Know Time Podcast

For another podcast/interview with me that was recently recorded, see Maths, Twistors & String Theory. Know Time is a series of podcasts that is a project of Shalaj Lawania, and I was impressed by the effort he put into trying to make sense of a complicated and inaccessible subject. For an excellent pairing with what I have to say, see his earlier interview with Matthew Kleban, who has a more positive take on string theory, the multiverse, etc.

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Spring Course

Starting next week I’ll be teaching a graduate topics course, with the general plan to develop much of the quantum field theory of the Standard Model in a form accessible to mathematicians, emphasizing the connections to representation theory. There’s a course web-page here, notes will start appearing here once the course gets underway. While the course will be aimed at mathematicians, I’m hoping that some physicists might find it interesting and worth trying to follow.

The last time I did something like this was back in fall 2003. At that time the course was aimed at getting math students to the point of understanding the TQFTs for Chern-Simons theory and Donaldson theory and was very much based on the path integral. This time I’ll be mostly sticking to flat space-time and using more representation theory. Also, a lot more about spinor geometry, as well about about how Euclidean and Minkowski space-time versions of QFT are related.

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String Theory Hype Fest

I just finished watching the video here, which was released today. Since this was advertised as a panel discussion on the state of string theory, I thought earlier today that it might be a good opportunity to write something serious about the state of string theory and its implications more generally for the state of hep-th. But, I just can’t do that now, since I found the video beyond depressing. I’ve seen a lot of string theory hype over the years, but on some level, this is by far the worst example I’ve ever seen. I started my career in awe of Edward Witten and David Gross, marveling at what they had done and were doing, honored to be able to learn wonderful things from them. Seeing their behavior in this video leaves me broken-hearted. What they have done over the past few decades and are doing now has laid waste to the subject I’ve been in love with since my teenage years. Maybe someday this field will recover from this, but I’m not getting any younger, so dubious that I’ll be around to see it.

Most shameful of the lot was Andy Strominger, who at one point graded string theory as “A+++”, another only “A+”. He did specify that very early on he had realized that actual string theory as an idea about unification was not going to work out. He now defines “string theory” as whatever he and others who used to do string theory are working on.

David Gross was the best of the lot, giving string theory a B+. At two points (29:30 and 40:13), after explaining the string theory unification vision of 1984-5 he started to say “Didn’t work out that way…” and “Unfortunately…”, but in each case Brian Greene started talking over him telling him to stop.

Funny thing is, I think even most string theorists are going to be appalled by this performance. Already, here’s what StringKing42069 has to say

🤮 these old jagoffs have thrown an entire generation of strings under the bus. Fuq them.

Update: I haven’t seen any negative reaction to this hypefest from anyone in the physics community other than from StringKing42069. The Black Hole Initiative at Harvard features the event prominently on its website here advertising Strominger’s participation (he’s a PI).

I’m finding it hard to believe that any of the participants in this thought of it as anything other than an advertising effort useful to try and prop up public support and grant funding. In particular, Strominger’s “A+++” is easier to understand once you realize the extent of the grant funding involved, e.g.:

The abstract of the last of these is A+++ hype in tune with the WSF video:

Vigorous efforts made over the last several decades have advanced our understanding of the fundamental laws of nature beyond the standard model of particle physics. Further advances would potentially include unification of the forces, the reconciliation of quantum mechanics and gravity, a derivation of the standard model couplings, a universal explanation of the area law for horizon entropy, and a theory for the origin of the universe.

For a much older example of successful use of hype to extract grant funding, there’s this Jeffrey Epstein story I hadn’t known about until recently.

Posted in This Week's Hype | 62 Comments

Recent Talk

I gave a “Spacetime is Right-handed” talk yesterday, part of a series entitled Octonions, standard model and unification. The slides are here, video should appear here.

Much of the talk was devoted to explaining the usual relation between spinors and vectors and how analytic continuation in complexified spacetime works then, from both the spinor and twistor point of view. This is contrasted to a new proposal for the relation between vectors and spinors in which the space-time degrees of freedom see only one of the two SL(2,C) factors of the usual complexified Lorentz group.

Nothing in the talk about using this for unification, where the idea is to exploit the other factor, which now appears as an internal symmetry. Starting from the point of view of Euclidean spacetime, the spacetime vectors and spinors that are related by Wick rotation to Minkowski spacetime degrees of freedom behave differently than usual, with a distinguished imaginary time direction. The general idea is that in standard Euclidean spacetime, where the geometry is governed by the rotation group SU(2) x SU(2), so splits into self-dual and anti-self-dual parts, one of these parts Wick rotates to spacetime symmetry, the other to an internal symmetry.

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P5 Report

There is a HEPAP meeting going on today, with release of the long-awaited P5 report prioritizing future HEP spending. The report is available here now, to be officially unveiled later in the day and discussed at the HEPAP meeting. The muon collider as a future project gets a strong endorsement as the “muon shot”.

The full report is now available here.

See press coverage of this at Nature and the New York Times.

There will be continued discussion of the P5 report at HEPAP tomorrow, and at a Town Hall at Fermilab on Monday.

While the theory side of HEP in principle is part of this report, the attention to theory is minimal, with the report recommendations about theory, in total:

  • The substance-less “Enhance research in theory to propel innovation, maximize scientific impact of invest-
    ments in experiments, and expand our understanding of the universe.”
  • A more substantive call to give university theorists on DOE grants more money, with no attempt to prioritize what the money would be for:

    Increase DOE HEP-funded university-based theory research by $15 million per year in 2023 dollars (or about 30% of the theory program), to propel innovation and ensure international competitiveness. Such an increase would bring theory support back to 2010 levels. Maintain DOE lab-based theory groups as an essential component of the theory community.

    In the page or so of text about theory, the emphasis is on the phenomenology part of theory in contact with experiment. About formal theory there is just

    Theorists uncover the mathematical patterns that describe the universe and explore alternate mathematical universes to deepen our understanding of nature. Theoretical investigations into quantum gravity have unlocked connections between extreme space-time geometries and information theory. The perspectives theorists bring to particle physics play an important role in inspiring young scientists.

Update: Sabine Hossenfelder has her reaction to the P5 report here. I’m sympathetic to her critique that, as far as experiments go, the report is an argument for “more of the same”. But I’m not at all sympathetic to her alternative: “Personally, I think what they should do is spend some money on serious theory development” instead of funding experiments. If there’s a part of science where money spent by the US has been much more of a waste than in HEP experiment, it’s HEP theory, which is now pretty much intellectually dead. There’s a good argument that the way HEP theory funding works has been a driving factor in this fatal illness, so that the problem with HEP theory is not too little funding but too much.

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Unification, Spinors, Twistors, String Theory

Last month I recorded a podcast with Curt Jaimungal for his Theories of Everything site, and it’s now available with audio here, on Youtube here. There are quite a few other programs on the site well worth watching.

Much of the discussion in this program is about the general ideas I’m trying to pursue about spinors, twistors and unification. For more about the details of these, see arXiv preprints here and here, as well as blog entries here.

About the state of string theory, that’s a topic I find more and more disturbing, with little new though to say about it. It’s been dead now for a long time and most of the scientific community and the public at large are now aware of this. The ongoing publicity campaign from some of the most respected figures in theoretical physics to deny reality and claim that all is well with string theory is what is disturbing. Just in the last week or so, you can watch Cumrun Vafa and Brian Greene promoting string theory on Brian Keating’s channel, with Vafa explaining how string theory computes the mass of the electron. At the World Science Festival site there’s Juan Maldacena, with an upcoming program featuring Greene, Strominger, Vafa and Witten.

On Twitter, there’s now stringking42069, who is producing a torrent of well-informed cutting invective about what is going on in the string theory research community, supposedly from a true believer. It’s unclear whether this is a parody account trying to discredit string theory, or an extreme example of how far gone some string theorists now are.

To all those celebrating Thanksgiving tomorrow, may your travel problems be minimal and your get-togethers with friends and family a pleasure.

Update: If you don’t want to listen to the whole thing and don’t want to hear about spinors and twistors, Curt Jaimungal has put up a shorter clip where we discuss among other things the lack of any significant public technical debate between string theory skeptics and optimists. He offers his site as a venue. Is there anyone who continues to work on string theory and is optimistic about its prospects willing to participate?

Update: For two more clips from the podcast, there’s one about spinors, and one about “spacetime is not doomed”.

Posted in Euclidean Twistor Unification, Uncategorized | 22 Comments

Spacetime is Right-handed v. 2.0 and Some Notes on Spinors and Twistors

I’ve just replaced the old version of my draft “spacetime is right-handed” paper (discussed here) with a new, hopefully improved version. If it is improved, thanks are due to a couple people who sent helpful comments on the older version, sometimes making clear that I wasn’t getting across at all the main idea. To further clarify what I’m claiming, here I’ll try and write out an informal explanation of what I see as the relevant fundamental issues about four-dimensional geometry, which appear even for $\mathbf R^4$, before one starts thinking about manifolds.

Spinors, twistors and complex spacetime

In complex spacetime $\mathbf C^4$ the story of spinors and twistors is quite simple and straightforward. Spinors are more fundamental than vectors: one can write the space $\mathbf C^4$ of vectors as the tensor product of two $\mathbf C^2$ spaces of spinors. Very special to four dimensions is that the (double cover of) the complex rotation group $Spin(4,\mathbf C)$ breaks up as the product
$$Spin(4,\mathbf C)=SL(2,\mathbf C)\times SL(2,\mathbf C)$$
where these two factors act on the spinor spaces.

While spinors are the irreducible objects for understanding complex four-dimensional rotations, twistors are the irreducible objects for understanding complex four-dimensional conformal transformations. Twistor space $T$ is a $\mathbf C^4$, with complex conformal transformations acting by the defining $SL(4,\mathbf C)$ action. A complex spacetime point is a $\mathbf C^2\subset T$ and conformally compactified complex spacetime is the Grassmannian of all such $\mathbf C^2\subset T=\mathbf C^4$. One of the spinor spaces at each point of complex spacetime is tautologically defined: it’s the point $\mathbf C^2$ itself (the other is of a different nature, with one definition the quotient space $T/\mathbf C^2$).

Real forms

While the twistor/spinor story for complex spacetime is quite simple, the story of real spacetime is much more complicated. When several different real spaces complexify to the same complex space, these are called “real forms” of the space. A real form can be characterized by a conjugation map $\sigma$ (an antilinear map on the complex space satisfying $\sigma^2=1$), with the real space the conjugation-invariant points. Using the obvious conjugation on $\mathbf C^4$, we get an easy to understand real form: the $\mathbf R^4$ with real coordinates, rotation group $SL(2,\mathbf R)\times SL(2,\mathbf R)$ and conformal group $SL(4,\mathbf R)$. Unfortunately, this real form seems to have nothing to do with physics, its invariant inner product is indefinite of signature $(2,2)$.

The real spacetime with Euclidean signature inner product has an unusual conjugation that is best understood using quaternions. If one picks an identification of the twistor space $T$ as $T=\mathbf C^4=\mathbf H^2$, then the conjugation is multiplication by the quaternion $\mathbf j$. The Euclidean conformal group is the group $SL(2,\mathbf H)$. The spinor spaces $\mathbf C^2$ are identified with two copies of the quaternions $\mathbf H$, with the rotation group now the group $Sp(1)\times Sp(1)$ of pairs of unit quaternions.

In this case the conjugation acts in a subtle manner. Since $\mathbf j^2$ is $-1$ rather than $1$, it’s not a conjugation on $T$, but is one on the projective space $PT=\mathbf CP^3$. It has no fixed points, so the twistor space has no real points. What is fixed are the quaternionic lines $\mathbf H\subset \mathbf H^2$, each of which corresponds to a point in the (conformally compacified, so $S^4=\mathbf HP^1$) real Euclidean signature spacetime. Using the decomposition as a tensor product of spinors, the action by $\mathbf j$ squares to $-1$ on each factor, but $1$ on the tensor product, where it gives a conjugation with fixed points the Euclidean spacetime.

The real spacetime with Minkowski signature is another real form of a subtle sort, with very different subtleties than in the Euclidean case. The conjugation $\sigma$ in this case doesn’t take the twistor space $T$ to itself, but takes $T$ to its dual space $T^*$. It takes spinors of one kind to spinors of the opposite kind (at the same time conjugating spinor coordinates to get anti-linearity). The Minkowski signature conformal group is the group $SU(2,2)$ and the rotation group is the Lorentz group $SL(2,\mathbf C)$ (acting diagonally on the two spinor spaces, with a conjugation on one side).

Some philosophy

The usual way in which the above real forms get used is that mathematicians ignore the Minkowski story and use the Euclidean signature real form to do four-dimensional Riemannian geometry, with the $Sp(1)\times Sp(1)$ decomposition at the Lie algebra level corresponding to the decomposition of two-forms into self-dual and anti-self-dual. Physicists on the other hand (especially Penrose and his school, but also those trying to do quantum gravity using Ashtekar variables) ignore the Euclidean story and use the Minkowski signature real form. In various places Penrose is quoted as explicitly skeptical of any relevance of the Euclidean story to physics. Working just with the Minkowski real form, one struggles with the fact that the Lorentz group is simple, but that one can get a very useful self/anti-self dual decomposition if one makes one’s variables complex.

The point of view I’m taking is that Wick rotation tells one that one should look simultaneously at both Euclidean and Minkowski real forms, understanding how to get back and forth between them. This is standard in usual geometry where one just looks at vectors, but looking at spinors and twistors shows that something much more subtle is going on. The argument of this new paper is that when one does this, one finds that the spacetime degrees of freedom can be expressed purely in terms of one kind of spinor (right-handed by convention), the one that twistor theory tautologically associates to each point in spacetime. The other (left-handed) half of the spinor geometry involves a purely internal symmetry from the point of view of Minkowski spacetime. This should correspond to the electroweak gauge theory, exactly how that works is still under investigation…

Update: Now posted on the arXiv here. Only reaction on social media I’ve seen so far is from Strinking42069, which seems to be a parody account trying to make fun of string theorists.

Posted in Euclidean Twistor Unification | 18 Comments

Analytic Stacks

Dustin Clausen and Peter Scholze are giving a course together this fall on Analytic Stacks, with Clausen lecturing at the IHES, Scholze from Bonn. Here’s the syllabus:

The purpose of this course is to propose new foundations for analytic geometry. The topics covered are as follows:
1. Light condensed abelian groups.
2. Analytic rings.
3. Analytic stacks.
4. Examples.

Yesterday Clausen gave the first lecture (video here), explaining that the goal was to provide new foundations, encompassing several distinct possibilities currently in use (complex analytic spaces, locally analytic manifolds, rigid analytic geometry/adic spaces, Berkovich spaces). These new foundations in particular should work equally well for archimedean and non-archimedean geometry and hopefully will be the right language for bringing together the Fargues-Scholze geometrization of local Langlands at non-archimedean places with a new geometrization at the archimedean place. He describes as “(very) speculative” the possibility of a geometrization of global Langlands (with Scholze more optimistic about this than he is).

Tomorrow Scholze will take over, giving the next six lectures. Perhaps this characterization is a bit over-the-top, but seeing lectures of this sort and of this ambition taking place at the IHES brings to mind the glory days of Grothendieck’s years lecturing at the IHES on new foundations for algebraic geometry. I fear that keeping up on the details of this as it happens will require the energy of someone much younger than I am…

Update: Scholze’s first lecture is here. He gives his version of the motivation for these new foundations.

Update
: This sort of thing didn’t happen back in the days of SGA.

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Spacetime is Right-handed

I’ve finally managed to write up something short about an idea I’ve been working on for the last few months, so now have a preliminary draft version of a paper tentatively entitled Spacetime is Right-handed. One motivation for this is the problem of how to Wick rotate spinor fields, given that Minkowski and Euclidean spacetime spinors are quite different. In particular, it has always been a mystery why a Weyl spinor field has a simple description in Minkowski spacetime, but no such description in Euclidean spacetime, where the Euclidean version of Lorentz symmetry seems to require introducing fields of opposite chirality. The argument of this paper is that the relation between Euclidean and Minkowski is not the usual chirally-symmetric analytic continuation but something where both sides use just one chirality (“right-handed”). It’s quite remarkable that the dynamics of gauge fields and of GR also has a chiral-asymmetric formulation.

In the ideas about unification using QFT formulated in Euclidean twistor space that I’ve been working on the past few years, it was always unclear why, when you analytically continued back to Minkowski signature, the left-handed Euclidean spin symmetry would not go to the Lorentz boost symmetry, but to an internal symmetry. One goal of this paper is to answer that question.

This past weekend I recorded a podcast with Curt Jaimungal, which presumably will at some point appear on his Theories of Everything site. It includes some discussion of the ideas behind the new paper.

Posted in Euclidean Twistor Unification | 17 Comments

Frenkel on String Theory

Curt Jaimungal’s Theories of Everything podcast has a new episode featuring a long talk with Edward Frenkel (by the way, I’ll be doing one of these next month). A few months ago I wrote about a Lex Fridman podcast with Frenkel here. While both of these are long, they’re very much worth watching.

While there’s some overlap between the two podcasts, some different topics are covered in the new one. In particular, one thing that happened to Frenkel since last spring is that he attended Strings 2023 and gave a talk there (slides here, video here). The experience opened his eyes to just how bad some of the long-standing problems with string theory have gotten, and starting around here in the podcast he has a lot to say about them.

It’s pretty clear that his reaction to what he saw going on at the conference was colored by his experience growing up in late Soviet-era Russia, where the failure of the system had become clear to everyone, but you weren’t supposed to say anything about this. He pins responsibility for this situation on senior leaders of the field, who have been unwilling to admit failure. As part of this, he acknowledges his own role in the past, in which he was often happy to get some reflected glory from string theory hype by playing up its positive influence on parts of mathematics while ignoring its failure as a theory of the real world. In any case, I urge you to watch the entire podcast, it’s well worth the time.

For a very different perspective on the responsibility of senior people for string theory’s problems, you might want to take a look at the bizarre twitter feed of stringking42069, which may or may not be some very high-quality trolling. In between replies and tweets devoted to weightlifting, weed and women, the author has some very detailed and mostly scornful commentary on the state of the field and the behavior of its leaders. His point of view is that the leaders have betrayed the true believers like himself, abandoning work on the subject in favor of irrelevancies like “it from qubit”, in the process tanking the careers of young people still trying to work on actual string theory. For a summary of the way he sees things, see here and here. Comments on specific people here and here.

This weekend here in New York if you’ve got $35 you can attend an event bringing together five of the people most responsible for the current situation. I doubt that the promised evaluation of “a mathematically elegant description that some have called a “theory of everything.”” will accurately reflect the state of the subject, but perhaps some of the speakers will have listened to what Edward Frenkel has to say (or read stringking42069’s tweets) and realized that a new approach to the subject is needed.

Update: Curt Jaimungal at the Theories of Everything podcast has a new episode, discussing quantum gravity with Jonathan Oppenheim. Around 1:10 Oppenheim has some comments about the current problem of few opportunities for young people to pursue new ideas in this field, including:

You know, it’s a multifaceted problem. I think part of it is that for whatever reason, people like to work on the same thing as everyone else. And I mean, we are social creatures, and we want to be part of the community. And so if there’s a big community doing something, then it’s very natural to want to be part of that community and do that research.

But it’s, I feel like it’s gotten to quite an extreme. It feels quite extreme at the moment, I feel like even when I was a student, you know, there were various researchers who, I would say, didn’t have a firm allegiance to say, string theory or loop quantum gravity, and you could kind of work with one of them and work on your own approach. Whereas I think now, for whatever reason, the landscape has just become a lot more divided into different communities who do different things, and it’s much harder to go off on your own. And maybe that’s just because it’s students’ worry that if they go off on their own, they won’t get a job. I think that’s probably a big part of it.

Update: Bringing together this and the last posting, if you’d like more Frenkel and more Langlands, there’s a new Numberphile video out.

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