This Week’s Hype

For the last thirty years or so, one tactic of those who refuse to admit the failure of string theory has been to go to the press with bogus claims of “we finally have found a way to get testable predictions from string theory!”. I’ve written about dozens and dozens of these over the years (see here). In recent years the number of these has tapered off considerably, as it likely has become harder and harder to find anyone who will take this seriously, given the track record of such claims.

Today though, Quanta magazine has a new example, with an article that informs us

An idea derived from string theory suggests that dark matter is hiding in a (relatively) large extra dimension. The theory makes testable predictions that physicists are investigating now.

This is about a proposal for a micron-scale large extra dimension, with no significant connection to string theory. I took a look at the “predictions” (see here) long enough to assure myself it’s more of the same, better to not spend more of one’s time on it. One positive thing to say about the article is that the writer did go ask string theorist experts about this, and while these experts tried to be polite, they clearly weren’t enthusiastic:

While physicists find the dark dimension proposal intriguing, some are skeptical that it will work out. “Searching for extra dimensions through more precise experiments is a very interesting thing to do,” said Juan Maldacena, a physicist at the Institute for Advanced Study, “though I think that the probability of finding them is low.”

Joseph Conlon, a physicist at Oxford, shares that skepticism: “There are many ideas that would be important if true, but are probably not. This is one of them. The conjectures it is based on are somewhat ambitious, and I think the current evidence for them is rather weak.”

Better though would have been to ask Sabine Hossenfelder what she thinks about this kind of thing (or not write about them at all)…

Update: Vafa has a new paper explaining the “prediction” of the extra dimension from Swampland conjectures. According to him

The most direct way to test the dark dimension scenario is to check Newton’s gravitational inverse square law (ISL) at micron scale. Due to O(1) number ambiguities one can only predict this to appear at length scales 1 − 10 microns. Experiments checking this length scale would need to improve the current range bounds by a factor of 10.

What if such experiments can be done but don’t see anything, even down to 1/10,000th of a micron? No problem at all, that would be a new discovery that you need to change one of the many Swampland conjectures:

We can only wait for the experimental verdict. Either way, we will learn exciting new physics!

Update: Sabine Hossenfelder explainer here.

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Particle Physics Is Not In Crisis

For a low-rent version of the self-congratulatory program discussed here, Bad Boy of Science Sam Gregson has a new video up entitled Particle Physics Is Not In Crisis – but we can make improvements. Cliff Burgess plays the Strominger role, explaining that the idea that there’s any problem with what’s going on in particle theory is “a nothing-burger” and “a complete non-issue”. Asked to rank any such problem on a scale of 0-10, he gives the Strominger-esque “.0001”. Martin Bauer goes for “1”.

The take on the question is much the same as Sean Carroll’s four-hour plus explanation that there is no problem, but shorter. It’s similar to Carroll in that no one who thinks there is a problem was invited to participate, or even gets mentioned by name. There’s a repeated reference to mysterious “Twitter influencers”, which I find very confusing because just about the only particle theorists I see spending time on Twitter going on about the state of the field are Bauer and Burgess. They can’t mean me since I’ve so far resisted the temptation to enter Twitter discussions. The idea of trying to have a serious discussion of complex scientific issues in the Twitter format never made any sense to me, and (StringKing aside) I find it hard to think of any tweets by anyone that shed any light on serious issues in this area.

The more serious part of the program was the discussion among the two HEP experimentalists of the state of their field, which got a 5-6 on the crisis level scale. I wrote about the problem there five years ago, and very little has changed, other than that we’re five years closer to the date when there will no longer be an energy frontier machine running anywhere in the world. The underlying problem wasn’t really explained. CERN is working on it, but there is as of now no specific plan with specific budget numbers for what to build next. Maybe I misunderstood, but it seemed that Bauer and others were talking about how the field just needed to convince funding agencies to support budget numbers of order \$100 billion, which is a pipe dream.

Update: Latest podcast from Sean Carroll has nothing to do with the crisis in particle physics, but he starts off anyway with this:

You may have heard there is a crisis in physics. No, there’s not. I mean, there’s little tiny crises, but that’s the very standard procedure if you’re doing science at the cutting edge, is all sorts of puzzles that we don’t know the answer to.

“Little tiny crises” is I guess his version of the Cliff Burgess “.0001” and Andy Strominger “A+++”.

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Quick Links

A few quick links:

  • There’s a one-day conference next Friday at the IHES, recognizing Dustin Clausen’s appointment to a new Jean-Pierre Bourguignon Chair. Should be several interesting talks, see here.
  • There’s an ongoing conference at the KITP on the topic of What is String Theory? So far, none of the online talks address that issue. Evidently there was a discussion of the topic last Wednesday, but not recorded. Were any readers here in attendance and willing to report on that event? Next chance to find out what string theory is will be a Monday Blackboard Lunch talk by Gopakumar.
  • In April there will be an IUT conference hosted by Zen University in Tokyo, see here. All the speakers but one are from RIMS. For news from the senior people devoted to IUT, Ivan Fesenko has moved to Westlake University in Hangzhou, and Shinichi Mochizuki is has been blogging here.
  • There’s a new Shanghai Institute for Mathematics and Interdisciplinary Science, headed by Shing-Tung Yau.
  • For those following what happens with the small number of permanent positions in particle theory, news from 4 gravitons.

Update: One more, which I’m quite interested in. Scholze will be giving a series of three Emmy Noether lectures at the IAS in March, topic Real local Langlands as geometric Langlands on the twistor-P1.

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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.

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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.

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