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 is 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.

]]>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…

]]>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.

]]>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.

]]>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 this 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).

]]>CERN on Wednesday is hosting a colloquium talk by Joseph Lykken, who supposedly will discuss Prospects for experimental quantum gravity. There’s by now a long tradition of string theorists dealing with criticism that their research program is inherently immune from experimental test by making bogus claims about experimental testability. Lykken has been at it for at least twenty years (see here), and this sort of misleading claim about testability is the latest in a long campaign.

If you read the abstract, it looks like what Lykken is actually talking about is numerical simulations of an SYK model with of order 100 Majorana fermions on a quantum computer. Ignoring the quantum computer hype (unclear how long it will really be before such simulations are feasible), keep in mind that the SYK model is a quantum mechanical toy model, not a model of quantum gravity in a physical dimension. The only thing a quantum computer could test would be the validity of certain approximations schemes in such a toy model. For comments by David E. Kaplan about similar testability claims, see the interview discussed in the previous posting, which includes:

]]>That there are actual people who are deciding string theory’s important, wanting to do string theory, and they’re even protecting the field. And some of those people are talking about how entropy now of a black hole can be described as a geometric thing, an entanglement, and that Hawking’s paradox about evaporating black holes is really wormholes, virtual wormholes coming from the inside to the outside, and all kinds of language. And you could test information theory of black holes using atomic physics experiments. And it’s literally bullshit.

There are people—prominent people—in physics who say, “I’m applying for this money from the DOE, but I know it’s bullshit.” And then there are experimental atomic physicists who don’t know and are shocked to learn that “What? String theorists don’t have a Hamiltonian? They don’t actually have a [laugh] description? What am I testing?”

There’s a long interview with David E. Kaplan (not the same person as David B. Kaplan…) by David Zierler at the AIP Oral Histories site. The whole thing is quite interesting and I recommend reading it, but I do want to point out that it shows that I’m a voice of moderation on the string theory issue. Some extracts follow:

About Ann Nelson and string theory in the 1990s:

She was extremely dismissive of string theory, and thought it was—you know, there was—my impression from her and from other people of that generation that weren’t doing string theory was that the string theorists were colluding in a sense, or were dismissing anything but string theory, and deciding that if you did string theory then you’re much smarter than the people who are not doing string theory. There was some unhappiness in the theoretical field. And the cancellation of the SSC probably added to that tension between the two.

But I don’t think she came of it from taking a side. I think she looked at the situation and said, “String theory is total bullshit.” In the mid-’80s, there were some realizations—there were some consistency checks that kind of worked in string theory, and people got super excited. Oh, my god, string—yeah, it could be the, you know, underlying thing to particle physics. But that was it.

The successes after that were few and far between. But there was an obsessive—like we’re studying the theory of quantum gravity. And it was deridingly called the theory of everything. And then they took that on, you know. We’re studying the theory of everything. And then the young people who want to do the greatest stuff would go to string theory. And there was a concern and some upset by the people not doing string theory that they’re absorbing a lot of people to do this crap, which is not very physics like. “It’s I believe the theory, and so I’m going to study all aspects of it, and maybe one day we’ll connect it with the physical world.” As opposed to I believe in the phenomenon, and I’m trying to explain that and more, and so I’m going to try out different theories and see what they’re consequences are.

And now I look back, and it’s obvious that string theory was bullshit in the sense of there were so many people working on it, and they were not manifesting any real progress externally. It was all internal consistency checks and things like that. And so at the time, you know, whenever it came up—and it didn’t come up much because there were no string theorists in Seattle—she was just very dismissive, like, you know, “What are those people doing? I don’t know what they’re doing.” [laugh]

About being a postdoc at SLAC:

There were a lot of string theorists at Stanford. I didn’t understand any of those talks. Or sometimes when the talks were not in strings, Lenny Susskind would yell at the speaker that this is bullshit or whatever, da, da, da, da—you know, abusive at some level. So Stanford was weird in that way.

About realizing what was going on in string theory, his evaluation of past (Strominger-Vafa) and current claims about string theory and black holes:

But—so I don’t—and it’s part of probably why I didn’t understand—I didn’t think of myself as a physicist because there’s a lot of physicists working very hard on what? I don’t know what they’re working on. It’s not—you know, I used to just think I’m too stupid to understand what they’re working on. And finally reading some of those papers, they’re not what—it’s stupid. There’s a lot of stupid stuff in there. String theory really is just stupid. It’s unbelievably stupid. There’s so many people who are working on it that don’t actually know physics that they can’t even describe a physical characteristic of the thing they’re calculating. They’re missing the whole thing.

…

So that’s when I realized string theory is like a video game. There are people just addicted to it. That’s all that’s happening. And it’s couched in the theory of everything and da, da, da, da.

So that’s all. I just kind of—I learned quite a bit about these things. And then I saw the people like Lenny Susskind, who was terrorizing people who work on regular physics, as just a plain asshole. That there are actual people who are deciding string theory’s important, wanting to do string theory, and they’re even protecting the field. And some of those people are talking about how entropy now of a black hole can be described as a geometric thing, an entanglement, and that Hawking’s paradox about evaporating black holes is really wormholes, virtual wormholes coming from the inside to the outside, and all kinds of language. And you could test information theory of black holes using atomic physics experiments. And it’s literally bullshit.

There are people—prominent people—in physics who say, “I’m applying for this money from the DOE, but I know it’s bullshit.” And then there are experimental atomic physicists who don’t know and are shocked to learn that “What? String theorists don’t have a Hamiltonian? They don’t actually have a [laugh] description? What am I testing?”

So I have converted a little bit to the opinions of my predecessors, only because I’ve actually done the work. I’ve actually tried to understand black holes of late, and I’ve gone back to those papers which are the breakthrough, celebrated, amazing papers about black holes, and there’s nothing in them. It’s really—it’s just a very simplistic picture where, look, if you take this hyper-simplistic picture, these numbers match these numbers, which means thinking about a black hole having entropy is correct, da, da, da, da, da.

No matter that the black hole they’re talking about is extremal. It doesn’t actually Hawking radiate. It’s a totally hyper-supersymmetric, multiple charges, free parameters. So now that I’ve finally dug into it, I realize that—not that all humanities fields are bad. But it’s much more like a humanities field where there are the prominent people in the field, and they decide what’s interesting. And that if you impress those people, you can get ahead. But that dictates then what research is done. And they’re not going to discover anything in that context. They’re not going to get anywhere. There’s not a lot of people doing—you know—thinking outside the box or just thinking diff…you know, doing different things, you know.

About the argument that string theory must be worthwhile because lots of people are doing it:

Zierler:What is your response to a string theorist who would say, and I know this because one has said this to me, “Look, four people were doing this in 1968, 20 people were doing it in 1984, 1,000 people were doing it in 2000, and now there’s 6,000 people who are doing string theory all over the world. And that’s proof that there’s something here that’s worthwhile”? What is your response to that line of reasoning?

Kaplan:[laugh] Take those numbers, continue the exponential, and apply it to Christianity—

Zierler:[laugh]

Kaplan:—and Islam and Judaism and Buddhism. Give me a fucking break. They’re describing a religion that can attract and addict people. That is exactly the kind of statement that shows it’s bullshit and non-scientific. They’ve proven it for me that they are not about discovering something. They’re about dominating the field for the purpose of what? That’s proof? Give me a break. Give me a fucking break. Slavery was very popular, and became widely used. Nazism. Come on. You can take extreme examples and show that that is so non-scientific and sick that the progress they have made is to get more people to work on something that isn’t producing anything. Oh, man, I wish you didn’t tell me that. [laugh]

About the current state of the field:

]]>There are so many things to think about. I don’t know what narrowed our field. I don’t see it as we’re dying because we’re coming to the limits of what we can do, the limits of what we can calculate in string theory, and the limits of how big of a ring we can build. I think most people are just doing useless stuff.

…

And so that’s why I—the whole depression or whatever, that’s a product of the non-willingness to feel stupid by the majority of our field. Expertise is more important to them than discovery. And that’s what I think is happening. And so what we’re seeing is not the death of the field, but the death of a direction that is being committed to by 98% of them.

A question that has always fascinated me about mathematics is that of how the field manages to stay healthy and not degenerate in the way I’ve seen theoretical physics do as it lost new input from experiment. On Twitter, Ash Joglekar gave a wonderful quote from von Neumann that addresses this question. The quote was from a 1947 essay “The Mathematician” (available here and here). von Neumann argues that:

…mathematical ideas originate in empirics, although the genealogy is sometimes long and obscure. But, once they are so conceived, the subject begins to live a peculiar life of its own and is better compared to a creative one, governed by almost entirely aesthetical motivations, than to anything else and, in particular, to an empirical science.

but warns

As a mathematical discipline travels far from its empirical source, or still more, if it is a second and third generation only indirectly inspired by ideas coming from “reality” it is beset with very grave dangers. It becomes more and more purely aestheticizing, more and more purely l’art pour l’art. This need not be bad, if the field is surrounded by correlated subjects, which still have closer empirical connections, or if the discipline is under the influence of men with an exceptionally well-developed taste. But there is a grave danger that the subject will develop along the line of least resistance, that the stream, so far from its source, will separate into a multitude of insignificant branches, and that the discipline will become a disorganized mass of details and complexities.

which describes all too well what has happened to string theory. What saves a field from this? “Men with an exceptionally well-developed taste”? He poses the general question this way:

What is the mathematician’s normal relationship to his subject? What are his criteria of success, of desirability? What influences, what considerations, control and direct his effort?

Normally mathematicians are loath to debate this kind of “soft” topic, but the rise of computer software capable of producing proofs has recently led several first-rate mathematicians to take an interest. Each year the Fields Institute in Toronto organizes a Fields Medal Symposium, structured around the interests of a recent Fields Medalist. This year it’s Akshay Venkatesh, and the symposium will be devoted to questions about the changing nature of mathematical research, specifically the implications of this kind of computer software. Last year Venkatesh wrote an essay exploring the possible significance of the development of what he called “Alephzero” (denoted $\aleph(0)$):

Our starting point is to imagine that $\aleph(0)$ teaches itself high school and college mathematics and works its way through all of the exercises in the Springer-Verlag

Graduate Texts in Mathematicsseries. The next morning, it is let loose upon the world – mathematicians download its children and run them with our own computing resources. What happens next – in the subsequent decade, say?

Among the organizers of the conference is Michael Harris, who has written extensively about mathematical research and issues of value in mathematics. Recently he has been writing about the computer program question at his substack Silicon Reckoner, with the most recent entry focusing on Venkatesh’s essay and the upcoming symposium.

Venkatesh

One of the speakers at the symposium will be Fields medalist Tim Gowers, who will be addressing the “taste” issue with Is mathematical interest just a matter of taste?. Gowers is now at the Collège de France, where his is running a seminar on La philosophie de la pratique des mathématiques.

I’ve tried asking some of my colleagues what they think of all this activity, most common response so far is “why aren’t they proving theorems instead of spending their time talking about this?”

]]>The hype campaign marches on, just three very recent examples:

]]>Heading to Oxford today, this evening I’ll give a talk there on Unified Theories of Physics. On Saturday I’ll try to find some way to get to the HTLGI Festival in London despite a national rail strike, where I’ll give a talk on Saturday and be on two panel discussions Sunday.

I’ll post slides after the talk tonight, one theme of which will be the failure of a series of attempts to extend the Standard Model, all of which were started in the mid-1970s (GUTs, SUSY, string theory). An opinion piece by Sabine Hossenfelder appeared yesterday in the Guardian, which takes a similar point of view on the current fate of extensions of the SM, but I strongly disagree with a lot of what she has to say.

The bad theory activity she points to has been going on for decades, but in recent years it seems to me to be a lot less popular. Most influential theorists have (quietly) agreed with her that particle physics is dead. In attacking bad model building in particle physics, I think she’s going after a small group of stragglers, not the center of theoretical activity (which has problems much more worth discussing).

What I most disagree with her about though is her treatment of HEP experiment and experimentalists. Yes, one can find people who have used bad theory to make bad arguments for building a new machine, but I don’t think those have been of much significance. For more on the current debate about this, see here. At the present time though, no one is spending money on building a new energy frontier machine any time soon. Money is being spent on running the LHC at high luminosity (CERN) and studying neutrinos (US), as well as studying the possibilities for going to higher energy. All of these activities are valuable and well-justified.

The LHC has been a huge success so far, with the old claims that it was going to see extra dimensions an embarrassment which doesn’t change the science that has happened. The discovery of the Higgs was a huge advance for the field, and the on-going effort to study its properties in detail is important. Another huge advance for the field has been the careful investigation of the new energy range opened up by the LHC, shooting down a lot of bad theory. Pre-LHC, the most influential theorists in the world heavily promoted dubious SUSY extensions of the SM, making these arguably the dominant paradigm in the field. LHC experimentalists have blown huge holes in that bandwagon, in some sense by doing exactly what Hossenfelder complains about (looking for evidence of badly motivated theories of new particles). In this story they’re not the problem, they’re the solution.

I’ll be busy this week with the talks mentioned and with attending math talks in Oxford, so little time to discuss more here or do a good job moderating a discussion. So, behave.

]]>**Some News:**

I’ll be in England later in the month, in Oxford much of the week of the 26th-30th. That week is the week of the 2022 Clay Research Conference and Workshops. The evening of Tuesday the 27th I’ll be giving a public talk on Unified Theories of Physics, sponsored by the Oxford Centre of the Institute of physics.

The 2022 HowTheLightGetsIn festival in London was supposed to be the weekend of September 17-18, but has been postponed two weeks because of the death of the Queen. It’s now scheduled instead for the weekend of October 1-2 and I’ll likely be there, participating in a couple of panel discussions.

**More of the Same:**

I’ve written too much here over the years about the problems with multiverse theories. For short versions, there’s also FAQ entries here and here, and a piece called Theorists Without a Theory I wrote for Inference. Seeing some recent things about this topic from people I generally agree with (e.g. here and here) leads to an uncontrollable urge to reiterate some of my arguments, so:

- You can’t argue against the concept of a multiverse in general, dismissing unobservable universes. If you had a very successful theory based on ideas that simultaneously implied successful predictions about what you can observe, as well as unobservable parallel universes, you could get indirect evidence for a multiverse. The strength of this evidence would depend on the details of the theory, but it’s logically possible that this could be strong evidence.
- Arguments pro or con about the “multiverse” that simultaneously engage with the many-worlds interpretation of quantum mechanics and inflationary or string theory landscape models are a waste of time. These are two completely different subjects, which raise completely different issues and have nothing to do with each other. For the rest of this I’ll stick to the second subject, ignore the first.
- If you want to have a serious discussion on this topic, it should be about a particular model or well-defined class of models. One popular class is inflationary models. Here people often write down a well-defined model, but the problem is that it’s a toy model (e.g. no SM fields, just gravity and a hypothetical inflaton field unrelated to any field for which we have a tested theory). Another popular class is the “string theory landscape”. Here the problem is that you don’t have a well-defined model. People who work on this work not with a well-defined theory but with a list of properties of a conjectured, currently non-existent, theory (e.g. “M-theory”). There’s nothing wrong with doing this to see if you get interesting predictions about the world, which would give you some confidence in the existence of the conjectural theory. There is something seriously wrong with doing this if after decades of work you find that the list of properties you have is vacuous in terms of explanatory power.
- It’s important to understand just how vacuous the “string theory landscape” class of models is. The problem is not just a measure problem on the space of possible universes, but much worse: one has no idea what this space is that you would like to put a measure on.
- “Pseudo-science” is an accurate description of “string theory landscape” research. People have complained to me that it is too harsh, should only be applied to activities of people who are abusing the good name of science for discreditable purposes. Doing something because you refuse to admit failure of a scientific idea you have a lot invested in seems to me a discreditable purpose.

I normally try and avoid getting into the vast topic of the hype problem in other subjects than string theory, but a couple things I’ve seen recently make it hard to resist. So, just this once…

**Quantum Computing**

Michio Kaku has a new book coming out next year, called Quantum Supremacy: How the Quantum Computer Revolution Will Change Everything. The publisher’s summary tells us that quantum computing “may eventually unravel the deepest mysteries of science and solve some of humanity’s biggest problems, like global warming, world hunger, and incurable disease.” More concisely:

There is not a single problem humanity faces that couldn’t be addressed by quantum computing.

For a very different take, see The quantum computing bubble at the Financial Times, where Nikita Gourianov argues that there’s a speculative bubble going on in this field, and:

Well, when exactly the bubble will pop is difficult to say, but at some point the claims will be found out and the funding will dry up. I just hope that when the music stops and the bubble pops, the public will still listen to us physicists.

For a response to this, see a later article at the Financial Times: Separating quantum hype from quantum reality.

I think Gourianov makes an important point for physicists to keep in mind. Having this sort of hype blow up in physicist’s faces is not going to help with the credibility problems physics already has with the public due to decades of hype about non-existent breakthroughs in fundamental physics.

**Nuclear Fusion**

Attempts to build a nuclear fusion-based power reactor have been going on for 70 years or so. Decades ago it had already become a joke that success was always “30 years off”. One would think that because of this there would be overwhelming skepticism about new claims in this field, but there’s continual new hype all the time. The Guardian recently had a long article about The race to give nuclear fusion a role in the climate emergency. If you read the article carefully, there’s no evidence of any change on the “30 years off” front, with one expert describing magnetic confinement-based reactors as highly unlikely before “after 2050” and laser-based schemes “another 50 years to go, if at all.”

One project that has been getting a lot of press is SPARC, a collaboration between MIT and a private start-up. Their claim seems to be that they’ve got a workable reactor design all ready to go, last year finished developing the needed 20T high temperature superconductor-based magnet, and by 2025 will have a working reactor putting out more energy than goes in. Then:

On this path, how long would it take before fusion energy is on the grid?MIT scientists and their collaborators believe that ARC — a fusion power plant that would produce electricity continuously — could be built and operating by early 2030.

This all seems highly implausible to me, but Bill Gates is putting money into the the project and I guess we’ll find out soon. For a skeptical take, see here.

About nuclear fusion, Michio Kaku tells us that:

Quantum computers could allow us to finally create nuclear fusion reactors that create clean, renewable energy without radioactive waste or threats of meltdown.

**Two more items:**

Getting back to the sort of claims about physics that don’t work out that I usually write about, the IAS website points to two recent items:

- Symmetry magazine interviews various physicists who appeared in the film Particle Fever (which I wrote about here).
- An electronic music producer interviews Edward Witten.

I see today via the LHC Page 1 Vistar that a problem at a cooling tower will cause part of the accelerator to need to be warmed up to room temperature, putting the LHC out of business for the next 4 weeks or so.

The LHC has just been coming out of long shutdown the past few months, starting its Run 3. In the past couple weeks it has started to get up towards its full luminosity potential, with over 2400 bunches in the beam. So far during Run 3 the machine has delivered an integrated luminosity of about 10 inverse fb to each of the experiments (ATLAS/CMS). The plan for Run 3 (which is expected to last through 2025) is to accumulate an integrated luminosity of about 300 inverse fb, doubling the 140 inverse fb of Run 2, at a slightly higher beam energy (6.8 TeV vs. 6.5 TeV).

]]>A random collection of things that may be of interest:

- September 17 and 18 I’ll be at the How the Light Gets In Festival in London, participating in discussions of the relation of math and physics, and theories of everything. I’m looking forward to the festival, which sounds like fun, and to spending some time in London. A week or so later, I’ll be in Oxford, attending the Clay Research Conference as well as a Physics from the Point of View of Geometry workshop in honor of Graeme Segal’s 80th birthday.
- I’ve been spending the summer trying to write up some details of the ideas I’ve been working on, specifically the claim that the geometry of spinors in four dimensions allows one to think of one of the SU(2)s in the Euclidean Spin(4) symmetry as an internal symmetry. Still learning more about how this works, hope to have something ready to publicize within the next month or so.
- For rest and relaxation I’ve been learning a bit more about various Langlands-related topics. The talks from the IHES summer school are mostly well-worth watching. Also very highly recommended are David Ben-Zvi’s lectures on
*The Langlands Program as Electric-Magnetic Duality*given a couple weeks ago at a workshop in Cambridge. - Still trying to finish reading Récoltes et Semailles and decide whether to write something here about this bizarre and fascinating document. If you want to read this yourself, Mateo Carmona has a freely available transcription here.
- There an interesting conversation about Ricci flow between my Columbia colleagues John Morgan and Richard Hamilton available here.
- Sometimes it takes great self-control to avoid responding to things I see on Twitter. In the case of a recent exchange between Noah Smith and various people defending string theory. I couldn’t help myself and started writing something, then soon hit the character limit. This returned me to sanity as I realized that trying to have an intelligible discussion in the twitter format about anything complicated is just absurd.
The gist of a lot of the discussion was that even string theory defenders now admit it was an overhyped failure as a “theory of everything”, but they then come up with new, improved hype. One argument seems to be that string theory has led to new developments in hype about black holes (for these, Scientific American has you covered here).

- Today on Twitter Sabine Hossenfelder explains her current academic employment situation (no permanent position, latest grant application denied.) She’s a very unusual case, and has a successful new book and other ventures that to some degree can replace a standard academic income. For everyone though, the way academic jobs in theoretical physics work, if you decide you want to pursue topics other than very conventional ones that a group is already working on, you’re going to have a very hard time. Getting older and having a life also tends to be inconsistent with pursuing the very few opportunities that might come up.

It’s getting late, but I can’t help myself. Reading too many wrong things about symmetry and physics on the internet has forced me to do this. And, John Baez says I don’t explain things. So, here’s what the relationship between symmetry and physics really is.

In the language of mathematicians, talking about “symmetries” means you are talking about groups (often Lie groups, or their infinitesimal versions, Lie algebras) and representations. The relation to physics is:

**Classical mechanics (Hamiltonian form)**

In classical mechanics the state of a system with $n$ degrees of freedom is given by a point in phase space $P=\mathbf R^{2n}$ with $n$ position coordinates $q_j$ and $n$ momentum coordinates $p_j$. Functions on this space are a Lie algebra, with Lie bracket the Poisson bracket

$\{f,g\}$. Dynamics is given by choosing a distinguished function, the Hamiltonian $h$. Then the value of any function on $P$ evolves in time according to

$$\frac {df}{dt}=\{f,h\}$$

The Hamiltonian $h$ generates the action of time translations. Applying the same formula, other functions generate the action of other groups (spatial translations, rotations, etc.). If your function satisfies $\{f,h\}=0$, it generates a “symmetry”, and doesn’t change with time (is a conserved quantity).

**Quantum mechanics**

Quantization of a classical system is something mathematically obvious: go from the above Lie algebra to a unitary representation of the Lie algebra. This takes elements of the Lie algebra (functions on $P$) to skew-adjoint operators on a Hilbert space, the space of quantum states. There’s a theorem (Stone-von Neumann) that says that (modulo technicalities) there’s only one way to do this, and it gives an irreducible unitary representation that works for polynomials up to degree two. For higher degree polynomials there will always be “operator ordering ambiguities”. The representation is given by

$$1\rightarrow -i\mathbf 1,\ \ q_j\rightarrow -iQ_j,\ \ p_j\rightarrow -iP_j$$

This is a representation because

$$\{q_j,p_k\}=\delta_{jk}\rightarrow [-iQ_j,-iP_k]=-i\delta_{jk}\mathbf 1$$

The right-hand side is the Heisenberg commutation relations for $\hbar=1$.

For more details, I wrote a whole book about this.

]]>David Zierler, the oral historian at the American Institute of Physics, has done many in-depth interviews with theoretical physicists in recent years. Today I came across a 2020 interview with Shelly Glashow, which was very interesting in general, and also answered a question I had always wondered about. Glashow was my undergraduate advisor at Harvard, where I was a student from 1975-79. From what I remember, his office was more or less next door to Steven Weinberg’s. It was well-known that they had been close friends, in the same class first at Bronx High School of Science, and then at Cornell. Towards the end of my time at Harvard I heard that their friendship was over and they were barely on speaking terms, but I never knew what had happened. In the fall of 1979, they were (together with Abdus Salam), awarded the Nobel Prize for their work on the unified electroweak theory.

In the interview, Glashow explains the story from his point of view:

Glashow:

by the late 1970s I began to think of myself as a Nobel contender. But I was under the impression that my old friend Steven Weinberg was doing everything in his power to keep the prize for himself and Salam. In particular—at a conference that he attended in Tokyo—he went out of his way to avoid mentioning my name at all while presenting the history of weak interaction theory. I got very upset by that omission. It was the issue which terminated our friendship. In the summer of 1979, I was invited to a meeting in Stockholm, to discuss the current state of physics ideas and others. Prior to the meeting, I sent a transcript of my talk to Steve. He was violently against my giving the talk. Because it examined various alternatives to what was then known as Weinberg/Salam theory. In fact, it was an open-minded talk in which I was discussing whether their—or more properly—our theory was a correct one or not. But it was such a heated discussion that I eventually had to simply hang up on him, because I had no intention of revising my talk. And I did not.Zierler:

Was his assessment of your paper accurate in your mind?Glashow:

I did talk about alternatives to the Weinberg-Salam theory. Yes. I was not yet convinced that it had to be true.Zierler:

And what was your sense of why this was so unacceptable to him?Glashow:

He thought it would endanger the Nobel Prize that he had campaigned for and anticipated for Salam and himself.

A copy of Weinberg’s Tokyo paper is here.

In the interview Glashow is scornful about Salam’s work and the campaign to get him a part of the Nobel Prize:

Glashow:

… Recall that Salam made a great deal of noise about why the prize should be given to he, Salam. I’ve been told that there were dozens and dozens of nominations of Salam. In fact, there’s a whole paper written about his shenanigans, which I can refer to you; written by Norman Dombey. Everything he says is true, to my knowledge….My Nobel Prize depended on that one paper written in 1960. Steve’s Nobel Prize depended exclusively on that one paper he wrote in 1967, a wonderful paper which applied the notion of spontaneous symmetry breaking to the—my electroweak model. So, the question arises, what did Salam do? He introduced the electroweak—the SU(2)XU(1) model in 1964. That was over three years after I did. He copied my work but did not cite me…

Zierler:

Do you want to comment on why then he would have been a co-recipient of the Nobel Prize with you for this copy of your work?Glashow:

I’ll explain it in a moment. But let me come back to—he also claims to the first to introduce spontaneous symmetry breaking in the paper that he wrote in 1968, one year after Steve wrote his paper. But that paper even cites Steve’s paper, so it is hardly the first time. He did what each of us had previously done, but much later. So why did he get a Nobel Prize? Very simply, he was nominated many times. Because he was Director of the International Center for Theoretical Physics in Trieste, Italy and he was very close with the directors of physics institutes in many countries; almost 100 of different institutions. And many of them wrote letters, by his instruction, using his words in some cases, encouraging the Nobel Committee to give the prize to him and also Steven. All of this documented, in fact, by the paper by Norman Dombey, who had access to Salam’s files in Italy, and has copies of the letters that he sent to other people encouraging them to nominate him. So, I think he shared the prize because he made a point of doing just that.

I wrote something on the blog about Donbey’s claims here.

Zierler also asks Glashow some questions about string theory, a topic on which Glashow’s views have been consistent from the beginning:

]]>Zierler:

In retrospect, Shelly—how well do you think—has both string theory and your criticism of it aged over the past 30 years?Glashow:

Well, it’s hard to answer that. String theory has become an established part of physics departments throughout the world, more so in Europe than in America. We still have some universities which are proudly string-free, like Boston University. We also have an awful lot of string theorists around who are twiddling their thumbs. It is not clear that string theory is going anywhere. I expect that string theorists would disagree with that assessment. But they are actually considering many other circumstances such as black holes in other spaces than ours, and there are all kinds of interesting things being done in mathematics, in physics, elsewhere by string theorists but with no relationship to the questions that interest me. They cannot answer the questions they set out to answer. That much is clear.Zierler:

That’s as clear to you—Glashow:

That was clear from the beginning, I think…Glashow:

… I no longer feel so strongly about string theory. Why beat a dead horse? String Theory does not answer the questions that I’m interested in. I’m sad about that. I hope that they’re wrong. I have no reason to think that their horse is, in fact, dead, but it’s dead from the point of view of being useful to my way of thinking about physics. And I think that many experimenters feel exactly the same way, because string theorists say nothing about experiments that have or could be done. They only speak of experiments that cannot be done, which is somehow not interesting.

There’s a new book out this month, Before the Big Bang: The Origin of the Universe from the Multiverse, about which we’re told:

One of the world’s most celebrated cosmologists presents her breakthrough explanation of our origins in the multiverse.

In recent years, Laura Mersini-Houghton’s ground-breaking theory, spectacularly vindicated with observational evidence, has turned the multiverse from philosophical speculation to one of the most compelling and credible explanations of our universe’s origins.

I spent a few minutes today looking through the book in the bookstore, trying to figure out where to find the details of the “spectacularly vindicated with observational evidence.” I didn’t see any references in the book, just a claim that in 2018 the author collaborated with Eleonora Di Valentino on showing vindication by observation. Presumably this is a reference to these three papers, but who knows. I don’t see anything like that in a quick look at the papers.

For many years I’ve spent a significant amount of time reading books and papers purporting to offer scientific evidence for a multiverse, trying to carefully understand the author’s arguments and write about them here (one example involved earlier claims by this author, see here). Few physicists though seem to care that bogus claims and pseudo-science about the multiverse have overrun their field and become its public face. I’ve come to the conclusion that best to not waste more time on this.

]]>Each summer for nearly a quarter-century there has been a big yearly conference bringing together the string theory community. I’ve often written about these conferences on the blog, see here. This year’s version will be held next week in Vienna, for more information see here.

Taking a look at the program, one thing that stands out is that the string theory community has almost completely stopped doing string theory. Looking at the program, only two out of 44 talks seem to be significantly about string theory. One of three parallel discussion sessions is entitled “Strings and the Real World” and will be chaired by Cumrun Vafa. I’m guessing this will mostly be about the swampland, not string theory.

A tradition at these conferences is one or more public talks designed to publicize string theory. This year’s versions will be given by Netta Engelhardt and Andy Strominger. They have nothing to do with string theory, but they do make very clear what the string theory community has found to replace string theory: black holes. Engelhardt’s title is “The Black Hole Information Paradow: A resolution on the horizon?” and Strominger’s is “Black Holes: the Most Paradoxical Objects in the Universe”.

Looking at the talk titles, the most common words in the titles are “holography” and “black holes”, with the center of gravity of the subject now for a couple decades the effort to use holography to say something about black holes. Maldacena’s title is “What happens when you look at supersymmetric black holes for a long time?” which seems also an interesting question about the field itself.

]]>The 2022 ICM is starting soon, in a virtual version organized after the cancellation of the original version supposed to be hosted in St. Petersburg (for how that happened, see here). The IMU General Assembly is now going on, moved from St. Petersburg to Helsinki. One decision already made there was that the 2026 ICM will be hosted by the US in Philadelphia. With the 2022 experience in mind, hopefully the IMU will for next time have prepared a plan for what to do in case they again end up having a host country with a collapsed democracy being run by a dangerous autocrat.

Registration for following the talks in real time has now been closed, but the talks are being recorded and will appear on the IMU Youtube channel. The program is here.

There will be quite a few other virtual events affiliated in some way with the main ICM, for a list see here. Some of these are traditional satellite conference which have been moved from their originally scheduled version in Russia. An example is this one organized by Igor Krichever, which was supposed to be held at Skoltech in Moscow, but was moved online and hosted by Columbia.

The Fields Medals will be announced at 10am local time in Helsinki on July 5, there will be a livestream here. This will be 3am here in New York, so I’ll likely be sleeping and find out what happened later in the morning. Since I just got back from vacation and it’s now a holiday weekend, I’ve been out of touch with my usual sources of math gossip and haven’t heard any informed rumors about who the medalists will be. One person who has been mentioned as a possibility is the Ukrainian mathematician Marnya Viazovska.

The last couple times (2014 and 2018) the IMU has put out the news about the Fields Medals to some of the press under unusual embargo terms that made reporting difficult for everyone except Quanta magazine which was given special access (for more about this see here). I haven’t heard anything about whether the same thing is happening this year.

]]>From today’s New York Times, Michio Kaku explains:

In physics, the concept of a multiverse is a key element of a leading area of study based on the theory of everything. It’s called string theory, which is the focus of my research. In this picture, subatomic particles are just different notes on a tiny, vibrating string, which explains why we have so many of them. Each string vibration, or resonance, corresponds to a distinct particle. The harmonies of the string correspond to the laws of physics. The melodies of the string explain chemistry.

By this thinking, the universe is a symphony of strings. String theory, in turn, posits an infinite number of parallel universes, of which our universe is just one.

In this universe I’m on vacation and in no mood to waste time commenting on this crap.

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