Publicity Stunt Fallout

Posted on December 6, 2022 by woit

Latest news this evening from Scott Aaronson at the IAS in Princeton:

Tonight, David Nirenberg, Director of the IAS and a medieval historian, gave an after-dinner speech to our workshop, centered around how auspicious it was that the workshop was being held a mere week after the momentous announcement that a wormhole had been created on a microchip (!!)—in a feat that experts were calling the first-ever laboratory investigation of quantum gravity, and a new frontier for experimental physics itself. Nirenberg speculated that, a century from today, people might look back on the wormhole achievement as today we look back on Eddington’s 1919 eclipse observations providing the evidence for general relativity.

I confess: this was the first time I felt visceral anger, rather than mere bemusement, over this wormhole affair. Before, I had implicitly assumed: no one was actually hoodwinked by this. No one really, literally believed that this little 9-qubit simulation opened up a wormhole, or helped prove the holographic nature of the real universe, or anything like that. I was wrong.

Scott has been the one person in this field I’m aware of who has tried to do something about the out-of-control hype problem that has been going from bad to worse. I do disagree with him about one thing. He goes on to write:

I don’t blame the It from Qubit community—most of which, I can report, was grinding its teeth and turning red in the face right alongside me. I don’t even blame most of the authors of the wormhole paper, such as Daniel Jafferis, who gave a perfectly sober, reasonable, technical talk at the workshop…

I do blame all those people. Unlike Scott, they’ve been either participating in hype for years, or staying quiet and enjoying the benefits of it. Grinding their teeth and turning red in the face is not enough. They need to finally say something and take action.

Update: Still unclear to me what the ultimate fallout of the publicity stunt will be. One thing that is becoming clear is that the publicity stunt is part of a vigorous and very effective campaign to mislead funding agencies and those making funding decisions. The goal is to convince them that “quantum gravity in a lab” is a real thing and the way forward for fundamental theoretical physics. The bogus Quanta story, video, headlines are not a bug, but a feature. Among the funding agencies, DOE is on board, their grant funding the publicity stunt, and they are advertising it prominently in their presentation to HEPAP today (see page 7 here). At the IAS, it seems director Nirenberg’s claims that the “first quantum gravity experiment on a chip” was possibly the biggest breakthrough in a century were not off-the-cuff comments based on what he had read in the paper or at Quanta, but prepared remarks based on conversations with IAS senior faculty. I gather that what he has been hearing from at least some of them is that the wormhole “experiment” vindicates their past research and justifies supporting them in the direction they are choosing for the future. He has though now been hearing other viewpoints.

If researchers in this field want to know what they can do about the problem, contacting places like Quanta to get them to fix their coverage is one thing, another is contacting people with funding responsibilities (ie. program officers at funding agencies, directors of institutes) who seem to have been misled by the hype campaign.

Update: Quanta hasn’t done anything more to fix the wormhole article, but they have now updated their original “Physicists have built a wormhole and successfully sent information from one end to the other.” tweet. New one reads “Experimental physicists built the mathematical analog of a wormhole inside a quantum computer by simulating a system of entangled particles.”

Update: Today at HEPAP the Fermilab director was prominently advertising the wormhole publicity stunt as a Fermilab initiative (see slide 67 here). She describes future plans for more of the same, with these calculations being performed not on one quantum computer, but on two spatially separated quantum computers connected by a quantum network. This would somehow allow for a big increase in the “quantum gravity in the lab” hype with a new Nature cover story: “FNAL scientists connect two quantum computers by a wormhole between two labs”. A question for those in the “It from Qubit” field. Are you willing to contact those responsible for funding this, who are now prominently advertising this work as a major success and new direction of research they intend to fund (e.g. Glen Crawford at DOE, and Lia Merminga at FNAL)?

Update: 4gravitons has a blogpost about the Quanta article, concentrating on the issue of “tone” of the coverage. That’s relevant for the usual problematic sort of physics coverage, but in this case something much more unusual is going on. This was a well-organized publicity stunt designed to justify funding “quantum gravity in a lab” research. Quanta was taken in more so than many other journalism venues. But the really disturbing part of this story is who else was taken in: the IAS director, the Fermilab director, the DOE division director and others, who are sophisticated consumers of science journalism, and independently getting their information from senior scientists in the field.

Posted in This Week's Hype, Wormhole Publicity Stunts | 29 Comments

The Wormhole Publicity Stunt

Posted on December 3, 2022 by woit

The best way to understand the “physicists create wormholes in the lab” nonsense of the past few days is as a publicity stunt (I should credit Andreas Karch for the idea to describe things this way), one that went too far. If the organizers of the stunt had stuck to “physicists study quantum gravity in the lab” they likely would have gotten away with it, i.e. not gotten any significant pushback.

There have already been a lot of claims about “quantum gravity in the lab” made in recent years, and surely many more will be made in the future. It’s important to understand that these all have been and always will be nothing but publicity stunts. In all cases, what is happening in these labs is some manipulation and observation of electron and electromagnetic fields at low energies. None of this has anything to do with gravitational degrees of freedom. One cannot possibly learn anything about the gravitational field or quantum gravity this way. If there is a dual theoretical description of QED in terms of a “gravitational” theory, this dual description is about other variables that have nothing to do with space-time and gravity in this world.

I’m hoping that journalists and scientists will learn something from this fiasco and not get taken in again anytime soon. It would be very helpful if both Nature and Quanta did an internal investigation of how this happened and reported the results to the public. Who were the organizers of the stunt and how did they pull it off? Already we’re hearing from Quanta that the problem was that they trusted “leading quantum gravity researchers”, and presumably Nature would make the same argument. Who were these “leading quantum gravity researchers”? Why weren’t any of the many other physicists who could have told them this was a stunt consulted?

It’s pretty clear that one of the organizers was Joe Lykken. After I wrote about his talk at CERN a month ago, someone told me that Dennis Overbye at the NYT was looking into writing about Lykken’s claims. I found it odd that the NYT would be interested in this, now it’s clear that the behind-the-scenes publicity campaign was starting already a month ago. If you look at Lykken’s slides, there’s no mention at all of the work he had done and knew was about to appear in Nature, but the whole talk is structured around arguing that such a quantum computer calculation would be a huge achievement. I still don’t know what to make of his claims in the Quanta video that the result of the Google quantum computer calculation was on a par with the Higgs discovery. Does he really believe this (he’s completely delusional) or not (he’s intentionally dishonest)?

It’s extremely unusual to not distribute a result like this on the arXiv before publication, to instead keep it confidential and go to the press with embargoed information. By doing this though you control the first wave of publicity, since you pick the press people you deal with and the terms of the embargo. One thing that first mystified me about this story is why Natalie Wolchover at Quanta was quoting comments from me on a different issue in her story, but hadn’t asked me about the article and its “physicists create wormholes in a lab” claims. One possible explanation for this is that the terms of the embargo meant she could not discuss the Nature article with me. I have to admit that if I had heard from her or any other journalist that a group was about to hold a press conference and announce publication in a major journal of claims about quantum gravity in a lab, and would I respect embargo terms so they could share info with me and get a quote, I would have said no. Likely I (and others in a similar situation) would immediately have gone and written a blog entry about how a publicity stunt was about to happen.

Update: I just noticed that the “It from Qubit” community will be gathering Monday thru Wednesday in Princeton and Thursday thru Friday in New York. One of the Princeton talks will be from one of the Nature authors (Jafferis), talking about “Emergent Gravitational Dynamics in Quantum Experiments” (no abstract, may or may not be explaining how he created the wormholes). This would be an excellent occasion I think for this community to discuss what can be done to stop publicity stunts like this one from discrediting their subject. The New York component will be invitation only, at the Simons Foundation. Presumably the Quanta people will be there to discuss with them the huge damage to their reputation they just suffered because of the publicity stunt. I’d be curious to hear how this goes from anyone participating.

Update: Something I should have linked to before is Scott Aaronson’s blog posting about this, and the comments there. One that I think is of interest explains that SYK at large N is not precisely dual to a 2d gravity theory as one often sees claimed, and has other useful explanations of issues with duality claims.

Update: According to Spiropulu on Twitter, at 2:15 Eastern Time today you can watch Jafferis talk about this stuff to a workshop at Princeton here.

Update: Just watched the livestream of the Jafferis talk. He went over in detail the paper. At the end, a few technical questions. At this point I’m seeing no evidence that anyone (other than Scott Aaronson) in this community has any problem with the outrageous hype and publicity stunts like this one being used to promote their field to the public and attract more funding.

Update: Something from Ethan Siegel, who as usual, gets it right:

There are no lessons to be learned about quantum gravity here. There are no lessons to be learned about traversable wormholes or whether they exist within our Universe. There are not even any lessons to be learned about the uniqueness or capabilities of quantum computers, as everything that was done on the quantum computer can be done and had previously (without errors!) been done on a classical computer. The best that one can take away is that the researchers, after performing elaborate calculations of the Sachdev-Ye-Kitaev model through classical means, were able to perform an analogous calculation on a quantum computer that actually returned signal, not simply quantum noise…

Wormholes and quantum computers will likely both remain topics that are incredibly interesting to physicists, and further research into the Sachdev-Ye-Kitaev model will likely continue. But the connection between wormholes and quantum computers is virtually non-existent, and this research — despite the hype — changes absolutely nothing about that fact.


Update: To get a taste of the utter nonsense people are now getting as “News” because of this publicity stunt, try watching this ABC News segment.

Posted in This Week's Hype, Wormhole Publicity Stunts | 59 Comments

Igor Krichever 1950-2022

Posted on December 1, 2022 by woit

I just heard the sad news that Igor Krichever passed away this morning at the age of 72. Igor was a great scholar, a wise man, and a wonderful human being. He will be sorely missed by his colleagues at Columbia and elsewhere. My condolences to his family, which includes another first-rate mathematician, his son-in-law Sasha Braverman. During the past year Igor had been suffering from a progressive neuro-degenerative disease. Fortunately he was still in good enough health to fully participate in and enjoy his 70th birthday conference, which took place at Columbia in early October.

In recent years Igor had been spending only one semester each year at Columbia, much of the rest of the time was in Moscow, where he was director of Skoltech’s Center for Advanced Studies. He came to Columbia in the mid-90s, with his hiring the beginning of a period of successful expansion and improvement in the math department. He was a gentle and friendly person, and it was always a pleasure to have a chance to talk to him about one topic or another. When he became chair of the department I remember thinking that it seemed unlikely that someone as scholarly and laid-back as him, with a somewhat typical Russian mathematician’s other-worldliness, could deal well with the challenges of the university bureaucracy. I was very, very wrong, as it became clear that he was extremely wise in the ways of the world and a great department chair. I guess that after growing up with Soviet bureaucracy, dealing with the Columbia version was child’s play.

Igor was a very distinguished mathematician, one of the leading figures working at the intersection of integrable systems and algebraic geometry. For more about his scientific work, there’s a biographical notice written by some of his colleagues at the time of his 60th birthday (which was also celebrated at Columbia with a conference, see here).

Posted in Obituaries | 2 Comments

This Week’s Hype

Posted on November 30, 2022 by woit

This morning Quanta Magazine informs us that Physicists Create a Wormhole Using a Quantum Computer, promoting the article on Twitter with BREAKING: Physicists have built a wormhole and successfully sent information from one end to the other and Physicists have used Google’s quantum computer to send a signal through a wormhole, a shortcut in space-time first theorized by Einstein and Rosen in 1935.

This work is getting the full-press promotional package: no preprint on the arXiv (unless I’m missing something?), embargoed info to journalists, with reveal at a press conference, a cover story in Nature, accompanied by a barrage of press releases (see here, here, here, with Harvard, MIT and Google to come). This is the kind of PR effort for a physics result I’ve only seen before for things like the Higgs and LIGO gravitational wave discoveries (OK, and the primordial gravitational wave non-discovery). It would be appropriate I suppose if someone actually had built a wormhole in a lab and teleported information through it, as advertised.

An additional part of the package is the Quanta coverage, with a very long article by Natalie Wolchover and an over-the-top seventeen minute film How Physicists Created a Wormhole in a Quantum Computer, with abstract

Almost a century ago, Albert Einstein realized that the equations of general relativity could produce wormholes. But it would take a number of theoretical leaps and a “crazy” team of experimentalists to build one on Google’s quantum computer.

The two senior physicists behind this, Joe Lykken and Maria Spiropulu, have histories that go way back of successfully promoting to the press nonsense about exotic space-time structures appearing in experiments that have nothing to do with them. Back in 1999, the New York Times published Physicists Finally Find a Way to Test Superstring theory, which featured Joe Lykken. In 2003, they featured Maria Spiropulu explaining how she was going to find extra dimensions (or “something just as ‘crazy””) at the Tevatron, or failing that, the LHC.

I just saw that the New York Times also has a big story about this: Physicists Create ‘the Smallest, Crummiest Wormhole You Can Imagine’. At least this article has some sensible skeptical quotes, including:

“The most important thing I’d want New York Times readers to understand is this,” Scott Aaronson, a quantum computing expert at the University of Texas in Austin, wrote in an email. “If this experiment has brought a wormhole into actual physical existence, then a strong case could be made that you, too, bring a wormhole into actual physical existence every time you sketch one with pen and paper.”

An odd thing about the Quanta article is that it contains a couple quotes from me, that aren’t at all about the wormhole business. They’re about the attempt to use AdS/CFT to either solve QCD or get a viable theory of quantum gravity. Back in June Wolchover contacted me with some questions about AdS/CFT. It seems that she was planning a long piece on AdS/CFT, one which somehow many months later got amalgamated with the wormhole nonsense. I had forgotten that I was thinking of turning what I sent her back then into a blog posting but never got around to it, so just earlier today posted it here.

On the substance of what is really going on here, it’s exactly the same as what was discussed extensively a month ago in this posting and in its comment section. The claim that “Physicists Create a Wormhole” is just complete bullshit, with the huge campaign to mislead the public about this a disgrace, highly unhelpful for the credibility of physics research in particular and science in general.

Update: Here’s the promotional piece from Google, and Will Kinney’s reaction.

Update: Physics World has Quantum teleportation opens a ‘wormhole in spacetime’ with a quote from Witten saying positive things about this experiment (“a ‘milestone’ in developing control over microscopic quantum systems”), nothing about the wormholes.

Update: I tried reading the paper in some more detail. Almost all the calculations in the paper were done on paper or on a classical computer. As far as I can tell, all they did was perform elaborate SYK calculations on a classical computer, together with simulations of noise on the Google quantum computer, trying to find a possible calculation on the quantum computer that would have signal, not just noise. Once such an N=7 SYK calculation was identified, they used a 9 qubit quantum computer and the noisy result matched the simulation result from the classical computer, exactly as expected. Seeing the completely expected match between results from a 9 bit noisy quantum computer and the results of the simulation of this on a classical computer caused Maria Spiropulu to say that “I was shaken” and “It was nuts. It was nuts”, while Joe Lykken felt that the moment was on a par with discovery of the Higgs particle.

I hadn’t noticed that the Nature issue comes with an article by Brown and Susskind, A holographic wormhole traversed in a quantum computer. Amidst the hype, they do at least point out:

because nine qubits can be easily simulated on a classical computer, the results of this experiment cannot teach us anything that could not be learnt from a classical computation, and will not teach us anything new about quantum gravity.

New Scientist is the sober one here, with their headline the relatively reasonable A quantum computer has simulated a wormhole for the first time

Update: MSN is going for the larger context: physicists didn’t just create a wormhole in a lab, also This tiny 2D wormhole could finally solve the biggest problem in physics

Update: Andreas Karch on Twitter I think has an accurate characterization of this “mostly a publicity stunt”:

Experimentally it’s of course cool they can do SYK – as a demonstration they have control over their device. They can couple 9 qbits in a pre-specified way. But I guess we knew they could do this before. Going after SYK in particular, in my mind, is mostly a publicity stunt.

Update: Quanta has changed the title of their article from “Physicists Create a Wormhole” to “Physicists Create a Holographic Wormhole”.

The MIT press release is out, and it’s comical in the other direction, explaining the huge breakthrough as MIT researchers use quantum computing to observe entanglement.

Chad Orzel is getting flashbacks to 2006, which I can well understand. Many of the worst offenders in this hype campaign were hard at work doing the same thing back then (and earlier), and I was, as now, ineffectually trying to do something about it (the first edition of “This Week’s Hype” dates back to that year).

Update: Quanta has also deleted the original “BREAKING: Physicists have built a wormhole and successfully sent information from one end to the other” tweet. Davide Castelvecchi at Nature as a more sober story, ending with

The theory tested at the Google lab “only has a very tangential relationship to any possible theories of quantum gravity in our Universe”, says Peter Shor, a mathematician at the Massachusetts Institute of Technology in Cambridge.

Update: More coverage of this here, here, here and here. Quanta and Wolchover are, quite appropriately, blaming the “some of the best-respected physicists in the world” who sold them this nonsense, see here, here and here.

Posted in This Week's Hype, Wormhole Publicity Stunts | 37 Comments

Comments on AdS/CFT

Posted on November 30, 2022 by woit

This is something I wrote back in June, for context see the next posting.

First of all, there’s the following, which is not strictly scientific, but very relevant to how one decides to evaluate progress in a subject.

  • The Maldacena AdS/CFT paper is almost 25 years old and has nearly 18,000 citations. Trying to exploit ideas based on AdS/CFT has been the main goal of thousands of the best theorists in the world for decades. Questions like “what about getting this to work in the more physical case of dS?” are not new but very old and have been the subject of tens of thousands of person-years of unsuccessful effort. This doesn’t mean it can’t be done, I think it does mean that what’s needed are some quite different ideas, there’s little point in further banging away at ones that haven’t worked for this long, after this much effort.
  • Some of the hype surrounding AdS/CFT has been outrageous. One example is the claim that AdS/CFT gives a good way to calculate things about heavy-ion physics. This is just not true, and the people saying things like this should know better. Seeing people do things like this make me question their arguments about whether other ideas work or not (or have good prospects for working).
  • As time goes on, people start using “AdS/CFT” to mean a wider and wider array of things. It often now denotes very general and vague conjectures about duality relations between gauge theory and gravity systems, or holography, or entanglement. It becomes impossible at some point to have a coherent discussion about the subject since there is no well-defined thing to talk about.

Sticking to the specific meaning of a duality between a specific superstring theory on AdS_5 x S^5 and N=4 super Yang-Mills on the conformal boundary, back in 1997 there were two reasons to get excited about this:

  • Reading the duality as telling you about gauge theory in terms of string theory, you could hope that the duality could be extended to non-supersymmetric Yang-Mills, providing the long-sought string dual to QCD, allowing reliable strong-coupling QCD calculations. After a few years post 1997, it started to become clear this wasn’t working, and why. N=4 SYM has zero beta-function and is conformally invariant, so the effective coupling and physics are the same at all scales. QCD has a running coupling constant, with weak-coupling and strong-coupling physics very different. AdS/CFT allows strong-coupling calculations on the gauge theory side using weakly-coupled strings, but this has the same problems that we’ve always had with QCD: there are ways to write down strong-coupling expansions, but no way to match those to weak coupling physics, no way to capture the way physics changes from strong to weak coupling.

    By the way, I noticed the Simons Foundation has just announced a collaboration to study QCD and strings

    Foundation Announces the Simons Collaboration on Confinement and QCD Strings


    and this doesn’t even mention AdS/CFT. People have tried really, really hard over decades to use AdS/CFT to say something about QCD, with very limited results.

  • Reading the duality as telling you about strings and quantum gravity in terms of gauge theory, the hope is to understand quantum gravity this way. There are a bunch of problems with this:

    There’s the gravity in AdS rather than dS problem that you mention. As noted above, back in 1997 it was reasonable to expect a useful extension to dS. After 25 years of failed efforts, if there is such a thing it has to be something very different.

    You want gravity in 4d, not 5d. This may not be a serious issue since you can take 5d with one small dimension, or brane or whatever to get rid of a dimension.

    There’s a fundamental problem with doing gravity this way: string theory-based quantum gravity uses weakly coupled strings with the graviton a weakly-coupled mode. But this theory is dual to strongly-coupled gauge theory where you can’t calculate anything. So, AdS/CFT is telling you nothing about the usual picture of how gravity arises from string theory. What it supposedly tells you about are strongly coupled strings (using weakly coupled gauge theory), but then the connection to gravity is something very different than what was originally advertised for string theory.

    Put together, the problem is that, to the extent AdS/CFT is telling you something about strings and quantum gravity, it’s telling you about the wrong kind of space-time (AdS) in the wrong dimension (5) with the wrong kind of strings (strongly-coupled). The general philosophy seems to be that at least it’s telling us about some kind of quantum gravity, which is a reasonable motivation, but leaves one far from real physics, in the land of general issues like resolving the black hole information paradox. But 20 years ago we were being told that it was resolved by AdS/CFT, then ten years later we were being told it wasn’t (the “Firewall”). Again, given the level of hype people operate with, it’s hard to evaluate any of this kind of thing with no relation to anything measurable.

I’m all in favor of good toy models, and from what I can see the main activity in AdS/CFT these days is trying to understand lower dimensional toy models. This leads to lots of interesting things to study, but you seem to end up with very complicated things happening even in much lower dimensions (0+1 SYK models, 1+1 JT gravity models), far from the 3+1 dimensions one wants. There are no physical gravity degrees of freedom below 3+1 dimensions, so it’s all too possible that what one is studying in these lower dimensional models is exactly the things of no physical relevance to the real problem.

Finally, my feeling has always been that the difficulty of measuring purely quantum gravitational effects means that the only convincing quantum gravity will be one unified with the rest of physics, fitting together well with what we can observe. The danger with studying pure quantum gravity is that you’ll end up with not one theory, but an infinite number of them, empty of any predictive value. The landscape is a realization of that danger.

Update: By the way, this is roughly the 25th anniversary of AdS/CFT, Scientific American has a piece by Anil Ananthaswamy.

Posted in Uncategorized | 5 Comments

The Mystery of Spin

Posted on November 22, 2022 by woit

Scientific American has a new article today about the supposedly mysterious fact that electrons have “spin” even though they aren’t classical spinning material objects. The article doesn’t link to it, but it appears that it is discussing this paper by Charles Sebens. There are some big mysteries here (why is Scientific American publishing nonsense like this? why does Sean Carroll say “Sebens is very much on the right track”?, why did a journal publish this?????).

These mysteries are deep, hard to understand, and not worth the effort, but the actual story is worth understanding. Despite what Sebens and Carroll claim, it has nothing to do with quantum field theory. The spin phenomenon is already there in the single particle theory, with the free QFT just providing a consistent multi-particle theory. In addition, while relativity and four-dimensional space-time geometry introduce new aspects to the spin phenomenon, it’s already there in the non-relativistic theory with its three-dimensional spatial geometry.

When one talks about “spin” in physics, it’s a special case of the general story of angular momentum. Angular momentum is by definition the “infinitesimal generator” of the action of spatial rotations on the theory, both classically and quantum mechanically. Classically, the function $q_1p_2-q_2p_1$ is the component $L_3$ of the angular momentum in the $3$-direction because it generates the action of rotations about the $3$-axis on the theory in the sense that
$$\{q_1p_2-q_2p_1, F(\mathbf q,\mathbf p)\}=\frac{d}{d\theta}_{|\theta=0}(g(\theta)\cdot F(\mathbf q,\mathbf p))$$
for any function $F$ of the phase space coordinates. Here $\{\cdot,\cdot\}$ is the Poisson bracket and $g(\theta)\cdot$ is the induced action on functions from the action of a rotation $g(\theta)$ by an angle $\theta$ about the $3$-axis. In a bit more detail
$$g(\theta)\cdot F(\mathbf q,\mathbf p)=F(g^{-1}(\theta)\mathbf q, g^{-1}(\theta)\mathbf p)$$
(the inverses are there to make the action work correctly under composition of not necessarily commutative transformations) and
$$g(\theta)=\begin{pmatrix}\cos\theta&-\sin\theta&0\\ \sin\theta &\cos\theta &0\\ 0&0&1\end{pmatrix}$$

In quantum mechanics you get much same story, changing functions of position and momentum coordinates to operators, and Poisson bracket to commutator. There are confusing factors of $i$ to keep track of since you get unitary transformations by exponentiating skew-adjoint operators, but the convention for observables is to use self-adjoint operators (which have real eigenvalues). The function $L_3$ becomes the self-adjoint operator (using units where $\hbar=1$)
$$\widehat L_3=Q_1P_2-Q_2P_1$$
which infinitesimally generates not only the rotation action on other operators, but also on states. In the Schrödinger representation this means that the action on wave-functions is that induced from an infinitesimal rotation of the space coordinates:
$$-i\widehat L_3\psi(\mathbf q)=\frac{d}{d\theta}_{|\theta=0}\psi(g^{-1}(\theta)\mathbf q)$$

The above is about the classical or quantum theory of a scalar particle, but one might also want to describe objects with a 3d-vector or tensor degree of freedom. For a vector degree of freedom, in quantum mechanics one could take 3-component wave functions $\vec{\psi}$ which would transform under rotations as
$$\vec{\psi}(\mathbf q)\rightarrow g(\theta)\vec{\psi}(g^{-1}(\theta)\mathbf q)$$
Since $g(\theta)=e^{\theta X_3}$ where
$$X_3=\begin{pmatrix}0&-1&0\\ 1&0&0\\0&0&0\end{pmatrix}$$
when one computes the infinitesimal action of rotations on wave-functions one gets $\widehat L_3 + iX_3$ instead of $\widehat L_3$. $S_3=iX_3$ is called the “spin angular momentum” and the sum is the total angular momentum $J_3=L_3 + S_3$. $S_3$ has eigenvalues $-1,0,1$ so one says that that one has “spin $1$”.

There’s no mystery here about what the spin angular momentum $S_3$ is: all one has done is used the proper definition of the angular momentum as infinitesimal generator of rotations and taken into account the fact that in this case rotations also act on the vector values, not just on space. One can easily generalize this to tensor-valued wave-functions by using the matrices for rotations on them, getting higher integral values of the spin.

Where there’s a bit more of a mystery is for half-integral values of the spin, in particular spin $\frac{1}{2}$, where the wave-function takes values in $\mathbf C^2$, transforming under rotations as a spinor. Things work exactly the same as above, except now one finds that one has to think of 3d-geometry in a new way, involving not just vectors and tensors, but also spinors. The group of rotations in this new spinor geometry is $Spin(3)=SU(2)$, a non-trivial double cover of the usual $SO(3)$ rotation group.

For details of this, see my book, and for some ideas about the four-dimensional significance of spinor geometry for fundamental physics, see here.

Update: I realized that I blogged about much this same topic a couple years ago, with more detail, see here. One thing I didn’t write down explicitly either there or here, is the definition of spin in terms of the action of rotations on the theory. It’s very simple: angular momentum is the infinitesimal generator of the action of rotations on the wave-function, spin angular momentum is the part coming from the point-wise action on the values of the wave-function (orbital angular momentum is the part coming from rotating the argument). Using a formula from my older posting, for a rotation about the z-axis, the total angular momentum operator $\widehat J_z$ is by definition
$$\frac{d}{d\theta}\ket{\psi(\theta)}=-i\widehat J_z \ket{\psi(\theta)}$$
The spin operator $\widehat S_z$ is what you get for $\widehat J_z$ when you act just on the wave-function values. For a spin n/2 state particle, the wave-function will take values in $\mathbf C^{n+1}$. For the spin 1/2 case the action of rotations is by 2 x 2 unitary matrices of determinant one (the spinor representation). For a rotation by an angle $\theta$ about the z-axis, this is
$$e^{-i\theta\frac{\sigma_3}{2}}$$
so the spin operator is
$$\widehat S_3=\frac{1}{2}\sigma_3$$

Posted in Quantum Mechanics | 45 Comments

Math Job Rumors

Posted on November 17, 2022 by woit

I noticed yesterday a website named Math Job Rumors that has been operating for a couple months. No idea what the story behind it is other than that it’s clearly a descendant of Economics Job Market Rumors, which had some small participation by mathematicians, but is somewhat of a dumpster fire of misinformation, trolling, misogyny and various sorts of juvenile behavior. It looks like someone is trying to provide something similar aimed specifically at mathematicians, with some improvement over the EJMR environment.

One aspect of the site are threads devoted to rumors about tenure track and postdoc hiring in pure math, I don’t know if there has been something like this before. In theoretical physics there’s the venerable Theoretical Particle Physics Jobs Rumor Mill and the HEP Theory Postdoc Rumor Mill, but these are run in a very different way, with all information posted coming from one or more people who run the site, based on information sent to him/her/them.

The problem with the EJMR or Math Job Rumors model is that anonymity is needed for the whole thing to work, but once you start allowing people to post things anonymously, if you don’t moderate what is posted, you’ll quickly get overrun by idiots, trolls and other sorts of bad actors. Some kind of moderation is going on at the new site, but it’s unclear who is doing it or on what basis.

After starting with the Official Peter Woit blog hate thread, I moved on to reading a few other threads. Lots of dumb stuff, lots of inside jokes, lots and lots of trolling. I confess though that in one case the trolling was clever enough to make me laugh out loud, but it’s aimed at a really small audience. I did learn one piece of information that appears to be true, that prominent string theorist Shamit Kachru has gone on leave from his position at Stanford to work as a consultant in the finance industry.

In summary, for those mathematicians who read this blog and feel that they are not wasting enough time on mostly dumb internet stuff, you might want to take a look…

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Career Prospects for HEP-TH Students

Posted on November 14, 2022 by woit

Guangyu Xu, a student just finishing his Ph.D. at the Centre for Particle Physics at Durham University, recently sent me a public letter he wrote, explaining the story of his job search, in hopes that it might be useful to others in a similar situation. As he acknowledges, his research record has been rather weak, so not surprising that his postdoc applications were not successful.

Back when I was writing Not Even Wrong, I did some detailed research into whatever information I could find about the HEP-TH job market, but I haven’t tried to do this more recently. Erich Poppitz did some analysis of data from the Theoretical Particle Physics Jobs Rumor Mill (available here), but only up to 2017. Given the large investment of various government agencies in the support of Ph.D. students, I would think that there would be data on career outcomes gathered by such agencies, but haven’t tried to look. Any pointers to this kind of data from anyone who has been looking into it would be appreciated.

Also of interest would be any up-to-date job search advice from those like Guangyu Xu who have been going through this recently.

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No Landau-Siegel zeros?

Posted on November 10, 2022 by woit

A couple weeks ago rumors were circulating that Yitang Zhang was claiming a proof of a longstanding open conjecture in number theory, the “no Landau-Siegel zeros” conjecture. Such a proof would be a very major new result. Zhang was a little-known mathematician back in 2013 when he announced a proof of another very major result, on the twin prime conjecture. Before that, he had a 2007 arXiv preprint claiming a proof of the Landau-Siegel zeros conjecture, but this was never published and known to experts to have problems such that at best the argument was incomplete.

Zhang now has a new paper on the arXiv, claiming a complete proof. The strategy of the proof is the same as in the earlier paper, but he now believes that he has a complete argument. At 110 pages the argument in the paper is quite long and intricate. It may take experts a while to go through it carefully and check it. Note that this is a very different story than the Mochizuki/abc conjecture story: Zhang’s argument use conventional methods and is written out carefully in a manner that should allow experts to readily follow it and check it.

For an explanation of what the conjecture says and what its significance is, I’m not competent to do much more than refer you to the relevant Wikipedia article. For a MathOverflow discussion of the problems with the earlier proof, see here, for consequences of the new proof, see here.

Update: I’m hearing that the above is not quite right, that what Zhang proves is weaker than the conjecture, although strong enough for many of its interesting implications. Perhaps someone better informed can explain the difference…

Update: Davide Castelvecchi at Nature has a news story here.

Update: Via David Roberts on Twitter, Zhang answers some questions about the paper here.

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Physical Mathematics c. 2022

Posted on November 9, 2022 by woit

The arXiv today has a very comprehensive survey of a conventional point of view on where “Physical Mathematics” is in 2022 and where it is going, written by a group of six authors. “Physical Mathematics” is a term popularized by one of them, Greg Moore (see here and here, with some commentary here), and it’s an expansion of a Snowmass white paper. A separate paper by Nikita Nekrasov covering the material listed in Section 10 is advertised as forthcoming with the title “The Ghosts of Past and Future Ideas and Inspirations on Interface of Physics and Mathematics”.

The term “Physical Mathematics” is a play on the more conventional name of “Mathematical Physics” to describe work being done at the intersection of math and physics. In its usage by Moore et al. it refers to a point of view on the relation of math and physics which heavily emphasizes certain specific topics that have been worked on intensively during the last four decades. These topics mostly have roots in seminal ideas of Witten and his collaborators, and involve calculational methods developed in quantum field theory and string theory research. The huge volume of this research is reflected in the fact that the survey reference section contains 62 pages giving 1276 separate references. A major problem for anyone taking up an interest in this field has been the sheer scale and complexity of all this work, and this survey should be helpful in providing an overview.

While some of these 1276 papers could equally well be simply characterized as “Mathematics”, it’s hard to describe exactly what makes a lot of the rest “Physical Mathematics” rather than “Physics”. Part of the answer is that these are not physics papers because they don’t answer a question about physics. A striking aspect of the survey is that while a lot of it is about QFT, the only mention at all of the QFT that governs fundamental physics (the standard model) is in a mention of one paper relevant to some supersymmetric extensions of the SM. The only other possible connection to fundamental physics I noticed was about the landscape/swampland, something only a vanishingly small number of people take seriously.

Also striking is the description of the relation of this field to string theory: while much of it was motivated by attempts to understand what string/M-theory really is, section 3.1 asks “What Is The Definition Of String Theory And M-Theory?” and answers with a doubly-boxed

We don’t know.

with commentary:

This is a fundamental question on which relatively little work is currently being done, presumably because nobody has any good new ideas.

In the background of this entire subject is the 1995 conjecture that there is a unique M-theory which explains various dualities as well as providing a unified fundamental theory. After nearly 30 years of fruitless looking for this, the evidence is now that there is no such thing, and maybe the way forward is to abandon the M-theory conjecture and focus on other ways of understanding the patterns that have been found.

I share a faith in the existence of deep connections between math and physics with those doing this kind of research. But the sorts of directions I find promising are very different than the ones being advertised in this survey. More specifically, I’m referring to:

  • the very special chiral twistor geometry of four-dimensions (no twistors in the survey)
  • the subtle relation of Euclidean and Minkowski signature (only a mention of the recent Kontsevich-Segal paper in the survey)
  • the central nature of representation theory in quantum physics and number theory (very little representation theory in the survey)

Looking back at Greg Moore’s similar 2014 survey, I find that significantly more congenial, with a more promising take on future directions (in particular he emphasizes the role of geometric representation theory).

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