Scholze and Stix on the Mochizuki Proof

As discussed here a couple months ago, Peter Scholze and Jakob Stix believe they have found a serious problem with Mochizuki’s claimed proof of the abc conjecture, and traveled to Kyoto in March to discuss it with him. Their write-up is now available here. Mochizuki has made public his response to this, creating a web-page available here. There’s also an updated version of Ivan Fesenko’s take on the story, as well as a possibly relevant FAQ on IUTeich from Go Yamashita.

Erica Klarreich has an excellent long and detailed article about this story at Quanta.

Update: Looking through these Scholze/Stix/Mochizuki documents, my non-expert opinion is that Mochizuki does not seem to effectively address the Scholze-Stix objections, which are aimed at a very specific piece of his argument. Unfortunately, he also does his own credibility a huge amount of damage by including over-the-top attacks on the competence of Scholze and Stix, in typefaces that make him look unserious. For instance, there’s

I can only say that it is a very challenging task to document the depth of my astonishment when I first read this Remark! This Remark may be described as a breath-takingly (melo?)dramatic self-declaration, on the part of SS, of their profound ignorance of the elementary theory of heights, at the advanced undergraduate/beginning graduate level.

or the last couple pages of his report.

Posted in Uncategorized | 15 Comments

This Week’s Hype

The Stanford string theory group is not taking the attack by Harvard’s Cumrun Vafa lying down. After an arXiv barrage of papers defending KKLT (see here), they’ve now enlisted the Stanford press office, which has produced a five part promotional series about the scientific glories of the string theory landscape. The first part of the series is online today, the rest to come soon.

The great thing about having your university press office write stories like this for you is that they will just print whatever you want, unlike journalists, who might ask your critics what they think and even quote them. Even better than not having to hear from your critics, you can try and discredit them as close-minded reactionaries unethically thwarting the search for truth, by misrepresenting their arguments:

“One dominant view in the community is that believing in the Landscape might have the negative effect of leading people away from fundamental physics, so we shouldn’t even discuss it,” said Shamit Kachru, who holds the Wells Family Directorship of the Stanford Institute for Theoretical Physics (SITP).

I’ve never heard anyone argue that “we shouldn’t even discuss it”. There is a dominant view in the field that what the theorists at Stanford are doing is not science, but the arguments for this are scientific, not arguments about what is or what isn’t good PR. Will we see any of these arguments in the rest of the series?

Update: All five parts of this are now on-line. No critics of the string landscape are named and their serious arguments are ignored (they are described as “hating” the idea, creatures of their out-of-control emotions). In the context of the old arguments of the string wars, two things to note are

  • This could be accurately described as a campaign by people who are losing in the scientific marketplace of ideas to, instead of doing science, start a PR effort aimed at the public.
  • It’s once of the best examples of the kind of extreme tribalism and “group-think” Lee Smolin was pointing to that I’ve ever seen. Stanford is portrayed as uniformly of one opinion about this, other opinions are wrong and only held elsewhere. If you are (or want to be) at Stanford and have a different opinion, especially if you’re a postdoc or grad student, it’s being made very clear that you best keep this to yourself.

Update: For those who want to follow the latest on the “Swampland” challenge to the Stanford/KKLT landscape program being promoted by the Stanford press office, there’s a conference later this week in Madrid, talks here. Among the roughly 100 participants at the conference, no one from Stanford. Not invited? Invited, but refuse to participate in any scientific discussion critical of their program? Inquiring minds want to know…

Posted in Multiverse Mania, This Week's Hype | 19 Comments

Is Quantum Mechanics a Probabilistic Theory?

There is a simple question about quantum theory that has been increasingly bothering me. I keep hoping that my reading about interpretational issues will turn up a discussion of this point, but that hasn’t happened. I’m hoping someone expert in such issues can provide an answer and/or pointers to places where this question is discussed.

In the last posting I commented that I’m not sympathetic to recent attempts to “reconstruct” the foundations of quantum theory along some sort of probabilistic principles. To explain why, note that I wrote a long book about quantum mechanics, one that delved deeply into a range of topics at the fundamentals of the subject. Probability made no appearance at all, other than in comments at the beginning that it appeared when you had to come up with a “measurement theory” and relate elements of the quantum theory to expected measurement results. What happens when you make a “measurement” is clearly an extremely complex topic, involving large numbers of degrees of freedom, the phenomenon of decoherence and interaction with a very complicated environment, as well as the emergence of classical behavior in some particular limits of quantum mechanics. It has always seemed to me that the hard thing to understand is not quantum mechanics, but where classical mechanics comes from (in the sense of how it emerges from a “measurement”).

A central question of the interpretation of quantum mechanics is that of “where exactly does probability enter the theory?”. The simple question that has been bothering me is that of why one can’t just take as answer the same place as in the classical theory: in one’s lack of precise knowledge about the initial state. If you do a measurement by bringing in a “measuring apparatus”, and taking into account the environment, you don’t know exactly what your initial state is, so have to proceed probabilistically.

One event that made me think more seriously about this was watching Weinberg’s talk about QM at the SM at 50 conference. At the end of this talk Weinberg gets into a long discussion with ‘t Hooft about this issue, although I think ‘t Hooft is starting from some unconventional point of view about something underlying QM. Weinberg ends by saying that Tom Banks has made this argument to him, but that he thinks the problem is you need to independently assume the Born rule.

One difficulty here is that you need to precisely define what a “measurement” is, before you can think about “deriving” the Born rule for results of measurements, and I seem to have difficulty finding such a precise definition. What I wonder about is whether it is possible to argue that, given that your result is going to be probabilistic, and given some list of properties a “measurement” should satisfy, can you show that the Born rule is the only possibility?

So, my question for experts is whether they can point to good discussions of this topic. If this is a well-known possibility for “interpreting” QM, what is the name of this interpretation?

Update: I noticed that in 2011 Tom Banks wrote a detailed account of his views on the interpretation of quantum mechanics, posted at Sean Carroll’s blog, with an interesting discussion in the comment section. This makes somewhat clearer the views Weinberg was referring to. To clarify the question I’m asking, a better version might be: “is the source of probability in quantum mechanics the same as in classical mechanics: uncertainty in the initial state of the measurement apparatus + environment?”. I need to read Banks more carefully, together with his discussion with others, to understand if his answer to this would be “yes”, which I think is what Weinberg was saying.

Update: My naive questions here have attracted comments pointing to very interesting work I wasn’t aware of that is along the lines of what I’ve been looking for (a quantum model of what actually happens in a measurement that leads to the sort of classical outcomes expected, such that one could trace the role of probability to the characterization of the initial state and its decomposition into a system + apparatus). What I learned about was

In these last references the implications for the measurement problem are discussed in great detail, but I’m still trying to absorb the subtleties of this story.

I’d be curious to hear what experts think of Landsman’s claim that there’s a possible distinct “instability” approach to the measurement problem that may be promising.

Update: From the comments, an explanation of the current state of my confusion about this.

The state of the world is described at a fixed time by a state vector, which evolves unitarily by the Schrodinger equation. No probability here.

If I pick a suitable operator, e.g. the momentum operator, then if the state is an eigenstate, the world has a well-defined momentum, the eigenvalue. If I couple the state to an experimental apparatus designed to measure momenta, it produces a macroscopic, classically describable, readout of this number. No probability here.

If I decide I want to know the position of my state, one thing the basic formalism of QM says is “a momentum eigenstate just doesn’t have a well-defined position, that’s a meaningless question. If you look carefully at how position and momentum work, if you know the momentum, you can’t know the position”. No probability here.

If I decide that, even though my state has no position, I want to couple it to an experimental apparatus designed to measure the position (i.e. one that gives the right answer for position eigenstates), then the Born rule tells me what will happen. In this case the “position” pointer is equally likely to give any value. Probability has appeared.

So, probability appeared when I introduced a macroscopic apparatus of a special sort: one with emergent classical behavior (the pointer) specially designed to behave in a certain way when presented with position eigenstates. This makes me tempted to say that probability has no fundamental role in quantum theory, it’s a subtle feature of the emergence of classical behavior from the more fundamental quantum behavior, that will appear in certain circumstances, governed by the Born rule. Everyone tells me the Born rule itself is easily explicable (it’s the only possibility) once you assume you will only get a probabilistic answer to your question (e.g. what is the position?)

A macroscopic experimental apparatus never has a known pure state. If I want to carefully analyze such a setup, I need to describe it by quantum statistical mechanics, using a mixed state. Balian and collaborators claim that if they do this for a specific realistic model of an experimental apparatus, they get as output not the problematic superposition of states of the measurement problem, but definite outcomes, with probabilities given by the Born rule. When I try and follow their argument, I get confused, realize I am confused by the whole concept: tracking a mixed quantum state as it evolves through the apparatus, until at some point one wants to talk about what is going on in classical terms. How do you match your classical language to the mixed quantum state? The whole thing makes me appreciate Bohr and the Copenhagen interpretation (in the form “better not to try and think about this”) a lot more…

Posted in Quantum Mechanics | 74 Comments

Beyond Weird

Philip Ball’s Beyond Weird is the best popular survey I’ve seen of the contemporary state of discussions about the “interpretation” of quantum mechanics. It appeared earlier this year in a British edition (which I just read a copy of), with the US edition scheduled to come out next month. Since it’s already out in Britain, there are several reviews you can take a look at, an insightful one is Natalie Wolchover’s at Nature.

The topic of the “weirdness” of quantum mechanics is one receiving a lot of attention these days, with two other books also appearing this year: Adam Becker’s What is Real? (which I wrote about here), and Anil Ananthaswamy’s Through Two Doors at Once. Lack of time as well as not having much of interest to say about the book has kept me from writing about Through Two Doors at Once. It’s much more focused than the other two, giving close attention to the two-slit experiment and surprising variants of it that have actually been performed in recent years.

Some of what I very much liked about Beyond Weird is the way Ball avoids getting into the usual ruts that books on this topic often end up in (with the Becker book one example). He avoids the temptation to follow a historical treatment, something that is almost irresistible given the great story of the history of quantum mechanics. The problem is that the early history of quantum mechanics and the struggles of Bohr, Einstein and Heisenberg to understand what it was saying is a fascinating story, perhaps the most compelling in the history of physics, but it is one that has been well-told many times in many places. Books that cover the later history have found it hard to resist the temptation of revisionism, caricaturing Bohr, Heisenberg and the dominant “Copenhagen interpretation” while making heroes instead of David Bohm, John Bell and Hugh Everett.

Ball has little to say about the personalities involved, but instead seriously engages with the central troublesome issues of the quantum mechanical picture of the world. The Copenhagen interpretation is given a fair treatment, as a warning about the limits one runs up against trying to reconcile the quantum mechanical and classical pictures of reality.

Instead of spending a lot of time in the rut of Bohmian mechanics, Ball dismisses it quickly as

But it is hard to see where the gain lies… Even Einstein, who was certainly keen to win back objective reality from quantum theory’s apparent denial of it, found Bohm’s idea ‘too cheap.”

Dynamical collapse models like GRW also get short shrift:

It’s a bodge, really: the researchers just figured out what kind of mathematical function was needed to do this job, and grafted it on… What’s more of a problem is that there is absolutely no evidence that such an effect exists.

As for the “Many-Worlds Interpretation”, which in recent years has been promoted in many popular books, Ball devotes a full chapter to it, not because he thinks it solves any problem, but because he thinks it’s a misleading and empty idea:

My own view is that the problems with the MWI are overwhelming – not because they show it must be wrong, but because they render it incoherent. It simply cannot be articulated meaningfully… The MWI is an exuberant attempt to rescue the ‘yes/no’, albeit at the cost of admitting both of them at once. This results in an inchoate view of macroscopic reality suggests we really can’t make our macroscopic instincts the arbiter of the situation…
Where Copenhagen seems to keep insisting ‘no,no and no’, the MWI says ‘yes, yes and yes’. And in the end, if you say everything is true, you have said nothing.

There’s a lot of material about serious efforts to go beyond Copenhagen, by understanding the role that decoherence and the environment play in the emergence of classical phenomena out of the underlying quantum world. This discussion includes a good explanation of the work of Zurek and collaborators on this topic, including the concept of “Quantum Darwinism”.

The last part of the book is up to date on what seem to be some currently popular ideas about the foundations of quantum mechanics. One aspect of this goes under the name “Quantum Reconstruction”, the attempt to derive the supposedly hodge-podge axioms of quantum theory from some more compelling fundamental ideas, hopefully the kind your grandmother can understand. These ideas are conjectured to somehow have to do with “information” and limits on it. I’m not sympathetic to these, since the axioms seem to me not “hodge-podge”, but connected to the deepest unifying ideas of modern mathematics. At the same time, I remain confused about what “information” is supposed to be and how these new foundations are supposed to work. And, as far as I’ve ever been able to tell, these are not things your grandmother is likely to understand, unless your grandmother is Scott Aaronson…

Posted in Book Reviews | 14 Comments

Quick Links

A collection of links that may be of interest:

  • Talks from the SM at 50 conference held earlier this summer are available here.
  • A detailed expose of the “Fake Science Factory” is here, a related Nature story is here.
  • For those wondering what came out of this story, you might be interested in this.
  • If you want to know what happens to string theorists who leave the field, one answer is that they perform as Ninja Sex Party.
  • Burt Richter passed away last month at the age of 87, some obituaries are here, here and here. Blog postings here discussing talks or papers by him can be found with this search.
  • Terry Tao has come up with his own take on arithmetic geometry, available here.
  • A Capella Science is really too wonderful for words. For an example, check out William Rowan Hamilton. Tommaso Dorigo explains here that Tim Blais will be at CERN on Sept. 19.
  • October 10 there will be a program at the New York Academy of Science about The Mystery of our Mathematical Universe. I can’t help noticing something about discussions of the deep role of mathematics in physics: they rarely involve mathematicians.
  • I’ll do an online web interview on September 6, as part of the Festivalettura in Mantua.


Update
: Frank Wilczek has an insightful review of Lost in Math at Physics Today.

Posted in Uncategorized | 7 Comments

Quantum Supremacy

Hasn’t been much that I’ve heard about worth discussing here recently. Presumably everyone is on vacation. I’ll try and gather some things that may be of interest, starting first with the hot topic of “quantum computation”. It looks like this will be drawing an increasing amount of attention and resources in the field of physics research. For instance:

  • Slides and videos from the summer IAS program From Qubits to Spacetime are available here.
  • There will be a graduate seminar at Harvard this fall, blog post about it here.
  • In a few weeks Fermilab will host a workshop on Next steps in Quantum Science for HEP.
  • Moving through the US Congress is a National Quantum Initiative Act, which would provide over a billion dollars in funding for things related to quantum computation.
  • At the NSF MPS (Mathematics and Physical Sciences) they’re promoting NSF’s Quantum Leap. This is the first of four “Big Ideas” (discussed here) which will influence what gets funded. The other three are multi-messenger astrophysics, big data, and things related to biology.
  • Launching this week is The NSF 2026 Idea Machine, which is a competition for suggesting research questions, more “Big Ideas” for the NSF to fund. If you want to enter the competition that opens Friday, I’m guessing that invoking the word “Quantum” will help.
Posted in Uncategorized | 11 Comments

On Status of KKLT

(Warning, this is just more about the topic of the last posting, which for most people will be a good reason to stop reading now. On the other hand, if you’re obsessed with the controversy over string theory, you might find this interesting).

I finally got around to watching some more of the Simons Center Workshop on the Swampland talks, and noticed a remarkable exchange at the end of Thomas Van Riet’s talk On Status of KKLT (starting at 1:30). The first commenter (a German, Arthur Hebecker?) starts off saying “I think you are doing something that is very dangerous”, with the danger being that KKLT will get thrown out and people will think that it is a “theorem” that string theory has no dS vacua. He is interrupted by Vafa who tells him that “your statement is defamatory, let’s calm down”. The German goes on to explain to Vafa the significance of the danger he is concerned about:

Maybe for you in the US it’s fine at Harvard, for me it will be a pain because people will turn against me. The little standing that string theory and new physics at all has in Germany will be harmed by a backlash on us that we have been talking nonsense all the time, which is not true.

Van Riet after a while interjects that there is an even worse danger:

The opposite happened and actually back-reacted very badly. We had the books by Woit and Smolin and it was based on the existence of the multiverse as a correct statement, right? And that’s when the criticism of string theory took off, right?

Someone else in the audience (Iosif Bena?) comes in on the Vafa/Van Riet side of the argument, criticizing multiverse mania:

I think the main problem was that at the beginning people in the KKLT camp, they came up with, “OK string theory has the multiverse, we’re not going to do physics anymore, the anthropic principle…” They came up with all these ideas that hurt string theory much much worse, at least in Europe, at least in my part of Europe. And you know, essentially hurt us heavily… Then there were these books by Woit and Smolin that were very popular…

It’s remarkable to see publicly acknowledged by string theorists just how damaging to their subject multiverse mania has been, and rather bizarre to see that they attribute the problem to my book and Lee Smolin’s. The source of the damage is actually different books, the ones promoting the multiverse, for example this one. A large group of prominent theorists, especially many from the West Coast, including the group at Stanford and the late Joe Polchinski at Santa Barbara, used the existence of the KKLT construction to push very hard a pseudo-scientific excuse for why string theory wasn’t working out. I’ve often point this out, and I do think this has been very damaging to the public perception of string theory. But the underlying problem is the takeover of string theory by multiverse pseudo-science, not that I and Lee Smolin criticized it.

A striking fact about the Stony Brook workshop is that none of the participants were from Stanford, and none of the many prominent figures responsible for promoting KKLT were there. It looks like there is now a dramatic split going on, with Vafa leading the charge to try and fight back against what in recent years has been a seeming dominance of string theory by the pro-multiverse faction. I think such a split is long overdue, that most string theorists for years now have been making a terrible mistake by going along with multiverse pseudo-science. As Hebecker(?) explained though, fighting back publicly at this point carries its own dangers. In particular, many observers will be asking: “for years you told us about the 10500 vacua”, now you say that maybe there aren’t any. Which is it? Why can’t you tell? And do you really have a serious alternative for how to connect string theory to the real world?

Vafa tries to not take sides, to portray this as a simple technical question that will yield to further calculations by theorists. Where I disagree with him is that I’m very skeptical that this is a technical question with a well-defined answer. This is not a new controversy: theorists have been arguing about moduli stabilization and this de Sitter/no de Sitter issue for twenty years or so, without coming to any firm conclusions. If you watch the technical talks at the Stony Brook workshop, the degree of technical complexity of the arguments is striking, as is their often rather vague nature. What you don’t see is a specific set of equations that everyone agrees on. We’ll see what happens in coming months and years, there are likely to be a large number of papers written on this subject. Also to look out for, likely the efforts of Vafa and others to throw doubt on KKLT will not be taken lying down. The West Coast Empire will strike back…

Update: At CNN, Don Lincoln has an article about this, which ends with:

It’s not quite a WWE cage match, but it’s going to be fun to watch these theories fight it out.

Update: Tonight the West Coast Empire has struck back, defending here and here their dS vacua against the Swampland attack, and going on the offensive, accusing the conjecture of their attackers as being “ruled out by cosmological observations, at least at the 3 sigma level”.

Posted in Multiverse Mania, Swampland | 15 Comments

Theorists with a Swamp, not a Theory

In recent weeks string theory has been again getting a lot of press attention, because of claims that new progress is being made in the study of the relation of string theory and the real world, via the study of the “swampland”. This is a very old story, and I’ve often written about it here. I just added a new category, so anyone who wants to can go follow it by clicking on the Swampland category of posts.

Recent press coverage of this includes an article by Clara Moskowitz at Scientific American, entitled String Theory May Create Far Fewer Universes Than Thought. This motivated Avi Loeb to write his own Scientific American piece highlighting the dangers of string theory speculation unmoored to any possible experimental test, which appeared as Theoretical Physics is Pointless without Experimental Tests. Loeb reports:

There is a funny anecdote related to the content of this commentary. In my concluding remarks at the BHI conference we held at Harvard in May 2018, I recommended boarding a futuristic spacecraft directed at the nearest black hole to experimentally test the validity of string theory near the singularity. Nima Arkani-Hamed commented that he suspects I have an ulterior motive for sending string theorists into a black hole. For the video of this exchange, see

https://www.youtube.com/watch?v=WdFkbsPFQi0

Last week Natalie Wolchover reported on this controversy, with an article that appeared at Quanta magazine as Dark Energy May Be Incompatible With String Theory and at the Atlantic as The Universe as We Understand It May Be Impossible (the Atlantic headline writer misidentifies “we” as “string theorists”).

Wolchover accurately explains part of this story as a conflict between string theorists over whether certain solutions (such as the KKLT solution and the rest of the so-called “string theory landscape”) to string theory really exist. Vafa argues they may not exist, since the proposed solutions are complicated and “Usually in physics, we have simple examples of general phenomena.” In response Eva Silverstein argues:

They [Vafa and others] essentially just speculate that those things don’t exist, citing very limited and in some cases highly dubious analyses.

On Twitter, Jim Baggott explains the problem

Let’s be clear. This is not a ‘test’ of string theory. There is no ‘evidence’ here. This is yet another conjecture that ‘might be true’, on which there is no consensus in the string theory community.

and in a retweet, Will Kinney accurately notes that

The landscape is a conjecture. The “swampland” is a conjecture built on a conjecture.

and points to an earlier tweet thread of his about this. Sabine Hossenfelder replies with the comment that

The landscape itself is already a conjecture build on a conjecture, the latter being strings to begin with. So: conjecture strings, then conjecture the landscape (so you don’t have to admit the theory isn’t unique), then conjecture the swampland because it’s still not working.

The Simons Center summer workshop this year has been devoted to Recent Developments in the Swampland, videos are here (this was also the case in 2006, see here). Next month in Madrid a conference will be devoted to Vistas over the Swampland, and I’m sure many more such gatherings are planned.

Unfortunately I think the fundamental problem here somehow never gets clearly explained: String theorists don’t actually have a theory, what they have is an approximation to an unknown theory supposed to be valid in certain limits, and a list of properties they would like the unknown theory to have. If this is all you have, there’s no way to distinguish when you’re on dry land (a solution to string theory) from when you’re in the swamp (a non-solution to string theory). Different string theorists can generate different opinions, conjectures and speculations about whether some location is swamp or dry land, but in the absence of an actual theory, no one can tell who is right and who is wrong. I don’t know why Vafa back in 2005 chose “Swampland” as the metaphor for this subject, but it’s an unfortunately apt one: string theorists are stuck in a swamp, with no way of getting out since they can’t tell what’s dry land and what isn’t.

Posted in Swampland | 15 Comments

Back

Back now from vacation. On the global warming front, I can report that Northern Norway has gotten rather warm, Svalbard is still pretty cold.

While I was away the big mathematics news was from the ICM. As everyone expected, one of the Fields medalists was Peter Scholze. I was surprised to find a blog post of mine quoted about this in the NY Times, since normally the way this works is that journalists are told who the winners are in advance, and then contact experts in the field (which I’m definitely not one of) for quotes. Some tweets from Davide Castelvecchi at Nature about the unusual embargo rules may provide some explanation:

The whole situation was surreal from the beginning: the organizers gave reporters advance notice of the winners, but on condition that we would not contact them — even though the winners had already been told long in advance.

They also made no other sources available. In other words, we were supposed to write about these difficult concepts without talking to any experts.

Oh and I forgot to say: The email with the names of the winners had no information whatsoever on why they won – in other words, no prize citations.

I suspect one reason for the unusual rules is that the ICM people had decided to concentrate on getting stories out through Quanta magazine, which ran the results here. The stories are very well done, and Quanta magazine is great, but a more usual process involving the rest of the science journalism press would have been a good idea.

One other big piece of news from the ICM was the choice of St. Petersburg over Paris as the site for the 2022 ICM. I was sorry to hear this. Perhaps it’s just that I’d rather have an excuse to go to Paris than one to go to St. Petersburg. 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. My understanding is that Russia offered twice as much money, and that many feel that was the deciding factor.

Update: I hadn’t realized that the problems with the IMU embargo this year were not new, they were much the same as the problems four years ago with the announcement of the 2014 prizes. See here for discussion of the 2014 story (which, when reading it, I first mistook for a discussion of 2018), and here for a discussion of 2018.

The writer of the new story suggests that “Next time the IMU offers up an embargo agreement, reporters should just refuse” which I’d also semi-jokingly suggested in a comment. Actually, given the history of this, it seems to me that journalists seriously should plan to do this next time, and that sympathetic and well-informed mathematicians should help them find out in advance who the winners are. This would allow journalists to contact experts and do proper reporting, with no reason to wait until the ICM to write their stories.

Update:

  • The ICM Youtube channel still doesn’t have plenary talks from the ICM posted. Peter Scholze’s talk on Period maps in p-adic geometry is available now on a different channel. It’s an excellent overview of, not the technology of perfectoid spaces, but some of the results achieved using them.
  • The reason there are relatively few comments here about the decision to have the next ICM in Russia is that I’ve deleted most of them as they come in. Many commenters don’t believe Russia is any unusual threat to liberal democracy (or, if it is, that US/European liberal democracy is anything worth saving). Most also disagree with the idea that such a threat should have any effect on what mathematicians do. 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.

    Another frequent comment is “but, by your logic, the US would not be a good place to hold the next ICM!”. I fear the answer to that is that yes, Paris would be a much better choice than the US at this point.

Posted in Uncategorized | 32 Comments

Leaving Town

About to head out on vacation tonight, back in a couple weeks. On the hot topics in fundamental physics, two items are:

  • Concerning the “no dS string vacua” conjecture, a new preprint begins by explaining why the existence or non-existence of such vacua is a question that has not been resolved (and, it seems likely to me, can’t be resolved):

    classical no-go theorems such as [12] indicate that realizing de Sitter vacua in string theory requires quantum and/or stringy ingredients. The fact that corrections to classical 10d low energy supergravity are qualitatively important implies that dS compactifications, in contrast to AdS or Minkowski compactifictions, must live in a regime in which these corrections cannot be made arbitrarily small [13], hence perturbation theory cannot be made arbitrarily accurate. Moreover the absence of supersymmetry in dS, and perhaps more fundamentally the lack of a complete, nonperturbative formulation of string theory, make it hard to obtain exact results beyond perturbation theory. Thus a completely rigorous, parametrically controlled construction of individual de Sitter vacua in string theory has remained out of reach.

    The paper also explains why if you try and get known physics with a quintessence field rather than a CC, you immediately run into serious problems with coupling to the Standard Model.

  • Slides and video of the talks at this year’s PiTP summer school on “From Qubits to Spacetime” have started to appear. Once I get back from vacation I’ll try and watch some of the talks and hope to figure out how one is supposed to get our spacetime and its physics out of qubits.

Recently people have contacted me suggesting I blog about two physics-related topics likely to lead to vigorous debate. I’d begged off in both cases, since engaging in such a debate or moderating it would be on a short list of things I’d most like to avoid doing. This afternoon though, it struck me that there is an excellent, if cowardly, way to deal with this. I’ll mention the two topics briefly here, then shut off comments on the blog and leave town. So, some may find interesting and want to argue elsewhere about:

  • One of the PiTP lecturers, Aron Wall, has a blog on physics and theology, called Undivided Looking. Wall’s theological views include thinking he has a pretty good idea about how God wants people to behave, in particular he’s pretty sure that God doesn’t want them having homosexual relations. He wrote extensively about this in a blog entry (now deleted) back in 2015. He’ll be soon taking up a faculty position at Cambridge University, and some people are not happy about this, see for example this statement from the Cambridge University Student’s Union.
  • If you’d like to attend an early universe conference this September, one place you could do so is in the Israeli-occupied West Bank settlement of Ariel, where Ariel University is hosting a workshop on Inflation, Alternatives and Gravitational Waves.
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