Not Even Wrong

This past semester I taught our graduate class on Lie groups and representations, and spent part of the course on the Heisenberg group and the oscillator representation. Since the end of the semester I’ve been trying to clean up and expand this part of my class notes. I’m posting the current version, working title From Quantum Mechanics to Number Theory via the Oscillator Representation. This is still a work-in-progress, but I’ve decided today to step away from it a little while, work on other things, and then come back later perhaps with a clearer perspective on what I’d like to do with these notes. In a few days I’m heading off for a ten-day vacation in northern California, and one thing I don’t want to be thinking about then is things like how to get formulas involving modular forms correct.

There’s nothing really new in these notes, but this is material I’ve always found both fascinating and challenging, so writing it up has clarified things for me, and I hope will be of use to others. The basic relationship between quantum mechanics and representation theory explained here is something that I’ve always felt deserves a lot more attention than it has gotten.

In the past I’ve often made claims about the deep unity of fundamental physics and mathematics, One goal of this document is to lay out precisely one aspect of what I mean when making these claims. There are other much less well understood aspects of this unity, but the topic here is something well-understood.

One thing that struck me when thinking about this and teaching the class is that this is a central topic in representation theory, but one that often doesn’t make it into the textbooks or courses. Typically mathematicians develop theories with an eye to classifying all structures of a given kind. This case is a very unusual example where there is effectively a unique structure. The classification theorem here is that there is basically only one representation, but it is one with an unusually rich structure.

When I get back from vacation, I plan to get back to work on the ideas about twistors and unification that I’m still very excited about, but have set to the side for quite a few months while I was teaching the class and writing these notes. More about that in the next few months…

A few unrelated items:

• I’ve been hearing from several people about their plans to travel to China this summer, just realized that they’re all going there for the same reason, to participate in the First International Congress of Basic Science. This is something new and on a grand scale, featuring 240 or so invited speakers, award of a new million dollar – plus prize, together with prizes for “Best paper” over the last five years in 36 different categories. Yau is the main organizer, and the Chinese government is providing the funding. So, if it’s July 16-28 and you are wondering where your colleagues are, quite possibly the answer is Beijing.
• I’m doing my best to try not to think about the implications of recent AI developments for mathematics, but someone who is doing a lot of thinking about this is Michael Harris, who this week at his Silicon Reckoner substack discusses Google’s use of arXiv math papers to train their Minerva language model. Harris raises the interesting question of whether this use of arXiv papers violates the licenses of these papers, standard ones of which include language like
  

  You may not use the material for commercial purposes.

  Even if Google is massively violating the arXiv licenses for commercial purposes, it’s unclear whether anything can be done about this, especially given the legal resources Google can afford. In addition, I suspect that when hearing about this a more common response than “this is terrible, I want to sue” would be “this is great, how can I get this thing to write papers for me, or even better, get Google to pay me to help make this possible.”

• Last month Symmetry magazine had an article Whatever happened to the theory of everything? featuring some quotes from me and John Ellis. Ellis explains that the particle physics community has become skeptical of supersymmetry and string theory:
  

  Supersymmetry seemed less and less likely to be right, and superstring theory never materialized into something with testable and concrete predictions.

  “The rest of the community is asking, ‘Where’s the beef?’” Ellis says. “There hasn’t been any beef yet. Maybe particle physicists have turned a bit vegetarian and have lost interest in stringy beef.”

• Possibly in response to the problem for string theory that Ellis is pointing to, Witten next week is giving a non-technical theoretical physics colloquium talk at the ICTP on What Every Physicist Should Know About String Theory. Back in 2015 he published something with the same title in Physics Today, which I wrote about here. We’ll see if there are any new arguments on this now very old topic.

Update: The 2023 Shaw prize in mathematics is going to Drinfeld and Yau.

Update: I missed the fact that last there was a Breakthrough Prize ceremony last month. This year they’ve emphasized even more the “Oscars of science” idea by moving the ceremony from Silicon Valley to LA and having it at the Academy Museum of Motion Pictures. The announcement has none of the names of the scientists, just the names of the Hollywood stars that would attend.

Update: I see (from a Strumia tweet) that a Witten 2015 talk with the same title is available here, was given I guess as a public talk at Strings 2015. It’s all about the differences between the 1d single-particle path integral and the 1+1d worldsheet path integral, unclear to me why this is something every physicist needs to know about, or whether this year’s version will be different.

I want to make up for linking to something featuring Michio Kaku yesterday by today linking to the exact opposite, an insightful explanation of the history of string theory, discussing the implications of how it was sold to the public. It’s by a wonderful young physicist I had never heard of before, Angela Collier. She has a Youtube channel, and her latest video is string theory lied to us and now science communication is hard.

Instead of going on in detail about the video and what’s great about it, I’ll just give you my strongest recommendation that you should go watch it, now. It’s as hilarious as it is brilliant, and you have to see for yourself.

Yesterday afternoon there was an event at CUNY featuring a panel discussion on Chern-Simons terms. Nothing new there, although it was interesting to hear first-hand from Witten the story of how he came up with the Chern-Simons-Witten theory. One piece of news I heard from Nikita Nekrasov was that he was missing a talk that day at the Simons Center in Stony Brook by Maxim Kontsevich, who would be arguing that the Hodge and Tate conjectures were not true. The video of that talk has now appeared, see here.

I’m way behind in preparing for my class for tomorrow, so haven’t had time to watch the full video and ask experts about it. Will try and learn more tomorrow after my class, but it does seem that if Kontsevich is right that would be a dramatic development. If you are able to evaluate Kontsevich’s arguments, any comments welcome. Tomorrow I’ll also try and at least find some good references to suggest for anyone who wants to learn the background of what these conjectures say.

Update: I see there’s an older version of this idea described here.

Update: Having watched the video and talked to a few people about it, I fear that there’s not much new here, and nothing likely to convince experts that a falsification of the Hodge or Tate conjectures is on the horizon. Kontsevich himself introduces the talk as “not really a talk, but a kind of after-dinner rant.” He for a long time has been trying to find examples that could falsify the Hodge conjecture, with no success so far, and from what I can tell, he doesn’t have a new compelling proposal for where to look and how to do this.

Lex Fridman’s latest podcast features a nearly four hour long conversation with Edward Frenkel, under the title Reality is a Paradox – Mathematics, Physics, Truth & Love. Normally I’m fairly allergic to hearing mathematicians or physicists publicly sharing their wisdom about the larger human experience (since they tend to have less of it than the average person), and I’m pretty sure I’ve never before listened to a podcast/interview longer than an hour or so. But in this case I listened to and enjoyed the entire thing. Besides sharing Frenkel’s deep interests in the relation of representation theory and quantum mechanics, and views on the unity of mathematics (and physics…), I envy his positive and thoughtful outlook on life and his openness to a range of human experience. The interview left me with a lot to think about and I recommend it highly.

I recently heard from John Minkowski, whose father Jan Minkowksi was a student of Pauli’s in the late 1940s. He asked if I knew what the specific context of Pauli’s “Not Even Wrong” comment was, and I told him I didn’t. I referred to this early blog post, which explains that Karl von Meyenn (editor of Pauli’s correspondence) had pointed me to a biographical memoir about Pauli by Rudolf Peierls which includes:

Quite recently, a friend showed him the paper of a young physicist which he suspected was not of great value but on which he wanted Pauli’s views. Pauli remarked sadly ‘It is not even wrong.’

Looking around for any more information about this, Wikipedia links to a 1992 letter to the editor at Physics Today from Peierls, which states

Wolfgang Pauli’s remark “Das is nicht einmal falsch” (“That is not even wrong”) was made not as a comment on a seminar talk but as a reaction to a paper by a young theoretician, on which a colleague (I believe it was Sam Goudsmit) had invited Pauli’s opinion.

Google also turned up a translation of a talk by Peierls in this article by Mikhail Shifman, which includes:

Somebody showed to Pauli a work of a young theorist being well aware that the work was not too good but still willing to hear Pauli’s opinion. Pauli read the paper and said, with sadness: “It is not even wrong.”

Trying to guess what the article in question might have been, I’m tempted by the hypothesis that the discussion with Goudsmit was about Everett’s “Relative State” Formulation of Quantum Mechanics paper. The timing (“Quite recently”) would have been right, with the paper published in July 1957, Pauli’s death later in December 1958. Goudsmit at the time was editor-in-chief at Physical Review, so would have been interested in Pauli’s opinion of the paper.

Complicating this story, John Minkowki sent me some pages from his father’s 1991 book Through three wars: The memoirs of Jan Michael Minkowski, which included this (in a context describing his 1946-48 student days at ETH):

I remember a seminar in theoretical physics given by a visitor from another Swiss university. These seminars were presided over by Dr. Pauli, and after the speaker finished all eyes would turn to Pauli to pronounce the verdict in his commentary. This particular lecture was treated by Pauli with progressively faster twirling of his thumbs around and around one another and a growing benevolent smile. Bad sign, we thought. The more he smiled the more vicious he will be, we thought. And sure enough, he smiled some more and said “It isn’t even wrong.”

One possibility here is that Minkowski was mis-remembering something from forty years earlier, another is that the occasion that Peierls was referring to was not the first time Pauli had used the phrase. As evidence for the second hypothesis, see this interview with Konrad Bleuler, which points to the possibility of Stueckelberg as the “visitor from another Swiss university”:

So these seminars took place in a common seminar having also Professor Ernst Stueckelberg, then a Professor in Geneva, also Stueckelberg being a well-known theoretician, his work was very much, if I might remind you of that fact, acknowledged by Richard Feynman. For example, his idea of the particle going back in time being interpreted as an antiparticle came as far as I know originally from Stueckelberg and many other great ideas. I remember one special seminar in which, of course this seminar could be rather called. High Court, with scientific papers in the docket, sometimes really sentenced to death. From that one might record Pauli’s classification of scientific papers. There were two classes or else there were old and right. Or the other class, new and wrong. But hardly anything intermediate. If it was even worse, Pauli would have said “it’s not even wrong.” That was the kind of atmosphere. But all what is written in physics is either understood or else it’s thrown away, and not this half-and-half, what we see at present. But then in this connection it was a search for truth. And for Pauli, a lecture hall was a kind of a holy place where only truth was allowed. And a wrong statement was a sacrilege, and in that sense one should understand his rather extremely sharp remarks he might make to some lecturer who seemed not to present things in a quite logical way. But coming to that special, to another special seminar is the following: Stueckelberg always knew really special — I might say prophetic — ideas. He gave a lecture and of course Pauli — it happened very often — didn’t agree. And said “you are not allowed to say such things.” But you see, Stueckelberg being a prophet, he’s not so easily stopped uttering his prophecies. So Pauli in despair menaced Stueckelberg with a stick and it seemed — I was not present myself but I was told — that the seminar ended like the war of Troy, Pauli, rather corpulent, with his stick after Stueckelberg around the table in the lecture hall. That was the kind of attitude at this period.

I’m not sure what to make of all of this. Perhaps Pauli used the phrase both in the late 40s to criticize Stueckelberg (probably unfairly since many of Stueckelberg’s ideas were ahead of his time) and then Everett in the late 50s (in my opinion accurately, but I don’t want to start up the usual empty arguments about MWI here).

The US particle physics community has been going through a multi-year process designed to lead up this fall to a 10 year strategic plan to be presented to the DOE and the NSF. In particular, this will generate a prioritized list of what projects to fund over this period. The process began with the Snowmass self-study, concluded last year, and available here. Since last fall there have been two independent efforts going on:

• A National Academies study has been holding meetings, materials available here.
• A P5 (Particle Physics Project Prioritization Panel) is holding meetings, see here, and planning for a report to NSF and DOE by October.

Looking through all the materials relevant to particle theory, there seems to me little acknowledgement of the serious problems faced by the subject, or any new ideas for how to address these problems. Most of the effort though is devoted to where most of the money will be spent, on the experimental side. To a large degree, for the short-term it’s clear where funding has to go (to continue supporting the LHC into the HL-LHC era, and finish building the DUNE/LBNF US neutrino project). The longer-term is however very uncertain, as it is unclear whether there’s a viable energy-frontier project that could study higher energies than those accessible at the LHC.

Last week EPP2024 and P5 held Town Hall events at Fermilab, see here and here. There’s video of the EPP2024 event here. On the question of the long-term future, one issue that is getting a lot of attention is that of whether to prioritize development of a possible muon collider. In this presentation a young physicist gives a future timeline including their likely retirement and death dates, showing that a muon collider is their only hope for new energy frontier physics during their lifetime. For those of my age the situation is a bit different, since even a muon collider is not going to do the job. At the EPP2024 event (3:28 in the video) Nima Arkani-Hamed makes the case that:

I think the subject has not been so exciting for many, many decades, and at the same time our ability to experimentally address and solidly settle some of these very big questions has never been more uncertain. I don’t think it’s a normal time, it’s an inflection point in the history of the development of our subject, and it requires urgency… The confluence of the technical expertise for doing so and the enthusiasm amongst the young people who are willing to do it exists now and I very much doubt it will exist in 10 or 15 years from now. If we are going to do it, we have to start thinking about doing it now.

While his point is more general, he’s clearly making the case for starting a new energy frontier machine project soon, with the muon collider the one possibility for getting to higher energies than the LHC.

A few weeks ago there was a workshop at the KITP devoted to the muon collider question, with a news story here (anyone know why the video of the panel discussion is password-protected?). Arkani-Hamed gave a talk aimed at other physicists here. On the European front, a couple days ago there was this meeting.

Already twenty years ago when I was writing Not Even Wrong, it was clear that a muon collider was in principle a very attractive idea for how to get to higher energies and I wrote about this in the first chapter of the book. The much higher mass of the muon than the electron means that you don’t have the same synchrotron energy loss problem, so can build a much smaller storage ring at the same energy, or get to much higher energies with the same size. The problem though is that muons have a life-time of only 2.2 microseconds. This implies two serious difficulties:

• You need to produce, store, accelerate and collide the muons in a very short period of time.
• As the muons decay they’ll produce large numbers of high energy electrons and neutrinos, creating a difficult environment for detectors to operate in and significant radiation hazards.

Normally one thinks of neutrinos as virtually never interacting with anything, but the numbers and high energies of the neutrinos produced at a muon collider create a potential significant radiation hazard, one that cannot be dealt with by shielding.

While I might not be around to see the results from a muon collider, if such a thing is viable, I’d strongly support such a project, and would even buy a t-shirt. The US DOE HEP budget is about a billion dollars/year. One would think this should be enough to accommodate building demonstrator projects or a small collider ring on a 10 year timescale, and possibly even an energy-frontier ring on a 20 or more year timescale. What’s worrying me a bit is the fact that more visible progress on this hasn’t happened since I looked into it 20 years ago. Why no current demonstrator project? Have the potential radiation hazard issues found solutions? I’d be very curious to hear from anyone with expertise on these questions.