More Math and Physics Items

Yet more math items:

  • First of all, congratulations to my colleague Johan de Jong, recipient of the 2022 AMS Steele Prize for Mathematical Exposition. Johan’s Stacks Project is very much deserving of such recognition. It’s both huge in scale and very high in quality, with nothing else really comparable. While it has attracted many contributors, it has always been mostly a one-person effort. If you’re interested in helping, even those not so expert in the field can contribute by fixing any mistakes they might find when using this incredible resource.
  • On my currently favorite topic of the unity of math (and physics), there’s a talk by Barry Mazur, in which he begins by raising the question “What is it that unifies Mathematics?”. He goes on to turn around the question “What is the physical interpretation of the Jones polynomial?” asked by Atiyah (and answered by Witten’s Chern-Simons theory). Mazur asks:

    What is the Arithmetical-Algebraic-Geometric interpretation of the Jones polynomial?

    or of Chern-Simons theory?

    or of TQFT?

  • Mazur’s title is “Bridges between Geometry and Number Theory”. The metaphor of “bridges” to describe what unifies mathematics gets a workout in a recent Quanta article about Ana Cariani and the Langlands program entitled The Mathematician Who Delights in Building Bridges (and subtitled Ana Caraiani seeks to unify mathematics through her work on the ambitious Langlands program.)
  • At the same conference as the one with the Mazur talk, Maxim Kontsevich spoke on Geometry from the perspective of quantum mechanics and string theory. His talk was a great summary of various aspects of the problem of quantization, in both quantum mechanics and conformal field theory. There wasn’t much though about what has been going on since the early developments in conformal field theory that he discussed. Things got a bit worrisome at the end, when he announced that he can’t understand Kevin Costello these days (if he can’t, who can?), and ended with (here’s a google-aided transcript):

    You see that gauge theories and gravity appears in various interactions is it’s in nothing else in a sense, and geometric limits of various string theories or quantum field theories and what I claim that it’s in fact it’s something generally about complex systems and mathematics. You do some combinatorial problem, whatever it is you get some counting or something, and then maybe you look on asymptotic growth of the number of solutions. It could be something very simple but your arranged parameters became something more complicated and if you see something more complicated it’s kind of I think it’s unavoidable you see some physics in a very wide sense: some string theory, some membranes, whatever. Okay, thank you.

    I can’t really make much sense of this, but he seems to have some sort of vision of fundamental physics being linked with complexity, a point of view that seems increasingly common, while not leading anywhere promising.

Moving to purely physics topics:

  • Noah Miller was a student here at Columbia in one of my mathematics of QM courses. I’ve had some wonderful students in those classes, and he was one of the best. He has gone on to graduate study in physics at Harvard, and I just saw a beautiful new paper by him this week on the arXiv, From Noether’s Theorem to Bremsstrahlung: a pedagogical introduction to large gauge transformations and classical soft theorems. It’s an exposition for non-experts of some of the new ideas about gauge symmetry and physics that Strominger and collaborators have been working on, highly lucid and readable.
  • I very much recommend taking a look at the talk from earlier this year by Mikhail Shaposhnikov, Conformal symmetry: towards the link between the Fermi and the Planck scales. Shaposhnikov has done a lot of fascinating work over the years, developing in detail a point of view which hasn’t got a lot of attention, but that seems to me very compelling. He argues that the SM and GR make a perfectly consistent theory up to the Planck scale, with the “naturalness problem” disappearing when you don’t assume something like a GUT scale with new heavy particles. Watching the discussion after the talk, one sees how many people find it hard to envision such a possibility, even though all experimental evidence shows no signs of such particles. For more about what he is in mind, see the talk or some of the many papers he’s been writing about this.
  • Finally, skydivephil tells me he has managed to get David Gross and Carlo Rovelli to debate string theory vs. loop quantum gravity, with video to drop on Youtube tomorrow. I normally try to make it a policy to avoid getting into this particular debate, but this I have to see. While you’re waiting for this, you can watch an earlier pairing well worth seeing: Alan Guth and Roger Penrose debating the multiverse versus cyclic cosmology.

Update: I just watched the Gross/Rovelli debate, and thought Rovelli did a good job of making the case that string theory is a failed research program. Gross spoke uninterruptedly at length, but interrupted Rovelli constantly. I found it interesting that Gross acknowledged “supersymmetry hype” and hype back in 1984-5, while at the same time engaging in massive amounts of hype about the current state of string theory. On the time scale for progress in string theory, he says 80 years (end of the century) to understand how to use string theory to solve QCD, no time scale for getting unification out of string theory.

Gross’s main point he kept repeating is that “string theory” now means an overarching framework that includes the Standard Model, so there’s no distinction between the Standard Model and “string theory” and you can’t argue that “string theory” is a failure. This argument is so silly that it’s hard to engage with it in any sensible way, and Rovelli didn’t even try.

Update: There’s an interesting long interview with Andy Strominger here. Some of this brought back old memories, since Strominger overlapped with me a bit as an undergraduate at Harvard, although the story of that part of his life is very unusual. I hadn’t realized the extent to which from the very beginning he was focused on the problem of quantum gravity, which to some extent explains his lack of interest in particle physics extensions of the Standard Model.

One thing he makes clear is that at this point string theory has become completely disconnected from the possibility of saying something testable about the real world. The AIP interviewer kept trying to ask about that, leading to this exchange:

Zierler: So is there an experiment that you can conceive of that could disprove string theory?

Strominger: I guess I am not getting my point across.

Zierler: You’re saying that string theory is totally outside the world of experimentation.

Strominger: … So yes, I don’t think – not many string theorists will talk this way – but I don’t think that we are in my lifetime — and I’m planning to live a very long time — going to get direct experimental evidence for string theory.

On the issue of what the terms “string theory” now mean. Strominger makes it clear that from the point of view of him and many others, there’s no longer any possible critique of “string theory” as a fundamental physical theory:

For the last 30 years, everything new that we’ve discovered, as long as we can relate it to the ideas in string theory, we call it string theory. So, if we continue to call everything that we discover string theory, it’s virtually certain that– (both laugh) It’s certain that when we get to the answer, we’ll call it string theory!

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16 Responses to More Math and Physics Items

  1. lun says:

    Shaposhnikov’s lecture is about https://arxiv.org/abs/2110.05175
    right? They seem to completely ignore the issue of triviality of the theory
    (in the sense of https://en.wikipedia.org/wiki/Quantum_triviality )

  2. Peter Woit says:

    lun,
    No, the talk was not about that recent paper but about Shaposhnikov’s long-standing research program. He has lots of relevant papers, for an early one, see
    https://arxiv.org/abs/0708.3550

    The point he is making about no hierarchy problem if you have no GUT scale is a very simple one: if you just look at the SM and gravity, the only energy scales are electroweak and Planck. Since you don’t actually have a viable theory of what is going on at the Planck scale, the only thing you have to go on is a single-scale theory, and that doesn’t have the fine-tuning problem you get when you try to maintain two very different energy scales. Taking into account both scales, he suggests a possibility is that a unified theory just has one scale (Planck), with the electroweak scale an exponentially small non-perturbative effect.

    So, the hierarchy problem appears when you write down a GUT theory, or a unified theory including gravity which has Planck-scale states. Conventional GUT theories and string unification models have this problem, but there’s also zero evidence for them.

    Besides this simple point, he has a well-developed research program dealing with the issue of gravity and many others. I think it’s extremely interesting and should be getting a lot more attention than it does.

  3. Johan Smit says:

    I wonder what Cumrun Vafa and the people working on the Swampland would think about David Gross’s redefinition of string theory to encompass all of theoretical physics.

  4. Peter Woit says:

    Johan Smit,

    I think most string theorists are well aware that the argument Gross makes about string theory and the SM doesn’t pass the laugh test. Gross didn’t mention the “swampland” argument, I’d guess that he (like most string theorists) doesn’t find it a compelling as an argument for string theory.

  5. Bertie says:

    Skydive Phil has a poll up on twitter as to who won the Gross/Rovelli debate.
    IMO Gross did his cause no favours in hogging the conversation then getting all defensive when Rovelli spoke.

  6. WD says:

    After watching the Rovelli/Gross debate, I couldn’t help but feel somewhat sorry for Gross. Quite frankly, he came across as somebody well past his best, and desperately clinging to old ideas. Also, his body language was borderline disrespectful. I was not impressed.

  7. Peter Woit says:

    WD,
    I thought Rovelli handled this very well, comparing Gross to Einstein: a theorist who did extremely important work early in his career, but ended up in the last decades of his career chasing a failed research program.

  8. anonymous says:

    “For the last 30 years, everything new that we’ve discovered, as long as we can relate it to the ideas in string theory, we call it string theory. So, if we continue to call everything that we discover string theory, it’s virtually certain that– (both laugh) It’s certain that when we get to the answer, we’ll call it string theory!”

    So when will string theorists start to call number theory and algebraic geometry “string theory”, if they continue to discover and/or prove things in number theory and algebraic geometry like they have in the past 30 years?

  9. Peter Woit says:

    anonymous,
    Wouldn’t surprise me if there were physicists now calling algebraic geometry “string theory”. Number theory however I think is safe from this for now.

  10. SRP says:

    Soundsl like string theory is the opposite of (pre-boom) AI, where once a task was successfully automated we stopped calling it”AI.”

  11. Dimitris Papadimitriou says:

    Andy Strominger’s interview was really interesting.
    He seems to have an exciting life ( and not only in physics!).
    The era between the 60s and 70s were a unique period in the history of humans. ( I’m a bit jealous!).
    It seems also that he’s a quite honest and unpretentious person. Somewhere in the middle of the interview he mentions that most string theorists did not understood very well GR back then, and this is quite true:
    For a long period of time he and Gary Horowitz were among the few in the strings community that had a deep knowledge for the theory of gravity.
    Untill recently, some of them had a weird, almost hostile attitude towards some aspects of GR, as in the case of firewalls for example.
    They also underestimated the importance of the dynamical internal spacetime geometry of black holes, at least before the important paper of Christodoulou/ Rovelli ( about the growth of the slice independent maximal volume of the black hole interior), that revealed a potential danger for holography.

  12. sdf says:

    News to me from the title slide of the Kontsevich lecture: “Laurent Lafforgue, Huawei”!!

  13. Z Y says:

    sdf,

    Funny coincidence, I came today to this blog specifically to see if there was any comment regarding Lafforgue’s move to Huawei 🙂

  14. Mike M says:

    Oof, the Gross/Rovelli “debate” was tough to watch. I agree with Bertie’s comments above. It really seemed like Rovelli showed up prepared for a thoughtful debate, while Gross’ approach was much more casual. Early on when Rovelli politely asked to be permitted to give uninterrupted opening remarks, Gross countered with “Well, I want to be able to make corrections along the way…” which is kind of a microcosm for the larger cultural problem.

    I like Skydivephil’s channel, but I get a bit nervous about debates/conversations like this in the public view. Could a novice viewer could walk away with the impression that “physics” is really just a lot of fancy semantic arguments.

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