If one tried to pick a single most talented and influential figure of the past 100 years in each of the fields of pure mathematics and of theoretical physics, I’d argue that you should pick Alexander Grothendieck in pure math and Edward Witten in theoretical physics. This afternoon I’ve run across two excellent sources of information about each of them.
Alexander Grothendieck
This week’s New Yorker has The Mysterious Disappearance of a Revolutionary Mathematician by Rivka Galchen. It’s a very well-done survey of Grothendieck’s life and work, aimed at a popular audience. If, like many mathematicians, you’ve always been fascinated by Grothendieck’s story, you won’t find too much in the article you haven’t seen before. But, if you’ve never delved into this story, you should read the article. On a related note, a copy of Récoltes et semailles that I ordered recently has just arrived in the mail, and I’m looking forward to spending some time with that this summer.
Edward Witten
In theoretical physics a very different but equally off-the-scale talented and influential figure is Edward Witten, who is the subject of a recent long and in-depth interview by David Zierler as part of the Oral Histories program at the Niels Bohr Library and Archives.
I first met Witten probably in 1977, when I was an undergraduate at Harvard and he was a Junior Fellow, recently arrived from Princeton. Over the years since then he has done a mind-blowing quantity of highly impressive work which I’ve done my best to try to follow. You can find many places where I’ve written about this here on the blog, and there’s also a lot in my book Not Even Wrong. Much of what he discussed in the interview was familiar to me, but I learned quite a bit new from his recollection of the details of how his work came about and how he thought about it. On some of the specifics of what happened many decades ago one should keep in mind that memory is imperfect. For instance, he describes a short period as a graduate student in economics at the University of Michigan, which surprised me since in research for my book I’d read that this was at the University of Wisconsin. Maybe I got this wrong, but if so I’m not the only one (see for instance here).
Witten’s work in the area where pure mathematics and quantum field theory overlap has had an overwhelming influence on those like myself who are fascinated by both subjects and their interaction. The landscape of this area would be completely different (and highly impoverished) without him. At the same time, his equally large influence in the area of attempts to unify physics I believe has been much more problematic.
I’ll quote here with a little commentary some of the passages from the interview that I found striking or where I learned something new.
About his early years:
Witten:
I was very interested in astronomy when I was growing up. Well, I was not an exception; these were the days of the Space Race, so everybody was interested in astronomy. I was given a small telescope when I was about nine or ten. That’s certainly a vivid memory. Another vivid memory is learning calculus when I was eleven. My father sort of taught me calculus or gave me materials from which I could learn it. But I didn’t advance very much in math beyond that for quite a few years…Zierler:
And then [after college at Brandeis] initially you thought you would go and become an economist?Witten:
Yes.Zierler:
What were your interests there? Did you think that your mathematical abilities would be applied well in that field?Witten:
It’s again hard to remember reliably, but I might have thought that. And I might have also thought that I could make a contribution to international development. But I realized- well, I came to the same realization I had come to when I was working on the McGovern campaign, that it wasn’t a good match for me. I remember being very embarrassed when I told the people in the department at Michigan who had been quite kind to me, that I had decided to leave. But in hindsight, I understand something that wasn’t that clear to me at the time, that if a given graduate program isn’t a good match for a given student, the department and the student are both better off if that’s realized sooner rather than later. If I had understood that at the time, I would have been less embarrassed, probably, with what I told them.
How to learn general relativity in ten days:
Zierler:
Was general relativity considered popular or interesting at Princeton at the time that you were a graduate student?Witten:
Well, I was certainly interested in it. I learned general relativity in a very exciting period of about ten days, from the book of Steve Weinberg. I mean, I tried to learn more from the book of Misner, Thorne, and Wheeler, and I did learn more from it, but my opinion of the book was what it remains now, which is that it’s got a lot of great stuff in it, but it’s a little bit hard to use it to learn systematically. The book I found useful for studying systematically was by Steve Weinberg.
The Harvard Society of Fellows:
Zierler:
Ed, did you enjoy the Harvard Society of Fellows, the social aspects of it?Witten:
Well, I enjoyed it up to a point, but let’s just say that many other people thrive on that more than I did.
On how he experienced the First Superstring Revolution.
Witten:
I’m not exactly sure what I would have said if you had asked me. There’s no interview, so there’s no record of my thinking in 1982 or 1983, and I won’t be able to remember very well. But as I was telling you, I was interested enough to spend a whole summer reading John Schwarz’s review article, but a little bit wary of becoming too involved in it…Something that was obvious to me but wasn’t immediately completely obvious to everybody was this. Green and Schwarz had put string theory in the form where there was a very strong case that there was a consistent quantum theory that described gravity together with other forces. And the other forces could be gauge fields, somewhat like in the Standard Model. But there was something extremely conspicuous that was wrong in terms of phenomenology, and that was that the weak interactions couldn’t violate parity…
And as it existed in 1982 and 1983, string theory was a consistent theory of gravity unified with other forces, but it completely missed the chiral structure. So, to me, that was a huge siren blaring. Anyway, to set the stage, I want to just point out to you that it was clear by 1982 or 1983 that there were an incredible variety of delicate things that fit together perfectly to make it possible to have a theory of quantum gravity based on string theory. It was unbelievable that it could all be a coincidence. Yet it was markedly wrong for describing the real world because of this question of the chiral nature of the fermions. But then in 1984, Green and Schwarz discovered a more general method of anomaly cancellation, and everything changed…
So, anyway, what was really problematical for Green and Schwarz was the combination of fermion chirality and anomalies. Taking these together, it seemed that string theory could not work. But then, in August 1984, Green and Schwarz discovered a new mechanism for anomaly cancellation, and everything changed…
So, it was immediately obvious to me, once they made their discovery, that you could make at least semi-realistic models of particle physics, in that framework. But also, to me, I had done kind of an experiment in the following sense. I had spent two years watching this, wondering, could it be? Can it be that all the coincidences that had been discovered that made string theory possible were just coincidences? As far as I was concerned, the discovery they made in 1984 was an empirical answer of “no” to that question. If the miraculous-looking things that had been discovered up to 1982 and 1983 were truly coincidences, you’d then predict there wouldn’t be any more such coincidences. That had proved to be wrong when they made this miraculous-looking discovery about anomalies that enabled the theory to be much more realistic.
In explaining this to you, I’m trying to help you understand why this had so much of an impact on my thinking, watching from the outside for a couple years, wondering if this subject was as amazing as it appeared to me. And a “no” answer would have predicted there shouldn’t be more miraculous discoveries. And that was, to my satisfaction, disproved in August 1984. So, after that, the hesitation that had kept me from becoming more heavily involved earlier evaporated. Now, I realized that in the physics world, there were plenty of people who hadn’t lived through this two years of uncertainty that I had lived through, and in many cases they had never heard of the whole thing until August 1984. And they hadn’t done the experiment I had done. So, they didn’t react as I did.
Here Witten explains how one very specific technical calculation triggered for him a dramatic vision of a possibility of a unified theory of everything, a vision that has stayed with him to this day, nearly four decades later.
About his evangelism for string theory unification starting in 1984:
Zierler:
How much cheerleading did you do among your colleagues, both near and far, after this revolution in 1984, that this is what people should concentrate on? That we can have this figured out in the near term?Witten:
I wasn’t intentionally cheerleading, but I was very enthusiastic. And I actually think I was right to be enthusiastic. I wasn’t intentionally cheerleading, but to the extent that I encouraged other people to get involved, I’ve got no regrets about it at all (laughter).
Another very interesting recent interview in the same series is one with Cumrun Vafa. Here’s what Vafa remembers about that time:
Vafa:
I remember I was at my office, I had come back from a trip, from I think the summer school in Europe, in Italy. Had come back to my office in Princeton on the fourth floor, and Ed’s office is on the third floor. And he rarely came to our floor, fourth floor, but here he was, coming and knocking at my door, and then saying, “Have you heard about the revolution?”…I said, “What revolution?” He said, “The SO(32) revolution.” Okay, that was my first introduction to Green and Schwarz’s work. SO(32) revolution. I said, “No, what is it?” He said, and he was completely sure, confident, that physics is not going to be the same after this. He said, “Physics is going to change forever because of this, and now everybody is going to work on this.”
I had left Princeton for Stony Brook early that summer. During the next few years, reports I got from fellow postdocs who tried to talk to Witten about their work were pretty uniformly something like “he told me that what I’m doing is all well and good, but that I really should be working on string theory.”
Unlike the case in the interview with Vafa previously mentioned, Zierler doesn’t really try and pin Witten down on the subject of the problems of string theory. He does ask:
Zierler:
What was happening at the time or has happened since in the world of experimentation or observation that may get us closer to string theory being testable?
but lets Witten give a non-answer, which in effect is that the landscape means string theory unification is completely untestable, so he has pretty much given up:
So, if you talked to me in the 1980s, I’m sure I would have expressed some hope about seeing supersymmetry as part of the answer of the hierarchy problem. But I would have expressed a lot of confidence about observing something that would have explained the hierarchy problem. …
But ultimately, with the LHC, experiment has reached the point that it’s extremely problematic to have what’s called a natural explanation of the weak scale, a mechanism that would explain in a technically natural way why the Higgs particle is as light as it is, thus making all the particles light. It’s actually a baby version of the problem with the cosmological constant. So, to the extent that the multiverse is a conceivable interpretation of why the universe accelerates so slowly, it’s also a conceivable explanation of why the weak scale is so small. It might be the right interpretation. But if it is, it’s not very encouraging for understanding the universe. When the multiverse idea became popular around 1999, 2000, and so on, I was actually extremely upset, because of the feeling that it would make the universe harder to understand. I eventually made my peace with it, accepting the fact that the universe wasn’t created for our convenience.
You would think that having an untestable theory on your hands would mean that you would try something else, anything else, but Witten seems convinced that whatever its problems, it’s the only way forward:
[About the second superstring revolution and M-theory] It’s satisfying to know that there was only one candidate for superunification. There’s only one reasonable candidate now for the theory that combines gravity and quantum mechanics. Before 1995, there was more than one. It’s more satisfying to know that the theory seems to have a lot of possible manifestations, in terms of approximate vacuum states, but at a fundamental level, there’s only one fundamental theory or system of equations, that we admittedly don’t understand very well. That’s got to be an advance of some kind…
By the time he [Einstein] had the theory [GR], he had the right mathematical framework of Riemannian geometry. At least by the time the theory was invented, he had the ideas it was based on, and some of them he had had before.
String theory and M-theory have always been different. From the beginning, they were discovered by people who discovered formulas or bits and pieces of the theory without understanding what’s behind it at a more fundamental level. And what we understand now, even today, is extremely fragmentary, and I’m sure very superficial compared to what the real theory is. That’s the problem with the claim that supposedly I invented M-theory. It would make at least as much sense to say that M-theory hasn’t been invented yet. And you could also claim it had been invented before by other people. Either of those two claims is defensible (laughter). So I made some incremental advances in a subject that’s far from being properly understood.
This “we don’t know what the fundamental equations are, but we know that they are unique” argument has never made any sense to me.
On his relation to mathematics:
Zierler:
What did it feel like to win the Fields Medal as a physicist?Witten:
Well, it was a thrill, of course. It felt a little funny because I knew that obviously I was a non-standard selection. And I don’t like controversy about science, and I felt that I might have been a controversial choice in the math world. But on the other hand, I hadn’t selected myself, so I didn’t feel any controversy was my fault…What’s a little funny about my relation to the math world is that although some of my papers are of mathematical interest, they rarely have the detail of math papers. And I can’t provide that detail. I simply don’t have the right background. What I bring to the subject is an ability to understand what quantum field theory or string theory have to say about a math question. But quantum field theory and string theory are not in the precise mathematical form where such statements can usually be rigorous.
The “I don’t like controversy about science” quote makes clear that Witten and I are temperamentally very different…
About the birth of geometric Langlands:
By the late 1980s- I’m probably forgetting bits of the story, I should tell you- but by the late 1980s, Sasha Beilinson and Vladimir Drinfeld had discovered what they called a geometric version of the Langlands program, and it involved ingredients of quantum field theory. Tantalizing. But it was tantalizing because they were using familiar ingredients of quantum field theory in a very unfamiliar way. It looked to me as if somebody had put the pieces at random on a chess board. The pieces were familiar, but the position didn’t look like it could happen in a real chess game. It just looked crazy. But anyway, it was clear it had to mean something in terms of physics. I even worked on that for a while at the time.
I think I’ve gotten this slightly out of order. I think when I worked on it was actually before the work of Beilinson and Drinfeld, driven by other clues. And the Beilinson and Drinfeld work was one of the things that made me stop, because I realized that A, I couldn’t understand what they were doing at the time, and B, there were too many things I didn’t know that they knew, and that seemed to be part of the story. Anyway, as you can see, my memories from whatever happened in the late 1980s are pretty scrambled.
They wrote a famous paper that was never finished and never published. It’s 500 pages long. You can find it online, if you like. They have an incredibly generous acknowledgement of what they supposedly learned from me, which is way exaggerated. Based on a hunch, I told them about a paper of Nigel Hitchin, but I didn’t understand anything of what they attributed to me. At any rate, regardless, even if I didn’t understand what they did with it, the fact that I was able to point them to the right paper was another sign of the fact that what they were doing had something to do with the physics I knew. But I couldn’t make sense of the connection. And this kept nagging at me off and on for a long time.
He then goes on to tell the story of the IAS workshop on geometric Langlands and how it led to his work on a QFT version of geometric Langlands.
In recent years Witten has continued to work on geometric Langlands and other topological quantum field theory related topics at the mathematics end of things. As far as physics goes, he is following the very popular “it from qubit”, quantum gravity from information theory, line of thinking:
Witten:
And the third time [revolutions: first and second were two superstring revolutions] has been the last six or seven years. It’s actually hard to remember the evolution of my thinking (laughter). I reread an interview I had done in 2014 which told me what my thinking was in 2014 better than I could have remembered it reliably (laughter). And what I told the interviewer at that time was somewhat similar to what I’m telling you right now. So, this has gone on for a while, and despite that, I haven’t really found the right way to become involved myself. But I do suspect that something big is happening.Zierler:
What has happened since 2014, when you initially got excited about this?Witten:
There have been various striking developments, but a particularly dramatic one came in 2019 when there was success in understanding what is known as the Page curve in black hole evaporation… Lots of things have happened that show that there’s a conspiracy between gravity and quantum mechanics. Somehow gravity at the classical level knows about quantum mechanics and statistical mechanics…Zierler:
To bring the conversation right up to the present, as we discussed right at the beginning, your interest in quantum information. And you said you don’t yet know how you might break into the field. What might be some possible avenues?Witten:
Well, when I was a graduate student, I sat down one day with piles of paper preprints. We didn’t have the archive. I’d sit down with piles and piles of paper preprints, and go through them, trying to find something I might do. The most interesting calculation I did as a student- I told you about it- was this calculation of deep inelastic photon-photon scattering, which was inspired by a paper I saw by Roger Kingsley, who studied the question but not quite with the most modern QCD ideas. So, when I was a graduate student trying to break in, I would go through piles of preprints. I guess the equivalent now is to look at papers in the archive and try to see what I might do. And I have made some minor contributions, actually, but I don’t feel like I’ve fully become engaged with the subject, as I have with other subjects in the past.
Witten and the interviewer discuss the difficulty of finding something to work on that is not too hard but still significant, and he comments that this is:
…the difficulty I’ve had getting involved with quantum information theory and gravity. I found a few things that I could do, but they were a little bit too narrow to really make me think that I was getting involved where I wanted to. And I haven’t quite found the right avenue. But I haven’t given up (laughter). I do have the feeling that’s the direction where something big is most likely to happen. You see, there isn’t a general understanding of what string/M-theory mean. And there’s something missing in the general understanding of quantum gravity. The biggest hope would be that those two would somehow make contact with each other.
I can understand why Witten hopes that the mystery of quantum information theory and gravity will give insight into and resolve the mystery of what M-theory is, finally vindicating his 1984 vision, but this looks to me like a very, very long shot.
A couple points on the Grothendieck piece. The author attributes the introduction of categories and functors to Grothendieck. In fact categorical machinery was first used by Eilenberg and Maclane in 1945, roughly twenty years before Grothendieck’s seminal work on the Weil conjectures. Grothendieck though did apply functorial machinery to algebraic geometry in a transformative way.
The authors also note that Grothendieck developed the theory of motives as part of his solution to the Weil conjectures. I do not believe this is true. Nor did Grothendieck originate sheaves (which are due to Leray), but he did apply sheaves to algebraic geometry in a transformative way, through his “schemes.” His seminal theoretical contribution that enabled the proofs of three of four of the conjectures was his etale (l-adic) cohomology theory. I do wish the authors had explained something of the search for this “Weil cohomology theory,” and Grothendieck’s brilliant insight, that homological algebra could be done on linear objects varying over any site, not just over the open subsets of a topological space.
I’ve been thinking about writing a popular article along these lines (explaining about the Weil conjectures and etale cohomology).
Overall, though, a decent biopic on Grothendieck.
Incidentally, for readers interested in the life of Grothendieck, here’s another brilliant piece to see: https://theanarchistlibrary.org/library/konstantinos-foutzopoulos-the-man-of-the-circular-ruins?v=1620246019
Personally I prefer this to the New Yorker piece.
From the little I know about Grothendieck’s vision of motives, his Standard conjectures on algebraic cycles, which are inspired by Weil’s proof of his conjectures for curves, would be part of the package, and thus would yield, “immediately”, a motivic proof different from Deligne’s.
“If one tried to pick a single most talented and influential figure of the past 100 years in each of the fields of pure mathematics and of theoretical physics, I’d argue that you should pick Alexander Grothendieck in pure math and Edward Witten in theoretical physics.”
Really? Yang? Anderson? Schwinger? Bardeen? Weinberg? Nambu? Etc.
I think the list extends to many tens if not hundreds.
What “physics” has Witten actually done? He’s been very influential in mathematics.
Peter : This is one of the rare interview by a particle theorist where non-0 neutrino mass is mentioned. His exact quote:
“And the second are the neutrino masses, which are plausibly a signal coming from something close to grand unification, though unfortunately we don’t know for sure that that’s the correct interpretation.”
I wish the interviewee pinned him more on this that if non-0 neutrino mass is supposedly a sign if physics beyond standard model, why isn’t Witten and others working more feverishly on it. Does anyone know if Witten has published papers with his father (on aspects of classical GR?)
stoopid,
Yes, really. Note that I specified “most talented and influential”, not biggest accomplishments. On “talented” I don’t think there’s any argument, and on “influential”, I also don’t think there’s anyone who has come close to his influence.
In the posting there’s a lot about what happened in 1984 and years afterwards. Witten took a technical argument about anomaly cancellation and used it to convince almost everyone in the field to follow him down a very speculative path. Decades afterwards, when it has long been clear this doesn’t work, there are still thousands of people working on it, and here at Columbia we teach it to undergraduates. I don’t think there’s anything even close in the history of physics to that scale of (negative) influence. At the same time of course one can point to a very large number of extremely important and influential positive developments that Witten is responsible for.
Shantanu,
I may be wrong, but as far as I know Witten has not published papers with his father.
One remarkable thing about Witten is that he is extremely knowledgeable about the state of high energy experiment and about HEP phenomenology (some of this shows through at points in the interview), far more so than most theorists. He has worked in phenomenology, but that has not been a big focus of his efforts. One could argue that, post SM, no one has been able to make a major breakthrough in HEP (beyond SM) phenomenology. So his concentration on formal theory has been sensible not just because his talents may be stronger in that area, but because the lack of experimental clues has stymied any progress in BSM physics.
The reference to neutrino masses was part of some half-hearted remarks about GUTS, which he still holds out some hope for, while realizing that no significant evidence for them has appeared.
I was going to post something like what @stoopid said, but I see now that Peter already gave an answer. Still, it makes me cringe a bit to see Grothendieck to be put on the same foot as Witten, in their respective fields. Sure, in terms of influence and talent, maybe, but, to me, Grothendieck’s legacy is far superior. Witten will gradually be cornered by history to the areas of mathematics on which he has been influential, as well as some isolated important results in theoretical physics (say, his proof of the positive mass theorem in GR.)
Most of his huge talent was wasted due to a lack of self-awareness (to put it gently and not to talk about lack of scrupulous or good faith…) regarding the über speculative nature of the field, a bit of historical bad luck (zero new experimental results for bSM physics in his lifetime), and maybe some other reasons. I think Grothendieck had better luck in that. Still, Witten managed to make important contributions in other areas, due to his huge talent, evidently.
As a physicist from a much more younger generation, Witten is far from a “hero” to me, despite his talent, and I think this reflects the feeling of many people around my age, particularly outside the main US centers.
Alex,
I see Grothendieck and Witten as sharing an unparalleled off-the-charts talent together with a huge capacity for a lot of hard work, with those around them recognizing this, leading to a great deal of influence.
In other respects, they and their careers were very different. Grothendieck was only intensively active for about fifteen years (1955-70), whereas for Witten it’s about 45 years and counting. Grothendieck was focused on building new foundations for his subject, whereas Witten never has worked in that way. While Grothendieck’s new foundations changed the way people thought of the subject, one might argue that most of these changes would have happened sooner or later without him, since they were the natural evolution of the direction things were headed in.
Witten’s contributions to our understanding of non-perturbative quantum field theory seem to me of a different nature. Most of the great things he has accomplished I think would not have happened without him (as one example among many, I don’t think we’d have the Seiberg-Witten non-perturbative solution to a 4d SUSY gauge theory). I suspect that, in the distant future, once the damage from “string theory” is cleared out, some of Witten’s new ways of thinking about QFT will turn out to be fundamental to further developments.
As for negative influence, here I don’t think Witten is the main person to blame. Most theorists have speculative enthusiasms which drive their work, and one can’t really blame them for following those. The herd-like way so much of the theoretical physics community followed Witten down a blind alley, and still refuses to admit what happened isn’t mainly his fault.
Shantanu and Peter:
Large Radius Expansion of Superstring Compactifications
Louis Witten(Cincinnati U.), Edward Witten(Princeton U.)
(Apr, 1986)
Published in: Nucl.Phys.B 281 (1987) 109-126
Thanks Chris!
Peter,
I really don’t agree with your views regarding Witten’s contributions to non-perturbative qft. I mean, what real and relevant problems have been solved? Has the Yang-Mills non-perturbative rigorous existence and positive mass gap problem, the one for which there’s the Clay Institute prize, been solved? Has the rigorous non-perturbative quantization of the non-linear Einstein’s Eqs. been solved? To me, a real advance in non-perturbative qft should be able to tackle those real physics problems. I really only see promises that so far have failed to deliver. On the other hand, there have been lots of people with their feet on the ground and away from the flashes that have taken these problems seriously (i.e., at face value, without embedding them on grand, delusional speculations) and are, in my opinion, much more closer to solutions than Witten ever was (e.g., the AQFT approach is getting closer to the YM problem, while things like Thiemann’s master constraint programme are doing the same for the quantum EFEs). SUSY doesn’t exist, TQFTs do not describe any known fundamental forces (at most, boundary terms in GR are of this form). As for the unification of the forces, Connes’ approach is much more closer to success that anything Witten ever invented. Sure, all of this only reflects my tastes to some extent, but they do contain a core of truth.
Second, I do think Witten carries a lot of blame. True, the herd mentality was a disaster and wasn’t a necessary consequence of Witten’s status (for example, Einstein was left alone by the community during his quest for a unified field theory, since there were more promising things to do at that time, and I think it was the right choice, despite the fact I consider Einstein to be the greatest thinker of all times in physics). But, once you are made a leader by your peers, that carries a duty and a responsibility too. And Witten’s role as a leader was close to reckless if we consider how things developed.
I’m sorry if this sounds a bit ranty, I think there are strong generational and geographical distances between our experiences and viewpoints.
@Topologist guy: I concur with Amadou – this is surely referring to the proposed proof of the last Weil conjecture using the standard conjectures.
The standard conjectures are closely related to the category of Chow motives – they prove it has various nice categorical properties. If I remember correctly, it’s possible to formulate the proof that the standard conjectures imply the last Weil conjecture both with and avoiding the category of Chow motives.
Of course the great irony here is that the standard conjectures are much, much more difficult than the Weil conjectures, and the biggest progress on the standard conjectures since Grothendieck formulated them was arguably the proof of the Künneth type standard conjecture over finite fields by Deligne and Katz-Messing, which uses the Weil conjectures. (In fact, maybe this is not so ironic, as Grothendieck suggests in Récoltes et semailles that the standard conjectures should be viewed as a generalization of the Weil conjectures to arbitrary correspondences.)
I was a bit disappointed that the New Yorker article didn’t add any clarity to the part of the story that has always confused me, where Grothendieck is angry that Deligne proved the Weil conjectures in the wrong way. This confuses me because the complaint doesn’t really make much sense (how can you complain that someone proved something the wrong way when neither they, you, nor anyone else know how to prove it the right way?) and because I never saw a place in writing where Grothendieck expresses that anger, though there are places where he criticizes Deligne about other things. The article added a bit more detail than I’d heard before to some other aspects of the story, like Grothendieck leaving IHES, but not that.
I would argue that Langlands has been more influential, you can see this manifestly by the amount of generational talent that since the 70s has moved from their original research subjects to become involved in his program (Deligne, Scholze,Vincent Lafforgue, T. Hales, Venkatesh), Witten being one of them. And probably this list will continue to grow in the coming decade.
Alex,
I agree that Einstein is a good contrast to Witten. In his later career at the institute in the same sort of position as Witten he pursued speculative lines that weren’t working out, while the rest of the community ignored him. One difference is that I don’t know of any stories of Einstein telling younger people that they should drop everything and work on his latest idea. I actually was kind of appalled by Witten’s “no regrets at all” attitude about his evangelism starting in 1984.
About the problems you mention, you can’t fault Witten for not solving them since no one else has (or has even come close). I think he’s very aware of and motivated by those problems but also very aware that he doesn’t have a promising idea to solve them. He has a very quick mind and his style is not to go off and spend years thinking about a hard problem, but rather to quickly realize he doesn’t have a good idea that will solve the problem and so move on to looking for another problem which he can solve. About, eg., solving QCD, my guess is that we’re lacking the right idea, and likely the way to get the right idea is not by frontal attack but by developing tools solving other problems, such that some day one will have found the right tool to attack QCD.
@ Will Sawin: I think, when it comes to Deligne’s proof, the better term for Grothendieck’s reaction would be “disappointment” instead of “anger” (on this specific point I never felt, reading Récoltes et Semailles, that G expressed anger): he claimed to have wanted above all a complete theory of motives – the most profound theme he introduced in mathematics, in his words; the Standard conjectures (“the proper way” to prove the RH over finite fields) would yield such a theory. I guess, later in his mind (not in mine to be clear), Deligne’s proof came to symbolize the abandonment of “foundations building” (his style) in favor of “tricks” or shortcuts to quickly snatch the prized theorem. (see R&S, 3.3. Le décès du patron-Chantiers à l’abandon). I am not sure if this clarifies anything for you.
@Amadouh: It helps! But it doesn’t resolve my confusion about the discrepancy between what’s in Récoltes et Semailles and what some other people say – for example the paragraph in the New Yorker article about this is not a good summary of the reaction you describe. So my confusion is to what this other perspective where (as in the New Yorker article) Deligne “wronged” Grothendieck with this proof, who experienced a “massacre” and in turn “vilified” him, is based on, if not Récoltes et Semailles – maybe recollections of conversations people had with Grothendieck about feelings he had but got over before writing Récoltes et Semailles?
Another interesting thing in the section you wrote is Grothendieck’s list of topics he studied that were dropped:
“I no longer heard news about motives, topoi, the six functor formalism, De Rham and Hodge coefficients, nor about the “mysterious functor” which was supposed to unite under one umbrella De Rham and l-adic coefficients for all prime numbers, nor about crystals (except to learn that they remained at a standstill), nor about the “standard conjectures” and other conjectures which I had formulated and which, evidently, represented crucial questions. ”
If these topics were ignored at one point, I don’t think they’ve been recently. People are constantly producing the six functors formalism in new contexts, there’s really interesting fundamental work on what a six functors formalism even is (though maybe involving only three at a time), p-adic Hodge theory was developed and constructed the mysterious functor and now we have a single cohomology theory that underlies both, there’s a Topos Institute and various topos-based research programs unrelated to the work there, everyone’s talking about motives, ….
@Z Y: Yes, it’s terribly infectious. When I came to Princeton I was determined not to study automorphic forms, and when I left I had learned a lot about automorphic forms, and now have a few papers about them.
But I feel that it’s more about the intrinsic interest of the problems, rather than any influence of Langlands himself (perhaps using “influential” in an overly strict sense). Didn’t most of the transfers to Langlands you mention happen after Wiles’s work?
Maybe another way to say this is that the Langlands conjectures were very influential, possibly on the century-defining scale that Grothendieck’s work was, but his actual work towards those conjectures (Jacquet-Langlands, Langlands-Tunnell, Langlands-Shahidi, …) was only influential in the way that many good papers are influential. People who work on his conjectures are not necessarily working in his mathematical universe.
An interesting parallel or contrast to Grothendieck is the way Langlands has been disappointed with some of the directions people take his work – famously geometric Langlands but also I heard that he doesn’t like modularity lifting and is disappointed that everyone isn’t studying beyond endoscopy via the trace formula.
@Will
There’s an interesting point that I think is captured in the audio recordings of Grothendieck’s 1973 Buffalo lectures on topos theory and functorial algebraic geometry: the news that the last Weil Conjecture had been proved landed in the USA, but not the details or even sketch of the proof. So there’s Grothendieck waxing lyrical about how Deligne must have used techniques X, Y and Z in the style of Grothendieck’s own foundation-building toolbox, and how wonderful this was. And then he clearly found out, and by a decade or so later, was bitter his own style of work was not used.
I believe this is discussed in McLarty’s talk about the lectures; at the very least, the video description mentions a closely related point.
The past 100 years is the period 1922 – 2022. The most influential theoretical physicists must have been Schrödinger, Heisenberg and Dirac, no? After all, they discovered QM. That is a pretty influential theory, if I’m not mistaken.
Other than the Michigan/Wisconsin-Madison issue, I think it is very interesting that Witten doesn’t remember clearly why he chose Brandeis or history or other choices he made when he was young. On the other hand, he remembers very clearly about the issues in physics and maths since the graduate student days. Is it a kind of focused or selective memory loss or does he want not to discuss about those personal issues from younger days?
I came here to write something similar to stoopid’s comment, and then I read the reply to him/her.
Honestly, that reply should have been included in the body of the post to avoid a misunderstanding… It clarifies “influential” and once more shows how bad a state theoretical physics is in – and that “accomplishments” now means “social engineering”.
Pierre Deligne- The Abel prize interview 2013…, and 30:45 Grothendieck’s program as a hindrance to proving Weil’s 3-rd conjecture.
https://youtu.be/MkNf00Ut2TQ
Witten states:
“They wrote a famous paper that was never finished and never published. It’s 500 pages long. You can find it online, if you like.”
Could someone please post a link to said paper?
Peter,
QM, QED and the Standard Model are the most influential theories of the past 100 years, but in each case there is no single theorist responsible for the theory. Among Schrödinger, Heisenberg and Dirac, if you pick any one and ask what physics would look like without them, I think the answer is “not that different”, their discoveries would have been made a little bit later by someone else. If you ask the question of what the theoretical physics of the last 45 years would look like without Witten, the answer is “very, very different” (in both positive and negative ways…).
Richard,
Witten is referring to this paper
http://math.uchicago.edu/~drinfeld/langlands/QuantizationHitchin.pdf
I’ve been struck repeatedly by Witten’s unequivocal rejection of other approaches to QG and unification. He’s hardly the only “only-game-in-towner”, but he generally appears to choose his words very carefully and rarely comes across in any interview or article as undiplomatic. Nonetheless, I think he’s been on record several times declaring LQG essentially worthless. He may or may not be correct, but in such a highly speculative area of research, I find it hard to justify such stark dismissals based on anything I would conventionally characterize as evidence. Major, perhaps even fatal difficulties, sure. But no value whatsoever?
LMMI,
I don’t want to get involved in the string theory/LQG argument, but it is quite remarkable that, while Witten is normally extremely cautious in what he says about scientific issues, on the topic of string theory he abandons this caution. One reason for this may be the intense criticism he has gotten about string theory for a very long time, leaving him feeling he has no choice but to mount a strong defense.
Peter Woit,
Thanks for the link!
— Rich
@ Will Sawin: Regarding Grothendieck’s list of dropped topics, I think one should keep in mind, besides the time of his writing (1984-1988 ?) which is before some later developments in these subjects, that Grothendieck may not have been very aware of progress that was made in the 70’s and early 80’s (e.g. Fontaine’s work on the mysterious functor, his period rings and conjectures). If I were to speculate as to why, I would say that: (1) his correspondence with Serre, his most important source of mathematical information until then, essentially stops after 1969; (2) he was not an avid reader of the mathematical literature (especially after 1970). Also, he seems to be drawing from (not so reliable) memory only some of the material for R&S, correcting himself in footnotes of footnotes (see for example R&S, 13.3.3, “Poids en conserves…”).
Peter: you repeatedly treat `theoretical physics’ as synonymous with `theoretical high energy physics.’ Please don’t. Theoretical high energy physics is only a subset (and an increasingly small subset) of theoretical physics writ large.
Anonymous physicist,
I appreciate the point, usually try to use a different term, e.g. “fundamental” theoretical physics. The problem with “HEP theory” is that the traditional leadership of that field (e.g. consider the IAS theoretical physics faculty) has stopped doing that long ago, with the “having something to do with quantum gravity” now a more accurate description. I have no idea what the right terminology is for what people like Witten have been doing for the last forty years, or for what they are doing now.
Some younger people in that general field refer to it (Ie what the string theory community is now doing) as ‘formal theory.’ Perhaps that is as accurate a name as any. It has the advantage that it also connotes theory that is increasingly disconnected from the rest of physics, both theoretical and experimental. And indeed I think nowadays the majority of people who consider themselves theoretical physicists essentially ignore the entire field and almost everything its practitioners have done.
Sorry to evoke the Sting Wars, as my recollection was solely meant to illustrate. I believe you could substitute any other framework or theory, and find the degree to which it is differentiated from String theory would be inversely proportional to its worth in Witten’s judgement. Which, again, is striking, given what is otherwise characteristic about his statements. I don’t know, of course, but I’ve concluded that’s simply what he thinks, and in his mind so clear as to require no moderation. A lot of folks who look to me like zealots have been less stark. I simply find it amazing that someone of his brilliance and equanimity has ended up embracing the multiverse. A logical conclusion based on the overwhelming correctness of String/M theory, I guess. But a premise with zero empirical evidence to show for over half-a-century of work is one hell of a premise to be so convinced of. Especially for what may be the greatest brain of any living human.
On the topic of Grothendieck, the Notices of the AMS published several times biographical notes on him, the most extensive are perhaps this couple by Allyn Jackson, in case anyone wants something a bit more in depth.
https://www.ams.org/notices/200409/fea-grothendieck-part1.pdf
https://www.ams.org/notices/200410/fea-grothendieck-part2.pdf
On the interviews, the one with Vafa has an interesting reply from him on the sociology of string theory that I haven’t seen anyone else bring up: “So, I would say that the very fact that new ideas are blossoming from string theory has been the reason it has continued, despite the fact, despite the striking fact, there has been zero experimental connection.” To what extent are people working in this field because there’s a constant stream of not too difficult ideas coming in that people can spend some time on and get a result out of? Is there a contributing factor that PhD advisors are telling their students, “hey, there’s these ideas in string theory you can work on and I think you’ll definitely get some good results out of” versus them being unsure what kind of results they could get if they work on something else.
On the topic of picking out a single person to be the most influential/talented figure, I think it is a bit of a silly thing to spend time on, similar how you might get debates on various forums about who is the greatest or most important figure of the XXth century, etc. Perhaps before the “modern” times, say in the times of Poincaré or Hilbert or early in Einstein’s life it would be easier to give a reasonable scientific estimate because a) the fields weren’t too big and b) there weren’t as many people working on them (in 1900 the number of physics PhD awarded was 10). By the time of WW2 fields had become much larger and the number of people working in theoretical physics has only ever continued to increase. Thus there were probably far more physicists working on string theory in the 1990s and 2000s than there were physicists working on quantum theory in the 1920s or 1930s, and consequently the responsibility of any individual theorist would have gone down on average. Even on the ends of the bell curve, how would you compare someone like Witten with someone like Weyl? As he himself admits in the interview he thinks his influence is overrated, and for sure if he was doing something else then some connections wouldn’t have been made, but many things would have still been worked on by the dozens of others working on the theory regardless, which is a point he made in the interview, while it’s harder to make that argument the further you go back (ie with Weyl), particularly on topics that take inspiration from mathematical rather than experimental ideas.
On the topic of giving a name, given that the first sentence of the Wikipedia article on theoretical physics says that the field tries to “rationalize, explain and predict natural phenomena”, perhaps something like mathematical physics would be more appropriate?
And finally, besides LQG and strings, are there many other framework theories that have any serious hope of contributing towards a theory of quantum gravity?
Jonathan,
I do think it’s true that the continued huge research effort in “string theory” (or whatever you want to call it) is driven by the sociological fact that it is set up to provide things that people can work on and write papers about using the tools they’re now familiar with. The lack of any success of this effort for decades means that what’s really needed are some quite different tools and ideas, but that kind of research is difficult, not rewarded, and lacking any community support.
I don’t see any point in most comparisons “was X better than Y”, but I do think Grothendieck and Witten are rather special cases, with Witten an unparalleled case of someone having an overwhelming influence on his field. Without him I think the Green-Scharz anomaly cancellation result and superstring theory would have been just another speculative path to unification that would have attracted a small fraction of the field, and died off in not too many years as it went nowhere. Away from string theory, his immense contributions to mathematics and to QFT/topology would not have happened. The whole landscape of this kind of theoretical physics and of mathematics would be very different.
And no, “mathematical physics” is not an appropriate term. If you look at much of what is going on as “formal theory” (as an example, the “it from qubit” stuff), the mathematical content is minimal. The problem is not that physicists have pursued mathematics, but that they have pursued bad ideas about physics.
@David Roberts, and more generally re: the question of whether Grothendieck was angry about Deligne’s proof
I think you are extrapolating too far based off of what I remember to be just a few comments of Grothendieck that he had heard that Deligne had finished the proof of the Weil conjectures. Looking at the evidence is available to us, I find none (and in fact much to the contrary) that he was bitter about that proof in particular not being through the standard conjectures, while he was clearly upset about motives and surrounding ideas not being pursued in the years after (which is a completely different thing).
I believe that the claim that Grothendieck vilified or was at angry at Deligne for proving the Weil conjectures in the way he did is simply false, but close enough to the truth – not in the sense that it is almost true, but that the truth can be confused with it through a hasty paraphrase – that it is repeated a lot. Given what we know of Grothendieck’s life and personality, it should not be surprising that many claims about him are exaggerated or just false. Given all the inaccuracies I’ve heard about him, this would be a more understandable one, though it is unfortunate that it is so widespread.
Regarding evidence for my claim, I think Recoltes et Semailles is a reliable reference, because the question at hand is precisely what Grothendieck thought about a certain thing, and Grothendieck is clearly writing what he thinks there (regardless of whether his analysis is correct). Here Grothendieck speaks highly of both the fact that Deligne proved the Weil conjectures (in Weil I), and of the progress that Weil II represented. I never read any part where he insinuated that it was wrong for Deligne to use the methods he did, whereas he did say that establishing the truth of the Weil conjectures should have been taken as encouragement to continue to work on motivic ideas.
Grothendieck certainly makes no secret that he’s upset at the development/non-development of motives and other mathematics in the 15 or so years after he formally left the mathematical scene. How justified his stance was may be a difficult question, but I’d say that it is far more understandable than being upset about a particular paper because of its methods. Like I mentioned earlier, I would guess that the uniqueness of Grothendieck’s life and character would make it easier for such a rumor to spread.
Anyone who has read even small portions of récoltes et semaille (and is fluent in french) would understand how “angry” Grothendieck was at his former students. He repeatedly (and in fact it is one of the main subjects of the book) speaks about what he calls the ” funeral” i.e. the fact that he thinks that his students have purposefully tried to reduce the amount of credit given to him (especially about the developement of étale cohomology SGA 4 1/2 being a big point of anger) and have tried to make topos theory “disappear”.
I think that most people (me very much included) think that this is complete delusion on Grothendieck’s part. But this is not the case of everyone : for example Laurent Lafforgue has recently published a text that goes in Grothendieck’s direction (https://www.laurentlafforgue.org/Corrections_Lafforgue_entretien_Bourguignon_Grothendieck_RS.pdf). This passage is striking (although in my opinion completely wrong) :
“Grothendieck emploie le mot « enterrement » non pas du tout comme un acte de rupture avec la « communauté scientifique » mais comme le constat qu’il fait que des pans entiers de son œuvre mathématique qu’il considère particulièrement importants ont été non seulement délaissés par ses anciens élèves et collègues mais font l’objet de leur part d’un « dédain » parfois affiché, d’un sourd « mépris » et d’une hostilité qui en interdisent l’accès aux jeunes générations. Presque quarante ans après « Récoltes et Semailles », on peut constater que la plupart des thèmes dont Grothendieck déplorait alors qu’ils fussent dédaignés ou proscrits, comme les catégories dérivées ou les motifs, sont revenus en force et sont étudiés dans le monde entier. Cependant, le thème des topos, que Grothendieck plaçait en tête de la liste des thèmes importants proscrits, est toujours exposé à une grande hostilité dans le monde académique. En fait, nombreux sont les étudiants qui veulent se lancer dans ce sujet, mais ils font l’objet d’intimidations de la part de représentants du monde académique qui tentent de les dissuader de s’engager dans cette voie.”
Einstein wrote a paper claiming that gravitational waves don’t exist. String theorists similarly misunderstood what string theory tells, when they wanted to believe it’s a theory with some supersymmetric vacua.
typo “let’s Witten give a non-answer”
Witten was at U.W. Madison for a semester — Zierler probably transcribed it incorrectly.
David Brown,
Typo fixed.
Could be a transcription error, could be Witten misremembering (the 70s were a long time ago…)
Be careful Peter, when reading Récoltes et semailles, not to go down the rabbit hole. [In the 1980s, Grothendieck sent me a copy, and asked me whether I was a “knowing” or “unknowing” member of the conspiracy.]
To Peter,
“I can understand why Witten hopes that the mystery of quantum information theory and gravity will give insight into and resolve the mystery of what M-theory is, finally vindicating his 1984 vision, but this looks to me like a very, very long shot.”
Could you elaborate on this? What do you think of Witten’s prediction on quantum information and quantum gravity? Do you think it’s an area worth pursuing for young researchers today?
Thanks
Anonymous,
I think there’s zero chance for what Witten is hoping for (a vindication of M-theory through quantum information theory approaches to quantum gravity).
The QIT/QG business seems to be yet another example of the pathological sociology that has afflicted HEP/fundamental theory for decades now. Based on a minor intriguing result, the entire field orients itself around a very speculative idea almost sure to not work out. There are endless promotional talks, little realistic evaluation of whether the idea is going anywhere. Grants, conferences, talk invitations, awards, jobs, articles in the press, etc. all start flowing to those who seem to be working on the hot idea. If you’re a young researcher you’re in a really ugly position: to get a job you should work on the hot idea, even if it’s not going anywhere and already has too many people doing it. This pattern just goes on and on.
By the way, I was just taking a look at the AIP site which has interviews, now one with Lars Brink. Brink is a die-hard superstring enthusiast, but even he now thinks the way string theory was pursued was not desirable:
“So, sure, I think it has been overdone in a sense. I think there’s also been too many people working in string theory. There was a time in the ’80s and ’90s when every American university should have a string theory group. They were sort of vacuum cleaning the market for people. That’s never good. For a long time, people could survive by reading string papers, and they could then do some twist on it, and that has been a bit too much. We all have to pay for it now because the funding of fundamental physics as such is diminishing and even dwindling. Here in Sweden, it’s a disaster. My younger colleagues had good funding 10-15 years ago. Now they’re not getting any funding at all from our research council. They are putting much more money into say quantum information. Of course, I’ve only listened to some seminars in quantum information, but I think they will also follow, more or less, the same scheme. There will be simple problems that they can work on, and then they will get out in various directions. It’s not necessarily so but it will be more, again, mathematics of some kind.”
One of the problems with It from Qubit is that it’s really quite hard to tell the papers that are nonsense from the ones that aren’t. For example, Maldacena and Susskind’s ER=EPR paper is a speculative idea that has no chance of being correct (but listening to his most recent talk, Susskind hasn’t given up on it). And when you actually corner other people in the area they (or at least some of them) will admit that this paper has virtually no chance of being correct, but for some reason they aren’t willing to say this publicly.
There are undoubtedly other papers in this field which are equally improbable. But it seems to me that any field where you have to be in the cogniscenti to know which papers are the ones worth paying attention to is in deep trouble.
Peter Shor,
String theory at least in the mid-late 1980s came with a fairly specific conjecture about what the theory was and how it was going to connect to reality (approximate Calabi-Yau compactifications). This didn’t work out as hoped, and string theorists were driven to more and more complicated conjectural “solutions” to the theory, at some point early on passing the “Not Even Wrong” boundary into a framework incapable of making any sort of conventional testable (even in principle) prediction.
The ER=EPR/It from Qubit program on the other hand started out from the beginning “Not Even Wrong” in a stronger sense, without anything like a well-defined conjecture relevant to the real world. Looking at the 2013 ER=EPR paper
https://arxiv.org/abs/1306.0533
besides writing down a metric in the appendix, the paper is 43 pages of verbiage and pictures, with no non-trivial equations. The “cognoscenti” problem here is that you need access to one of a small number of people to explain to you which of the verbiage corresponds to something well-defined which you could write down an equation for, and which corresponds to an extremely vague hope/dream with nothing backing it.
Whenever I try and look into the literature of this field, all I can see that is well-defined are toy model calculations, often in 0+1 or 1+1 dimensions. These may be very interesting, but they don’t seem to come with any serious proposal for what they are supposed to imply about a realistic (even in the sense of having any physical gravitational degrees of freedom at all) theory.
Probably others have the same problem I have with writing anything publicly about this. The literature is huge and complicated, so it would be a full time job to master it to the point of being sure there is no there there. I’ve been through this before with string theory claims and wasted far too much time on that. Until the people working on this start producing review articles that clearly explain how what they are doing is supposed to connect to reality, what has worked and what hasn’t, it seems to me that the rest of the world should assume that, as far as a theory of fundamental physics goes, this is just another extremely speculative vague idea that is not working out.
I wonder on what grounds ER=EPR is supposed to have “no chance” of being correct. There is already the curious parallel of non-traversibility of wormholes, and non-transmission of information via entanglement alone; obtaining both of these limitations from a common origin is exactly the kind of beautiful conceptual connection one expects from a deep correct insight.
Perhaps I should also be asking what “It from Qubit” ideas *are* to be considered promising!
@Peter Shor
I’d be interested to hear why you think ER=EPR has no chance of being correct.
If we compare It from Qubit to “old-fashioned string theory,” I think we’d have to say that, yes:
– Both seem difficult to inform by any feasible experiments (apart from “experiments” that are really simulations, e.g. of one quantum system by a different one).
– Both have fundamental concepts that still lack clear mathematical definitions, except in special cases that are then speculatively extrapolated way beyond.
– Both have a strong predilection for toy models (with, e.g., unbroken supersymmetry, negative cosmological constant, different numbers of dimensions) that make clear departures from the observed world.
Having said, I’d submit to the people here that there’s at least one respect in which It from Qubit sharply differs in flavor from “old-fashioned string theory.” Namely, IfQ takes as its starting point a fundamental conceptual problem (black hole information loss) that would presumably need to be confronted eventually in any theory that encompassed both QM and GR. It tries to produce general insights that would interest anyone who cared about that problem, regardless of the unknown details of what might be happening at extremely high energies and short distances. It often uses string theory as a source of examples, but then (as it were) discards the strings like scaffolding, so that many of the results and open questions can be made surprisingly comprehensible to anyone who understands and accepts QM, plus some high-level facts from GR and QFT.
For instance, anyone, regardless of their speculative commitments about the Planck scale or lack thereof, can now be asked: so, OK, what do *you* think would happen if you did the AMPS experiment? If you wouldn’t encounter a firewall at the event horizon, then which of the assumptions leading to that apparent conclusion do you reject? Or (as in Susskind’s recent talk): could an observer jumping into a black hole see the answers to certain computational problems that are exponentially hard even for quantum computers? If not, then again: which of the assumptions seeming to point that way are false?
If we reach for analogies in the history of physics, none of this strikes me as analogous to any of the great triumphs—the experimentally-confirmed new theories—but much of it *does* strike me as analogous to the posing and sharpening of puzzles (e,g., Newton’s bucket argument, Einstein’s hole argument, Maxwell’s demon, EPR…) that often either preceded the triumphs or drew out their consequences after the fact.
Why do I think ER=EPR has no chance of being correct? I think the idea (somebody correct me if I’m wrong) is if you take a whole bunch of entangled pairs of particles, say in the state 1/sqrt(2)(|↑↓〉-|↓↑〉), and let them collapse into two black holes, you get an Einstein-Rosen bridge between the black holes.
Now, suppose you take a whole bunch of entangled particles 1/sqrt(2)(|↑↑〉-|↓↓〉) and let them collapse. This is the same thing as turning one of the two black holes 180 degrees, so shouldn’t they also form an Einstein-Rosen bridge? Now, suppose you take a whole bunch of particles, half of them 1/sqrt(2)(|↑↓〉-|↓↑〉) and half of them 1/sqrt(2)(|↑↑〉-|↓↓〉). Do they form a black hole as well? If not, why not? … you started with a lot of entanglement, it just wasn’t consistently oriented. But if they do, then it seems to lead to the conclusion that you can make an Einstein-Rosen bridge out of pairs of particles with no entanglement between them at all, because a probabilistic mixture of these two entangled states is equivalent to an unentangled state. And if they don’t, you need to answer the question of how much consistent orientation do you need before you get a bridge? And is there a continuum … if more of the particles are have the first orientation rather than the second, do you get a partial Einstein-Rosen bridge? How exactly does this work?
Now if the original paper had actually discussed questions like this, maybe I would take it seriously. But no, it was a grand hand-wavey idea that sounded good, but as far as I can tell, had utterly no thought given to the possibility that when you try to work out the details, they might turn out to be inconsistent.
Thanks Scott for the explanation of motivation for this. I do have to now discourage further technical discussion of these issues in this comment section, partly because they’re off-topic, partly because I’m incompetent to moderate such a discussion.
@Peter Shor: The ER=EPR argument starts from the observation that the thermofield double state of two entangled CFTs is holographically dual to an Einstein-Rosen bridge. This observation had actually already been made ten years earlier by Maldacena. However what Maldacena and Susskind did is observe that you could make a naive version of the AMPS paradox for the thermofield double state, but that it’s resolution is obvious (the interior partner of the Hawking mode and its purification in the opposite CFT are the same fundamental degree of freedom). When Lenny talks about collapsing entangled qubits into black holes to make a wormhole, he really means constructing the analogue of the thermofield double state in some hypothetical version of holography beyond AdS/CFT. A generic entangled state will not have any sort of short classical wormhole, and no one claims that it does.
They then argued that “morally” the same solution should work for actual evaporating black holes, because we should think of any pair of entangled particles as (in some poorly defined way) physically equivalent to a connected wormhole. This claim as they originally stated it is very imprecise – what on earth is the physical meaning of a “Planckian wormhole” connecting any Bell pair? – to the point where it’s “not even wrong”.
But a year or so later a paper by Engelhardt and Wall was published introducing the “quantum extremal surface prescription” for computing holographic entropies. And in that prescription classical geometry and entanglement of quantum fields are treated in exactly equivalent ways. This can be thought of as a precise realisation of the vision of ER=EPR in at least one important context. The 2019 developments that Witten referenced in his interview then applied those formulas to evaporating black holes in a way that essentially realises the vision of Maldacena and Susskind.
So sometimes (aspects of) grand hand-wavey ideas can eventually be turned into precise calculations, although it normally takes a lot of work.