Notes on the Twistor P1

Posted on January 29, 2022 by woit

I’ve just finished writing up some notes on what the twistor $P^1$ is and the various ways it shows up in mathematics.  The notes are available here, and may or may not get expanded at some point.  The rest of the blog posting will give some background about this.

One of the major themes of modern mathematics has been the bringing together of geometry and number theory as arithmetic geometry, together with further unification with representation theory in the Langlands program. I’ve always been fascinated by the relations between these subjects and fundamental physics, with quantum theory closely related to representation theory, and gauge theory based on the geometry of bundles and connections that also features prominently in this story.

The Langlands program comes in global and local versions, with the local versions at each point in principle fitting together in the global version. In the simplest arithmetic context, the points are the prime numbers p, together with an “infinite prime”. A major development of the past few years has been the recent proof by Fargues and Scholze that the arithmetic local Langlands conjecture at a point can be formulated in terms of the geometric Langlands conjecture on the Fargues-Fontaine curve.

Back in 2015 Laurent Fargues gave a talk at Columbia on “p-adic twistors”. I attended the talk, and wrote about it here, but didn’t understand much of it. The appearance of “twistors” was intriguing, although they didn’t seem to have much to do with Penrose’s twistor geometry that had always fascinated me. What I did get from the Fargues talk was that the analog at the infinite prime of the Fargues-Fontaine curve (which I couldn’t understand) was something called the twistor $P^1$, which I could understand. The relation to the Langlands program was a mystery to me. Some years later I did talk about this a little with David Ben-Zvi, who explained to me that his work with David Nadler (see for instance here) relating geometric Langlands with the representation theory of real Lie groups involved a similar relation between local Langlands at the infinite prime and geometric Langlands on the twistor $P^1$.

Over the past couple years I’ve gotten much more deeply involved in twistor theory, working on some ideas about how to get unification out of the Euclidean version of it. I’ve also been fascinated by the Fargues-Scholze work, while understanding very little of it. Back in October Peter Scholze wrote to me to tell me he had taken a look at my Brown lecture and was interested in twistors, due to the fact that the twistor $P^1$ was the infinite prime analog of the Fargues-Fontaine curve. He remarked that it’s rather mysterious why the twistor $P^1$ is what is showing up here as the geometrical object governing what is happening at the infinite prime. I was very forcefully struck by seeing that this object was exactly the same object that describes a space-time point in twistor theory and I mentioned this at the end of my talk in Paris back in late October.

Scholze’s comments inspired me to take a much closer look at the twistor $P^1$, beginning by trying to understand a bunch of things that were somehow related, but that I had never really understood. These ranged from Carlos Simpson’s approach to Hodge theory via the twistor $P^1$ to some basic facts about local class field theory, where one gets a simple analog for each prime p of the twistor $P^1$ and the quaternions. Along the way, I finally much better understood something else in number theory that had always fascinated me, see the story explained very sketchily in section 6.2. That the quantum mechanical formalism for a four-dimensional configuration space beautifully generalizes to all primes, with the global picture including an explanation of quadratic reciprocity is not something I’ve seen elsewhere in attempts to bring p-adic numbers into physics. I’d be very curious to hear if someone else knows of somewhere this has been discussed.

Anyway, these new notes are partly for my own benefit, to put what I’ve understood in one place, but I hope others will find something interesting in them. Now I want to get back to thinking about the open questions raised by the twistor unification ideas that I was working on before the last few months. A big question there is to understand what twistor unification might have to do with Witten’s ideas relating geometric Langlands with 4d QFT. Perhaps something I’ve learned by writing these notes will be helpful in that context.

Update: I’ve posted the notes, with an added abstract and a final section of speculations, to the arXiv, see here.

Posted in Euclidean Twistor Unification, Langlands | 8 Comments

This Week’s Hype

Posted on January 21, 2022 by woit

For many years, editions here of This Week’s Hype were mainly devoted to bogus claims that someone had found a way to get a testable prediction out of string theory or other “evidence for string theory”. Recently there have been many fewer such claims, with consensus in the string theory community that there is now no hope to get a prediction from string theory about observable physics at accessible energies. One can watch the recent talks here on Steven Weinberg and his legacy to get a good idea of what this current consensus looks like: you can’t test string theory since string effects occur at much too high an energy scale, and Weinberg showed that such things will just look like the Standard Model sort of QFT at observable energies. In addition, Weinberg is also credited with the anthropic CC argument, taken as evidence for the otherwise unobservable string theory landscape. Taken together, the consensus of leading particle theorists has become that there’s no point to trying to do any better than the Standard Model, with the only answer available to anyone who asks questions about higher energies is “string theory, whatever that is”.

With particle physics abandoned, theorists have focused on quantum gravity as the only legitimate issue to study. For many decades the hope was that a consistent answer to the unknown question of what string theory really is (often called “M-theory”) would be found, and that would provide a final end to the subject of fundamental physics. This final theory would be untestable, but it would self-consistently explain why one could not hope to test it. In recent years though, after decades of no progress towards a consistent M-theory, string theorists have essentially given up on this hope.

This situation has lead to a recent trend in string theory research: instead of looking for positive evidence for string theory, try to find an argument that resistance is hopeless, string theory is the only theory possible. The arguments of this kind I’ve seen make no sense to me, but they are gaining in influence. One place I noticed this is in this recent white paper about the interesting topic of celestial holography, which has little to do with string theory. There the authors write:

A crowning achievement for the celestial holography program would be for it to determine concretely whether string theories are the only consistent theories of (asymptotically flat) quantum gravity.

Today Quanta magazine has more of this sort of thing, with an article whose title shows up on the web as A Correction to Einstein Hints At Evidence for String Theory. The sub-headline tells us that

In a quest to map out a quantum theory of gravity, researchers have used logical rules to calculate how much Einstein’s theory must change. The result matches string theory perfectly.

which sounds pretty impressive. The article starts off with quotes such as:

The hope is that you could prove the inevitability of string theory using these [bootstrap] methods,” said David Simmons-Duffin, a theoretical physicist at the California Institute of Technology. “And I think this is a great first step towards that.

and

Irene Valenzuela, a theoretical physicist at the Institute for Theoretical Physics at the Autonomous University of Madrid, agreed. “One of the questions is if string theory is the unique theory of quantum gravity or not,” she said. “This goes along the lines that string theory is unique.”

The paper at issue is this one which appeared on the arXiv nearly a year ago. It’s not about string theory or about conventional quantum gravity in four space-time dimensions. The topic is graviton scattering in maximally supersymmetric theories in ten flat space-time dimensions, and the argument is that the basic principles of supersymmetry, Lorentz invariance, analyticity and unitarity imply a bound on the coefficient of the lowest order correction term. The only relation to string theory is that a string theory calculation of this correction coefficient satisfies the bound (as expected, since string theory is supposed to satisfy the assumed basic principles). Much is made of the fact that in string theory one can get any value of the coefficient consistent with the bound. This is taken as evidence for the “inevitability” of string theory, but I don’t see this at all. It’s more accurately evidence for the usual problem with string theory: it’s consistent with anything. If the authors of this paper had found that the string theory bound was different than their bound, they could have written a paper arguing that they had finally found a way to falsify string theory (measure the coefficient, if it was found to be in the region allowed by general principles but not by string theory, string theory would be falsified).

The article does get right the motivations behind these claims:

Some physicists hope to see string theory win hearts and minds by default, by being the only microscopic description of gravity that’s logically consistent. If researchers can prove “string universality,” as this is sometimes called — a monopoly of string theories among viable fundamental theories of nature — we’ll have no choice but to believe in hidden dimensions and an inaudible orchestra of strings.

To string theory sympathizers, the new bootstrap calculation opens a route to eventually proving string universality, and it gets the journey off to a rip-roaring start.

and it gives a little space to skeptics:

Other researchers disagree with those implications. Astrid Eichhorn, a theoretical physicist at the University of Southern Denmark and the University of Heidelberg who specializes in a non-stringy approach called asymptotically safe quantum gravity, told me, “I would consider the relevant setting to collect evidence for or against a given quantum theory of gravity to be four-dimensional and non-supersymmetric” universes, since this “best describes our world, at least so far.”

Eichhorn pointed out that there might be unitary, Lorentz-invariant descriptions of gravitons in 4D that don’t make any sense in 10D. “Simply by this choice of setting one might have ruled out alternative quantum gravity approaches” that are viable, she said.

Another critique, though, is that even if string theory saturates the range of allowed α values in the 10-dimensional setting the researchers probed, that doesn’t stop other theories from lying in the permitted range. “I don’t see any practical way we’re going to conclude that string theory is the only answer,” said Andrew Tolley of Imperial College London.

I don’t at all understand why Quanta chose to cover this. All it does is help to spread hype and further the cause of the “resistance is futile” campaign from proponents of a failed research program.

Update: This kind of hyped story turns into the expected PR result:

Evidence for String Theory –In a quest to map out a quantum theory of gravity, researchers have used logical rules to calculate how much Einstein’s theory must change. The result matches string theory perfectly, reports Natalie Wolchover for Quanta.

Posted in This Week's Hype | 30 Comments

Yet More Math and Physics Items

Posted on January 14, 2022 by woit

Various items that may be of interest:

Update: A very recent relevant paper from Joshi is this. It contains a detailed comparison of his point of view with Mochizuki’s, but avoids taking any position on the controversial Corollary 3.12 claimed by Mochizuki.

Update: To clarify the above. In this paper (Theorem 10.1.1) Joshi proves his version of Mochizuki’s Corollary 3.12. But importantly (in that paper): Along with Theorem 10.1.1, there is a discussion of why Joshi’s version of Corollary 3.12 is different from Mochizuki’s version and notably why his version does not imply Mochizuki’s version (according to Joshi, the two versions work with two different ambient sets to compute the theta-values locus–Joshi’s version uses a natural ambient set his theory provides–and it is deeply tied to Fargues-Fontaine Theory).

Posted in Uncategorized | 11 Comments

Igor and Grichka Bogdanoff 1949-2021/22

Posted on January 4, 2022 by woit

A few days ago I heard news from Paris of the death of Grichka Bogdanoff on Dec. 28, and this morning heard of the death yesterday of his twin brother Igor. There are many news stories online (e.g. here), and Lubos Motl has written about them here.

There’s a chapter in my book Not Even Wrong about “The Bogdanov Affair”, and quite a few blog postings here referred to the twins and their activities related to theoretical physics. The motivations for writing about them were always two-fold. That they had managed to get more or less nonsensical papers published in reputable physics journals in 2001-2 (Annals of Physics and Classical and Quantum Gravity) raised important questions about how one evaluates speculative theoretical physics research. But also, the whole story had many comic aspects (see for instance here). I always supposed that to some extent the brothers were in on the joke and I hope that was true. At one point they invited me to come see them when I was in Paris, but I decided not to take them up on the offer, since it seemed best to keep one’s distance from whatever they were doing. In recent years I hadn’t been following at all their activities.

There’s a darkly comedic aspect to this and other examples of prominent people opposed to COVID vaccinations succumbing themselves to the disease. I’m sorry that this happened to the brothers, putting a final all too avoidable tragedy at the end of their remarkable life stories.

Posted in Obituaries | 21 Comments

Witten Goes Anthropic

Posted on December 22, 2021 by woit

Multiverse mania started seriously among string theorists around 2003, with a defining event Susskind’s February 2003 The Anthropic Landscape of String Theory. At the time I was finishing up writing what became the book “Not Even Wrong”, and my reaction to Susskind’s paper was pretty much “This is great! Susskind’s argument implies that string theory can’t ever be used to predict anything. If people accept that, they’ll have to give up on string theory since it has come to the end of the line.” Over the next year or two it became clear that devotion to multiverse mania wasn’t just localized at Stanford (where Andrei Linde had always been pushing this, even before the string theorists climbed aboard). Other proponents of the string theory landscape were up and down the California coast, including Raphael Bousso at Berkeley and Joe Polchinski at UCSB. One West Coast holdout was David Gross, who that summer at Strings 2003 quoted Churchill’s words to his country during the Nazi bombardment of London: “Never, never, never, never, never give up”. On the East Coast, the center of the resistance was at the IAS in Princeton, where several people told me that Witten was privately strongly making the case that this was not physics.

I ended up adding an additional chapter to the book about this, and covering developments closely here on the blog. For many years I found it impossible to believe that this pseudo-scientific point of view would get any traction among most leaders of the particle theory community. How could some of the smartest scientists in the world decide that this was anything other than an obviously empty idea? After a while though, it became clear that this was getting traction and that there was a very real danger that particle theory would come to an end as a science, with most influential theorists giving up, justifying doing so by claiming they now had a solid argument for why there was no point in trying to go further. String theory is the answer, but the answer is inherently unpredictive and untestable.

It has become clear recently that we’ve now reached that end-point. From the new video of his discussion with Rovelli, it’s clear that David Gross has given up. No more complaints about the multiverse from him, and his vision of the future has string theory solving QCD 80 years from now, nothing about it ever telling us anything about where the Standard Model comes from. Today brought an extremely depressing piece of news in the form of a CERN Courier interview with Witten. Witten has also given up, dropping his complaints about the string theory landscape:

Reluctantly, I think we have to take seriously the anthropic alternative, according to which we live in a universe that has a “landscape”of possibilities, which are realised in different regions of space or maybe in different portions of the quantum mechanical wavefunction, and we inevitably live where we can. I have no idea if this interpretation is correct, but it provides a yardstick against which to measure other proposals. Twenty years ago, I used to find the anthropic interpretation of the universe upsetting, in part because of the difficulty it might present in understanding physics. Over the years I have mellowed. I suppose I reluctantly came to accept that the universe was not created for our convenience in understanding it.

I’ve never really understood the kind of argument he is making here, that the problem with the string theory multiverse is that it’s upsetting, but we just have to get control of our feelings. Feelings have nothing to do with it: the problem is not that the idea is upsetting, but that it’s vacuous.

The rest of the interview is also pretty depressing. At the high energy physics experimental frontier, Witten promotes “split supersymmetry”, something which does little more than try to keep on life support failed ideas about supersymmetry and “naturalness”:

There is also an intermediate possibility that I find fascinating. This is that the electroweak scale is not natural in the customary sense, but additional particles and forces that would help us understand what is going on exist at an energy not too much above LHC energies. A fascinating theory of this type is the “split supersymmetry” that has been proposed by Nima Arkani-Hamed and others.

On string theory, he follows Gross in referring to not “string theory” but “the string theory framework” and describes the situation as

We do not understand today in detail how to unify the forces and obtain the particles and interactions that we see in the real world. But we certainly do have a general idea of how it can work, and this is quite a change from where we were in 1973.

The situation with string theory unification is that it’s a failed idea, not that it’s a successful general idea just missing some details.

Finally, Merry Christmas and best wishes for the New Year. Fundamental physical theory may now be over, replaced with a pseudo-science, but at least that means that things in this subject can’t get any worse.

Posted in Multiverse Mania | 41 Comments

More Math and Physics Items

Posted on December 18, 2021 by woit

Yet more math items:

  • First of all, congratulations to my colleague Johan de Jong, recipient of the 2022 AMS Steele Prize for Mathematical Exposition. Johan’s Stacks Project is very much deserving of such recognition. It’s both huge in scale and very high in quality, with nothing else really comparable. While it has attracted many contributors, it has always been mostly a one-person effort. If you’re interested in helping, even those not so expert in the field can contribute by fixing any mistakes they might find when using this incredible resource.
  • On my currently favorite topic of the unity of math (and physics), there’s a talk by Barry Mazur, in which he begins by raising the question “What is it that unifies Mathematics?”. He goes on to turn around the question “What is the physical interpretation of the Jones polynomial?” asked by Atiyah (and answered by Witten’s Chern-Simons theory). Mazur asks:

    What is the Arithmetical-Algebraic-Geometric interpretation of the Jones polynomial?

    or of Chern-Simons theory?

    or of TQFT?

  • Mazur’s title is “Bridges between Geometry and Number Theory”. The metaphor of “bridges” to describe what unifies mathematics gets a workout in a recent Quanta article about Ana Cariani and the Langlands program entitled The Mathematician Who Delights in Building Bridges (and subtitled Ana Caraiani seeks to unify mathematics through her work on the ambitious Langlands program.)
  • At the same conference as the one with the Mazur talk, Maxim Kontsevich spoke on Geometry from the perspective of quantum mechanics and string theory. His talk was a great summary of various aspects of the problem of quantization, in both quantum mechanics and conformal field theory. There wasn’t much though about what has been going on since the early developments in conformal field theory that he discussed. Things got a bit worrisome at the end, when he announced that he can’t understand Kevin Costello these days (if he can’t, who can?), and ended with (here’s a google-aided transcript):

    You see that gauge theories and gravity appears in various interactions is it’s in nothing else in a sense, and geometric limits of various string theories or quantum field theories and what I claim that it’s in fact it’s something generally about complex systems and mathematics. You do some combinatorial problem, whatever it is you get some counting or something, and then maybe you look on asymptotic growth of the number of solutions. It could be something very simple but your arranged parameters became something more complicated and if you see something more complicated it’s kind of I think it’s unavoidable you see some physics in a very wide sense: some string theory, some membranes, whatever. Okay, thank you.

    I can’t really make much sense of this, but he seems to have some sort of vision of fundamental physics being linked with complexity, a point of view that seems increasingly common, while not leading anywhere promising.

Moving to purely physics topics:

  • Noah Miller was a student here at Columbia in one of my mathematics of QM courses. I’ve had some wonderful students in those classes, and he was one of the best. He has gone on to graduate study in physics at Harvard, and I just saw a beautiful new paper by him this week on the arXiv, From Noether’s Theorem to Bremsstrahlung: a pedagogical introduction to large gauge transformations and classical soft theorems. It’s an exposition for non-experts of some of the new ideas about gauge symmetry and physics that Strominger and collaborators have been working on, highly lucid and readable.
  • I very much recommend taking a look at the talk from earlier this year by Mikhail Shaposhnikov, Conformal symmetry: towards the link between the Fermi and the Planck scales. Shaposhnikov has done a lot of fascinating work over the years, developing in detail a point of view which hasn’t got a lot of attention, but that seems to me very compelling. He argues that the SM and GR make a perfectly consistent theory up to the Planck scale, with the “naturalness problem” disappearing when you don’t assume something like a GUT scale with new heavy particles. Watching the discussion after the talk, one sees how many people find it hard to envision such a possibility, even though all experimental evidence shows no signs of such particles. For more about what he is in mind, see the talk or some of the many papers he’s been writing about this.
  • Finally, skydivephil tells me he has managed to get David Gross and Carlo Rovelli to debate string theory vs. loop quantum gravity, with video to drop on Youtube tomorrow. I normally try to make it a policy to avoid getting into this particular debate, but this I have to see. While you’re waiting for this, you can watch an earlier pairing well worth seeing: Alan Guth and Roger Penrose debating the multiverse versus cyclic cosmology.

Update: I just watched the Gross/Rovelli debate, and thought Rovelli did a good job of making the case that string theory is a failed research program. Gross spoke uninterruptedly at length, but interrupted Rovelli constantly. I found it interesting that Gross acknowledged “supersymmetry hype” and hype back in 1984-5, while at the same time engaging in massive amounts of hype about the current state of string theory. On the time scale for progress in string theory, he says 80 years (end of the century) to understand how to use string theory to solve QCD, no time scale for getting unification out of string theory.

Gross’s main point he kept repeating is that “string theory” now means an overarching framework that includes the Standard Model, so there’s no distinction between the Standard Model and “string theory” and you can’t argue that “string theory” is a failure. This argument is so silly that it’s hard to engage with it in any sensible way, and Rovelli didn’t even try.

Update: There’s an interesting long interview with Andy Strominger here. Some of this brought back old memories, since Strominger overlapped with me a bit as an undergraduate at Harvard, although the story of that part of his life is very unusual. I hadn’t realized the extent to which from the very beginning he was focused on the problem of quantum gravity, which to some extent explains his lack of interest in particle physics extensions of the Standard Model.

One thing he makes clear is that at this point string theory has become completely disconnected from the possibility of saying something testable about the real world. The AIP interviewer kept trying to ask about that, leading to this exchange:

Zierler: So is there an experiment that you can conceive of that could disprove string theory?

Strominger: I guess I am not getting my point across.

Zierler: You’re saying that string theory is totally outside the world of experimentation.

Strominger: … So yes, I don’t think – not many string theorists will talk this way – but I don’t think that we are in my lifetime — and I’m planning to live a very long time — going to get direct experimental evidence for string theory.

On the issue of what the terms “string theory” now mean. Strominger makes it clear that from the point of view of him and many others, there’s no longer any possible critique of “string theory” as a fundamental physical theory:

For the last 30 years, everything new that we’ve discovered, as long as we can relate it to the ideas in string theory, we call it string theory. So, if we continue to call everything that we discover string theory, it’s virtually certain that– (both laugh) It’s certain that when we get to the answer, we’ll call it string theory!

Posted in Uncategorized | 16 Comments

Some Math and Physics Items

Posted on December 7, 2021 by woit

First some math news:

  • An anonymous commenter claims here that the 2026 ICM will take place in Philadelphia. I had heard that a US group was submitting a proposal, so this rumor is plausible.
  • Many mathematicians and physicists have signed an Open Letter on K-12 Mathematics pointing to problems with attempts to reform mathematics education such as the California Mathematics Framework. For more about this, see the blog entry posted here and on Scott Aaronson’s blog, and more detail here.

    While I’ve always had some sympathy for the general idea that there’s much that could be changed and improved about the US K-12 math curriculum, there’s a huge problem with all proposed changes based on the “algebra/pre-calculus/calculus sequence is too hard and not relevant to everyday life” argument. Students leaving high school without algebra and some pre-calculus are put in a position such that they’re unequipped to study calculus, and calculus is fundamental to learning physics. Without being able to learn physics, a huge range of possible fields of study and careers will be closed to them, from much of engineering through even going to medical school. Whatever change one makes to K-12 math education, it shouldn’t leave students entering college with a severely limited choice of fields they are prepared to study.

  • Davide Castelvecchi at Nature has a story about machine learning being useful in knot theory and representation theory. Given my personal prejudice that hearing endlessly about how AI and machine learning will take over everything is just depressing, I’m trying to ignore this kind of thing. But, together with stories like the success of proof assistants in solving a problem posed by Scholze, it’s harder and harder to believe what I would like to believe (that this is all a bunch of hype that should be ignored).

For some physics items:

  • Jim Baggott has an excellent article at Aeon about the “Shut up and calculate” meme, featuring a retraction by its originator, David Mermin

    In a quick follow-up discussion with me in July 2021, Mermin confessed that he now regrets his choice of words. Already by 2004 he had ‘come to hold a milder and more nuanced opinion of the Copenhagen view’. He had accepted that ‘Shut up and calculate’ was ‘not very clever. It’s snide and mindlessly dismissive.’ But he also felt that he had nothing to be ashamed of ‘other than having characterized the Copenhagen interpretation in such foolish terms’.

  • For some wisdom on the thorny issue of how to relate Euclidean and Minkowski signature metrics in gravity, see the recent IAS lecture by Graeme Segal on Wick Rotation and the Positivity of Energy in Quantum Field Theory.
  • In fundamental theoretical physics these days, it’s quantum information theory all the time, with conferences around now here, here, here, and here. I can’t figure out what the relevance of any of this is supposed to be to actual models describing reality. Best guess would be that this is supposed to “solve the black hole information loss paradox”, although in that case Sabine Hossenfelder has some apt comments here.
  • For something more inspirational, see Natalie Wolchover’s long piece at Quanta on the JWST.

Update: For more from Geordie Williamson about the math/AI story, see here. For more about the problems with the California Mathematics Framework and its co-author see here.

Posted in Uncategorized | 24 Comments

Lex Fridman Podcast

Posted on December 3, 2021 by woit

A couple months ago I recorded a podcast with Lex Fridman, it’s now available here.

A lot of Fridman’s other interviews are well worth watching or listening to, and I thought we had an interesting conversation. I can’t stand listening to or watching myself, so not sure how it turned out. But happy to answer here any questions about what we were discussing.

Posted in Uncategorized | 22 Comments

Unifying Foundations for Physics and Mathematics

Posted on November 28, 2021 by woit

During recent travels I attended two conferences (in Paris and Berkeley) and met up with quite a few people. At the Paris conference I gave an intentionally provocative talk to the philosophers of physics there, slides are here. The argument I was trying to make is essentially that more attention should be paid to evidence for a deep unity in much of modern mathematics, which at the same time is connected to our best unified theory of physics (the Standard Model and GR). Edward Frenkel has made some similar points, referring to the Langlands program and its connections to physics as a “Grand Unified Theory of Mathematics”. The specific structures underlying this unification seem to me to deserve attention as providing an important way of thinking about what’s at the “foundations” of both math and physics.

Another motivation for this talk was to make an argument against what I see as having become a widespread and standard ideology about the search for a unified theory in physics. Talking to many physicists and mathematicians interested in physics, I noticed that the conventional wisdom, shared by the establishment and contrarians alike, is that the SM and GR are likely low energy emergent theories, that some completely different sort of theory is needed to describe very short distances such as the Planck scale. Physics establishment figures tend to believe that following the path started with string theory, then AdS/CFT, lately quantum error correction or whatever, will someday lead to a dramatically different sort of theory, replacing space, time and maybe quantum mechanics. Contrarians often have their own favorite idea for a radically different starting point. For an example of this, take a look at Figures 2 and 3 of Mike Freedman’s The Universe from a Single Particle (he spoke about this in Berkeley). Figure 2 is the “establishment” picture, with AdS/CFT the fundamental theory, well-decoupled from the emergent SM + GR (since no one has any idea how to relate them). His Figure 3 shows his own proposal, even better decoupled from any connection to the SM + GR.

Given the extreme level of experimental success of the SM + GR, the obvious conjecture is that these are close to a unified theory valid at all distances. That the mathematical framework they are built on is closely connected to unifying structures in mathematics provides yet more evidence that what one is looking for is not something completely different. The odd thing about the present moment is that arguing that our well-established successful theories can provide a solid basis for further unification makes one a contrarian, with the “establishment” position that a revolution sweeping such theories aside is needed.

I hope to find time in the next few weeks to write up what’s outlined in the slides as a more detailed article of some sort. More immediately, I plan to write a blog entry and perhaps some more detailed notes about the “twistor $P^1$” mentioned at the end of the talk, explaining how it shows up in Euclidean twistor theory as well as in recent work on the Langlands program.

Posted in Uncategorized | 15 Comments

Back

Posted on November 26, 2021 by woit

I haven’t been posting here for a while, partly due to a lot of traveling, partly due to some personal time-consuming commitments, and largely due to a lack of much in the way of news that seemed worth much attention. For some examples of such news that might be of interest:

  • Due to discovery of a buckled RF finger, the LHC start-up (at 6.8 TeV/beam) has been delayed from end of next February to end of March or beginning of April. For details, see here.
  • As usual in the US for many years, no one knows what the Federal HEP physics budget for the current fiscal year is, although we’re a couple months into it. The formal US budgeting process involves a long process including an executive branch budget proposal and congressional committee hearings and debate. This however does not lead to actual budget numbers, which only emerge at the last minute, made in some way understandable to no one I’ve ever asked about this. From the latest news, the US might have a budget any day now, and then a bit later we’ll find out what the HEP budget will be.

    This year the process has involved a highly peculiar situation with the budget for US LHC contributions (prospects for large cuts, assumed to get fixed mysteriously in the last minute process). For the details of what is going on, there’s a news story here, and discussion at an HEPAP meeting here. For the first time I’m aware of, the HEPAP meeting videos are on Youtube (see links here), so one can follow the actual discussion between physicists and government officials there.

  • In non-news about the abc conjecture, the Japanese media appears to be reporting uncritically about IUT-based claims of proofs that are not accepted by the vast majority of experts in the subject. There have been a couple of workshops devoted to IUT (see here and here) recently, with those speaking about IUT almost all based at RIMS. Recently Mochizuki has posted a strange Invitation to view IUT workshop videos. To view the videos you have to apply, and promise not to use them for “non-mathematical purposes”. My guess is that one of the “non-mathematical purposes” at issue would be bloggers pointing out that nowhere in the talks does anyone discuss the fact that convincing arguments have been given by Peter Scholze and Jacob Stix that the IUT-based proof of abc is flawed and cannot possibly work. This problem is addressed with:

    Unfortunately, it has come to my attention that certain misunderstandings concerning IUT continue to persist in certain parts of the world. Perhaps the most famous misunderstanding concerns an asserted identification of “redundant copies”. This misunderstanding involves well-known, essentially elementary mathematics at the beginning graduate level concerning the general nonsense surrounding “gluings”. For instance, if one “applies” this misunderstanding to the well-known gluing construction of the projective line, then one concludes that the two copies of the affine line that appear in this gluing are “redundant’’, hence may be identified. This identification leads immediately to a contradiction, i.e., to a “proof” that the projective line cannot exist! More details may be found in the Introduction to [EssLgc] and the references given there.

    In case anyone thinks it’s plausible that Peter Scholze is making errors in elementary mathematics at the beginning graduate level, David Roberts has an explanation of what’s going on here.

On the string theory front, it’s become impossible to figure out how to have any sort of scientific debate about most of the public defenses of “string theory”. For two recent examples:

  • In an article about What We Will Never Know, David Gross rather explicitly acknowledges that prospects for testing ideas about string theory are now an issue of “faith”, with no hope of turning into science any time soon:

    There’s faith that one way or another we should be able to test these ideas… It might be very indirect—but that’s not something that’s a pressing issue.

  • For Nabil Iqbal, string theory is now to be understood at the pre-scientific level of parable. In his parable, human beings trying to understand the equations of string theory are like fish trying to understand the equations governing the behavior of water. I’m trying to think of a sensible comment about this, but I’ve got nothing.
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