Some Math and Physics Interactions

Quanta magazine has a new article about physicists “attacking” the Riemann Hypothesis, based on the publication in PRL of this paper. The only comment from a mathematician evaluating relevance of this to a proof of the Riemann Hypothesis basically says that he hasn’t had time to look into the question.

The paper is one of various attempts to address the Riemann Hypothesis by looking at properties of a Hamiltonian quantizing the classical Hamiltonian xp. To me, the obvious problem with an attempt like this is that I don’t see any use of deep ideas about either number theory or physics. The set-up involves no number theory, and a simple but non-physical Hamiltonian, with no use of significant input from physics. Without going into the details of the paper, it appears that essentially a claim is being made that the solution to the Riemann Hypothesis involves no deep ideas, just some basic facts about the analysis of some simple differential operators. Given the history of this problem, this seems like an extraordinary claim, backed by no extraordinary evidence.

I suspect that the author of the Quanta article found no experts in mathematics willing to comment publicly on this, because none found it worth the time to look carefully at the article, since it showed no engagement with the relevant mathematical issues. A huge amount of effort in mathematics over the years has gone into the study of the sort of problems that arise if you try and do the kind of thing the authors of this article want to do. Why are they not talking to experts, formulating their work in terms of well-defined mathematics of a proven sort, and referencing known results?

Maybe I’m being overly harsh here, this is not my field of expertise. Comments from experts on this definitely welcome (and those from non-experts strongly discouraged).

While these claims about the Riemann Hypothesis at Quanta look like a bad example of a math-physics interaction, a few days ago the magazine published something much more sensible, a piece by IAS director Robbert Dijkgraaf entitled Quantum Questions Inspire New Math. Dijkgraaf emphasizes the role ideas coming out of string theory and quantum field theory have had in mathematics, with two high points mirror symmetry and Seiberg-Witten duality. His choice of mirror symmetry undoubtedly has to do with the year-long program about this being held by the mathematicians at the IAS. He characterizes this subject as follows:

It is comforting to see how mathematics has been able to absorb so much of the intuitive, often imprecise reasoning of quantum physics and string theory, and to transform many of these ideas into rigorous statements and proofs. Mathematicians are close to applying this exactitude to homological mirror symmetry, a program that vastly extends string theory’s original idea of mirror symmetry. In a sense, they’re writing a full dictionary of the objects that appear in the two separate mathematical worlds, including all the relations they satisfy. Remarkably, these proofs often do not follow the path that physical arguments had suggested. It is apparently not the role of mathematicians to clean up after physicists! On the contrary, in many cases completely new lines of thought had to be developed in order to find the proofs. This is further evidence of the deep and as yet undiscovered logic that underlies quantum theory and, ultimately, reality.

I very much agree with him that there’s an underlying logic and mathematics of quantum theory which we have not fully understood (my book is one take on what we do understand). I hope many physicists will take the search for new discoveries along these lines to heart, with progress perhaps flowing from mathematics to physics, which could sorely use some new ideas about unification.

Update: Some comments sent to me from a mathematician that I think give a good idea of what this looks like to experts in number theory:

The “boundary condition” is imposing an identification with zeta zeros by fiat, so the linkage of any of this to RH is basically circular. The paper at best just redefines the problem, without providing any genuine new insight. More specifically, as the experience of more than 100 years has shown, there are a zillion ways to recast RH without providing any real progress; this is yet another (if it makes any rigorous sense, which it does not yet do, yet the absence of rigor is not the reason for skepticism about the value of this paper, whatever the pedigree of the authors may be).

One has to find a way of encoding the zeta function that is not tautological (unlike the case here), and that is where deep input from number theory would have to come in. This is really the essential point that all papers of this sort fail to recognize.

Real insight into the structures surrounding RH have arisen over the past decades, such as the work of Grothendieck and Deligne in the function field analogue that provided a spectral interpretation through the development of striking new tools inspired by novel insights of Weil. In particular, the appearance of the appropriate zeta functions in such settings is not imposed by fiat, but is the outcome of a massive amount of highly non-trivial constructions and arguments. In another direction, compelling evidence and insight has come from the “random matrix theory” of the past couple of decades (work of Katz-Sarnak et al.) was inspired by observations originating with Dyson merged with work of the number theorist Montgomery.

Number theorists making a major advance on the puzzles of quantum gravity without providing anAbdelmalek Abdesselam identifiable new physical insight is about as likely as physicists making a real advance towards RH without providing an identifiable new number-theoretic insight. There is no doubt that physical insights have led to important progress in mathematics. But there is nothing in this paper to suggest it is doing anything more than providing (at best) yet another ultimately tautological reformulation by means of which no progress or insight should be expected.

Update: Another way to state the problem with this kind of approach to the RH is that without number theoretic input, it is likely to give a much too strong result (proving analogs of the RH for functions that don’t satisfy the RH). For example, see the comment here (I don’t know if this correct, but it explains the potential problem).

Update: Nature Physics highlights the Bender et al. paper with “Carl Bender and colleagues have paved the way to a possible solution [of the RH] by exploiting a connection with physics. Some wag there has categorized this work as work with subject term “interstellar medium”.

Update: There’s an article about the Bender et al. paper here, with extensive commentary from oneAbdelmalek Abdesselam of the authors, Dorje Brody, who addresses some of the questions raised here (for example, why PRL if it’s not a physics topic?).

Update: Belissard has put up a short paper on the arXiv explaining the idea of the Bender et al. paper, as well as the analytical problems one runs into if one tries to get a proof of the RH in this way.

Update: One of the authors has posted on the arXiv a note with more precise details of the construction of a version of the operator discussed in the PRL paper.

Posted in Uncategorized | 21 Comments

New LHC Results

This week results are being presented by the LHC experiments at the Moriond (twitter here) and Aspen conferences. While these so far have not been getting much publicity from CERN or in the media, they are quite significant, as first results from an analysis of the full dataset from the 2015+2016 run at 13 TeV, This is nearly the design energy (14 TeV) and a significant amount of data (36 inverse fb/experiment). The target for this year’s run (physics to start in June) is another 45 inverse fb and we’ll not start to hear about results from that until a year or so from now. For 14 TeV and significantly larger amounts of data, the wait will be until 2021 or so.

The results on searches for supersymmetry reported this week have all been negative, further pushing up the limits on possible masses of conjectured superparticles. Typical limits on gluino masses are now about 2.0 TeV (see here for the latest), up from about 1.8 TeV last summer (see here). ATLAS results are being posted here, and I believe CMS results will appear here.

This is now enough data near the design energy that some of the bets SUSY enthusiasts made years ago will now have to be paid off, in particular Lubos Motl’s bet with Adam Falkowski, and David Gross’s with Ken Lane (see here). A major question now facing those who have spent decades promoting SUSY extensions of the Standard Model is whether they will accept the verdict of experiment or choose a path of denialism, something that I think will be very damaging for the field. The situation last summer (see here) was not encouraging, maybe we’ll soon see if more conclusive data has any effect.

If the negative news from the LHC is getting you down, for something rather different and maybe more promising, I recommend the coverage of the latest developments in neutrino physics here.

Update: Lubos has paid off his bet with Jester. Losing the bet hasn’t dimmed his enthusiasm for SUSY. No news on whether David Gross has conceded his bet.

Posted in Experimental HEP News | 60 Comments

This Time It’s For Real

Several months ago I was advertising a “Final draft version” of the book I’ve been working on forever. A month or two after that though, I realized that I could do a more careful job with some of the quantum field theory material, bringing it in line with some standard rigorous treatments (this is all free quantum fields). So, I’ve been working on that for the past few months, today finally got to the end of the process of revising and improving things. My spring break starts today, and I’ll be spending most of it in LA and Death Valley on vacation, blogging should be light to non-existent.

Another big improvement is that there are now some very well executed illustrations, the product of work in TikZ by Ben Dribus.

I’m quite happy with how much of the book has turned out, and would like to think that it contains a significant amount of material not readily available elsewhere, as well as a more coherent picture of the subject and its relationship to mathematics than usual. By the way, while finishing work on the chapter about quantization of relativistic scalar fields, I noticed that Jacques Distler has a very nice new discussion on his blog of the single-particle theory.

There’s a chance I might still make some more last-minute changes/additions, but the current version has no mistakes I’m aware of. Any suggestions for improvements/corrections are very welcome. Springer will be publishing the book at some point, but something like the current version available now will always remain available on my website.

Update: After writing to someone to answer a question and what is and isn’t in the book, and other things to read, I thought maybe I’d post here part of that answer:

For the main topics about QM and representation theory that I cover in the book, I don’t know of a better reference, even assuming an excellent math background. That’s one of the main reasons I wrote the thing… The problem with other books on QM for mathematicians (e.g. Hall, which is very good on the analysis point of view) is that they don’t do much from the representation theory point of view. Weyl’s book was written very early, when a lot of what was going on was still unclear, I don’t think it’s a very good place to try and learn this material from. One topic that is in there that I don’t cover at all is basically Schur-Weyl duality, but even for that arguably Weyl is not a good place to learn that theory.

One thing to keep in mind about my book is that the early chapters are deceptive. I wanted to start out with very simple things, make the simplest examples accessible to as many people as possible, mathematicians or physicists. If you know basic facts about Lie groups, Lie algebras, finite dim unitary representations, Fourier analysis and how to use it to solve e.g. the heat equation, then the first quarter of the book is only going to be of interest in telling you about some applications of math you know. Mathematicians generally should be learning the basic rep theory elsewhere (lots of good books on these topics, and the main reason I’m doing many things in a mathematically sketchy way is that doing them in full would take too long, and has been done better elsewhere). In early chapters, all I’m really doing is working out very special cases of Lie groups/algebras that are rank one or products of rank one, and the irreps of sl(2,C). I never touch higher rank or general semisimple theory (would argue this actually doesn’t get used much in physics, other than some simple SU(3) examples).

Around chapter 12 though, things get much more non-trivial. From a high mathematical level, a lot of what’s going on in the middle part of the book is the representation theory of the Heisenberg group (over R and C) and the implications of the action by the symplectic group by automorphisms (e.g. the metaplectic representation). This is done in a very detailed and concrete way, together with the relation to QM, although for some of the trickier parts of the mathematics (especially the analysis, e.g. the proof of the Stone-von Neumann theorem) I just give references. This is followed by discussing Clifford algebras, the orthogonal group and spinors (over R and C), in a very parallel way (interchanging symmetric and antisymmetric). I wish I knew of a good pure mathematics source for this material aimed at students, stripped of the quantum mechanics apparatus, but I don’t. It (as well as material about reps of the Euclidean groups) is not covered in any conventional rep theory textbook I’m aware of.

Much of the last third of the book, on quantum field theory, I think is just inherently quite challenging, for either mathematicians or physicists. From the representation theory point of view, the basic framework is that of an infinite dimensional Heisenberg group or Clifford algebra, but this is a difficult mathematical subject, and I think the physics point of view helps make clear why. For this stuff the rigorous treatments are quite specialized, I try and do some justice to what the main issues are and give references that provide the details.

Posted in Quantum Theory: The Book | 39 Comments

Can the Laws of Physics be Unified?

There’s a new book out this week from Princeton University Press, Paul Langacker’s Can the Laws of Physics Be Unified? (surely this is a mistake, but there’s also an ISBN number for a 2020 volume with the same name by Tony Zee). It’s part of a Princeton Frontiers in Physics series, in which all the books have titles that are questions. The other volumes all ask “How…” or “What…” questions, but the question of this volume is of a different nature, and unfortunately the book unintentionally gives the answer you would expect from Hinchliffe’s rule or Betteridge’s law.

This is not really a popular book, rather is accurately described by the author as “colloquium-level”. Lots of equations, but not much detail explaining exactly what they mean, for that some background is needed. The first two-thirds of the book is a very good summary of the Standard Model. For more details, Langacker has a textbook, The Standard Model and Beyond, which will have a second edition coming out later this year.

The last third of the book consists of two chapters addressing the question of the title, beginning with “What Don’t We Know?”. Here the questions are pretty much the usual suspects:

  • Why the SM spectrum, with its masses and mixing angles?
  • The hierarchy problem.
  • The strong CP problem.
  • Quantum gravity.
  • Problems rooted in the cosmological model: Baryogenesis, dark matter, dark energy and the CC,

In addition, there are problems listed that are only problems if you philosophically think that a good unified model should be more generic than the SM, leading you to ask: why no FCNC? why no EDM?, why no proton decay?

The last chapter “How will we find out?” lists the usual suspects for ideas about BSM physics: SUSY, compositeness, extra dimensions, hidden sectors, GUTS, string theory. We are told that this is a list of “many promising ideas”. While in general I wouldn’t argue with most of the claims of the book, here I think the author is spouting utter nonsense. The ideas he describes are ancient, many going back 40 years. In many cases they weren’t promising to begin with, introducing a large and complex set of new degrees of freedom without explaining much at all about the SM. Decades of hard work by theorists and experimentalists have not been kind to these ideas. No compelling theoretical models have emerged, and experimental results have been strongly negative, with the LHC putting a large number of nails into the coffins of these ideas. They’re not “promising”, they’re dead.

Langacker does repeatedly point out the problems such ideas have run into, but instead of leaving it at “we don’t know”, he unfortunately keeps bringing up as answer “the multiverse did it”. On page 151 we’re told the most plausible explanation for the CC is “the multiverse did it”, on page 160-163 we’re given “multiverse did it” anthropic explanations for interaction strengths, fermion masses, the Higgs VEV, and the CC. Pages 167-173 are a long argument for “the multiverse did it”. The problem that this isn’t science because it is untestable is dismissed with the argument that it “may well be correct”, and maybe somebody someday will figure out a test. On page 203 we’re told that string theory provides the landscape of vacua necessary to show that “the multiverse did it”.

The treatment of string theory has all of the usual problems: we’re assured that string theory is “conceptually simple”, despite no one knowing what the theory really is. The only problem is that of the “technical details” of constructing realistic vacua. I won’t go on about this, I once wrote a whole book…

In the end, while Langacker expresses the hope that “sometime in the next 10, 50, or 100 years” we will see a successful fully unified theory, there’s nothing in the book that provides any reason for such a hope. There is a lot that argues against such a hope, in particular a lot of argument in favor of giving up and signing up for a multiverse pseudo-scientific endpoint for the field. I suspect the author himself doesn’t realize how much the argument of the book is stacked against his expressed hope and in favor of a negative answer to the title’s question.

Update: If you just can’t get enough multiverse mania, you can watch Joseph Silk’s talk Should We Trust a Theory? (more talk materials here). I’m not quite sure, but I think we agree that the multiverse is not currently science (he writes “The multiverse might or might not exist, but no physicist should waste his or her time chasing the unchaseable”), but not about about string theory. I have no idea what is behind his claim that “String theory has been very successful”, and, since he’s not a string theorist, I suspect that neither does he.

Posted in Book Reviews, Multiverse Mania | 25 Comments

Reality is Not What It Seems

This Sunday’s New York Times has a rather hostile review by Lisa Randall of Carlo Rovelli’s popular book Reality is Not What It Seems, which has recently come out in English in the US. Rovelli responds with a Facebook post. Another similar recent book by Rovelli got a much more positive review in the NYT, his Seven Short Lessons on Physics.

I haven’t written about these two books mainly because I don’t think I have anything interesting to say about either of them (although if someone had asked me to review one of them I might have tried to come up with something). They’re aimed very much not at physicists but at a popular audience that doesn’t know much about physics. From the parts I’ve read they seem to do a good job of writing for such an audience, and I noticed nothing that seemed to me either objectionable or particularly unusual. Rovelli’s two slightly different angles on this topic are an interest in the ancient history of speculation about physics and a background in loop quantum gravity rather than HEP theory/string theory. Instead of wading into the controversy over string theory, he just ignores it and writes about what he finds interesting.

I’m not so sure why, since to me this seems harmless if not particularly compelling, but Randall strongly objects to Rovelli’s attempts to draw connections between modern physics and classical philosophy:

Wedging old ideas into new thinking is analogous to equating thousand-dollar couture adorned with beads and feathers and then marketed as “tribal fashion” to homespun clothing with true cultural and historical relevance. Ideas about relativity or gravity in ancient times weren’t the same as Einstein’s theory. Art (and science) are in the details. Either elementary matter is extended or it is not. The universe existed forever, or it had a beginning. Atoms of old aren’t the atoms of today. Egg and flour are not a soufflé. Without the appropriate care, it all just collapses.

She’s also quite critical of the way Rovelli handles the unavoidable problem of writing about a complicated technical subject for the public:

The beauty of physics lies in its precise statements, and that is what is essential to convey. Many readers won’t have the background required to distinguish fact from speculation. Words can turn equations into poetry, but elegant language shouldn’t come at the expense of understanding. Rovelli isn’t the first author guilty of such romanticizing, and I don’t want to take him alone to task. But when deceptively fluid science writing permits misleading interpretations to seep in, I fear that the floodgates open to more dangerous misinformation.

Here I’m a bit mystified as to why she finds Rovelli any more objectionable than any other similar author (or maybe she doesn’t, and he just happened to be the lucky one to have the first such book she was asked to review in the New York Times). As should be clear from this blog and book reviews that I’ve written, I agree with Randall about a problem that she leads off the review with:

Compounding the author’s challenge is the need to distinguish between speculation, ideas that might be verified in the future, and what is just fanciful thinking.

However, to me it seemed that Rovelli met this challenge better than many, far better than any of the huge popular literature about supersymmetry, string theory and the multiverse. She may be right that someone not paying careful attention could get the wrong idea from Rovelli about cosmological loop quantum gravity models. It’s equally true though that readers of her own books about extra dimensions, dark matter and the dinosaurs might come away not understanding exactly what the strength of evidence was for those speculations.

Note added for clarification 3/6/2017: the following is not part of the commentary on Randall’s review, it’s another related topic I thought readers would find interesting. The relation between the two parts is that they both have to do with the question of distinguishing solid argument/speculation, but it’s not about Randall, and the context is different (communicating with other physicists versus communicating with the general public}.

On this question of how/whether physicists (here mathematicians are very, very different) make clear what is a solid argument and what is just speculation, another interesting case is that of Nima Arkani-Hamed, who came to prominence in particle theory with Randall, both of them working on extra dimensional models. Both of them got a huge amount of attention for this, from the public and from within physics, although these ideas were always highly speculative and unlikely to work out.

There’s a wonderful new “Storygram” by George Musser of a great profile by Natalie Wolchover of Arkani-Hamed. It’s all well worth reading, but related to the topic at hand I was struck by the following:

Arkani-Hamed considers his tendency to speculate a personal weakness. “This is not false modesty, it’s really a personal weakness, but it’s true, so there’s nothing I can do about it,” he said. “It’s important for me while I’m working on something to be very ideological about it. And then, of course, it’s also important after you are done to forget the ideology and move on to another one.”

Arkani-Hamed is an incredibly compelling speaker, but his talks often have struck me as putting forward very strongly some particular speculative point of view, while ignoring some of the obvious serious problems. If you’re not pretty well-informed on the subject, you might get misled… From the quote above he seems to have a fair amount of self-awareness about this. Also interesting in this context is his talk last year at Cornell on The Morality of Fundamental Physics. He gives an inspiring account of the intellectual value system of theoretical physics at its best. On the other hand, he pays no attention to the very real tension between that value system and the way people actually pursue their work, often very “ideologically”. For particle theory in particular and the current situation it finds itself in, this seems to me an important issue for practitioners to be thinking about.

Posted in Uncategorized | 19 Comments

Bertram Kostant 1928-2017

I was sorry to just hear via a comment here about the recent death of Bert Kostant, at the age of 88. MIT has a story about him here.

Kostant was a major figure in the field of representation theory, and perhaps the leading one during the second half of the twentieth century among those with a serious interest in the relations between representation theory and quantum theory. These relations have for a long time now been a deep source of fascination to me, and Kostant’s work has had a great impact on how I think about the subject.

I’ll just list here some of his major papers that I’ve spent significant amounts of time with, characterized by a few major themes:

Borel-Weil-Bott, Lie algebra cohomology, BRST and Dirac cohomology

Quantization of the dual of a Lie algebra, W-algebras

The dual of a Lie algebra is a Poisson manifold, and you can ask what happens when you quantize this. For semisimple Lie algebra, reduction with respect to the nilradical is an idea that Kostant pursued, with two examples the following two papers. Applied to loop groups, this is a central idea of the geometric Langlands program. The theory of W-algebras is also an outgrowth of this.

Geometric quantization theory and co-adjoint orbits

Starting around 1970 Kostant did a great deal of work developing the theory of “geometric quantization” and the idea of quantizing co-adjoint orbits to get representations (other figures to mention in this context are Kirillov and Souriau). Some of his papers on this are:

All of the three general themes above are closely intertwined, and the relations between them indicate that there is still a lot more to be understood about how quantum theory and representation theory are related, with Kostant’s work undoubtedly playing a large role in developments to come.

Posted in Uncategorized | 4 Comments

Various News

First some mathematics items:

  • Igor Shafarevich, one of the great figures of twentieth century algebraic geometry and algebraic number theory, died this past weekend at the age of 93. Besides his many contributions to mathematics research, he was also a remarkably lucid expositor. His two volume Basic Algebraic Geometry is a wonderful introduction to that subject, his survey volume Basic Notions of Algebra emphasizes the connections to geometry, and his volume on number theory (with Borevich) struck the AMS reviewer as “delectable”.

    Shafarevich was also known for his religiously-motivated nationalistic views which to many were distressingly anti-Semitic. In the spirit of respect for the recently deceased, I’ll just link to a quite interesting recent discussion (very sympathetic to Shafarevich) of the issue by David Mumford here (and ruthlessly delete attempts to argue about this in the comment section).

  • The AMS Notices has a set of articles in honor of Andrew Wiles and his work, which include some great explanations of the mathematics, as well as a long in-depth interview.
  • For another detailed interview with a mathematician, see Quanta magazine for a piece by Siobhan Roberts about Sylvia Serfaty of the Courant Institute.

On the physics front, there’s:

  • For his contribution to the Why Trust a Theory? conference (see here and here), Helge Kragh has a new paper which examines the question of whether history of science can help evaluate recent claims about the need to change the way theories are assessed. He sees in the unsuccessful “vortex theory” of the late nineteenth century an analog of string theory, with many of the same claims and justifications for lack of success. He quotes as a typical example of the enthusiasm of the time:

    I feel that we are so close with vortex theory that – in my moments of greatest optimism – I imagine that any day, the final form of the theory might drop out of the sky and land in someone’s lap. But more realistically, I feel that we are now in the process of constructing a much deeper theory of anything we have had before and that … when I am too old to have any useful thoughts on the subject, younger physicists will have to decide whether we have in fact found the final theory!

    but then explains that this is actually a quote from Witten, with “string” replaced by “vortex”.

  • Scientific American this month has an article (also available here) about the problems with the theory of inflation. The authors end by pointing out the dangers to science of multiverse inflationary scenarios (which they call the “multimess”):

    Some scientists accept that inflation is untestable but refuse to abandon it. They have proposed that, instead, science must change by discarding one of its defining properties: empirical testability. This notion has triggered a roller coaster of discussions about the nature of science and its possible redefinition, promoting the idea of some kind of nonempirical science.

    A common misconception is that experiments can be used to falsify a theory. In practice, a failing theory gets increasingly immunized against experiment by attempts to patch it. The theory becomes more highly tuned and arcane to fit new observations until it reaches a state where its explanatory power diminishes to the point that it is no longer pursued. The explanatory power of a theory is measured by the set of possibilities it excludes. More immunization means less exclusion and less power. A theory like the multimess does not exclude anything and, hence, has zero power. Declaring an empty theory as the unquestioned standard view requires some sort of assurance outside of science. Short of a professed oracle, the only alternative is to invoke authorities. History teaches us that this is the wrong road to take.

  • Nautilus has an article by Juan Collar about the increasing skepticism about Wimps as dark matter candidates, and the interest in alternatives.

Update: With results from the full 13 TeV dataset just a few weeks away, SUSY enthusiasts have given up hope for the LHC. A new paper just out argues that pre-LHC claims that naturalness + SUSY implied a gluino mass upper bound of 350 GeV (the latest LHC limits are more like 1900 GeV, likely to go up next month) were misguided. According to these authors, the right number for the upper bound is 5200 GeV and the “HE-LHC with [cm energy] 33 TeV is required to either discover or falsify natural SUSY”. So, claims that the LHC could falsify natural SUSY are no longer operative now that it has done so by earlier metrics, and such discovery or falsification is still just around the corner. All that’s needed is to rebuild the LHC into a higher energy version (that’s what the HE-LHC proposal is, may take a while…).

Update: Another excellent article by Natalie Wolchover at Quanta, this time about progress in studying conformal quantum field theories in higher dimensions (above 2). Definitely one of the more interesting things going on in theory at the moment. The reference in the subtitle to “geometry underlying all quantum theories” I don’t think though is really justified, this is really just about conformal field theories.

There’s probably lots more to be learned about these, with this conformal symmetry still not fully exploited. I’m somewhat fond of the point of view that you really shouldn’t try and think of QFTs just as effective theories for some different physics at short distances. Rather, what might be going on at short distances is not some new kind of theory at the cutoff scale, but a conformal theory valid at all scales.

Update: From the comments, unfortunately two other deaths to report, those of Bert Kostant (I’ve written something here) and Ludwig Faddeev.

Posted in Multiverse Mania, Uncategorized | 15 Comments

A Big Bang in a Little Room

There’s a review in today’s Wall Street Journal by me of Zeeya Merali’s A Big Bang in a Little Room. If their version is behind a paywall you might find also find it elsewhere (for instance here). I’ll reproduce parts of the review below with some comments more appropriate for the blog venue. As always, the editors at the WSJ did an excellent job of improving the first draft I sent them.

Merali has a website about the book here, and last week Nature published this review by Andreas Albrecht. Albrecht criticizes the book for “sloppy interplay between science and religion”, but I think he misses the important point that the most serious problem here is the sloppiness about what is science and what isn’t. When physics journals decide to publish articles like this one, it’s not surprising that science writers make the mistake of taking them seriously and writing about them (Merali’s first chapter is about this paper).

Here are some extracts from the review, with some comments:

What happened at the Big Bang—or before—is an irresistible question but one that, for now, as science, lies in the realm of the purely speculative.

In “A Big Bang in a Little Room,” science writer Zeeya Merali turns the question around, asking instead whether physicists can create a “baby universe,” born in its own Big Bang. Indeed, one prominent theorist she interviews has suggested that our own universe might be a baby universe created by a “physicist hacker,” with the complex pattern of fundamental particle masses intended as some sort of message to us. thereby learning more about the beginnings of the “old” one.

The reference here is to Andrei Linde and this 1991 paper.

[Merali] explains that her interest in this topic is tied up with her religious beliefs: If we ourselves could play God and create a new universe, wouldn’t that creation amount to a theological discovery, showing the likelihood that some higher intelligence was responsible for the Big Bang? She structures her narrative around interviews with prominent theoretical physicists; they mostly discuss science, but religious questions sometimes play a role, with often fascinating results. While some refuse to engage, she gets others to discuss such topics as the relation of the laws of physics to God’s happiness, the possibility of a physical “consciousness field,” and what the quantum mechanics of the Big Bang might indicate about the possibility of life after death and resurrection.

Don Page is the one interested in God’s happiness, Abhay Ashtekar in the “consciousness field”, and Andrei Linde in resurrection.

Mr. Linde is the central figure in this story, and Ms. Merali describes him as “a showman: bombastic, passionate, and fueled by the certain belief that inflation theory, which he helped to invent, is correct.” While Ms. Merali takes all of this seriously, there are very good reasons why most physicists don’t. Readers of “A Big Bang in a Little Room” would be well-advised to enjoy the ride but stay skeptical. Inflationary models can to some degree be confronted with observation and tested (a topic covered in other books but not this one).

About the string theory landscape:

Ms. Merali gives a disturbing version of this, contemplating the possibility that “string theory and inflation may be conspiring against us in such a way that we may never find evidence for them, and just have to trust in them as an act of faith.”

This comes after an explanation of the anthropic multiverse point of view from HEP experimentalist Greg Landsberg, where he adds the twist of anthropics explaining why the string scale is at such high energy, and thus unobservable. The full paragraph in the book is

In other words, the physics of string theory and inflation may be conspiring against us in such a way that we may never find evidence for them, and just have to trust in them as an act of faith. The multiverse truly works in mysterious ways!

If that paragraph doesn’t make a scientist’s blood run cold and see the danger physics is facing, I don’t know what will. I end the review with

In an era where “post-truth” was the word of the year, scientists and science writers need to make clear that science is not a species of theological or philosophical speculation and not about belief or entertainment value. Legitimate scientific claims are those that can be backed up with evidence, and unfortunately the wonderful and exciting story told well here contains none at all.

My concern about the topic of the book is that it’s Fake Physics, not that religion is motivating the author (and likely motivating the Templeton Foundation to fund this project). A book about the religious views of physicists would be an interesting one that I’d certainly read, and the material in this book on that topic is quite interesting. One of the odder twists here is that the two blurbs from physicists promoting the book are from Sean Carroll and Martin Rees, with Carroll writing

So you want to make your own universe. Zeeya Merali’s new book won’t quite give you an instruction kit—but it’s the closest thing we have at the moment. A fun and mind-expanding ride through modern ideas of how universes come to be.

I don’t see how you can be devoted to fighting for science against religiously-driven pseudoscience, and think that this book is one you’d like to see be the public face of what “modern ideas” about cosmology are.

Posted in Book Reviews, Fake Physics | 21 Comments

Various Links

The Columbia Math department has been doing extremely well in recent years, with some wonderful mathematicians joining the department. A couple items first involving some of them:

  • Kevin Hartnett at Quanta Magazine has a great article about developments in the field of technical issues in the foundations of symplectic topology. This explains work by my colleague Dusa McDuff, who together with Katrin Wehrheim has been working on such issues, trying to resolve questions raised by fundamental work of Kenji Fukaya and collaborators. For technical details, two places to start looking are here and here.

    The Hartnett story does an excellent job of showing one aspect of how research mathematics is done. Due to the complexity of the arguments needed, it’s not unusual for early papers in a new field to not be completely convincing to everyone, with unresolved questions about whether proofs really are airtight. The way things are supposed to work, and how they worked here, is that as researchers better understand the subject proofs are improved, details better understood and problems fixed. Along the way there may be disagreements about whether the original arguments were incomplete or not, but almost always people end up agreeing on the final result.

    Also featured in the article is another of my Columbia colleagues, Mohammed Abouzaid, who provides characteristically wise and well thought out remarks on the story.

  • Via Chandan Dalawat, I learned of an interesting CIRM video interview with another colleague, Michael Harris. The same site has this interview with Dusa McDuff, as well as a variety of other interviews in English and French.

For some other non-Columbia related links:

  • The 70th birthday of Alain Connes is coming up soon, and will be celebrated with a series of public lectures and conferences on noncommutative geometry in Shanghai.
    This year will be the last series of lectures by Connes at the College de France. They’re appearing online here, and I highly recommend them. He’s taking the opportunity to start the series with a general overview of the point of view about the relationship of geometry and quantum theory that he has been developing for many years.
  • For employment trends in theoretical particle physics, there are some updated graphs of data gleaned from the particle theory jobs rumor mill created by Erich Poppitz and available here. In terms of total number of jobs, there has been some recovery in the past couple years, with about 15 jobs/year, above the 10 or so common since the 2008 financial crisis (before 2008 numbers were higher, 20-25). As always, an important thing to keep in mind about this field is that this number of permanent jobs/year is a small fraction of the number of Ph.Ds. in the subject being produced each year at US universities.

    The numbers for distribution of subfields separate out “string theory” and lattice gauge theory. There have always been few jobs in lattice gauge theory, appear to be no hires in that subject for the past two years. I’m putting “string theory” in quotes, because it’s very hard these days to figure out what counts as “string theory”. With Poppitz’s choice of what to count, hiring in string theory has recovered a bit, now around 25% of the total for the past two years, up from more like 15% typical since 2006 (earlier on the numbers in some years were around 50%).

  • As pointed out here by commenter Shantanu, on Wednesday John Ellis gave a talk on Where is particle physics going? at Perimeter. I’d characterize Ellis’s answer to the question as “farther down the blind alley of supersymmetry”. He spins the failure to find SUSY so far at the LHC as some sort of positive argument for SUSY. The question session was dominated by questions about SUSY, with Ellis taking the attitude that there’s no reason to worry about the failure so far of the fine-tuning argument for SUSY, all you need to do is “ratchet up your pain threshold”. I fear that’s some sort of general advice where this line of research is going.

    About the failure to find any evidence for SUSY wimps that were supposed to explain dark matter, Ellis explained that he had been working on this idea for 34 years, first writing about it in 1983, so with that much invested in it, he’s not about to give up now.

Update: Davide Castelvecchi points me to another new mathematics story at Nature.

Update: One more. A profile of Roger Penrose by Philip Ball. Penrose explains that his main problems with string theory come from two sources. One is the instability problem of extra dimensions, the other is his aesthetic conviction that sticking to four space-time dimensions is a good idea since it is only in four dimensions that you get the beautiful geometry of twistors. Ball raises the interesting question of whether Penrose could have a successful scientific career if he were starting out today:

Worst of all, the career structures and pressures facing young researchers make it increasingly hard to find the time simply to think. According to several early-career scientists interviewed by Nature, the constant need to bring in grant money, to produce papers and administer groups, leaves little time to do any research, still less indulge anything so abstract and risky as an idea.

Posted in Uncategorized | 23 Comments

Perfectoid Woodstock

Every year in Tucson the Arizona Winter School takes place, with a five day program on some topic in arithmetic geometry aimed mainly at advanced graduate students, designed to get them involved in current research-level topics. This year’s topic (Perfectoid Spaces) is drawing a huge number of people there next month, with about 450 participants expected (in the past numbers were more like 100). This should be a veritable Woodstock of arithmetic geometry, with no one I’ve talked to quite able to figure this out, thinking that there probably weren’t 450 people worldwide interested at all in arithmetic geometry. It seems everyone in the field will be there and then some.

Peter Scholze is the opening and closing act. The other lecturers who will take the stage have started to put lecture notes for their lectures on the school website.

Some are dubious that there really are 400 or so students in the world with the background necessary to understand this material. See for example MathOverflow where nfdc23 isn’t very encouraging to a student who doesn’t know any rigid analytic geometry, but plans to attend the AWS. In any case, I hear Tucson is quite nice in March.

At some kind of other end of the spectrum of such things, a couple months later experts will gather in Germany to discuss this field (see here). Also for about five days, at the Schloss Elmau Luxury Spa and Cultural Hideaway, the sort of place heads of state go for G7 meetings. Rooms run $600 a night or so, but in this case the tab is being picked up by the Simons Foundation. Sorry, by invitation only.

Posted in Uncategorized | 22 Comments