All Langlands, all the time

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 P1, 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-P1), 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 Mathew has a Youtube channel of videos of talks run out of Chicago.
Posted in Langlands | 6 Comments

Richard S. Hamilton 1943-2024

I heard this morning that Richard Hamilton passed away yesterday early this morning. 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 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.

Update: Frank Calegari has some memories of Walter Neumann here.

Posted in Obituaries | 6 Comments

Is Spacetime Unraveling?

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 “Spacetime 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. 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 giving 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 concept 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.

Update: John Horgan has some commentary here, taking the point of view that discussions of “Beyond Space-time” are fine, as long as you realize what you’re doing is “ironic science” not science.

Posted in Uncategorized | 20 Comments

This Week’s Hype

Today’s Washington Post has an opinion piece from Brian Greene, running under the demonstrably false title Decades later, string theory continues its march toward 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 any definitive, 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.

Update: I recommend checking out Sabine Hossenfelder’s latest youtube piece, which is mostly devoted to the Brian Greene wormhole publicity event stunt discussed earlier here. Near the end of the video, she tells a story that explains a lot about why this kind of thing keeps going on (see here). She had been writing a regular column for Quanta Magazine, but they stopped publishing her after she wrote a column in which she argued that physicists should not be misleading the public by claiming that the “black holes” supposedly on the other side of a duality from a given quantum system were actual physical black holes.

What she was warning about in 2019 is an essential part of the wormhole publicity stunt, and of other similar continuing efforts that have been going on for years. One impetus behind this nonsense has always been clear: there’s attention to be gotten, and money to be made. Another factor though is the one Hossenfelder explains here. Press outlets devoted to science want to publish positive news about scientific advances, want nothing to do with authors who explain that this positive news is nothing but hype.

Posted in This Week's Hype | 48 Comments

Podcast About String Theory, Other Items

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.
Posted in Uncategorized | 23 Comments

Podcast on Unification

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.

Posted in Euclidean Twistor Unification | 21 Comments

The Terrifying Power of Mathematics

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”.

Posted in Uncategorized | 7 Comments

The Elegant Universe: 25th Anniversary Edition

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 2001 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 The 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 The 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.

Posted in Book Reviews | 17 Comments

Two More

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.

Posted in Langlands, Uncategorized | 13 Comments

Quick Links

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.

Posted in Uncategorized | 9 Comments