## A Few Items

Some short items and links:

• Among possible futures that I never would have dreamed of during my student days was that someday my Nobel-prize-winning undergraduate advisor would
“try to rile” my Nobel-prize-winning graduate school professor at a Bohr Centennial celebration by quoting me. I hope the quote at least was one I would agree with.
• Also on the topic of hoping I agree with what I say publicly, there’s an NHK documentary about Mochizuki and the abc conjecture that has recently been finished, was supposed to air in Japan this weekend, now delayed til next month due to more timely news from Ukraine. I did an interview with the filmmakers here in NYC last year and they talked to many other people. No idea how they’ll manage to deal with this controversial story, coming from a Japanese perspective.
• At Quanta magazine, another article about the “naturalness problem”, headlined A Deepening Crisis Forces Physicists to Rethink Structure of Nature’s Laws. This has the usual problem with such stories of assigning to the Standard Model something which is not a problem for it, but only for certain kinds of speculative attempts to go beyond it. John Baez makes this point in this tweet:

Indeed, calling it a “crisis” is odd. Nothing that we really know about physics has become false. The only thing that can come crashing down is a tower of speculations that have become conventional wisdom.

James Wells has a series of tweets here, starting off with

The incredibly successful Standard Model does not have a Naturalness problem. And if by your criteria it does, then I can be sure your definition of Naturalness is useless.

He points to a more detailed explanation of the issue in section 4 of this paper.

• My criticisms of some Quanta articles are motivated partly by the fact that the quality of the science coverage there is matched by very few other places. If you want to work there, they have a job open.
• But if you really want to cash in on gazillionaire money going into mathematics, you might want to try for some of the $20 million that crypto entrepreneur Charles Hoskinson is giving Carnegie Mellon to establish the Hoskinson Center for Formal Mathematics. Early in his career Hoskinson was in a Ph.D. program in analytic number theory, but bailed and later joined Ron Paul’s presidential campaign, and ended up in crypto since “When Bitcoin came out, it was like the spiritual successor to what Ron Paul was talking about” (see here). • Someone who is not going to be getting Hoskinson funding is Michael Harris, whose The Silicon Reckoner you should follow for an alternate take on “formal mathematics”. For the reaction to such criticism from the formalizers, you can check out this Zulip Chat archive, and then responses from Harris here. • For Grothendieck news, see here, here and here. Update: There’s a statement out today from Breakthrough Prize Laureates strongly criticizing Russia’s invasion of Ukraine. There’s also a truly appalling statement from the Breakthrough Prize Foundation itself, not in the least critical of Russia or Putin and abusing the memory of Stephen Hawking. Witten characterizes the Foundation statement as “disappointingly vapid”. Update: Milner seems to have realized that refusing to criticize Putin was not a tenable position. A new statement from the Breakthrough Prize Foundation starts off with: As the terrible war in Ukraine continues, with casualties and atrocities mounting, the Breakthrough Prize Foundation strongly condemns Russia’s invasion of Ukraine and its unprovoked and brutal assaults against the civilian population. and announces a further \$ 3 million donation:

the Foundation today pledges a further \$3 million in funding to support physicists, life scientists and mathematicians who have been forced to flee from Ukraine. We hope that this donation will help talented researchers contribute to human knowledge in such dark times. The Breakthrough Prize Foundation stands together with the Ukrainian people, its scientists and their families. Posted in Uncategorized | 32 Comments ## ICM 2022 and the Invasion of Ukraine The news this evening that Russia is sending troops into the Eastern Ukraine and in effect announcing annexation of at least part of the Ukraine carries extremely disturbing implications for the whole world. On a much more minor scale of importance, I don’t see how the IMU has any choice but to cancel this year’s ICM planned for St. Petersburg in July. Four years ago when the IMU chose St. Petersburg over Paris for the 2022 ICM I commented here on this blog: It does seem to me though that in these worrisome times, when offered the choice between the world’s most active opponent of liberal democracy and one of the great remaining healthy liberal democracies, the other choice than the one the IMU made would have been the better one… I agree that in general it’s best to keep mathematics and the ICM out of politics. A question to think about though for those who know the history of the 1930s is that of whether there was some point during the rise of Fascism that one would stop thinking it was a good idea to have the ICM in a Fascist capital. We’re not yet far along the horrific path of the 1930s, but maybe that just means that all should be thinking about what can be done to keep the world from going down that path again. I sympathize with many who felt that the decision to hold the ICM in Russia was an important way to support Russian mathematicians and a reasonable gamble that Putin would not take his country down the path he now appears to have chosen. But right now it’s looking like that gamble failed and the IMU will have to figure out what to do about its mistake. I don’t want to host a general political discussion here, especially not with the all too many people I’ve heard from who don’t have a problem with burying liberal democracy. If your comment is not about the ICM, please don’t submit it. Update : On February 10 an organization of Ukrainian mathematicians emailed the ICM invited speakers asking them to cancel their talks (and on January 31 had emailed the AMS leadership). I’m curious to know if any responded to this, and if the Russian military invasion will lead to some decisions to cancel talks. Update : According to this from @UkrainianMath, the AMS position was recently that “the AMS leadership is closely tracking the situation surrounding the ICM and believes that it is still premature to advocate a boycott”. The “premature” indicates that there is some point at which AMS leadership agrees that the ICM should be canceled. Is the situation of Russian troops occupying the Eastern Ukraine still “premature”, or will the AMS wait for them to take Kiev? Update: I noticed there’s an AMS-NSF-Simons-ICM Travel Grant program to fund ICM participation by US mathematicians. It was supposed to announce awards this month. Will this program go forward or will the grants be canceled? Update: Many Russian mathematicians likely feel the same way about this as Edward Frenkel who calls this “a catastrophe for Russian people and all Slavic people”. Update: The AMS has issued a statement urging the IMU to cancel the ICM and has suspended the AMS-NSF-Simons-ICM travel grant program Update: There’s a statement out signed by invited ICM speakers. Unfortunately it has been overtaken by events, with little more than a request that the IMU “elaborate and announce contingency plans” in case of war, something that would have made sense a month ago, but not now. Nothing yet that I’m aware of from the IMU or other mathematical societies than the AMS. Update: The French SMF has a statement calling on the IMU to not hold the ICM in Russia during 2022. In another statement, the London Mathematical Society “strongly recommends that the IMU not hold the ICM in Russia in July 2022.” Also in France, INSMI at the CNRS has this. Update: There’s a long twitter thread about this here. It includes a contribution from Ian Agol: “As a chair of the topology selection committee, I requested @ICM2022 that the opening ceremony not be presided by a head of state (presumably Putin), but they were not willing to consider this.” This makes clear the fundamental problem with deciding to hold the ICM in a country ruled by a fascist dictatorship. If you do this, you end up putting the conference under the control of the dictator, because anyone inside the country cannot oppose them. Those outside the country end up having to either go along with the dictator, or cancel the conference, and this is where the IMU is now. Update: The IMU has issued a (rather empty) statement, saying that “The Executive Committee of the IMU is now assessing the situation” Update: More statements from national math societies: Italy, Canada, Poland, Lithuania. Updates: The IMU this morning has on their website: The IMU Executive Committee is currently assessing the highly disturbing events that are taking place in Ukraine and their implications for the IMU. We will return with a statement as soon as it is available. There are new statements calling for canceling the ICM from the European Mathematical Society, the Australian Mathematical Society, the Swedish Mathematical Society and others. Update: Via @UkrainianMath, the latest from the IMU Secretary: The IMU EC has been sitting in meetings for two days now, discussing the situation and how to respond properly. I ask for your understanding that it is more difficult for a global organization to meet and discuss this issue. Of particular concern to us is how to find a possible way to carry out a General Assembly and an ICM if possible, but outside Russia. Furthermore, we do not want to cause damage to our Russian colleagues, who have spent endless hours preparing for an ICM. The IMU webpage does contain a statement that we are working on this, and until we have reached a decision, which will be very soon, this is the best we can do. Update: The IMU has announced that the ICM will take place as scheduled, but as a free fully virtual conference, not in-person in St. Petersburg. The IMU General Assembly will take place in-person, but at a different location still to be chosen, outside Russia. Update: The ICM website (icm2022.org) no longer exists, with that address redirected to the IMU site mathunion.org. There had been no activity on the @ICM2022 Twitter account since Feb. 11, but now there’s a statement from four of the Russian mathematicians who had been involved in organizing the ICM: We condemn the madness, the injustice, and the irreversibility of war that threatens the very existence of humanity. While our losses cannot be compared to the losses and the suffering of millions of people in the Ukraine, we are devastated to see all of our dreams and all of our work of many years ruined. The goals towards which we worked could not have been further from the horror that is happening and those responsible for it. Still, amid the ruins of our dreams, we feel left with an insurmountable debt that may take much longer than the life of our generation to be forgiven. D. Belyaev, A. Okounkov, J. Pevtsova, S. Smirnov Update: See here for a letter to the IMU from some mathematicians arguing against the decision to hold the ICM online. Posted in Uncategorized | 51 Comments ## Seminar talk on Euclidean Twistor Unification and the Twistor P1 Today I gave a talk via Zoom at the Algebra, Particles and Quantum Theory seminar series organized by Nichol Furey. The slides from the talk are here (I gather the talk was recorded and video might be available at some point). This talk emphasized explaining the twistor geometry, integrating some of what I’ve learned over the last few months thinking about the “twistor$P^1$” (see here). For instance, one way to think of the basic object of Euclidean twistor theory is as$\mathbf {CP}^3$, together with a different real structure (the twistor real structure) than the usual one given by conjugation of complex coordinates. One thing that struck me while writing up these slides is that the Euclidean twistor story gets a lot of mileage out of identifying$\mathbf C^2$and$\mathbf H$, together with taking as fundamental$\mathbf H^2$. It has always seemed possible that the octonions might have a role to play here; one way into that might be to think about identifying$\mathbf H^2$with$\mathbf O$in some analogous way to the$\mathbf C,\mathbf H$story. There’s nothing new here about any of the many open questions of how to use this geometrical framework to get a fully worked out dynamics that would include the Standard Model and gravity. After a detour into number theory and hyper-Kähler geometry for several months, I’m now getting back to thinking about those questions. Update: Video of the talk is now available here. Posted in Euclidean Twistor Unification | 17 Comments ## This Way to the Universe There’s a new popular book out this week by string theorist Michael Dine, This Way to the Universe, as well a a new Sean Carroll podcast interviewing him about the book and the state of particle theory research. According to Carroll, Dine represents the “insider view” of what is really going on in fundamental physics: you’re getting what basically is the closest to a consensus view of what state particle theory and fundamental physics is right now. Much of the book is a very conventional and straightforward attempt to explain modern particle theory/GR/cosmology to a general audience, featuring some explanations from Dine about specific attempts to go beyond the Standard Model that he has worked on. The last quarter or so of the book is about string theory and the multiverse. One odd thing about this is that the jacket copy is fraudulent, stating: People assume string theory can never be tested, but Dine intrepidly explores how the theory might be investigated experimentally. whereas there’s nothing like that in the book that I could find. Instead, on page 253 one finds about string theory it’s not clear it’s right, or that it even makes definite predictions at all… Many readers will know that string theory has been a lightning rod for criticism. In this chapter, we’ll understand why, on the one hand, the subject is so seductive, and on the other, its critics may have a point. On page 295 there’s In fact, the existence of states in string theory that really look similar to what we see around us is highly conjectural. This hasn’t stopped me nor my colleagues from writing many papers speculating on a stringy reality. Unfortunately, none of these papers can be said to be making a prediction from string theory. Typically the author likes one particular solution of string theory or another, and selects one feature that is distinctive and goes beyond the Standard Model. But apart from the arbitrariness of this choice, the author has closed his or her eyes to two huge problems with their proposal [the cosmological constant and, perhaps, supersymmetry breaking]. On the Carroll podcast, there’s this exchange (starting around 1:25): MD: There are people who work actively trying to… On what they would call string phenomenology, but I think that at the moment, this is a hard topic and we just don’t understand well enough how in detail the theory could be related to nature… …strings are rather simple things, but the steps from there to things that look like the standard model, that look like general relativity, are pretty elaborate, and along the way, there are steps we don’t really understand… SC: … Let me ask you how you respond to sort of the hardcore critics who might say something like this: In the 1980s, the first superstring revolution, people are going around saying like, yeah, we’re going to unify everything, we’re going to predict the mass of the electron and everything is going to be finished in 10 years. Then not only has string theory not made any predictions that you can test in an accelerator, but once we have the landscape of string theory, we’re saying that string theory is compatible with almost any set of particle physics you can have, and at that point, shouldn’t you just give up and move on to something else? It’s not a thing that’s going to give you any testable predictions at any point in the future. MD: Well, I would basically say that that, all that is fair, but at some gut level, I don’t exactly agree. So first of all, I would say that in 1985, already, in this era of the first superstring revolution, Nathan Seiberg and I pointed out what has come to be known as the Dine-Seiberg problem, a very basic and fundamental obstacle to relating string theory to nature. And people have proposed possible solutions, some of which are interesting, but really, there’s… In the subsequent nearly 40 years, people have not put forward. So I’m on safe ground, I sort of took both sides of this issue. SC: .. why not just give up if we think that string theory could predict anything at all given the landscape problem? MD: Well, I think my own attitude is to sit somewhere on the fence, not to devote huge amounts of energy to it, but to allow string theory to inform my thinking about various kinds of issues. Dine is referring here to the “Dine-Seiberg problem”, described in a 1985 paper with abstract We argue that if the superstring is to describe our world, it is probably strongly coupled. Several other (unlikely) possibilities are discussed. The paper is specifically about the effective potential for the dilaton, but the problem is generic and fundamental: you can’t get anything like the real world out of the perturbative superstring and you don’t know what strongly coupled string theory is (one can argue that AdS/CFT tells you what strongly coupled string theory is, but again, that looks nothing like the real world). The really odd thing about Dine’s current comments about testability (besides that they contradict the jacket of his book) is that 15-20 years ago he was for a while one of the theorists most prominently making the case that string theory and the landscape could be tested. I wrote about this often here on the blog, see for instance here and here. The second of these postings is about a 2007 Physics Today article by Dine entitled String theory in the era of the Large Hadron Collider that claimed: A few years ago, there seemed little hope that string theory could make definitive statements about the physics of the LHC. The development of the landscape has radically altered that situation. An optimist can hope that theorists will soon understand enough about the landscape and its statistics to say that supersymmetry or large extra dimensions or technicolor will emerge as a prediction and to specify some detailed features. The Physics Today piece was rather explicitly an answer to my criticisms of the string theory landscape as untestable pseudo-science, with a subtitle The relationship between string theory and particle experiment is more complex than the caricature presented in the popular press and weblogs. Fifteen years later, in this new book Dine says nothing about his earlier claims about testing string theory at the LHC, or that others clearly pointed out at the time what was wrong with them. He ends with this summary of the situation: … one can adopt the landscape viewpoint, but then one has to acknowledge that, at this point in time, we have nothing like a complete theoretical framework in which to make any scientific investigation, and that there are facts hard to reconcile with this viewpoint. I, for one, find this quite unsettling. His experience of the last fifteen years does not seem to have made him think any more charitably of string theory critics, who get this sneering description on page 269-70: [they] view the subject with total disdain, often wearing their ignorance of even its most rudimentary aspects as a badge of honor. One telling mistake in the book is its reference (page 117) to the “Clay Mathematics Institute of Peterborough, New Hampshire”, an indication of the all too typical theoretical physicist’s lack of knowledge of anything about mathematicians and the mathematics community. Update: There’s an interesting conversation between Dine and Lisa Randall about the book and these issues, see here. Posted in Book Reviews, Multiverse Mania | 9 Comments ## Notes on the Twistor P1 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

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

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

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

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

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