible that some very different generalized or “string-inspired” theory might have something to do with the real world but that:

we don’t know and we don’t know if String theory will help us find those things…. We are still uncertain about whether whatever it is: “generalized”,

“boundaries pushed”, “string-inspired theories”. We don’t know and I think that’s the bottom line now.

As for the idea that we just need to understand how to break the superstring supersymmetry to get the real world:

People will say oh all you have to do is spontaneously break supersymmetry, blah blah well it’s been 25 30 40 years by now that nobody’s figured out how to do that.

On the “failure” description, he thinks String theory has not been a failure in the sense of showing gravitation and QM can coexist, but, as for particle theory:

Whether it’s been a failure in producing a theory of Elementary particles I would guess remains to be seen but String theory (with a capital S) is not the right theory.

On the wormhole publicity stunt (1:38):

Not a very good experiment… the experimental implementation of it left more than a little bit to be desired. That got much too much hype, yeah.

Krauss brings up the the string theory hype problem, with

we owe it to the public I think to be careful in what we say. I understand we get excited and it’s fine for physicists to get excited with each other but we have to be careful of what we say we can do because if we don’t it’ll come down and bite us in the butt.

Susskind’s response is:

I completely agree with that, but on the other hand there is a tension between that and the importance of keeping excited and letting the public know why we’re excited.

I’d have liked to hear Susskind’s thoughts on what should be done when a bunch of theorists write popular books hyping ideas that don’t work. Whose job is it to explain to the public that they were misled by overenthusiastic scientists? If he’s not going to do that, would he at least be publicly supportive of those who do this job?

Another question I’d have liked to ask him would be: given that he agrees that the idea of using string theory to understand particle physics hasn’t worked and we don’t know that “string-inspired” is the right direction to go, what next? If “string-inspired” is not the way to go, should we just give up on going beyond the SM? If not, how would he encourage young people to work on non-“string-inspired” ideas about unification that might take us beyond the SM?

]]>I had thought that the Wormhole Publicity Stunt could now be safely ignored, with almost everyone in the physics community agreeing that this was an embarrassing disaster that was dead and buried. Even the people at Quanta had realized that they had been misled into helping promote something that wasn’t at all what it claimed to be. The Quanta promotional video that was a big part of the publicity stunt is still on Youtube, but they’ve added this text:

UPDATE: In February 2023, an independent team of physicists presented evidence that the research described in this video did not create any wormholes, holographic or otherwise.

Today though, the World Science Festival put out a Zombie revival of the publicity stunt, under the bizarre title Did Einstein Crack the Biggest Problem in Physics…and Not Know It? It starts off with Brian Greene explaining that this may be the “Holy Grail” connecting string theory/quantum gravity to experiment, with such experiments not needing an expensive collider or space telescope, just a Google quantum computer.

Brought in for the discussion are the three architects of the publicity stunt, Daniel Jafferis, Joe Lykken, and Maria Spiropulu. At a couple points there is a mention that something might be “controversial”, but there’s zero explanation of what the “controversy” might be. After starting out with some background about wormholes and entanglement, the rest of the program is basically outrageous and misleading hype, without a hint of why anyone might be skeptical about it.

I’ve now wasted too much of my life trying to debunk bogus claims of this kind, with the wormhole nonsense just the latest and most egregious example. One learns over the years that it’s impossible to stop this kind of thing, there’s no way to kill off the Test of String Theory/Fake Physics enterprise. Even if you think something has been completely debunked, its proponents will always find some way to emerge from the grave and keep going. If anyone is aware of a source for the right kind of silver bullet to stop this, let me know.

]]>A few items of different kinds:

- The Harvard Math department website has a wonderful profile of Dick Gross.
- The second International Congress of Basic Science ended a few days ago in Beijing. A huge number of interesting talks, video and slides available here. My Columbia colleague Richard Hamilton was one of the winners of a Basic Science Lifetime Award, unclear how much wealthier this makes him and his fellow awardees.
- Alphaxiv is a new website allowing for research discussion of arXiv papers.
- The Gates Foundation evidently is no longer going to pay publishing costs for open access journals. The problem is that this kind of funding incentivizes some sorts of bad publishing practices. They refer to

unsavory publishing practices by poor actors (paper mills, questionable quality review, unchecked pricing)

- The Perimeter Institute last week had a summer school on Celestial Holography. This panel discussion explains some of what the people involved are trying to do.
- Curt Jaimungal has been planning a series of programs on
*Rethinking the Foundations of Physics*, with the topic “What is Unification?”. For the first program, featuring Neil Turok, see here. I’ll record something on Friday, part of the plan evidently is a lot of questions. If you have one, you can try leaving it as a comment and I’ll try and get some of them to Curt.

The past few years I’ve been noticing more and more claims like this one, supposedly finding a way to “connect string theory to experiment”. When you look into such claims you don’t find anything at all like a conventional experiment/theory connection of the usual scientific method, giving testable predictions and a way to move science forward. As for what you do find, for many years I tried writing about this in detail (see here and here), but that’s clearly a waste of time.

One thing that mystifies me about such claims is that I find it very hard to believe that most theorists take them seriously, always assumed that the great majority was with Nima Arkani-Hamed, who recently characterized the track record of this kind of thing as “really garbage”. But if most theorists think this is garbage, why am I seeing more and more of it? A hint of an answer comes from the paper with the supposed connection, which describes the Harvard Swampland Initiative as the place the work initiated.

I hadn’t been aware there was a Harvard Swampland Initiative, but it it is a Research Center at Harvard, running an “immersive program” in which “participants collectively navigate the Swampland”. More importantly, it has no less than ten associated postdoc positions. On the scale of different ways of having influence on a field, being able to hand out ten postdoc positions at Harvard is right up there. This goes a long way towards explaining to me what I’ve been seeing in recent years. It also makes me quite depressed: when I started my career in that department in the late seventies, the idea that fifty years later this is what it would come to is something beyond any one’s worst nightmare at the time.

]]>A few items, all involving Peter Scholze in one way or another:

- A seminar in Bonn on Scholze’s geometrization of real local Langlands is finishing up next week. This is working out details of ideas that Scholze presented at the IAS Emmy Noether lectures back in March. Until recently video of those lectures was all that was available (see here, here and here), but since April there’s also this overview of the Bonn Seminar, and now Scholze has made available a draft version of a paper on the subject.
- In three weeks there will be a conference in Bonn in honor of Faltings’ 70th birthday. Scholze’s planned talk is entitled “Are the real numbers perfectoid?”, with abstract

Rodriguez Camargo’s analytic de Rham stacks play a key role in the geometrization of “locally analytic” local Langlands both over the real and p-adic numbers. In both settings, one also uses a notion of perfectoid algebras, with the critical property being that “perfectoidization is adjoint to passing to analytic de Rham stacks”. This suggests a “global” definition of perfectoid rings. We will explain this definition, and present some partial results on the relation to the established p-adic notion.

- On the abc conjecture front, Kirti Joshi has a new document explaining his view of The status of the Scholze-Stix Report and an analysis of the Mochizuki-Scholze-Stix Controversy. To some extent what’s at issue is what was discussed by Scholze and others on my blog back in April 2020 (see here). Joshi is trying to make an argument that there is a way around the problem being discussed there, but I don’t think he has so far managed to convince others of his argument (Mochizuki refuses to even discuss with him). He ends with the following:

Meanwhile, Scholze and I are having a respectful and professional conversation (on going) as I work to clarify his questions; while I continue to wait for Mochizuki’s response to my emails.

He also clarifies that he has not yet finished a water-tight proof of abc along Mochizuki’s lines:

My position on whether or not Mochizuki has proved the abc-conjecture is still open (as my preprint [Joshi, 2024a] still remains under consideration). In other words, I’m currently neutral on the matter of the abc-conjecture. However, I continue to work on [Joshi, 2024b,a] to tie up all the loose ends.

A common theme in discussions online of the problems of fundamental theoretical physics is that the subject has gotten “lost in math”, losing touch with “physical intuition”. In such discussions, when people refer to “math” it’s hard to figure out what they mean by this. In the case of Sabine Hossenfelder’s “Lost in Math” you can read her book and get some idea of what specifically she is referring to, but usually the references to “math” don’t come with any way of finding out what the person using the term means by it. Here I’ll mostly leave “math” in quotation marks, since the interesting issue of what this means is not being addressed.

“Physical intuition” is also a term whose meaning is not so clear. Sometimes I see it used in an obviously naive way, referring to our understanding of the physical world that comes from our everyday interaction with it and the feeling this gives us for how classical mechanics, electromagnetism, thermodynamics work. Some people are quite devoted to the idea that this is the way to understand fundamental physics, sometimes taking this as far as skepticism about subjects like quantum mechanics.

Usually though, the term is not being used in this naive sense, but as meaning something more like “the sort of understanding of physical phenomena someone has who has spent a great deal of time working out many examples of how to apply physics theory, so can use this to see patterns and guess how some new example will work out”. This is contrasted to the person lacking such intuition, who will have to fall back on “math”, in this situation meaning writing down the general textbook equations and mathematically manipulating them to produce an answer appropriate for the given example, without any intuitive understanding of the result of the calculation. This is what we expect to see in students who are just learning a new subject, haven’t yet worked out enough examples to have the right intuition.

If the question though is not how to apply well understood fundamental theory to a new example, but how to come up with a better fundamental theory, I’d like to make the provocative claim that “physical intuition” is not going to be that helpful. New breakthroughs in fundamental theory have the characteristic of being unexpectedly different than earlier theory. The best way to come up with such breakthroughs is from new experimental results that conflict with the standard theory and point to a better one. But, what if you don’t have such results? It seems to me that in that case your best hope is “math”.

Here’s a list of the great breakthroughs of fundamental physics in the 20th century, with some comments on the role of “physical intuition” and “math”.

**Special relativity**: According to physical intuition, if I’m emitting a light ray and speed up, so will the the speed of the light ray. The crucial input was from experiment (Michelson-Morley), which showed that light always travels at the same speed. Finding a sensible theory of mechanics with this property was largely “math”.**General relativity**: There’s a long argument about the role of “math” here, but I think the only way to develop “physical intuition” about curved spacetime is to start by learning Riemannian geometry.**Quantum mechanics**: Here again, a crucial role was played by experimental results, those on atomic spectra. A large part of the development of the subject was applying “math” to the mysterious spectra for which there was zero “physical intuition”. Later on, a better understanding of the theory and better calculational methods involved bringing in a large amount of new “math” to physics, especially the theory of unitary representations of groups.**Yang-Mills theory**: This was pretty much pure “math”: replacing a U(1) gauge theory by an SU(2) gauge theory.- G
**ell-Mann’s eight-fold way**: Pure “math”. **The Anderson-Higgs mechanism**: The funny thing here is that Anderson did get this out of “physical intuition”, based on what he knew from superconductivity. Particle theorists ignored him (especially when it came time for a Nobel Prize), and their papers about this were often mainly “math”, more specifically argumentation about how the mathematics of gauge symmetry could give a loophole to a theorem (the Goldstone theorem).**The unified electroweak theory**: Looks to me more like “math” than “physical intuition”.**QCD and asymptotic freedom**: David Gross famously had the “physical intuition” that the effective coupling grows in the ultraviolet for all QFTs, based on experience with a wide range of examples. He set a mathematical problem for his student (Frank Wilczek), and when the “mathematics” was finally sorted out, they realized the usual physical intuition for QFTs had to be replaced by something completely different.

Making a list instead of the great disasters of 20th century theoretical physics, there’s

**Supersymmetry**: OK, this one is “math”. I suspect though that the problem here is that the “math” is not quite right, but missing some other needed new ideas.**String theory**: As we’re told in countless books and TV programs, this starts with a new “physical intuition”: instead of taking point particles as primitive objects, take the vibrational modes of a vibrating string. Developing the implications of this certainly involves a lot of “math”, but the new fundamental idea is a physical one (and it’s wrong, but that’s a different story…).

PRL has just published this paper (preprint here), with associated press release here. The press release explains that the authors have discovered how to use string theory to provide “an easier way to extract pi from calculations involved in deciphering processes like the quantum scattering of high-energy particles.”

The press release has led to stories here, here and here, as well as commentary from Sabine Hossenfelder.

As for applications of this, the press release refers to Positron Emission Tomography, while one of the stories linked above gives the more modest explanation of what this is good for:

]]>The series found by IISc researchers combines specific parameters in such a way that scientists can rapidly arrive at the value of pi, which can then be incorporated in calculations, like those involved in deciphering scattering of high-energy particles, the release said.

*The following makes no claims to originality or any physical significance on its own. For a better explanation of some of the math and the physical significance of the use of quaternions here, see this lecture by John Baez. *

*I’ve been spending a lot of time thinking about spinors and vectors in four dimensions, where I do think there is some important physical significance to the kind of issue discussed here. See chapter 10 here for something about four dimensions. A project for the rest of the semester is to write a lot more about this four-dimensional story.*

Until recently I was very fond of the following argument: in three dimensions the relation between spinors and vectors is very simple, with spinors the more fundamental objects. If one uses the double cover $SU(2)=Spin(3)$ of the rotation group $SO(3)$, the spinor (S) and vector (V) representations satisfy

$$ S\otimes S = \mathbf 1 \oplus V$$

which is just the fact well-known to physicists that if you take the tensor product of two spinor representations, you get a scalar and a vector. The spinors are more fundamental, since you can construct $V$ using $S$, but not the other way around.

I still think spinor geometry is more fundamental than geometry based on vectors. But it’s become increasingly clear to me that there is something quite subtle going on here. The spinor representation is on $S=\mathbf C^2$, but one wants the vector representation to be on $V_{\mathbf R}=\mathbf R^3$, not on its complexification $V=\mathbf C^3$, which is what one gets by taking the tensor product of spinors.

To get a $V_{\mathbf R}$ from $V$, one needs an extra piece of structure: a real conjugation on $V$. This is a map

$$\sigma:V\rightarrow V$$

which

- commutes with the $SU(2)$ action
- is antilinear

$$ \sigma(\lambda v)=\overline \lambda v$$ - satisfies $\sigma^2=\mathbf 1$

$V_{\mathbf R}$ is then the conjugation-invariant subset of $V$.

If we were interested not in usual 3d Euclidean geometry and $Spin(3)$, but in the geometry of $\mathbf R^3$ with an inner product of $(2,1)$ signature, then the rotation group would be the time-orientation preserving subgroup $SO^+(2,1)\subset SO(2,1)$, with double cover $SL(2,\mathbf R)$. In this case the usual complex conjugations on $\mathbf C^2$ and $\mathbf C^3$ provide real conjugation maps that pick out real spinor ($S_{\mathbf R}=\mathbf R^2\subset S$) and vector

$(V_{\mathbf R}=\mathbf R^3\subset V=S\otimes S)$ representations.

For the case of Euclidean geometry and $Spin(3)$, there is no possible real conjugation map $\sigma$ on $S$, and while there is a real conjugation map on $V$, it is not complex conjugation. To better understand what is going on, one can introduce the quaternions $\mathbf H$, and understand the spin representation in terms of them. The spin group $Spin(3)=SU(2)$ is the group $Sp(1)$ of unit-length quaternions and the spin representation on $S=\mathbf H$ is just the action on $s\in S$ of a unit quaternion $q$ by left multiplication

$$s\rightarrow qs$$

(we could instead define things using right multiplication).

There is an action of $\mathbf H$ on $S$ commuting with the spin representation, the right action on $S$ by elements $x\in \mathbf H$ according to

$$s\rightarrow s\overline{q}$$

(this is a right action since $\overline {q_1q_2}=\overline q_2\ \overline q_1$).

This quaternionic version of the spin representation is a complex representation of the spin group, since the right action by the quaternion $\mathbf i$ provides a complex structure on $S=\mathbf H$. While there are no real conjugation maps $\sigma$ on the spin representation $S$, there is instead a quaternionic conjugation map, meaning an anti-linear map $\tau$ commuting with the spin representation and satisfying $\tau^2=-\mathbf 1$. An example is given by right multiplication by $\mathbf j$

$$\tau (q)=q\mathbf j$$

Note that in the above we could have replaced $\mathbf i$ by any unit-length purely imaginary quaternion and $\mathbf j$ by any other unit-length purely imaginary quaternion anticommuting with the first.

In general, a representation of a group $G$ on a complex vector space $V$ is called

- A real representation if there is a real conjugation $\sigma$. In this case the group acts on the $\sigma$-invariant subspace $V_\mathbf R\subset V$ and $V$ is the complexification of $V_\mathbf R$.
- A quaternionic representation if there is a quaternionic conjugation $\tau$. In this case $\tau$ makes $V$ a quaternionic vector space, in a way that commutes with the group action.

Returning to our original situation of the relation $S\otimes S= 1 \oplus V$ between complex representations, $S$ is a quaternionic representation, with a quaternionic conjugation $\tau$. Applying $\tau$ to both terms of the tensor product the minus signs cancel and one gets a real conjugation $\sigma$ on $V$.

What’s a bit mysterious is not the above, but the fact that when we do quantum mechanics, we have to work with complex numbers, not quaternions. We then have to find a consistent way to replace quaternions by complex two by two matrices when they are rotations and and complex column vectors when they are spinors (so $S=\mathbf C^2$ rather than $\mathbf H$).

In my book on QM and representation theory I use a standard sort of choice that identifies $\mathbf i,\mathbf j,\mathbf k$ with corresponding Pauli matrices (up to a factor of $i$):

$$1\leftrightarrow \mathbf 1=\begin{pmatrix}1&0\\0&1\end{pmatrix},\ \ \mathbf i\leftrightarrow -i\sigma_1=\begin{pmatrix}0&-i\\ -i&0\end{pmatrix},\ \ \mathbf j\leftrightarrow -i\sigma_2=\begin{pmatrix}0&-1\\ 1&0\end{pmatrix}$$

$$\mathbf k\leftrightarrow -i\sigma_3=\begin{pmatrix}-i&0\\ 0&i\end{pmatrix}$$

or equivalently identifies

$$q=q_0 +q_1\mathbf i +q_2\mathbf j + q_3\mathbf k \leftrightarrow \begin{pmatrix}q_0-iq_3&-q_2-iq_1\\q_2-iq_1 &q_0 +iq_3\end{pmatrix}$$

Note that this particular choice incorporates the physicist’s traditional convention distinguishing the $3$-direction as the one for which the spin matrix is diagonalized.

The subtle problem here is the same one discussed above. Just as the vector representation is complex with a non-obvious real conjugation, here complex matrices give not $\mathbf H$ but its complexification

$$M(2,\mathbf C)=\mathbf H\otimes_{\mathbf R}\mathbf C$$

The real conjugation is not complex conjugation, but the non-obvious map

$$\sigma (\begin{pmatrix}\alpha&\beta \\ \gamma & \delta\end{pmatrix})= \begin{pmatrix}\overline\delta &-\overline\gamma \\ -\overline\beta & \overline\alpha \end{pmatrix}$$

Among mathematicians (see for example Keith Conrad’s Quaternion Algebras), a standard way to consistently identify $\mathbf H$ with a subset of complex matrices as well as with $\mathbf C^2$, (giving the spinor representation) is the following:

- Identify $\mathbf C\subset \mathbf H$ as

$$z=x+iy\in \mathbf C \leftrightarrow x+\mathbf i y \in \mathbf H$$ - Identify $\mathbf H$ as a complex vector space with $\mathbf C^2$ by

$$q=z +\mathbf j w \leftrightarrow \begin{pmatrix}z\\ w\end{pmatrix}$$

Note that one needs to be careful about the order of multiplication when writing quaternions this way (where multiplication by a complex number is on the right), since

$$z+w\mathbf j= z+\mathbf j\overline w$$ - Identify $\mathbf H$ as a subset of $M(2,\mathbf C)$ by

$$q=z +\mathbf jw \leftrightarrow \begin{pmatrix}z&-\overline{w}\\ w& \overline z\end{pmatrix}$$

This is determined by requiring that multiplication of quaternions in the spinor story correspond correctly to multiplication of an element of $\mathbf C^2$ by a matrix.

With this identification

$$\mathbf i\leftrightarrow \begin{pmatrix}i&0\\ 0&-i\end{pmatrix},\ \ \mathbf j\leftrightarrow \begin{pmatrix}0&-1\\ 1&0\end{pmatrix},\ \ \mathbf k\leftrightarrow \begin{pmatrix} 0&-i\\ -i&0\end{pmatrix}$$

This is a bit different than the Pauli matrix version above, but shares the same real conjugation map identifying $\mathbf H$ as a subset of $M(2,\mathbf C)$.

There’s been very little blogging here the past month or so. For part of the time I was on vacation, but another reason is that there just hasn’t been very much to write about. Today I thought I’d start looking at the talks from this week’s Strings 2024 conference.

The weird thing about this version of Strings 20XX is that it’s a complete reversal of the trend of recent years to have few if any talks about strings at the Strings conference. I started off looking at the first talk, which was about something never talked about at these conferences in recent years: how to compactify string theory and get real world physics. It starts off with some amusing self-awareness, noting that this subject was several years old (and not going anywhere…) before the speaker was even born. It rapidly though becomes unfunny and depressing, with slides and slides full of endless complicated constructions, with no mention of the fact that these don’t look anything like the real world, recalling Nima Arkani Hamed’s recent quote:

“String theory is spectacular. Many string theorists are wonderful. But the track record for qualitatively correct statements about the universe is really garbage”

The next day started off with Maldacena on the BFSS conjecture. This was a perfectly nice talk about an idea from 25-30 years ago about what M-theory might be that never worked out as hoped.

Coming up tomorrow is Jared Kaplan explaining:

why it’s plausible that AI systems will be better than humans at theoretical physics research by the end of the decade.

I’m generally of the opinion that AI won’t be able to do really creative work in a subject like this, but have to agree that likely it will soon be able to do the kind of thing the Strings 2024 speakers are talking about better than they can.

The conference will end on Friday with Strominger and Ooguri on *The Future of String Theory*. As at all string theory conferences, they surely will explain how string theorists deserve an A+++, great progress is being made, the future is bright, etc. They have put together a list of 100 open questions. Number 83 asks what will happen now that the founders of string theory are retiring and dying off, suggesting that AI is the answer:

train an LLM with the very best papers written by the founding members, so that it can continue to set the trend of the community.

That’s all I can stand of this kind of thing for now without getting hopelessly depressed about the future. I’ll try in coming weeks to write more about very different topics, and stop wasting time on the sad state of affairs of a field that long ago entered intellectual collapse.

]]>I had thought that the universally negative reaction to the fall 2022 wormhole publicity stunt meant that we’d never hear more about this, with even the editors of Quanta magazine having understood that they’d been had. While away on vacation though, I learned from Dulwich Quantum Computing that all the authors of the original stunt are back, now claiming not just wormhole teleportation, but Long-range wormhole teleportation.

I’d also thought that no one at this point could possibly think it was a good idea to help these authors go to the public with their claims about creating wormholes in a lab. It seems though that this coming weekend if you’re here in NYC you can buy tickets to listen to some of them explain in person

]]>the mind-bending speculation that we may be able to create wormholes—tunnels through spacetime—in the laboratory.