## 50 Years of Electroweak Unification

The 50th anniversary of electroweak unification is coming up in a couple days, since Weinberg’s A Model of Leptons paper was submitted to PRL on October 17, 1967. For many years this was the most heavily cited HEP paper of all time, although once HEP theory entered its “All AdS/CFT, all the time” phase, at some point it was eclipsed by the 1997 Maldacena paper (as of today it’s 13118 Maldacena vs. 10875 Weinberg). Another notable fact about the 1967 paper is that it was completely ignored when published, only cited twice from 1967 to 1971.

The latest CERN Courier has (from Frank Close) a detailed history of the paper and how it came about. It also contains a long interview with Weinberg. It’s interesting to compare his comments about the current state of HEP with the ones from 2011 (see here), where he predicted that “If all they discover is the Higgs boson and it has the properties we expect, then No, I would say that the theorists are going to be very glum.”

Today he puts some hope in a non-renormalizable Majorana mass term for neutrinos as evidence for new physics. As for the future:

As to what is the true high-energy theory of elementary particles, Weinberg says string theory is still the best hope we have. “I am glad people are working on string theory and trying to explore it, although I notice that the smart guys such as Witten seem to have turned their attention to solid-state physics lately. Maybe that’s a sign that they are giving up, but I hope not.”

On this last sentiment, I have the opposite hope. He also shares what I think is a common hope for what will save the field (a smart graduate student with a new idea):

Weinberg also still holds hope that one day a paper posted in the arXiv preprint server by some previously unknown graduate student will turn the SM on its head – a 21st century model of particles “that incorporates dark matter and dark energy and has all the hallmarks of being a correct theory, using ideas no one had thought of before”.

Perhaps current training of graduate students in theory should be rethought, to optimize for this.

Update: A colloquium talk by Weinberg on this topic will be live-streamed here on October 17.

Posted in Uncategorized | 10 Comments

## Various Topics in Interpretation of Quantum Mechanics

A couple of recent discussions about quantum mechanics that may be of interest:

• There’s a recent paper out by Don Weingarten that looks looks like it might have a different take on the fundamental “many-worlds” problem of, as he writes:

how in principle the definite positions of the macroscopic world emerge from the microscopic matter of which it is composed, which has only wave functions but not definite positions.

My naive feeling about this has always been that the answer should lie in a full understanding of the initial state of the measurement apparatus (+ environment), that it is our imperfect probabilistic understanding of the initial state that limits us to a probabilistic understanding of the final state. I found Weingarten’s investigation of this intriguing, although I’m not sure that the language of “hidden variables” is a good one here, given the use of that language in other kinds of proposals. By the way, Weingarten is an ex-lattice gauge theorist who I had the pleasure of first meeting long ago during his lattice gauge theory days. He at some point left physics to go work for a hedge fund, I believe he’s still in that business now.

Luckily for all of us, Jess Riedel has looked at the paper and written up some detailed Comments on Weingarten’s Preferred Branch, which I suggest that anyone interested in this topic look at. Discussion would best be at his blog, a much better informed source than this one.

• Gerard ‘t Hooft has a remarkable recent preprint about quantum mechanics, with the provocative title of Free Will in the Theory of Everything. I fear that the sort of argument he’s engaging in, trying to ground physics in very human intuitions about how the world should work, is not my cup of tea at all. Instead, what has always fascinated me about quantum mechanics has always been its grounding in very deep mathematical ideas, and the surprising way in which it challenges our conventional intuitions by telling us about an unexpected new way to think about physics at a fundamental level.

For more discussion of the paper, there are Facebook posts by Tim Maudlin here and here in which he argues with ‘t Hooft. I confess that I wasn’t so sure whether to take the time to read these, and after a short attempt gave up, unable to figure out precisely what the argument was about (and put off by Maudlin’s style of argument. Do philosophers really normally behave like that?). Links provided here in case you have more interest in this than I do, or better luck getting something out of it.

Posted in Quantum Mechanics | 17 Comments

## The Big Bang Theory and the Death of SUSY

If you’re a fan of The Big Bang Theory, perhaps you’ve seen the latest episode, The Retraction Reaction. If not, you might be interested in the following transcript (taken from here). The show has always done a good job of getting the science right, for an interview with their physics consultant David Saltzberg, see here.

The episode begins with a Science Friday interview of physicist Leonard Hofstadter by Ira Flatow:

FLATOW: So, it has been five years since the discovery of the Higgs boson– what’s the next big thing gonna be?

LEONARD: Wow, that’s hard to say. There’s so much going on. We’ve been collecting tons of data that could revolutionize the way we understand the universe. For instance, there’s a particle called a squark, which could prove supersymmetry.

FLATOW: That is interesting. Have you found it?

LEONARD: What, the squark?

FLATOW: Yes.

LEONARD: No, no. Wouldn’t that be exciting? But we’re also looking for the selectron, the gluino and the neutralino.

FLATOW: Well, and have you found that?

LEONARD: No. Another fun sidenote– I went to high school with a girl named Theresa Gluino, but it didn’t cost $2 billion to find her. She was smoking behind the gym. (laughs) FLATOW: So, what have you found? LEONARD: Uh, nothing, actually. We’ve got the best equipment and the best minds all working on it. Although, some days I’m, like, ugh we’ve spent so much money. Why haven’t we found anything? What are we doing? After a segment in which neuroscientist Amy explains that she doesn’t tell physicist boyfriend Sheldon about her new lab equipment since AMY: We’ve been getting so much more funding than physics, he’s been a little sensitive. another scene features Leonard called into the office of a university administrator: LEONARD: I have to say I’m a little nervous. Ms. DAVIS: You should be. LEONARD: Look, I know I screwed up, but it was only one interview. How much damage could it have caused? Ms. DAVIS: Would you like for me to read you the e-mails from donors asking why are they giving us money if physics is a dead end? LEONARD: I didn’t say it was a dead end. I just said that I was worried it might be. Ms. DAVIS: So if I just said I was worried you might not have a job next week, how would you feel? LEONARD: Light-headed, and glad you asked me to sit down. Okay, just tell me what I can do. Ms. DAVIS: I’m gonna need you to make a statement saying that you misspoke, and that you’re confident the physics community is close to a major breakthrough. LEONARD: You want me to lie. Ms. DAVIS: Look, Dr. Hofstadter, I’m counting on you. I think that you are the smartest physicist at this university. LEONARD: Really? Ms. DAVIS: See? Lies. They’re not that hard. Leonard then has this exchange with Penny: PENNY: Hey, come on, look, you said a few dumb things on the radio– what is the worst that could happen? LEONARD: I may get fired. PENNY: Okay, well, even if you did, you could find another job. LEONARD: Yeah, who wouldn’t want to hire the physicist who publicly said physics is dead? Well, I wouldn’t put that under “special skills”. I can fix it, I just need to write a retraction I don’t believe in– basically sell out to keep my job. PENNY: Great, I’ll leave you to it. He then goes to talk to string theorist Sheldon Cooper: LEONARD: Sheldon, it’s me. SHELDON: What? LEONARD: Look, I know you’re mad, but I have to write a statement that says the physics community is close to a breakthrough, and since you actually believe that, I could really use your help. SHELDON: Sorry, I can’t. LEONARD: Come on, don’t be like that. SHELDON: What? Look. (sighs) Not all science pans out. You know, we’ve been hoping supersymmetry was true for decades, and finally, we built the Large Hadron Collider, which is supposed to prove it by finding these new particles, and it-it hasn’t. And maybe supersymmetry, our last big idea, is simply wrong. LEONARD: Well, that sounds awful. Now I get why everyone hates me. Penny later comes in: PENNY: So you guys are upset because the collider thing disproved your theories? LEONARD: It’s worse than that. It hasn’t found anything in years, so we don’t know if we’re right, we don’t know if we’re wrong. We don’t know where to go next… PENNY: Come on. You guys are physicists. Okay? You’re always gonna be physicists. And sure, sometimes, the physics is hard, but isn’t that what makes it boring? The episode ends with a visit to the grave of Richard Feynman, and a reference to Feynman’s story about how he got himself out of a slump in his work when he was at Cornell: WOLOWITZ: He did so much. And here we are, stuck and letting him down. You know, Feynman used to say he didn’t do physics for the glory or the awards, but just for the fun of it. He was right. Physics is only dead when we stop being excited about it. All in all, a pretty accurate portrayal of the situation in high energy physics theory, with a reasonable take on what to do about it. Update: A correspondent points me to a rather Leonard Hofstadter-ish interview with Steven Weinberg back in 2011, where he says: It may be that they’ll only discover the Higgs boson and nothing else, and we’ll be left looking at our toes and wondering what we’re going to do next. There may be nothing really new that can be reached with the LHC, I have fears… If all they discover is a Higgs boson with roughly the properties that the theory predicts and nothing else, I don’t know where the field is going to go. When asked a rather Ira Flatow-ish question: “Wouldn’t you say to a young person that now would be a very exciting time to go into physics?” his answer is Whether or not it would be a good career move depends on what they are going to discover. If all they discover is the Higgs boson and it has the properties we expect, then No, I would say that the theorists are going to be very glum. Posted in Uncategorized | 35 Comments ## 2017 Nobel Prize in Physics At this point, Kip Thorne and Rainer Weiss of LIGO have (deservedly) won just about every scientific prize out there, for the first observation of gravitational waves. I don’t know of anyone who doesn’t believe they’ll be getting the Physics Nobel tomorrow morning. With an open spot in the usual limitation to three (Ronald Drever passed away earlier this year), perhaps Barry Barish will also get the nod. Most appropriate would be to use the third slot to give an award to the entire LIGO collaboration, but it seems likely that the tradition of not honoring collaborations will continue. There will be a live webcast of the announcement at 5:45am EST available here. Update: Congratulations to the winners. I think Natalie Wolchover speaks for all science journalists when she writes: Thrilled they won, thrilled not to spend this morning speed-reading about some bizarre condensed matter phenomenon. Update: A couple things I’ve learned from comments and other coverage of this: • Some physicists have no sense of humor and are either unaware of or ungrateful for the excellent job Natalie Wolchover and others at Quanta magazine have been doing in writing high-quality stories about a wider range of topics in physics than anyone else (see here and here, related here). • All evidence is that on October 16th we’ll get announcement of observation of gravitational waves with an optical counterpart, with details at this conference in Baton Rouge. Posted in Uncategorized | 53 Comments ## Vladimir Voevodsky 1966-2017 I was very sorry to hear yesterday of the announcement from the IAS of the untimely death of Vladimir Voevodsky, at the age of 51. Last year I had the chance to meet Voevodsky and talk with him for a while at the Heidelberg Leader’s Forum (which I wrote about here). He was a gracious and modest person, and it was fascinating to learn a bit about what he was trying to do, and his earlier experiences doing mathematics that had led him down this path. There was no indication at that time that he was ill, and I don’t know what led to his death. Back in 2012 I wrote a blog post about him and his work, linking to various things that may be of interest if you’d like to know more about him. Among more recent sources of information, there’s a video interview here, a popular article here, lecture slides here, here and here, and a piece by Siobhan Roberts which covers some of the same topics that Voevodsky told me about when I met him last year. Update: See here for remembrances of Voevodsky on the HoTT mailing list. Update: There will be a gathering at the IAS to remember Voevodsky this Sunday, a funeral service and conference in Moscow December 27-28, and a conference in Princeton September 29-30, 2018. More information available here. Update: A longer obituary of Voevodsky, from the IAS. Update: The New York Times has an obituary here. Video of the IAS gathering is available here. Especially informative and touching is the talk given there by his ex-wife Nadia Shalaby, who gave a detailed look at his life, mathematical and personal, including a frank discussion of his problems with mental illness, depression and sometimes self-destructive ways of dealing with this. Also see this story at Quanta, where Shalaby gives the cause of his death as an aneurysm. Posted in Obituaries | 6 Comments ## Various and Sundry • I don’t know if I ever mentioned this, but quite a while ago I replaced the “latexrender” TeX plugin being used here by a mathjax one. As I find time, I’m now going back and editing old posts to get rid of latexrender tags and make the equations more mathjax friendly. As far as comments are concerned, you can add TeX content by using standard math delimiters \$, or \$\$ for displayed math. If you want to comment about US dollars, put a backslash before your dollar signs to avoid the interpretation as TeX.

One reason I hadn’t advertised this much is that I know it’s hard to get TeX right the first time, so people’s comments with TeX would be likely to often not work properly. I’ve added a plugin that lets you edit your comment for 5 minutes after you write it. This should be useful for typos, as well as for fixing TeX problems (note that you need to refresh the page to get the math to display).

• For a philosopher’s take on evaluating string theory, see this talk by James Ladyman, on Cosmic Dreams. Material on string theory is near the end, and just makes the obvious point that having no experimental evidence for the theory is a huge problem, no matter what efforts are made to change the usual way scientific theories are evaluated.
• A hot topic these days in the math community is the conjecture that local Langlands can be understood as geometric Langlands for the Fargues-Fontaine curve. My attempts to learn about this so far haven’t had a lot of success, but I now have new-found hope. At Harvard there’s a seminar going on this semester on the topic, and it has a website which so far features explanations of some of the mathematics involved from Jacob Lurie and Dennis Gaitsgory. In London, the London Number Theory Seminar also has a study group devoted to this topic (website here, although seems to have disappeared for the moment).
• LQP2 (Local Quantum Physics Crossroads, v.2.0) is a website that gathers various information about relativistic quantum theory.
• In November Perimeter will host what should be an interesting workshop on the question of how to make sense of the Path Integral for Gravity.
• A memorial for Maryam Mirzakhani will take place at Stanford on October 21, with a live feed available here.
• As always, Quanta magazine keeps publishing a wide range of very high quality articles about math and physics, covering different topics than everyone else. Most recently, on the math side, see an article by Erica Klarreich on Pariah Moonshine and on the physics side, Robert Henderson on possible searches for long-lived particles possibly from a “hidden sector”..

Update: Commenter sdf points out this historical article by Pierre Colmez about the Fargues-Fontaine curve, preprint of a preface to an Asterisque volume.

Posted in Uncategorized | 17 Comments

## Special Relativity and Classical Field Theory

For quite a while Leonard Susskind has been giving some wonderful courses on physics under the name “The Theoretical Minimum”, pitched at a level in between typical popularizations and standard advanced undergraduate courses. This is a great idea, since there is not much else of this kind, while lots of people inspired by a popular book could use something more serious to start learning what is really going on. The courses are available as Youtube lectures here.

Book versions of some of the courses have now appeared, first one (in collaboration with George Hrabovsky) about classical mechanics, then one (with Art Friedman) about quantum mechanics. I wrote a little bit about these here and here, thought they were very well done. When last in Paris I noticed that there’s now a French version of these two books (with a blurb from me for the quantum mechanics one).

The third book in the series (also with Art Friedman) is about to appear. It’s entitled Special Relativity and Classical Field Theory, and is in much the same successful style as the first two books. Robert Crease has a detailed and very positive review in Nature which does a good job of explaining what’s in the book and which I’d mostly agree with.

The basic concept of the book is to cover special relativity and electromagnetism together, getting to the point of understanding the behavior of electric and magnetic fields under Lorentz transformations, and the Lorentz invariance properties of Maxwell’s equation. Along the way, there’s quite a lot of the usual sort of discussion of special relativity in terms of understanding what happens as you change reference frame, a lot of detailed working out of gymnastics with tensors, and some discussion in the Lagrangian language of the Klein-Gordon equation as a simpler case of a (classical) relativistic field theory than the Maxwell theory. Much of what is covered is clearly overkill if you just want to understand E and M, but undoubtedly is motivated by his desire to go on to general relativity in the next volume in this series.

At various points along the way, the book provides a much more detailed and leisurely explanation of crucial topics that a typical textbook would cover all too quickly. This should be very helpful for students (perhaps the majority?) who have trouble following what’s going on in their textbooks or course due to not enough detail or motivation. Besides non-traditional students in a course of self-study, the book may be quite useful for conventional students as a supplement to their textbook.

One of the most annoying things someone can do while reviewing a book is to start going on about their own different take on the material, criticizing the author for not writing a very different book. So, the rest of this posting is no longer a review of the book, it’s now about the very different topic of what I think about this material, nothing to do with Susskind’s valuable and different approach.

This semester I’m teaching a graduate level course on geometry, and by chance the past week have been discussing exactly some of the same material about tensor fields that Susskind covers. The perspective is quite different, starting with trying to explain a coordinate-invariant point of view on what these things are, only then getting to the formalism Susskind discusses. I can’t help thinking that, with all the effort Susskind (and pretty much every other physics textbook…) devotes to endless gymnastics with tensors in coordinates, they could instead be providing an understanding of the geometry behind this story. It’s unfortunate that many if not most of those who study this material in physics don’t ever get exposed to this point of view. Thinking in geometrical terms, the vector potential and field strength have relatively simple interpretations, and using differential forms the equations needed for the part of E and M Susskind covers are pretty much just:

F=dA, dF=0, and d*F=*J

Similarly, for the special relativity material, there’s a danger of the basic simplicity of the story getting lost in calculations of how things appear in coordinates with respect to different reference frames. What you fundamentally need is mainly that objects are described by a (conserved in the absence of forces) energy-momentum p, which satisfies p2= -m2, with Lorentz transformations taking one such p to another. The wider principle is that things are described by solutions to wave equations, with special relativity saying that the Lorentz group takes solutions to solutions.

I’d like to believe that such a very different course and very different book would be possible, quite possibly am very wrong (I’ve never taught special relativity to anyone). Maybe some day someone, inspired by Susskind’s project, might try to do something at a similar level, but from a more geometric point of view.

Posted in Book Reviews | 30 Comments

## QCD at $\theta=\pi$

Earlier this week Zohar Komargodski (who is now at the Simons Center) visited Columbia, and gave a wonderful talk on recent work he has been involved in that provides some new insight into a very old question about QCD. Simplifying the problem by ignoring fermions, QCD is a pure SU(3) Yang-Mills gauge theory, a simple to define QFT which has been highly resistant to decades of effort to better understand it.

One aspect of the theory is that it can be studied as a function of an angular parameter, the so-called $\theta$-angle. Most information about the theory comes from simplifying by taking $\theta=0$, which seems to be the physically relevant value, one at which the theory is time reversal invariant. There is however another value for which the theory is time reversal invariant, $\theta=\pi$, and what happens there has always been rather mysterious.

The new ideas about this question that Komargodski talked about are in the paper Theta, Time Reversal and Temperature from earlier this year, joint work with Gaiotto, Kapustin and Seiberg. Much of the talk was taken up with going over the details of the toy model described in Appendix D of this paper. This is an extremely simple quantum mechanical model, that of a particle moving on a circle, where you add to the Lagrangian a term proportional to the velocity, which is where the angle $\theta$ appears. You can also think of this as a coupling to an electromagnetic field describing flux through the circle.

Even if you’re put off by the difficulty of questions about quantum field theories such as QCD, I strongly recommend reading their Appendix. It’s a simple and straightforward quantum mechanics story, with the new feature of a beautiful interpretation of the model in terms of a projective representation of the group O(2), or equivalently, a representation of Pin(2), a central extension of O(2). In the analogy to SU(N) Yang-Mills, it is the $\mathbf Z_N$ symmetry of the theory that gets realized projectively.

Komargodski himself commented at the beginning of the talk on the reasons that people are returning to look again at old, difficult problems about QCD. The new ideas he described are closely related to ones that are part of the recent hot topic of symmetry protected phases in condensed matter theory. It’s great to see that this QFT research may not just have condensed matter applications, but seems to be leading to a renewal of interest in long-standing problems about QCD itself.

Besides the paper mentioned above, there are now quite a few others. One notable one is very recent work of Komargodski and collaborators, Time-Reversal Breaking in QCD4, Walls and Dualities in 2+1 Dimensions.

Posted in Uncategorized | 11 Comments

## Modern Theories of Quantum Gravity

Quanta magazine today has a column by Robbert Dijkgraaf that comes with the abstract:

Reductionism breaks the world into elementary building blocks. Emergence finds the simple laws that arise out of complexity. These two complementary ways of viewing the universe come together in modern theories of quantum gravity.

It struck me that at this point I don’t know what a “modern theory of quantum gravity” is. Much of the article is a clear explanation of the usual story of the renormalization group and effective field theory, but towards the end, when quantum gravity comes up, I have trouble following. String theory has gone from being an exciting new idea to being part of historical tradition:

Traditional approaches to quantum gravity, such as perturbative string theory, try to find a fully consistent microscopic description of all particles and forces. Such a “final theory” necessarily includes a theory of gravitons, the elementary particles of the gravitational field.

That “reductionist” tradition is opposed to a new “emergent” holographic theory, and we’re told that

The present point of view thinks of space-time not as a starting point, but as an end point, as a natural structure that emerges out of the complexity of quantum information, much like the thermodynamics that rules our glass of water. Perhaps, in retrospect, it was not an accident that the two physical laws that Einstein liked best, thermodynamics and general relativity, have a common origin as emergent phenomena.

In some ways, this surprising marriage of emergence and reductionism allows one to enjoy the best of both worlds. For physicists, beauty is found at both ends of the spectrum.

Dijkgraaf seems to be saying that a viable emergent theory of four-dimensional quantum gravity based on the complexity of quantum information has been found, but I seem to have missed this. Can someone point me to a paper describing it?

Posted in Uncategorized | 20 Comments

## Modern Geometry

This semester I’m teaching the first semester of Modern Geometry, our year-long course on differential geometry aimed at our first-year Ph.D. students. A syllabus and some other information about the course is available here.

In the spring semester Simon Brendle will be covering Riemannian geometry, so this gives me an excuse to spend a lot of time on aspects of differential geometry that don’t use a metric. In particular, I’ll cover in detail the general theory of connections and curvature, rather than starting with the Levi-Civita connection that shows up in Riemannian geometry. I’ll be starting with connections on principal bundles, only later getting to connections on vector bundles. Most books do this in the other order, although Kobayashi and Nomizu does principal bundles first. In some sense a lot of what I’ll be doing is just explicating Kobayashi and Nomizu, which is a great book, but not especially user-friendly.

A major goal of the course is to get to the point of writing down the main geometrically-motivated equations of fundamental physics and a few of their solutions as examples. This includes the Einstein eqs. of general relativity, although I’ll mostly be leaving that topic to the second semester course.

Ideally I think every theoretical physicist should know enough about geometry to appreciate the geometrical basis of gauge theories and general relativity. In addition, any geometer should know about how geometry gets used in these two areas of physics. I’ve off and on thought about writing an outline of the subject aimed at these two audiences, and thought about writing something this semester. Thinking more about it though, at this point I’m pretty sick of expository writing (proofs of my QM book are supposed to arrive any moment…). In addition, I just took a look again at the 1980 review article by Eguchi, Gilkey and Hanson (see here or here) from which I first learned a lot of this material. It really is very good, and anything I’d write would spend a lot of time just reproducing that material.

Posted in Uncategorized | 26 Comments