Various Math Items

Some math-research items:

  • Mura Yakerson has been doing a really wonderful series of interviews with mathematicians, available at her math-life balance web-page or Youtube channel. I’ve just started listening to some of them, including ones with Peter Scholze and Dustin Clausen (Clausen is John Tate’s grandson, the latest AMS Notices has a memorial article).
  • There’s a remarkable report out from Peter Scholze about the progress of the Liquid Tensor experiment. Back when I first heard about this, I figured it was a clever plot by Scholze to get other people to help with a very complicated part of a proof, by getting them to work out the details, with the excuse being that they would be doing a computer check of the proof. Seemed to me very unlikely you could check such a proof with a computer, but that by forcing humans to try to disambiguate things carefully enough in preparation for a computer proof, he’d get a human-checked proof. Looks like I was wrong.
  • For yet more Scholze news, the Fields Medal symposium this year will be devoted to his work.
  • Trying to find something of interest in math, that wasn’t Scholze-related, I noticed this site devoted to the case of Azat Miftakhov, where there will be an online Azat Miftakhov Day program. Foiled though on the Scholze front, since he’s a speaker there, talking about Condensed Mathematics.
  • The list of those giving plenary lectures at next years ICM is here.

Update: Kevin Hartnett at Quanta has a good new article up about quantum field theory and mathematics (an inexhaustible topic…)

Update: Also from the Simons Foundation, there’s a wonderful profile of my Columbia colleague Andrei Okounkov, who has been very active in bringing together mathematics and ideas from quantum field theory.

Posted in Uncategorized | 8 Comments

Non-empirical Physics

I haven’t been paying much attention in recent years to the philosophers of science studying “Non-empirical” or “Post-empirical” physics or theory confirmation. At various times I did write fairly extensively about this, see for instance here, here and here. By 2015 there was a conference in Munich on the topic, which led in 2019 to a volume of papers entitled Why Trust a Theory?

There’s a new paper out along similar lines, String theory, Einstein, and the identity of physics: Theory assessment in absence of the empirical, evidently to appear in a journal special issue from a 2019 conference on Non-Empirical Physics from a Historical Perspective.

The reaction of most physicists to this sort of thing is exemplified by Will Kinney’s tweet about the paper:

WTAF

In the past few years I’ve been writing less and less here and elsewhere about the issue of evaluating string theory as physics, for several reasons:

  • String theory has effectively gone completely post-empirical, decoupling from any possible relation to experiment. This Week’s Hype used to be a regular feature here, devoted to debunking the numerous bogus claims regularly being made for how to “test string theory”. One rarely sees these anymore, with the string theory community now having given up on this and somehow comfortably moved into a completely post-empirical mode.
  • I’m actually much more sympathetic than most people to the idea that there is a serious and very interesting question about how to evaluate ideas about theoretical fundamental physics in the absence of viable experimental tests. But I haven’t had much luck finding others who share my views. The reaction to blogposts like this recent one tends to be pretty uniformly scornful, that I’m just Lost in Math. The post-empirical philosophers of science deal with me differently, pretty much doing their best to ignore me (I don’t make it into the extensive bibliography of the new paper on the arXiv).
  • There are two other projects that seem to be a much better way to spend my time (the twistor unification stuff, and improving the textbook on QM and representation theory).

By the way, I notice that there is an arXiv trackback already for another blog entry about this paper, wondering if trackbacks here are still censored.

Well, that’s all about this for now, best to take my own advice and go think about something else.

Update: I just ran across this AIP interview with John Schwarz from last year. Schwarz seems to feel that string theory unification is a huge success, despite the testability problem. On the failure to find the superpartners he and other string theorists expected, that’s a problem for experimental physics, not for string theory:

As I said, if supersymmetry is not discovered, there’s a danger that experimental particle physics will die. If that happens, it would be tragic, but it wouldn’t be the end of string theory. String theory will continue, regardless, and will continue to advance.

On the topic of answering those who argued that superpartners would not be found back in the 2000s, and who have put forward detailed criticisms of string theory unification, here’s what he has to say:

There were a couple popular books that attacked string theory about a decade or so ago. The authors clearly had chips on their shoulders. For people without a physics background it’s not possible to assess whether what they’re reading makes sense or not. But anyone with at least an undergraduate education in physics I think can recognize that they should not be taken seriously.

Posted in Uncategorized | 27 Comments

The Evolution of the Physicist’s Picture of Nature

Reading this Nautilus article about Julian Barbour led me recently to something I don’t think I’ve ever read before, Dirac’s 1963 Scientific American article The Evolution of the Physicist’s Picture of Nature. There is a very famous quote from this article that I’ve often seen:

It is more important to have beauty in one’s equations than to have them fit experiment

but I was unaware of the context of that quote, in which the famous part is prefaced by “I think there is a moral to this story, namely that…” The story that Dirac had in mind was that of the discovery of the Schrödinger equation.  Famously, Schrödinger first wrote down a relativistic wave equation (now known as the Klein-Gordon equation).  This equation is what one quickly gets if one follows de Broglie’s idea that matter is described by waves, and uses the relativistic energy-momentum relation.   Here’s the full story, as told by Dirac, giving his famous quote in context:

I might tell you the story I heard from Schrödinger of how, when he first got the idea for this equation, he immediately applied it to the behavior of the electron in the hydrogen atom, and then he got results that did not agree with experiment. The disagreement arose because at that time it was not known that the electron has a spin. That, of course, was a great disappointment to Schrödinger, and it caused him to abandon the work for some months. Then he noticed that if he applied the theory in a more approximate way, not taking into ac­ count the refinements required by relativity, to this rough approximation his work was in agreement with observation. He published his first paper with only this rough approximation, and in that way Schrödinger’s wave equation was presented to the world. Afterward, of course, when people found out how to take into account correctly the spin of the electron, the discrepancy between the results of applying Schrodinger’s relativistic equation and the experiments was completely cleared up.

I think there is a moral to this story, namely that it is more important to have beauty in one’s equations than to have them fit experiment. If Schrodinger had been more confident of his work, he could have published it some months earlier, and he could have published a more accurate equation. That equation is now known as the Klein-Gordon equation, although it was really discovered by Schrödinger, and in fact was discovered by Schrödinger before he discovered his nonrelativistic treatment of the hydrogen atom. It seems that if one is working from the point of view of getting beauty in one’s equations, and if one has really a sound insight, one is on a sure line of progress. If there is not complete agreement between the results of one’s work and experiment, one should not allow oneself to be too discouraged, because the discrepancy may well be due to minor features that are not properly taken into account and that will get cleared up with further developments of the theory.

There’s another remarkable aspect of this Scientific American article, something about it that would be completely inconceivable today: they write down three equations, including both the famous non-relativistic Schrödinger equation for the Coulomb potential, as well as the relativistic Klein-Gordon version.

Dirac notes that Schrödinger found his formulation of quantum mechanics in a very different way than Heisenberg found his:

Heisenberg worked keeping close to the experimental evidence about spectra that was being amassed at that time, and he found out how the experimental information could be fitted into a scheme that is now known as matrix mechanics. All the experimental data of spectroscopy fitted beautifully into the scheme of matrix mechanics, and this led to quite a different picture of the atomic world.

whereas

Schrödinger worked from a more mathematical point of view, trying to find a beautiful theory for describing atomic events, and was helped by De Broglie’s ideas of waves associated with particles. He was able to extend De Broglie’s ideas and to get a very beautiful equation, known as Schrödinger’s wave equation, for describing atomic processes. Schrodinger got this equation by pure thought, looking for some beautiful generalization of De Broglie’s ideas, and not by keeping close to the experimental development of the subject in the way Heisenberg did.

At the end of the article, Dirac makes the case that progress in fundamental physics may not come from a theorist like Heisenberg finding a scheme to match experimental results, but from a theorist like Schrödinger pursuing mathematical beauty:

It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power, needing quite a high standard of mathematics for one to understand it. You may wonder: Why is nature constructed along these lines? One can only answer that our present knowledge seems to show that nature is so constructed. We simply have to accept it. One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe. Our feeble attempts at mathematics enable us to understand a bit of the universe, and as we proceed to develop higher and higher mathematics we can hope to understand the universe better.

This view provides us with another way in which we can hope to make advances in our theories. Just by studying mathematics we can hope to make a guess at the kind of mathematics that will come into the physics of the future. A good many people are working on the mathematical basis of quantum theory, trying to understand the theory better and to make it more powerful and more beautiful. If someone can hit on the right lines along which to make this development, it may lead to a future advance in which people will first discover the equations and then, after examining them, gradually learn how to apply them. To some extent that corresponds with the line of development that occurred with Schrodinger’s discovery of his wave equation. Schrödinger discovered the equation simply by .looking for an equation with mathematical beauty. When the equation was first discovered, people saw that it fitted in certain ways, but the general principles according to which one should apply it were worked out only some two or three years later. It may well be that the next advance in physics will come about along these lines: people first discovering the equations and then needing a few years of development in order to find the physical ideas behind the equations. My own belief is that this is a more likely line of progress than trying to guess at physical pictures.

The context for his famous quote is thus an argument for pursuing fundamental physics by looking for mathematical beauty, not giving up on a beautiful equation just because it doesn’t seem to fit experiment. As in Schrödinger’s case, more effort may be needed to understand the actual relationship of the equation to reality.

Besides this argument, which I’ve always been well aware of and sympathetic to (despite not knowing the context in which Dirac was making it), there’s something else I found very striking about the 1963 article. Dirac begins by explaining that the four-dimensional Lorentz symmetry of relativity is in a sense broken by the choice of a way of describing the state of the world:

What appears to our consciousness is really a three-dimensional section of the four-dimensional picture. We must take a three-dimensional section to give us what appears to our consciousness at one time; at a later time we shall have a different three-dimensional section. The task of the physicist consists largely of relating events in one of these sections to events in another section referring to a later time. Thus the picture with four­ dimensional symmetry does not give us the whole situation. This becomes particularly important when one takes into account the developments that have been brought about by quantum theory. Quantum theory has taught us that we have to take the process of observation into account, and observations usually require us to bring in the three-dimensional sections of the four-dimensional picture of the universe.

The special theory of relativity, which Einstein introduced, requires us to put all the laws of physics into a form that displays four-dimensional symmetry. But when we use these laws to get results about observations, we have to bring in something additional to the four-dimensional symmetry, namely the three-dimensional sections that describe our consciousness of the universe at a certain time.

Dirac also refers to work on canonical formulations of general relativity, aimed at quantizing gravity:

… if one insists on preserving four-dimensional symmetry in the equations, one cannot adapt the theory of gravitation to a discussion of measurements in the way quantum theory requires without being forced to a more complicated description than is needed bv the physical situation. This result has led me to doubt how fundamental the four-dimensional requirement in physics is. A few decades ago it seemed quite certain that one had to express the whole of physics in four­-dimensional form. But now it seems that four-dimensional symmetry is not of such overriding importance, since the description of nature sometimes gets simplified when one departs from it.

Thinking about twistor unification has led me to some similar thoughts: a Euclidean formulation of quantum theory requires picking a choice of imaginary time direction and breaking SO(4) symmetry in order to define states. Dirac thinks of our consciousness as giving us access to the state of the universe defined on a 3d slice, but the twistor point of view is even more directly related to our conscious experience. A point in space time is defined by the sphere of light rays through the point, and it is this sphere that our vision gives us direct access to, with 3d space something we make up out of these spheres.

A common argument against Dirac’s point of view is that it’s engaging in mysticism. For another recent article that touches in a different way on the mystical nature of a discovery about fundamental physics, see this interview with Frank Wilczek, where he tells this story:

The mystical moment came while I was visiting Brookhaven National Laboratory, on Long Island. Somehow—I don’t remember how, exactly—I wound up alone, standing on a jerry-rigged observation platform above a haphazard mess of magnets, cables, and panels. This was a staging area for assembling detectors and renovating pieces of the main accelerator there, the Alternating Gradient Synchotron (AGS). I must have gotten separated from my host for a few minutes. In any case, there I was, alone inside an aircraft-hangar-sized metallic box, staring down at the kind of equipment that people use to explore the fundamentals of Nature experimentally.

And then it happened. It came to me, viscerally, that the intricate calculations I’d done using pen and paper (and wastebasket) might somehow describe this entirely different realm of existence—namely, a physical world of particles, tracks, and electronic signals, created by the kind of machinery I was looking at. There was no need to choose, as philosophers often struggled to do, between mind or matter. It was mind and matter. How could that be? Why should it be? Yet I somehow, I suddenly knew that it could be so, and should be so.

That was my mystical experience. I warned you that it was ineffable.

Posted in Uncategorized | 20 Comments

Some History

I’m heading out soon for a 10 day vacation in the Rocky Mountains, blogging likely to change from sparse to non-existent for the next couple weeks. I’ve come across the following things that people with an interest in the recent history of mathematics may find worthwhile:

  • S. T. Yau over the past year has organized a series of talks on the recent history of mathematics, featuring prominent people in the subject giving expository talks on a topic, sometimes writing something up. The talks are available here, the write-ups here. I can especially recommend Nigel Hitchin’s detailed explanation of the work of Michael Atiyah relevant to physics, much of which he was personally involved in.
  • Lieven Le Bruyn at neverendingbooks points to some wonderful French math YouTube videos. Don’t miss Alain Connes interviewing Serre, with Serre explaining that he doesn’t know (or care) what a topos is.
  • For a good account of the fascinating life of Alexander Grothendieck, there’s Luca Signorelli’s The Man of the Circular Ruins. I hadn’t realized that some of the weirder writings from Grothendieck’s later life are now readily available, for instance La Clef des Songes.
  • For a long recent account by Langlands both of his recent ideas about geometric Langlands and his fascination with languages (including White Russian language instructors), see this letter to Yvan Saint-Aubin.
Posted in Uncategorized | 5 Comments

Finished Some Things

I’ve now finished with two things that I’ve been working on over the last year or so:

  • The paper explaining my proposal for “Twistor Unification” is now done and uploaded to the arXiv, see here.
  • I’ve finished lecturing for the course on quantum mechanics for mathematicians that I’ve been teaching this academic year. Because of the Covid-required online format for the lectures, they could easily be put on Youtube, where they’re available here. I’m hoping to never ever have to teach this way again, so don’t expect to ever again be producing Youtube lectures. The lectures pretty closely follow my book, and I had been hoping to work on improving and expanding the text. Unfortunately, partly due to laziness and partly due to the twistor stuff, while I found a lot in the book that needs improvement, I didn’t find the time to do the necessary rewriting and writing. I do however have a notebook full of notes on what needs to be done.

For the future, I’m hoping to go on some sort of vacation in a couple weeks, and soon get back to work on some of the major issues raised by the unification proposal (much of which is very sketchy, a lot to be done). I hope to do quite a bit of traveling the rest of this year, likely won’t be teaching in the fall, but probably will be teaching the quantum course again next year during the spring semester. At that point perhaps I’ll get finally get around to the project of rewriting and expanding the quantum book.

Posted in Uncategorized | 22 Comments

Hawking Hawking

There’s a very good new book about Stephen Hawking that just came out, Charles Seife’s Hawking Hawking. Some detailed reviews can be found at Prospect Magazine (Philip Ball) and the New York Review of Books (James Gleick). Seife has chosen to write the story of Hawking’s life starting at the end and ending at the beginning, which takes some getting used to, but provides a different perspective.

Hawking was a huge world-wide celebrity, widely considered by the public and the press to be the modern-day analog of Einstein, dominating the field of theoretical physics. His personal story, involving a long life battling a disease that left him quadraplegic and severely disabled, added greatly to the phenomenon he became. His life has been the subject of various books, films and TV shows, but only now, three years after his death, has something appeared that gives an account of this life corresponding not to myth but to reality.

The reality of this story is that Hawking was a very good theorist, with a high point of his career his work on Hawking radiation in 1974. I remember attending lectures by him at Princeton in the early 1980s, when he was actively working on Euclidean quantum gravity. His speech was hard to follow, so one of his graduate students or postdocs would translate for the audience. Unfortunately, the disease continued to take its toll, and after he nearly died from it in 1985, losing the ability to speak to a tracheostomy, all evidence I’ve seen is that he was no longer able to continue to do research at the highest level. From then on he lived a remarkable and full life for another 33 years, including some collaborative work with other theorists, but he was no longer the driving force behind any new research programs. Seife quotes extensively many physicists who worked with Hawking during this time, including Andy Strominger and Hawking’s student Marika Taylor, who give a fairly good idea of what it was like to work with him.

During the early 80s Hawking was quite fond of the idea that N=8 supergravity would be a successful unified theory, famously giving a talk about it entitled Is the end in sight for theoretical physics?. The advent of string theory coincided with the serious deterioration in his health and ability to communicate. From then on he was reliant on others to explain to him what was going on in string/M-theory:

[Marika] Taylor didn’t yet know how difficult the task ahead of her was. Her thesis was going to be on M-theory, but Hawking was not an expert on the subject. Taylor would largely have to guide herself straight to the frontier of an incredibly difficult branch of theoretical physics, digest all the important work of the past few years, and then teach Hawking what she had learned before even being able to come up with a thesis idea. On top of that, Hawking wasn’t particularly enthusiastic about the string-theoretic parts of the theory: he just cared about supergravity. “As I was starting to go into those areas, I wouldn’t say that he was skeptical,” Taylor says. “He was just not interested… Actually I think the real truth is that he didn’t want to engage with people on territory he was unfamiliar with.”

Soon after I started this blog in 2004, I wrote here and here about Hawking’s heavily publicized talk in Dublin announcing that he had figured out how to resolve the black hole information paradox. I was baffled by reports of his talk and his paper, and not the only one. Seife tells the story of this in some detail, and I think the consensus is that there was no there there.

A large part of Hawking’s celebrity and income derived from his work as a popular author. His 1988 popular book, A Brief History of Time, was a huge success. Seife tells the story of how that book came about, partly motivated by the need for a new source of income. An initial manuscript due to Hawking was edited and improved a great deal before the published version was done. Many other books followed, and if you go to any bookstore with a science section, you’re likely to find quite a few of them for sale. The problem is that, on the whole, they’re not any good, and they’re not written by Hawking. Seife documents this sorry tale in some detail.

I first noticed this when I ran across a copy of God Created the Integers, a thick anthology of writing on mathematics, supposedly edited by and with commentary by Hawking. At least he’s listed as the sole author. Given the topic and the volume of material, it seemed highly implausible to me that Hawking was actually the author. For a review of the book, see here. Seife explains in detail that much of it is essentially plagiarized from other sources, and that to this day, it seems to be unknown who wrote the material (just that it clearly wasn’t Hawking).

At least this sort of thing got little attention, which unfortunately was not true of his 2010 The Grand Design, co-written with Leonard Mlodinow. I wrote about this book in some detail here. Put bluntly, it was an atrocious rehash of the worst nonsense about M-theory and the string theory landscape, with an argument for atheism thrown in to get more public attention. This is the sort of thing that has done a huge amount of damage to both the public understanding of fundamental physics, and even to the field itself. James Gleick’s otherwise excellent review of the Seife book ends with

Hawking promoted the theory of everything with a vengeance. He made it part of his brand. It was the title of the 2014 biopic in which Eddie Redmayne played Hawking. The much-quoted ending of A Brief History of Time raised the prospect of a complete theory—a final theory: “It would be the ultimate triumph of human reason—for then we would know the mind of God.” At the 1998 White House event, Hawking told the assembled dignitaries:

We shall have to rely on mathematical beauty and consistency to find the ultimate Theory of Everything. Nevertheless I am confident we will discover it by the end of the 21st century and probably much sooner. I would take a bet at 50-50 odds that it will be within twenty years starting now.

He would have lost that one, too. It was hubris—but it sold, and it is part of his legacy. He showed younger colleagues how to chase grand theories and best-selling books. Hawking is not the only physicist guilty of hawking.

The theory of everything is a false idol. Why should the universe, which grows more gloriously complex the more we see, be reducible to one set of equations and formulae? The point of science is not the holy grail but the quest—the searching and the asking. Let us hope there will never be a final theory.

We now live in an environment where the idea that there may be a deeper, more unified theory has become completely discredited, through the efforts of many, with Hawking playing an unfortunate part.

If you have any interest at all in Hawking’s story, you owe it to yourself to read this book. It’s a rich and thoughtful examination of his life and work, pushing aside the myth and bringing out the much more interesting reality behind it.

Update: There’s now a review of the book by Frank Wilczek in the New York Times.

Posted in Book Reviews | 19 Comments

Muon g-2 Result

The long awaited FNAL muon g-2 result was announced today, you can watch a video of the seminar here, look at the paper and a discussion of it at Physical Review Letters, or read stories from Natalie Wolchover at Quanta and Dennis Overbye at the New York Times. Tommaso Dorigo has an extensive discussion at his blog. In terms of the actual new result, it’s not very surprising: quite similar to the previous Brookhaven result (see here), with similar size uncertainties. It’s in some sense a confirmation of the Brookhaven result. If you combine the two you get a new, somewhat smaller uncertainty and ($a_\mu=\frac{1}{2}(g-2)$)
$$a_\mu(Exp)=116592061(41)×10^{−11}$$

The measurement uncertainties are largely statistical, and this is just using data from Run 1 of the experiment. They have accumulated a lot more data since Run 1, and once that is analyzed the FNAL experiment should be able to provide an experimental value with much lower uncertainty.

The big excitement over the g-2 experimental number has to do with it being in conflict (by 4.2 sigma now) with the Standard Model theoretical calculation, described here, which gives
$$a_\mu(Theory)=116591810(43)×10^{−11}$$
An actual discrepancy between the SM theory and experimental value would be quite exciting, indicating that something was missing from our understanding of fundamental particle physics.

The problem is that while the situation with the experimental value is pretty clear (and uncertainties should drop further in coming years as new data is analyzed), the theoretical calculation is a different story. It involves hard to calculate strong-interaction contributions, and the muon g-2 Theory Initiative number quoted above is not the full story. The issues involved are quite technical and I certainly lack the expertise to evaluate the competing claims. To find out more, I’d suggest watching the first talk from the FNAL seminar today, by Aida El-Khadra, who lays out the justification for the muon g-2 Theory Initiative number, but then looking at a new paper out today in Nature from the BMW collaboration. They have a competing calculation, which gives a number quite consistent with the experimental result:
$$a_\mu(BMW)=116591954(55)×10^{−11}$$

So, the situation today is that unfortunately we still don’t have a completely clear conflict between the SM and experiment. In future years the experimental result will get better, but the crucial question will be whether the theoretical situation can be clarified, resolving the current issue of two quite different competing theory values.

Update: Also recommended, as always: Jester’s take.

Posted in Experimental HEP News | 41 Comments

The God Equation

When I was out for a bike ride yesterday I stopped by a large book store and looked to see if they had a copy of Michio Kaku’s new book The God Equation. They didn’t, but did have plenty of copies for sale of his various previous efforts to promote string theory, such as 1987’s Beyond Einstein, 1994’s Hyperspace and 2005’s Parallel Worlds. If someone interested in fundamental physics walks into a bookstore, and looks in the Science section for something to read written by a well-known physics professor, these books are what they’re likely to end up taking home and reading.

When I got back from the bike ride, several people had forwarded me a link to this story from the Guardian which gives a good idea of what’s likely in the book, claims like:

Well, string theory has also created a tremendous amount of interest, as well as a backlash. People say, well, where is the proof? Quite frankly we don’t have the proof, in the same way that Newton did not have the proof of his inverse square law back in 1666. Sometimes, the mathematics and the ideas are ahead of the concrete experimental data. That’s where the Large Hadron Collider comes into play…

The Standard Model is the theory of almost everything. It works spectacularly well but it’s one of the ugliest theories proposed so far. There’s this avalanche of experimental numbers you have to put in by hand. But in string theory the Standard Model just pops right out. With just a few assumptions you get the entire Standard Model. So the point here is that we need experimental proof and the LHC may give us hints of a deviation in the Standard Model and that’s where this post-LHC physics comes into play.

This is just complete and unadulterated bullshit, of exactly the same sort Kaku and a host of others well-credentialed physicists have been heavily and successfully promoting for the last 35 years. I started writing about this 20 years ago, and there have been some changes since then (for one thing, we have Sabine Hossenfelder). I’m still waiting though for any of the leading figures in the physics community responsible for the string-theory hype campaign to do anything at all to try and stop Kaku and the rest of the Fake Physics onslaught that they unleashed.

Usually with books like this, once I get a copy of the book I try and write here a careful review quoting the writer accurately and explaining the problems with what they’ve written, but this time I think I’ll pass on the grounds that this would be a waste of time.

The funny thing though is that I probably agree with Kaku far more than most people about the possibility of unification, although I wouldn’t use the terminology “God equation” to describe a unified theory. Unfortunately Kaku has done far more than most physicists to discredit the search for a better unified theory, through the endless nonsense he has put out about the subject in books like this. I do think we’ll find a better, more unified theory, and I even think I know a couple of the crucial equations, which, leaving God out of it, are:
$${D\mkern-11mu/}_A\psi=0$$
and
$$F_A^+=0$$

Update: You can read the book’s introduction here. It seems that Kaku has conceptualized the book as a response to criticism of string theory. Near the end of the introduction, he assures us:

This book will hopefully give you a balanced, objective analysis of string theory’s breakthroughs and limitations.

This morning he’s on Morning Joe.

Posted in Book Reviews, This Week's Hype | 32 Comments

Twistor Unification

I’ve finally finished writing up a new version of some ideas that I first wrote about here last summer. The latest draft is here, I may set up a web page with more info here.

Several people had very helpful comments on what I wrote last summer, especially in pointing out that I wasn’t providing sufficient justification for the most radical claim I was making, that the problems with analytic continuation of spinor fields indicated that one could interpret one of the Euclidean space rotation group SU(2)s as an internal symmetry. I then spent a lot of time mastering aspects of Euclidean QFT I had never properly understood. Section two of the current paper is the result. It’s in some sense quite elementary, people may find it of independent interest, even if you’re not interested in the ideas involving twistors. Section three, an exposition of relevant aspects of twistors, is pretty much unchanged. Section 4 is an outline of the ideas about how to get a unified theory out of twistors, much there is still sketchy. I understand a lot better than last year how what I’m proposing fits into some standard ideas about “chiral” formulations of gravity, also have learned a bit more about previous attempts to formulate chiral gravity and gauge theory on twistor space. Some highly speculative remarks that this might all be somewhat related to N=4 super Yang-Mills have been added.

Here’s a little bit more here about the hardest to believe claim being made (about analytically continuing spinors). The standard assumption (this is what I always thought) has been based on the analytic continuation behavior of correlation functions: Schwinger and Wightman functions are analytic continuations of each other, and one might think there’s nothing more to analytic continuation between Euclidean and Minkowski space theories. After learning more about the Euclidean QFT literature, I was struck by how different this is from the physical Minkowski space formalism: states and fields don’t just analytically continue, they’re quite different sorts of objects in the Euclidean case. Anyway, this is all explained in detail in the paper…

Update: No, this is not an April Fool’s joke. I’ve now created a twistor unification page where I’ll try and maintain updated information about this unification proposal

Posted in Twistor Unification | 11 Comments

The Future of Fundamental Physics

IAS director Robbert Dijkgraaf will be giving the CERN colloquium tomorrow, with the title The Future of Fundamental Physics. Here’s the abstract:

The reports of the death of physics are greatly exaggerated. Instead, I would argue, we are living in a golden era and the best is yet to come. Not only did the past decades see some amazing breakthrough discoveries and show us the many unknowns in our current understanding, but more importantly, science in general is moving from studying `what is’ to `what could be.’ There will be many more fundamental laws of nature hidden within the endless number of physical systems we could fabricate out of the currently known building blocks. This demands an open mind about the concepts of unity and progress in physics.

I don’t know of any “reports of the death of physics”, but there are a lot of reports of the death of string theory (Dijkgraaf’s specialty) and of the larger subject of attempts to go beyond the Standard Model, experimentally or theoretically. CERN yesterday announced new results from LHCb testing lepton universality (a prediction of the Standard Model). LHCb sees a ratio of decays to muons vs. electrons in a certain process that is off from the Standard Model prediction by 3.1 sigma.

If this result is confirmed with better data and careful examination of the theory calculation, that will be a dramatic development, indicating a significant previously unknown flaw in the Standard Model. BSM theory and experiment would be very much undeniably alive (no known relevance of this though to the troubles of string theory). Unfortunately, the experience of the past few decades is that 3 sigma size violations of Standard Model always go away after more careful investigation (see for instance the 750 GeV diphoton excess). It’s exactly this pattern that has people worried about the health of the field of high energy physics.

Dijkgraaf’s claim that “we are living in a golden era” is an odd one to be making at CERN, which has seen some true golden eras and is now facing very real challenges. Even odder is arguing at CERN that the bright future of science is due to it “moving from studying `what is’ to `what could be.’” CERN is at its core a place devoted to investigating “what is” at the most fundamental level. I’m curious to hear what those at CERN make of his talk.

Dijkgraaf’s abstract to me summarizes the attitude that the best way to deal with the current problems of HEP theory is to change the definition of the goals of the field, thereby defining failure away. The failure of heavily promoted ideas about string theory and supersymmetric extensions of the Standard Model is rebranded a success, a discovery that there’s no longer any point to pursue the traditional goals of the subject. Instead, the way forward to a brighter future is to give up on unification and trying to do better than the Standard Model. One is then free to redefine “fundamental physics” as whatever theorists manage to come up with of some relevance to still healthy fields like condensed matter and hot new topics like machine learning and quantum computing. I can see why Dijkgraaf feels this is the way forward for the IAS, but whether and how it provides a way forward for CERN is another question.

Update: I just finished watching the Dijkgraaf talk, together with the question session afterwards. Dijkgraaf basically just completely ignored HEP physics and the issues it is facing. He advertised the future of science as leaving the river of “what is” and entering a new ocean of “what can be”, with the promising “what can be” fields biotech, designer materials and AI/machine learning. He hopes that theorists can contribute to these new fields by trying to find new laws governing emergence from complexity, perhaps via new ideas using quantum field theory tools.

With nothing at all to point to as a reason to be optimistic about HEP, a couple questioners asked whether his river of “what is” might be now hitting not an ocean but a desert, and he didn’t have much of an answer. All in all, I’m afraid that the vision of the future he was trying to sell is not one in which high energy physics has any real place. It fits well with the depressing increasingly popular view of the field, as one which had a great run during the twentieth-century, but now has reached an end.

Update: For more discussion of the reliability of the LHCb result, see comments here and here, as well as Tommaso Dorigo’s blog post.

Update: Tommaso puts his money where his mouth is.

Posted in Uncategorized | 30 Comments