A grab-bag of unrelated topics and links:

- Continuing the subject of budget cuts from the last posting, I heard today that the NSA is not funding this year the grant program that the AMS has been running for it, called the NSA Mathematical Sciences Program. In typical NSA fashion, no real reason given:

after much deliberation our senior management has decided that the MSP will not have the resources to make new awards in FY2017.

Even less information is available than in the case of the similarly mysterious DOE HEP Theory cuts, since all information about the NSA budget, even the total, is classified (although from Snowden and others, it seems that it’s about $10.5 billion).

- The IHES has a new website.
- This spring Peter Scholze will give a series of six lectures at the IHES on the latest about the local Langlands conjectures.
- Via David Roberts, the LMS has some videos about mathematicians here. Kevin Buzzard explains Langlands:

The Langlands philosophy? Yeah, that’s like Birch-Swinnerton-Dyer on crack, isn’t it?.

- Tate’s collected works are finally available from the AMS.
- Turning to physics, there’s a very good new article at Quanta from Natalie Wolchover about the unsuccessful search for proton decay and what this means for grand unification ideas. Glashow has now given up, with the simplest GUTs now conclusively ruled out:

Glashow, for one, largely lost interest in the whole affair when SU(5) was ruled out. “Proton decay has been a failure,” he said. “So many great ideas have died.”

Not everyone has given up though, with fans of the “flipped SU(5)” SUSY GUT explaining things this way:

Barr, one of the originators of the still-viable “flipped SU(5)” GUT model, compared the situation to waiting for your spouse to come home. “If they’re 10 minutes late, there’s simple explanations for that. An hour late, maybe those explanations become a little less plausible. If they’re eight hours late … you begin to worry that maybe your husband or wife is dead. So the point is, at what point do you say your theory is dead?”

Right now, he said, “we’re more at the point where the spouse is 10 minutes late, or maybe an hour late. It’s still completely plausible that grand unification is correct.”

Besides the current wishful thinking, this particular model has a strange history. You can read here about how it follows from Vedic Science. Over the years it has been about to come home many times, see this from 2012, which assures us that:

The CMS and ATLAS experiments have also observed tantalizing hints of the unique signature predicted by the Flipped SU(5) model.

At this point, it seems to me to be way more than an hour late, time for its nearest and dearest to admit that it’s dead (or maybe has run off with its TM instructor).

- Also in Quanta, you can read about Janet Conrad and sterile neutrinos here.
- I don’t always agree with Sabine Hossenfelder about math, but I very much agree with the conclusion of this posting:

In lack of experimental guidance, what we need in the foundations of physics is conceptual clarity. We need rigorous math, not claims to experience, intuition, and aesthetic appeal. Don’t be afraid, but we need more math.

- There’s a Recent Developments in Fields, Strings, and Gravity conference going on this week at the new Center for Quantum Mathematics and Physics at Davis.
- Videos of the talks at the recent John Schwarz 75th birthday conference at Caltech are available here.
- Multiversal Journeys is an organization devoted to promoting theoretical physics, with a heavy dose of multiverse mania as part of their story. They have a new book coming out, Quantum Physics, Mini Black Holes and the Multiverse, supposedly “Debunking Common Misconceptions in Theoretical Physics”. It seems that one of these common misconceptions is that the multiverse is pseudo-science. To fight this, they’ve also produced a promotional video.
- Bert Schroer has an interesting preprint with a lot of material about Rudolf Haag and algebraic quantum field theory.
- Another intriguing preprint recently out is from Arkani-Hamed and collaborators. In the past Arkani-Hamed has been vehement about gauge symmetry just being a worthless redundancy in our description of physics, for instance stating:

What’s as a misnomer called gauge symmetry, whose beauty is extolled at length in all the textbooks on the subject, is completely garbage. It’s completely content free, there’s nothing to it.

In the new paper, instead of gauge invariance being useless, there’s a conjecture that locality and unitarity, instead of being fundamental principles, follow from gauge invariance.

There’s a long tradition in the philosophy of physics literature of arguing over whether gauge symmetry is a fundamental idea or a useless redundancy. I’m on “fundamental idea” side, but of course exactly what the role of gauge symmetry is in fundamental physics is something that we have yet to fully comprehend.

What are you thoughts on the likelihood of a multiverse? Will take a link if you have already discussed it.

Ben,

That’s a meaningless question, the multiverse is pseudo-science. I’ve written endlessly about this on the blog, see

http://www.math.columbia.edu/~woit/wordpress/?cat=10

and some of the questions in the blog FAQ.

One thing to notice about the many multiverse promotional efforts like this is that they never include multiverse critics (and I think being critical of the multiverse as not science is a majority point of view among physicists). Their only discussion of criticism of the multiverse as pseudo-science is to counter straw-man arguments.

That said, the last thing I want is another discussion here of exactly the same arguments as always. If you have something new, please comment, otherwise please restrain yourself, I’m just going to delete attempts to carry on old arguments.

“One thing to notice about the many multiverse promotional efforts like this is that they never include multiverse critics ” – this is actually proof that multiverse theories are wrong. If they were true, there would be many promotional efforts that focussed on the negative aspects. (sorry if the joke falls flat)

Thanks for the link 🙂

Gauge symmetry can both be useful and be redundant, I don’t see why these are two exclusive categories. One could say that thermodynamics is redundant, to pick a not-quite random example, but that doesn’t make it useless.

Dear Peter, I too think that gauge theory is a fundamental building block of quantum nature and is not an indication of some redundancy. Frequently what appears to be reduntant from the point of view of classical physics has a deep meaning in quantum reality. A nice discussion of this phenomenon can e.g. be found in the second volume of Richard Feynman about electrodynamics concerning the vector potential.

Interesting article by Wolchover. I am interested in learning more on the relationship of proton decay to SUSY. As I understand it, there are SUSY and non-SUSY GUTs. I suppose the LHC results make SUSY GUTs a whole lot less interesting, but what about non-SUSY GUTs like minimal SO(10)? I am surprised Glashow threw in the towel on GUTs just because his SU(5) was ruled out. Are there other problems with these higher symmetry non-SUSY GUTs?

neil,

Minimal non-SUSY SO(10) is also already ruled out, I doubt the (not very large since they’re both rank 4) difference between SO(10) and SU(5) models was that significant to Glashow.

Nanopoulos explains well the general problem of why, even if you can make a more complicated model than the SU(5) or SO(10) ones, specially designed to evade conflict with experiment, you might not want to:

SO(10) is D_5, and is rank 5. SU(5) is A_4, and is rank 4.

I think Glashow threw in the towel ~ 30 years ago. He (in my way of thinking) has been faithful to principle. The beauty/simplicity/falsifiability of Georgi and his GUTS model was minimal SU(5). Perhaps I misremember, but I think he walked away back when proton decay contradicted this model . He didn’t introduce additional degrees of freedom to clutter the model in order to tune it in order to save it from being falsified–i.e., make it no longer predictive.

Chris Austin,

Thanks, that’s right, my mistake about the ranks, I was thinking of something else (SU(5) is the subgroup of SO(10) that preserves a complex structure).

Peter,

it might be less well known that various people who worked on the the standard model – several of them with Swedish prizes – do think that the search for a unique gauge group is misguided. After all, the electroweak model is not a real unification, as it still requires two independent coupling constants. And in the standard model, SU(3) has a third, independent constant. Both experiment and theory show that it is not possible to describe nature with SU(5) or SO(10) or another single group with only one coupling constant. Nature has three gauge forces, not one.

But there is an important reason to cling to grand unification: it is predicted, or at least suggested, by string theory. So we are again in the difficult situation that experiment is against grand unification, whereas string theory is in favor of it. (The situation is similar to supersymmetry.) It seems that theory will make progress only once all the people believing in GUT and SUSY are gone.

Peter, I agree with Glashow. looking for proton decay is looking for El Dorado.

That said I know several grad students who continue to be lured into doing thesis on proton decay.

nothing wrong with experimental theses on proton decay – always good to push any measurement to a higher level of sensitivity, almost independent of theoretical motivation.

(and proton decay experiments have already won one Nobel Prize…..)

Frank,

The basic problem with GUTs and SUSY is similar: you postulate a more unified theory using a larger symmetry group (or supergroup), but then have to somehow break the symmetry to explain why we don’t see representations of this larger symmetry group. The ad hoc symmetry breaking sector makes the whole idea much less compelling and predictive. These ideas were born 40 years ago around the same time, back then everyone thought they would either lead somewhere in a few years or get abandoned. It’s remarkable that instead they entered the textbooks and became institutionalized as a seemingly permanent part of the subject.

Shantanu,

Just because finding proton decay is less likely doesn’t mean one shouldn’t do such experiments. I’m no expert, but my impression was that many such detectors are now configured to do double-duty as neutrino experiments.

You are right Peter. Proton decay was the primary purpose of Super-K, but with the Kajita Nobel prize much of the research there is on neutrino oscillations. And the DUNE neutrino observatory has a proton decay experiment.

Proton decay seems less and less likely for the reasons stated but, wow, baryon number violation would be a huge discovery.

The ‘wife showing up late’ comment is interesting, but is missing a major aspect. The prior probability of your wife’s continued existence and intent to return home should be much higher than the prior probability that your favourite theory which isn’t known to be inconsistent with experiment is an accurate extension of current models. At least for most marriages. Its more like you’re attending a dinner event in the city your crush lives in and you’re judging the probability that you’ll to run into them.

Or maybe I’m just asking for a bit too much from analogies.

Louis,

You’re right, it’s a strange analogy. Until you realize that the particle theory community has been living with GUT/SUSY speculation for so long that it is like a close family member, one whose death (due to a conclusive experimental result) would be unexpected and heart-breaking. Better to do anything to keep it alive and not face that.

how do these new experimental limits on proton decay + LHC results affect supersymmetry GUT such as SUSY GUT SU(5) or SO(10)?

it’s my understanding adding SUSY to GUT increases proton lifetime enough to evade these bounds.

Bee writes:

In lack of experimental guidance, what we need in the foundations of physics is conceptual clarity. We need rigorous math, not claims to experience, intuition, and aesthetic appeal. Don’t be afraid, but we need more math.

Allow me to partly disagree. Conceptual clarity is needed. But it is *not* achieved with math. Math cannot help to decide whether the Planck scale has a fundamental importance or not. Math cannot decide whether GUT or SUSY are correct. Math cannot decide whether strings are correct. Math cannot tell which symmetry is correct. Math cannot tell how many dimensions nature has. If math would help to get conceptual clarity, we would have found the TOE already years ago.

Conceptual clarity is not achieved with math, it is achieved by checks with experimental data. GUT is mathematically sound, but wrong. So is SUSY. So are strings.

Math helps to draw correct conclusions. But it does not help in finding the foundations. Math leads to conceptual consistency. Math does not lead to conceptual clarity. And in the history of physics, it never did.

Take the issue of symmetry. If you know that a flower has fivefold symmetry, you still do not know the shape of a petal. You just know how the other four look like if you have only one. Math (in this case symmetry) helps; but it does not provide the full information. Experiment does. We have the same issue with nature.

Frank,

I think what Bee has in mind is the situation in her field of quantum gravity. There many of the research topics (ER=EPR, firewall paradox, Verlinde’s entropic gravity, etc, etc) suffer from the problem she identifies: people are manipulating very vague, ill-defined speculative ideas, claiming “intuitive”, “physical” understanding, but you can’t pin down exactly what these ideas are. Before you can confront your theories with experiment, you first need to have a well-defined theory, and it is mathematics that can provide you with this.

serious question here,

There’s a graphic in the Quanta article that addresses this, showing in particular most of the range for supersymmetric SO(10) already ruled out. One problem though is that these theories have a lot of undetermined parameters, so claims about their “predictions” tend to have a bunch of built-in assumptions. If you look at the history of these “predictions”, my impression is that they have tended to creep up as experimental bounds move up. For an example of the calculations involved, see

https://arxiv.org/abs/hep-ph/0007213

“Why String Theory?” is Physics World’s book of 2016:

http://physicsworld.com/cws/article/news/2016/dec/14/robust-defence-of-string-theory-wins-physics-world-2016-book-of-the-year

Peter/others:

I am not objecting to building/operating such detectors. My own thesis was on such a one. I am surprised that gullible students continue to work on analysis of proton decay.

Dear Peter,

I recommend your readers to read a new review

https://arxiv.org/pdf/1501.01886.pdf

Minimal non-SU(5) was ruled out by the wrong relation between the down quark and charged leptons masses. Even before you compute the lifetime of the proton the model is ruled out. Now, once you write down a consistent model for fermion masses it is possible to achieve unification without supersymmetry in a simple SU(5) theory, see for example for a recent paper:

https://arxiv.org/pdf/1604.03377.pdf

Best,

Pavel

Peter wrote:

It’s less strange if you remember why people actually like the SO(10) grand unified theory. In this theory, each generation of fermions and antifermions fits neatly into a single family of particles, the spinor representation of SO(10) (or really Spin(10)). This theory “explains” why quarks have charges 2/3 and -1/3 while leptons have integer charge, and much more. All sorts of facts that otherwise seem strange and random suddenly fit together in a beautiful way.

However, there’s a lot that it

doesn’texplain, like the masses of particles, and one must invoke extra Higgs bosons to break the symmetry from Spin(10) down to SU(3) x SU(2) x U(1).So, it’s absolutely heart-breaking that this theory seems to be wrong, but we can hope that there’s something right about the underlying algebraic patterns that make it tick.

Unfortunately we may not live to see the next really interesting development in this mystery. So, unless one has a really promising new idea, it’s better to think about something else.

John,

I agree that the fact that a generation fits into the spinor rep of SO(10) is something very appealing, an indication of something right about the idea (and less right about the original SU(5). The problem with GUTs has always been that the unification is a bit of a fake, since you don’t have a compelling idea about why it breaks (introducing a special set of new Higgs fields isn’t very pretty…)

My guess is that the hint here is that there is some sense (one we don’t understand) in which there are five fundamental degrees of freedom, with a generation the exterior algebra on these five degrees of freedom. The relation to the spinor rep is that you can construct the spinor rep of Spin(2n) using the complex exterior algebra on n-dimensional complex space (i.e. as the state space of five fermionic oscillators, see discussion in my book).

Maybe of some interest:

A question that appeared on Stackexchange: Which were some major mathematical breakthroughs 2016?

Peter,

FYI, the responses to the 2017 Edge.org annual question have been posted. This year’s question was, “What scientific term or concept ought to be more widely known?” Martin Rees suggested “multiverse”: https://www.edge.org/response-detail/27129

Vedic Science a la John Hagelin and the Maharishi University makes lousy science, but good art! I was in the MIT Physics Dept. circa 1986, and a particle theorist had a large multi-color poster showing how an incarnation of SU(5) accorded with purported Hindu constructs. But the craziness was mostly in the margin. Most of it recalled the lovely illustrations of the Eightfold Way etc. from 1960’s Scientific American. Can I get one of these?