Not Even Wrong

There’s a very intriguing new article out today by Kevin Hartnett at Quanta magazine, entitled Secret Link Uncovered Between Pure Math and Physics (also a video here). It’s about ideas relating number theory and physics from arithmetic geometer Minhyong Kim. He’s evidently on tour talking about them, with two talks on Gauge theory in arithmetic and a colloquium talk on “Gauge theory in geometry and number theory” in Heidelberg, and a talk on Gauge theory in arithmetic geometry in Paris.

In recent years Kim has been working on what he calls “arithmetic Chern-Simons” theory. For details about this, there are papers here, here, here and here, a workshop here, talks here and here. These ideas grew out of a beautiful and well-known analogy between topology and number theory that goes under the name “Arithmetic Topology”. For more about this, see the book Knots and Primes by Morishita, or the course notes by Chao Li and Charmaine Sia.

While these ideas look quite interesting and I have some idea what they’re about, the Quanta story seems to indicate that Kim has something new, an idea about “Diophantine gauge theory” going beyond the arithmetic Chern-Simons business, and with potential applications to deep problems in arithmetic geometry. Unfortunately the mathematical background here is beyond me (you can try to look at Jordan Ellenberg here, and this earlier paper of Kim’s), and as far as I can tell, the only source for details on the conjectured relations to gauge theory is Kim’s recent talks, which aren’t documented anywhere I can see.

I’m sure we’ll be hearing more about this as time goes on. It joins a host of other ideas relating gauge theory and number theory (in the context for instance of the Langlands program), and promises deeper links to come between fundamental ideas about physics and about mathematics.

Update: Some personal background on this story from John Baez.

Update: More about this story here, including a discussion of the use of Kim’s methods to deal with the “Cursed Curve”.

Update: Reddit has a report of the Heidelberg talk here, unfortunately giving just enough information about the talk to make it sound very interesting, too little to figure out what the ideas discussed actually were. For yet more frustration on this front, Kim gave a general talk on the subject last year here with video supposedly available, but no browser I’ve tried can access it. I do hope we’ll soon see slides, notes, a paper, something, anything, so we can figure out what the Quanta article actually was about.

Update: Kim now has a paper out explaining these new ideas: Arithmetic Gauge Theory: A Brief Introduction.

Quanta magazine has an interesting new piece up, an interview of Witten by Natalie Wolchover.

One topic covered in the interview is the question discussed in a recent posting, that of whether a different formulation of QFT exists, one not based on a choice of Lagrangian. Here Witten is non-committal, leaning to the idea such a thing might exist only in special cases:

Now, Nati Seiberg [a theoretical physicist who works down the hall] would possibly tell you that he has faith that there’s a better formulation of quantum field theory that we don’t know about that would make everything clearer. I’m not sure how much you should expect that to exist. That would be a dream, but it might be too much to hope for; I really don’t know…

I find it hard to believe there’s a new formulation that’s universal. I think it’s too much to hope for. I could point to theories where the standard approach really seems inadequate, so at least for those classes of quantum field theories, you could hope for a new formulation. But I really can’t imagine what it would be.

The standard example of where such a formulation might be needed is the 6d superconformal (2,0) theory, about which Witten says:

From the (2,0) theory’s existence and main properties, you can deduce an incredible amount about what happens in lower dimensions. An awful lot of important dualities in four and fewer dimensions follow from this six-dimensional theory and its properties. However, whereas what we know about quantum field theory is normally from quantizing a classical field theory, there’s no reasonable classical starting point of the (2,0) theory.

About the current state of M-theory, there’s this exchange:

You proposed M-theory 22 years ago. What are its prospects today?

Personally, I thought it was extremely clear it existed 22 years ago, but the level of confidence has got to be much higher today because AdS/CFT has given us precise definitions, at least in AdS space-time geometries. I think our understanding of what it is, though, is still very hazy. AdS/CFT and whatever’s come from it is the main new perspective compared to 22 years ago, but I think it’s perfectly possible that AdS/CFT is only one side of a multifaceted story. There might be other equally important facets.

What’s an example of something else we might need?

Maybe a bulk description of the quantum properties of space-time itself, rather than a holographic boundary description. There hasn’t been much progress in a long time in getting a better bulk description. And I think that might be because the answer is of a different kind than anything we’re used to. That would be my guess.

Are you willing to speculate about how it would be different?

I really doubt I can say anything useful. I guess I suspect that there’s an extra layer of abstractness compared to what we’re used to. I tend to think that there isn’t a precise quantum description of space-time — except in the types of situations where we know that there is, such as in AdS space. I tend to think, otherwise, things are a little bit murkier than an exact quantum description. But I can’t say anything useful.

The hope of 22 years ago was that it was non-perturbative string theory which would provide the desired “description of the quantum properties of space-time itself”. Over the years though studies of gauge-gravity duality have moved away from the use of string theory to provide this bulk description. Witten’s take on the current situation: “There hasn’t been much progress in a long time in getting a better bulk description. And I think that might be because the answer is of a different kind than anything we’re used to.” seems reasonable.

It’s interesting to hear that Witten was going back to Wheeler to see if he had any inspiration to offer the current “It from Qubit” program. This requires a patience for the “vague but inspirational” that Witten has more of these days than he used to:

Why do you have more patience for such things now?

I think when I was younger I always thought the next thing I did might be the best thing in my life. But at this point in life I’m less persuaded of that. If I waste a little time reading somebody’s essay, it doesn’t seem that bad.

This patience is not infinite though: among Witten’s many admirable qualities are the way he responds to:

Do you have any ideas about the meaning of existence?

No. [Laughs.]

First, two local events, involving well-known physics bloggers:

• Last Thursday I had the pleasure of attending an event at NYU featuring Sabine Hossenfelder and Natalie Wolchover in conversation. You can watch this for yourself here. If you’re not following Hossenfelder on her blog and at Twitter (and planning to read her forthcoming book), as well as reading Wolchover’s reporting at Quanta magazine, you should be.
• Next week there will be an event out in Brooklyn advertised as covering the Scientific Controversy over string theory. The idea seems to be to address this controversy by bringing to the public two well-known and very vocal proponents of one side of it.

For a Q and A with another well-known physics blogger, there’s Tommaso Dorigo at Physics Today.

For a couple of encouraging indications that the theoretical physics community may finally be taking seriously the need to give up on failed thinking and try something new, there’s

• A conference next month in Italy on Weird Theoretical Ideas (Thinking outside the box).
• An interesting talk at a recent IPMU conference by Yuji Tachikawa. I like his conclusion:
  

  Basically, all the textbooks on quantum field theories out there use an old framework that is simply too narrow, in that it assumes the existence of a Lagrangian.

  This is a serious issue, because when you try to come up e.g. with a theory beyond the Standard Model, people habitually start by writing a Lagrangian … but that might be putting too strong an assumption.

  We need to do something

In General Relativity related news, there’s a new edition out of Misner, Thorne and Wheeler, the book from which many of us learned both geometry and GR. It comes with new prefaces from David Kaiser as well as Misner and Thorne (which an appropriate search on the Amazon preview might show you…). In other Wheeler-related news, Paul Halpern has a new book out, The Quantum Labyrinth, which tells the entangled stories of Feynman and Wheeler.

Finally, also GR related, the Perimeter Institute has announced the formation of a new cosmology-focused “Centre for the Universe”, funded by an anonymous 10-year $25 million donation. It will be led by cosmologist Neil Turok, who is soon to step down as director of Perimeter.

The Breakthrough Prizes for 2018 will be awarded at a ceremony on December 3, I believe at the usual NASA Hangar 1 in Mountain View. The next day Stanford will host the 2018 Breakthrough Prize symposium, which one will be able to watch live from the Breakthrough Prize Facebook page.

The symposium schedule is available here, and while it does not list the Prize awardees, it does appear to list the titles of the talks. From this it looks like the math \$3 million will go to a geometer, who will talk about “Geometry at Higher Dimensions”. There may be several \$100,000 New Horizons Prizes for younger mathematicians, but at least one will be to an analytic number theorist, who will talk about “Analytic Number Theory in Everyday Life”.

For the \$3 million physics prize, it looks like it is going to be split five ways and go to cosmologists/astrophysicists. The talks by laureates are “The Next Decade in Cosmology”, “Gravitational Waves and Cosmology”, “Search for Extraterrestrial Intelligence”, “A New Instrument for Listening to the Universe” and “The Beginning and End of the Universe”.

Update: Some details about the prize ceremony here. Perhaps there really is a problem with the public understanding of mathematics:

This year, a total of seven \$3 million prizes will be awarded – five in life sciences, one in fundamental physics, two in mathematics.

Update: The \$3 million for physics went to the WMAP team. For mathematics, it was Hacon and McKernan. The posted titles for the mathematics prize winners were a red herring, they have been changed to “A Tour of Algebraic Geometry” (McKernan) and “Sphere Packing in High Dimensions” (Viazovska).

A few links that may be of interest. Mathematics first:

• A seminar “Lectures Grothendieckiennes” on the mathematical ideas of Alexander Grothendieck is taking place this year in Paris, and has just recently started up.
• My ex-Columbia colleague Jeff Achter is one of the authors of an unusual new math paper: Hasse-Witt and Cartier-Manin matrices: A warning and a request. The paper points out that papers of Manin at some points confused an operator and its dual, leading to potential sign errors in later papers that reference Manin’s results. I’m quite sympathetic to the problem, having at various points fallen victim to similar confusions while writing my book (I hope they have all been resolved in the final version, wouldn’t bet anything really valuable on it…).
• Nature has an excellent obituary of Vladimir Voevodsky, written by Dan Grayson.

On the physics side:

• The LHC has now ended data-taking at 13 TeV for the year (a recent summary is here) and will start up again next spring. The machine ended up delivering about 50 inverse fb each to CMS/ATLAS (bettering the goal of 45), of which about 45 was recorded. Results published so far typically use 36 inverse fb from previous year’s data, so next year we should start seeing results based on a total 13 TeV data set of up to 80 inverse fb.
• Still no WIMPs. Frank Wilczek surveys searches for his favorite dark matter alternative here.
• At Big Think, Eric Weinstein has a take on what’s gone wrong with theoretical physics over the past 40 years that I’m mostly in agreement with.

Since returning from a vacation partly spent isolated from the internet, I’ve been catching up and noticed that some of the most prominent sources of funding for math and physics research have been making the news:

• The New York Times and other sources have extensive reports based on leaked records from an offshore law firm that specializes in helping you avoid inconvenient US tax and reporting requirements. The story starts out with the example of Jim Simons, who has become the largest non-governmental funder of math and physics research. His Simons Foundation has been doing an excellent job of providing such funding. They have about \$3 billion in assets, annual income of around \$500 million. The Times reports that Simons (with a net worth of about \$18.5 billion) has an offshore version of the Foundation, the Simons Foundation International, with assets of \$8 billion, dwarfing the onshore version.
• The assets of these Foundations are presumably largely invested in the secretive and extremely successful Renaissance Technologies hedge fund, which also is the employer of quite a few physicists and mathematicians. I’ve asked many people over the years, but have never found anyone who knows (or will admit to knowing) what it is that RenTech does that is so successful. A peculiar aspect of the coming age of private math/physics research funding is that no one getting this funding really knows where the money comes from.

  In other news while I was away the CEO of RenTech, Robert Mercer, was finally induced to leave. Mercer had drawn a lot of attention recently since he in recent years has been taking the opposite tack to Simons, funding institutions devoted to promoting untruth over truth (e.g. Breitbart News), achieving fantastic success last year. He also has branched out from doing whatever secretive things RenTech does to make mountains of money using computers and data, starting up a firm called Cambridge Analytica, a firm involved in secretively using computers and data to undermine democracy in the US and elsewhere. I had been wondering for quite a while what Simons thought of Mercer’s activities. My understanding of highly-paid finance jobs was that your employer pays you a lot of money in return for having your full attention and devotion to not having negative stories about them come to public attention, so Mercer’s continued employment was surprising. It seems that Simons finally had enough, after realizing how much damage Mercer was doing to his firm, in particular by creating a situation that would discourage many people from wanting to work there (there also was a campaign underway to get institutions to divest from investments with RenTech).

• Another high profile source of funding for math and physics, in this case for cash prizes to mathematicians and physicists, has been venture capitalist Yuri Milner, with his Breakthrough Prize organization. New prizes will be announced in three weeks at a December 3 prize ceremony (I also believe there will be an associated Breakthrough Prize symposium held at Stanford shortly thereafter). It has always been well-known that much of Milner’s wealth derived from investments in Facebook and Twitter. Less well-known and recently revealed was that a major source of the funds for these investments was Russian state organizations closely tied to Vladimir Putin.
• Turning to sources of public funding, there’s not very positive news about a possible ILC collider in Japan, with reports of a cutback of the proposal from a 500 GeV to a 250 GeV machine (which would still cost about $7 billion).
• Foreign policy magazine has an article discussing the proposal for a huge new collider in China (discussed here). The point of view of the article is quite critical of the idea of locating a huge new project in a country with an increasingly authoritarian regime:
  

  China’s next-generation supercollider will unlock secrets of the universe — and destroy the ideals of the scientists running it.

  Luckily, for another more local prominent large country with an increasingly authoritarian and xenophobic regime, the issue of a possible problem with locating an international collider project there isn’t likely to come up since its leaders have no interest in funding such projects.

A few short items:

• My graduate school roommate Nathan Myhrvold has a new book coming out this month, a five-volume series about the science of bread, based on several years of research into the subject at his laboratory near Seattle. Robert Crease has gone out to visit, and gives a wonderful detailed report on The physics of bread in this month’s Physics World.
• An article at FQXI on multiverse research they are funding seemed to finally give me an understanding of what this is all about:
  

  These are the two conceptually hardest questions in cosmology, according to Raphael Bousso, a theoretical physicist at the University of California, Berkeley. They go to the core of what it means to exist as a human being making sense of the universe we find ourselves in. And, he adds, unfortunately, there is very little physical knowledge to go on when it comes to working out the answer.

  Undaunted by the lack of tools to help them, theatrical physicists Eugene Lim of King’s College London, UK, and Richard Easther of the University of Auckland, New Zealand, are…

  This all of a sudden made things clear: what is going on is “theatrical physics”, not “theoretical physics”. Going on like this about the multiverse is performance art.

  Unfortunately I just noticed that this page has been edited (new version here), removing the enlightening characterization of what this is about.

• I’m glad to see that Natalie Wolchover has just won an AIP award for her writing about physics, in particular for a piece on how physicists are dealing with the “nightmare scenario”. While she’s perhaps the best professional journalist writing about these topics, for coverage of this from a professional physicist, the best you can find is Sabine Hossenfelder’s blogging at Backreaction. I’m pleased to hear that the two of them will be appearing at an event here next month in NYC, talking about Making Sense of Mind-Blowing Physics at NYU on Nov. 16.

Update: Sabine Hossenfelder has a book coming out next year, which should be fascinating (although I suspect I’ll have something to disagree with…).

Gian Francesco Giudice has a long essay about the status of particle physics, post-negative LHC results. For better and worse, I think it captures well the view of many mainstream theorists.