John Tate, who was responsible for some of the most important developments in number theory and arithmetic geometry during the second half of the twentieth century, has passed away at the age of 94. Tate was a faculty member in the Harvard math department when I was an undergraduate there, moving on to UT Austin in 1990, then retiring from there in 2009.
The work that Tate is famous for includes “Tate’s thesis”, his 1950 doctoral thesis, which may be the most influential doctoral thesis of modern mathematics. For a book-length explanation of Tate’s thesis, see Ramakrishnan and Valenza’s Fourier Analysis on Number Fields. The later generalization of the GL(1) case of Tate’s thesis to the non-abelian GL(n) case is one of the founding pillars of the Langlands program.
Tate was the Abel Prize laureate in 2009, and one can learn a lot more about him from an interview conducted around the time of the award. For an extensive discussion of Tate’s mathematical work, see this article from James Milne, or this review by Milne of Tate’s Collected Works.
A mathematician was explaining his work to Tate, who looked bored. Eventually the mathematician asked “You don’t find this interesting?” “No, no” said Tate, “I think it is very interesting, but I don’t have time to be interested in everything that’s interesting”.
As a thesis topic, Tate gave me the problem of proving a formula that he and Mike Artin had conjectured concerning algebraic surfaces over finite fields. One day he ran into me in the corridors of 2 Divinity Avenue and asked how it was going. “Not well” I said, “In one example, I computed the left hand side and got p13; for the other side, I got p17; 13 is not equal to 17, and so the conjecture is false.” For a moment, Tate was taken aback, but then he broke into a grin and said “That’s great! That’s really great! Mike and I must have overlooked some small factor which you have discovered.” He took me off to his office to show him. In writing it out in front of him, I discovered a mistake in my work, which in fact proved that the conjecture was correct in the example I considered. So I apologized to Tate for my carelessness. But Tate responded: “Your error was not that you made a mistake — we all make mistakes. Your error was not realizing that you must have made a mistake. This stuff is too beautiful not to be true.”
During a seminar at Harvard, a conjecture of Lichtenbaum’s was mentioned. Someone scornfully said that for the only case that anyone had been able to test it, the powers of 2 occurring in the conjectured formula had been computed and they turned out to be wrong; thus the conjecture is false. “Only for 2” responded Tate from the audience. [And, in fact, I think the conjecture turned out to be correct except for the power of 2.]
Tate’s father, John Torrence Tate Sr., was a physicist, editor of the Physical Review between 1926 and 1950. In one famous story, Tate Sr. stood up to Einstein by insisting that one of his papers be refereed in the usual way. Einstein was outraged (but it turned out the paper was incorrect). A few years ago I was at a talk here in New York at the Simons Foundation, during which the speaker put up a slide referring to Tate (Jr.)’s work, with a picture of Tate. After a moment, from the back of the room we heard “that’s not me, that’s my father!”.
Some links related to the foundations of math and physics:
Kevin Hartnett at Quanta has a long article on Jacob Lurie and his work on infinity categories. Unfortunately Lurie didn’t participate in the article himself, so comments are only from others. The article does a good job of giving at least a vague sense of what these very abstract foundational ideas are about, as well as examining the math community’s struggle to absorb them. Lurie’s work on this is spread out over more than 900 pages here and more than 1500 pages here. Recently he has been putting together an online textbook/reference version of this material as Kerodon, which is modeled after and uses much of the same software as Johan de Jong’s Stacks project.
In the new (November) issue of the AMS Notices John Baez has a review of a recent collection of articles about the foundations of mathematics and physics. The book, Foundations of Mathematics and Physics One Century After Hilbert, contains contributions about both math and physics, although in his review Baez concentrates on issues related to physics. He notes “The elephant in the room is string theory.”
The same issue of the Notices contains an informative long article about Michael Atiyah and his career, written by Alain Connes and Joseph Kouneiher (Kouneiher is the editor of the book reviewed by Baez).
The 2019 Physics Nobel Prizes were announced this morning, half going to Jim Peebles for his work on big bang cosmology, half to Michel Mayor and Didier Queloz for discovery of an exoplanet.
You can read elsewhere more details about the prize winners and their work, but I do want to point out that this announcement means (since there will be no further Physics Nobel Prize awards before the start of 2020) that John Horgan has won his 2002 bet with Michio Kaku, with \$2000 going to the Nature Conservancy. The winning prediction from Horgan was:
By 2020, no one will have won a Nobel Prize for work on superstring theory, membrane theory, or some other unified theory describing all the forces of nature.
If one looks at the comments back then, Gordon Kane signs on to an even stronger variant of the Horgan/Kaku bet:
By 2020 there will be a Nobel Prize for a string- or unification- or supersymmetry-based theory or explanation or experimental discovery.
Luckily for him he doesn’t seem to have put up any money for this, since he has now lost this bet.
For my own comments at the time, see here (this was a couple years before this blog was started). As I explained there, I was willing to sign up on Horgan’s side of the bet if the “other unified theory” clause was eliminated. Unlike Horgan, I’m not a sceptic at all of the existence of a unified theory, or of humanity’s ability to find it. My argument (which I think has held up well) was that we’re not going to get there by pursuing superstring theory or anything like it. In a better world, the LHC would have found not a vanilla Higgs, but something unexpected that gave us a new idea about electroweak unification, one that pointed to a successful new idea about a fully unified theory. I didn’t think this was likely, but I thought it was possible, and I wasn’t interested in betting against the possibility I would most like to have seen.
What shocks me about where we are now that Kaku and Kane have lost their bets is not that they lost, which was to be expected, but that this loss seems to have had zero effect on their behavior. Kane’s endless replacement of failed predictions by new ones is a well-known story. For Kaku, one can get some idea of his current point of view from this interview:
Yahoo News: So tell us about your work in string field theory. You’re trying to finish Einstein’s equation?
Michio Kaku: That’s right. We want to find the “God Equation” — the ultimate theory that explains the entire universe. We want an equation that’s maybe 1 inch long that would allow us to “read the mind of God” — those are Einstein’s words.
Yahoo News: And how’s it going?
Michio Kaku: We think we have it! It’s called string theory. It’s not in its final form, and it’s not testable yet, [but] we have the Large Hadron Collider outside Geneva.
We’re testing the periphery of the theory, but the theory itself is a theory of the universe — so it’s very hard to test. But we physicists are optimistic. We think we will be able to test the theory. And we think it is the final theory. So physics ends at that point. Another era opens up, but one era ends when we finally prove this is the Theory of Everything….
If string theory is correct, it means that all the subatomic particles — the electrons, the protons — are nothing but musical notes on a tiny vibrating rubber band. So that physics is nothing but the harmonies of the vibrating rubber bands. Chemistry is nothing but the melodies you can create from the vibrating strings. The universe is a symphony of strings.
And the mind of God is cosmic music resonated through hyperspace.
I don’t know of other bets on string theory, but there were quite a few bets about SUSY. I assume David Gross has now paid off his lost bets on SUSY, haven’t heard though anything about that. At the Copenhagen SUSY bet event, the losers (Arkani-Hamed, Gross and Shih) showed no signs that losing a bet on a scientific outcome had any effect at all on these scientist’s views on the issue they were willing to bet on.
Update: Horgan has posted his own take on this here.
The physics briefing book for the ongoing update to the European Strategy for Particle Physics is now available, for more see here. This describes the physics that one might hope to do with various proposed new machines. The hard part comes in the next few months: coming up with a proposal that has some chance of getting funded.
There’s an ongoing Cosmic Controversies conference in Chicago this week, which tonight will feature a panel discussion on “Do we need the Multiverse and can it made turned into a scientific theory?”. Tomorrow the panel topics will be more promising: “What more can we learn from particle physics about cosmology?“ and “Convergence or Disruption”. You can find video posted from the conference here including a live stream.
This evening I noticed that a recent documentary about Abdus Salam, entitled Salam: The First ****** Nobel Laureate, has just appeared on Netflix, and I spent some time watching it. The title is a reference to Salam’s membership in the Ahmadiyya sect of Islam, which in Pakistan has been declared heretical, and thus Salam not Muslim.
I enjoyed watching the film, and learned a lot I didn’t know about Salam, but there’s not a great deal in the film about his actual work in theoretical physics. While starting to write more here about the film based on some notes I took while watching it, I noticed that Matin Durrani last year at Physics World wrote an excellent detailed review of the film, and I recommend you consult that for more details.
Among those interviewed are Chris Isham and Michael Duff, who have interesting comments on what it was like to work with him. I was pleased to see that one old photograph had him standing in front of a blackboard that prominently featured “Unitary G-reps”.
Update: For another detailed review of the film, see here.
Photographer Jessica Wynne has been taking photographs of mathematician’s blackboards, and there’s a story about this in the New York Times. Many of her photographs have been taken here at Columbia, where we happen to have, besides some excellent mathematicians, also some excellent blackboards.
A non-Columbia excellent mathematician I’ve sometimes written about here is Bonn’s Peter Scholze. If you want to get some idea of the field he works in (arithmetic geometry) and what he has been able to accomplish, a good place to learn is Torsten Wedhorn’s new survey article On the work of Peter Scholze.
On the string theory front:
Arguments about the failure of string theory as a unified theory have been going on so long that they are now a topic in the history of science. For detailed coverage of many events in the long history of these arguments, you can consult historian of science Sophie Ritson’s 2016 University of Sydney doctoral dissertation. It and some of her other work is available at her academia.edu website.
For the latest in content-free argumentation about the failure of string theory unification, Steve Mirsky has a podcast discussion with string theory fan Graham Farmelo (see discussion of his recent book here), in which Mirsky challenges Farmelo about the problems of string theory. Farmelo has spent a lot of time at the IAS and basically takes the attitude that the point of view of certain unnamed string theorists there is what should be followed. I’d describe it as basically “we’ve given up working on string theory unification, but will keep insisting it is the best way forward until someone proves us wrong by coming up with a completely successful alternate idea.”
For the absolute latest attempt to extract some sort of “prediction” from string theory, see this week’s Navigating the Swampland conference in Madrid. Today there was a discussion session, with results shown of a survey of the views of those attending the conference. Note that, on the contentious topic of the reliability of supposed metastable de Sitter solutions of string theory, the Stanford group defending this reliability does not seem to be represented at the conference. I’ve been trying to understand what picture of physics this research has in mind, given that one main goal is to torpedo the metastable de Sitter solutions, and thus the usual “anthropic string landscape” picture. Looking at page seven, most participants seem to want to replace single field inflation models with more complicated quintessence or multi-field inflation models.
In Hirosi Ooguri’s talk he gives a supposed “unparalleled opportunity for string theory to be falsified”, I gather by claiming string theory somehow implies a small value of r. He quotes Arkani-Hamed as saying that string theorists should have reacted to the bogus BICEP2 measurement of r=.2 by saying “if this is true string theory is falsified.” They didn’t do that. When the topic came up at the time, what they had to say was:
Theoretical physicist Eva Silverstein of Stanford says she disagrees that string theory-based models of inflation are in any sort of trouble. “There is no sense in which we are forced to start over,” she says. She adds that in fact a separate class of theories that involve both axions and strings now look promising.
Linde agrees. “There is no need to discard string theory, it is just a normal process of learning which versions of the theory are better,” he says.
Several physicists now have pieces up explaining why Sean Carroll’s claim that “the Multiverse did it” (i.e. all you have to do is believe in multiple worlds) isn’t a real solution to the measurement problem. Beside the previously mentioned Chad Orzel, there’s also Sabine Hossenfelder and Philip Ball. I agree with Ball’s conclusion:
Here, then, is the key point: you are not obliged to accept the “other worlds” of the MWI, but I believe you are obliged to reject its claims to economy of postulates. Anything can look simple and elegant if you sweep all the complications under the rug.
Update: A video of the discussion session at the Swampland conference is here. It seems that I’m not the only one confused about what assumptions people working on this are making and what they are or are not accomplishing.
I’ve often added material to recent posts as “updates”, while aware that some who might be interested would likely not realize the added material was there. To improve the situation, I’ve just added a “Recently Modified Posts” widget on the right. The ordering is by modification time. I’ll try and figure out how to avoid having the modification time change when I do something like fix a typo (right now some old film reviews are appearing on the list because I recently added a “Film Reviews” category).
Among recent updates, I recommend the updates to this posting. Someone pointed me to a quite remarkable exchange earlier this week between Mike Peskin and Nima Arkani-Hamed.
Multiverse mania seems to have been dying down recently, with this only the third entry in that category here so far this year, after 10 in 2018, 13 in 2017, 10 in 2016, 17 in 2015, 18 in 2014, 12 in 2013, 9 in 2012, 15 in 2011. Bringing up the rear (hopefully…) is The Number of the Heavens, Tom Siegfried’s new book out today from Harvard University Press.
Siegfried is about the worst of the many journalists covering fundamental physics that I’ve run into over the years (only real competition is K.C. Cole). For some of his efforts as a journalist over the years, see here, here, here, here, here, and here. It’s not surprising that his multiverse book is an atrocious piece of propaganda.
It’s basically a compendium of arguments for string theory and the multiverse, with a bit of extra history tacked on. You get to read long sections of all the usual pro-string landscape and multiverse arguments from the usual suspects: Carroll, Deutsch, Guth, Greene, Linde, Polchinski, Rees, Susskind, Tegmark, and Weinberg. There’s the usual chapter on the MWI, ending with the acknowledgement that this has nothing at all to do with what the rest of the book is about. There’s a chapter about the glories of supersymmetry, brane-world scenarios, nothing about negative results from the LHC.
The way Siegfried handles criticism of string theory, etc. is very simple: pretend it doesn’t exist. As far as I can tell, there’s nothing anywhere in the book that even acknowledges that there’s another side to this story: for instance, no Baggott, Hossenfelder, Smolin, Penrose, or any reference to any book at all critical of string theory or multiverse hype. While there’s zero criticism of string theory, there are, as far as I can tell, just two appearances of multiverse critics:
On pages 223-8, remarks by Burt Richter at a panel discussion in 2006 get two paragraphs, followed by four pages of arguments from Linde, Susskind, Polchinski and Carroll explaining why he’s wrong. The prominent multiverse critic David Gross makes a brief appearance in these pages, with no mention of the fact that he is a multiverse critic.
Pages 262-9 are labeled a section on “Multiverse Deniers”, but there’s only one multiverse denialist quoted, George Ellis, with the only source given for his arguments this paper. In these pages short excerpts of his arguments are interleaved with long explanations from the author (as well as Weinberg, Wilczek, Carroll, Donoghue and Rees) about why Ellis is wrong.
Th one thing I can’t figure out about this book is how it got to be published by a reputable university press. My understanding has always been that university presses have some commitment to ensuring scholarly excellence in what they publish, for instance by having a manuscript about a controversy reviewed by experts from both sides. That obviously can’t have happened in this case, so I must be mistaken about how places like Harvard University Press now operate.
Chad Orzel has a piece at Forbes which I like a lot, where he argues that the “Many Worlds” of the MWI interpretation should be taken metaphorically, and thus the MWI really should be the “Metaphorical Worlds Interpretation”. I urge you to take a look (and argue about this with him, not me…).
Update: Natalie Wolchover suggests renaming MWI as the “Many Cakes Interpretation”, since
there’s a lot of having of cakes and eating them as soon as things get awkward.
There was a workshop last week at the Harvard CMSA, focusing on new ideas about physics rooted in topology. Talks are available on the workshop webpage, and those interested in high energy physics might be most interested in the ones from the first session. There was an interesting introductory talk by Dan Harlow, in which he lays out his view (which I think is a very mainstream one) of the current situation of HEP theory.
He begins by noting the problem of building higher energy accelerators (claiming that the problem is that technological limits make the maximum energy of collisions go as the square root of the radius of the machine, but I think really for proton-proton machines it is linear in the radius, for electron-positron machines the fourth root of the radius). Given the lack of new data, he describes one tactic for theorists as to change fields, e.g. to machine learning or biophysics.
If one does want to persist, he argues there still is a list of things incompatible with the Standard Model (gravity, dark matter, neutrino masses, baryogenesis, inflation) and these are not just “aesthetic” problems (here he refers to misunderstandings in the “popular media”, a clear reference to Sabine Hossenfelder and her book). From there he focuses on quantum gravity, essentially arguing that the other problems can be addressed by BSM models, but none of these seem particularly nice, so without new data progress is unlikely.
He describes quantum gravity as the ideal situation for theorists, since according to him there’s no self-consistent theory that fits the data we already have (I guess he’s saying string theory models are inconsistent…). He describes current work on this as based on two main strategies, with AdS/CFT providing a link between them:
“Study the non-realistic corners of string theory where mathematical control is possible”, i.e. pick some non-physical string theory background (e.g. AdS/CFT) where you think you can do self-consistent calculations and do those, hoping to get some more general insight.
“Set aside gravity for the moment, and focus on understanding the mathematical properties of QFT.” He gives a few examples of general questions being studied (which unfortunately have no obvious relevance to addressing the problem of quantum gravity, or basic problems like that of non-perturbative QCD.)
In the question section, there was an exchange between Harlow and Seiberg, based on Harlow’s reference to changing fields because of no data and to something he said during the talk (at 2:06):
Harlow: So then, what are we supposed to do in the meantime, right? You know we need to keep writing papers and posting them to hep-th and so on, so what do we do?
This was a beautiful summary, spectacular, except that one thing was fundamentally wrong and certainly should not be said. It’s not that we’re doing what we’re doing because we have to fill the time (audience laughter). We’re doing what we’re doing because it’s very important (audience laughter). I don’t think about “maybe we should write some books and this and that, until we have more information” I think this is wrong and this should not be [inaudible]
Harlow: I’m doing it, right, I don’t like wasting my time, so, I think it’s worth my time. I do think it’s important. We have this list of phenomena that we can see and can’t explain.
Seiberg: Comments like these have been used against us (audience laughter), in addition to the fact that they are wrong.
Harlow: OK, yeah, yeah, I’m not talking to the New York Times, right. (audience laughter).
Dam Son?: Is it recorded?
Harlow: I don’t know actually (audience laughter), I’ve said much worse things that were recorded, so.
HEP theory is at a very difficult point in its history, and it seems that the older generation struggling with this is not particularly amused to hear what sounds like flippant takes on the problem from the younger generation.
I originally was officially an elementary particle physicist. Elementary particles is not going so well, there’s no new experimental input and nobody knows what to do. It’s sort of reaching a point of, should I call it diminishing returns? It could change, it could easily change. I don’t think it’s doing very well. It’s not the fault of the physicists, it’s just the fact that they’ve reached a barrier, with no possible access experimentally to things that we’re not doing very well figuring out theoretically. So that’s not doing exceptionally well. My guess is the same thing may happen to cosmology. That they will eventually run, and they’re very close to it now, running out of new data, so there may be a barrier there.
Update: This week in Chicago there’s a workshop on the CEPC (proposed large new electron-positron collider in China). The first talk Monday was from Nima Arkani-Hamed. At the end of it, the question period started, with an exchange that resonates with the Harlow-Seiberg one:
Mike Peskin: So, let me make a quick summary of this talk: “my prediction is that when we go to high precision with the Higgs we will see no deviation from the Standard Model, but that will be a good thing because theorists will be inspired to think about these fundamental questions.”
Nima Arkani-Hamed: Absolutely. I’ve said it many times. Many people don’t believe me, but I believe it 100 percent. If we see some deviation, fantastic, great, people will have a lot of fun figuring it out, if we don’t see a deviation that’s a much, much bigger gauntlet thrown down at the feet of theorists to try to figure out what is happening.
Mike Peskin: But on the other hand you’re not promising any concrete discovery, just we reconfirm the Standard Model at a much higher level of energy.
Nima Arkani-Hamed: Reconfirming the Standard Model would just crank up the screws that are put on our theoretical imaginations even more.
Mike Peskin: How many billions of dollars do you expect people to spend to reach this conclusion?
Nima Arkani-Hamed: … However many billions it takes.
I’ll review some arguments that may be well-known to many of us—but which I find are not necessarily well-known to students, some of whom are being taught that there is no motivation to search for BSM physics.
and gives this I think accurate characterization of the problem:
The better way to frame the problem, and the role of fine-tuning, is that we are seeking a theory that explains the origin of the EW scale.
If, within that theory, the EW scale is extremely sensitive to input parameters, it’s not a very good explanation. The theory does not generically describe a universe like the one we live in.
If moving around in parameter space just produces modest changes in the low-energy physics, that’s a compelling theory that predicts a world like ours.
This characterization makes clear what the correct interpretation of the null LHC results should be: they provide significant evidence that the picture of a very high energy scale GUT/string theory with lots of parameters, generically producing the weak-scale physics that we see, is just wrong. There never has been any evidence for this anyway, so the failure of the hierarchy argument was to be expected. To the extent that you believe the hierarchy problem is the motivation for BSM physics, students who are being taught to give up on BSM physics by Harlow and others are not really being misled.
My own take on all of this: what Harlow and Arkani-Hamed get wrong is their claim that thinking about fundamental issues of quantum gravity is some new, exciting question that has just come up post-LHC null results. These issues have been there for decades; they were obvious at the time I was a grad student in the early eighties. The problem is what to do facing several decades of failure by theorists, and I don’t think the answer is to make outrageous claims about how wonderful the current situation is. The motivation for a new collider is the one Reece points to, ignoring the business about the hierarchy problem: we don’t understand at all the origin of the EW scale. This is the best argument for studying the scales just above it that the LHC has started to enter. If we can get some new insight into the EW scale from a detailed study of the scales just above it, that will revolutionize physics (not just be “a lot of fun”). If we can’t, we’re facing a very, very tough time, especially if we insist on pursuing fundamental theory the way it has been pursued in the past.