Now back from vacation, and as far as I can tell, not much happened while I was away. Here are a few things I’ve seen that may be of interest:

- Mochizuki has posted a long progress report on “activities devoted to the verification of IUTeich.” New Scientist has an article about this here, which quotes Minhyong Kim making comments I think most experts would agree with:

Some mathematicians say Mochizuki must do more to explain his work, like simplifying his notes or lecturing abroad. “I sympathise with his sense of frustration but I also sympathise with other people who don’t understand why he’s not doing things in a more standard way,” says Kim. It isn’t really sustainable for Mochizuki to teach people one-on-one, he adds, and any journal would probably require independent reviewers who have not studied under Mochizuki to verify the proof.

Lieven Le Bruyn has a less charitable take (see here and here):

If you are a professional mathematician, you know all too well that the verification of a proof is a shared responsability of the author and the mathematical community. We all received a referee report once complaining that a certain proof was ‘unclear’ or even ‘opaque’?

The usual response to this is to rewrite the proof, make it crystal-clear, and resubmit it.

Few people would suggest the referee to spend a couple of years reading up on all their previous papers, and at the same time, complain to the editor that the referee is unqualified to deliver a verdict before (s)he has done so.

Mochizuki is one of these people.

His latest Progress Report reads more like a sectarian newsletter.

There’s no shortage of extremely clever people working in arithmetic geometry. Mochizuki should reach out to them and provide explanations in a language they are used to.

Mochizuki’s progress report strikes me as quite an odd document, especially in its insistence that experts need:

to

*deactivate the thought patterns*that they have installed in their brains and taken for granted for so many years and then to start afresh, that is to say, to*revert to a mindset*that relies only on*primitive logical reasoning*, in the style of a student or a novice to a subject.He at times seems to be arguing that his ideas are nearly disconnected from the rest of known mathematics, and the only way to understand why the abc conjecture is true. This is highly implausible, since the great beauty and strength of mathematics is the way in which deep ideas are interconnected, with many paths from one place to another. If he wants to convince people that he really has what he claims, the best way to do it would be to follow the conventional route: write himself a document giving an exposition of a proof of abc, in as clear and simple terms as possible.

Unfortunately, that doesn’t seem to be what he has planned, with his efforts devoted to getting others to start from the beginning and master his long series of papers. If this works, at some point there will be others able to write up a proof of abc using his ideas, and when that happens, experts may have something they can work with. This looks now like a story that is going to go on for a long time…

- The last couple weeks in Jerusalem there was a Winter School on General Relativity. It included a final session (video here) largely devoted to defending string theory as the one true path to quantum gravity. This included a panel discussion where Carlo Rovelli held his own in a battle of the LQG/string wars, with him ganged up on by Gross and Arkani-Hamed. Mostly I don’t think there were any new arguments, just a rehash of the tediously familiar. Gross did give an enthusiastic call for all students to read the Dawid book discussed here.

For yet another promotional effort about strings, one that seems like it could have been written exactly the same way twenty years ago, see here. - One new argument from the Rovelli side was to point out that “Nature talks”, and what it has said at the LHC so far is that SUSY is not there, blowing a big hole in the expectations of the superstring theory community. The Economist has a piece about how the upcoming LHC run at 13 TeV will be:

the last throw of the dice for the theory, at least in its conventional form.

As often the case though, the article misrepresents the strength of arguments for SUSY:

But, though the Standard Model works, it depends on many arbitrary mathematical assumptions. The conundrum is why these assumptions have the values they do. But the need for a lot of those assumptions would disappear if the known particles had heavier partner particles: their supersymmetric twins.

This is pretty much complete nonsense, since the problem with SUSY has always been that it doesn’t actually explain why the SM model parameters take the values that they do, and this has always been the best reason to be skeptical about it.

On the other hand, the Economist and Rovelli do get the basic story right: Nature talks, and if what it says in LHC Run 2 is that the theoretical physics community has been barking up the wrong tree for the last forty years, it will be interesting to see if theorists are still willing to listen.

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Peter, happy new year.

On a light-hearted note, an interesting poster has been seen around CERN after the winter break…

http://i57.tinypic.com/2yvs8b6.jpg

While it may be implausible that there aren’t connections between the rest of mathematics and IUTech, that doesn’t mean that Mochizuki or anyone else knows what they are … it might take some time indeed to find them … and it seems there’s still a question of whether it will ever be studied enough to be.

Mochizuki does seem enamoured with his work and he may well want to believe that it is truly isolated, as that would add substantially to the degree of his achievement. Given this, he might not be looking too hard.

Definitely a good candidate for automated proof checking as I saw someone mentioning on one of those linked blogs, perhaps a task for one of his acolytes. That would make people stand up and take notice. I know that tends to take years, but in this situation the alternative could take longer …

I do wonder if some of his acolytes are giving too much deference to Mochizuki in not pushing for more rework of the papers.

And there would also seem to be lots of reasons a person might not want to ever travel (unrelated to mathematics) and most they wouldn’t necessarily want to talk about. I’m aware Mochizuki has been abroad before but things change …

acTeVist – that’s great. I love how 200 years from now one of the focus topics is how condensed matter physicists still don’t “get it”.

acTeVist,

Thanks! Although I’m not sure how funny it is….

“Mochizuki has posted a long progress report ”

I found Mochizuki’s remarks on the Langlands program quite interesting.

“it will be interesting to see if theorists are still willing to listen”

They have been willing to listen for at least a decade, the problem is that nobody can find an alternative.

Nature has already spoken, the electron EDM measurement of the ACME collaboration essentially rules out SUSY partner masses up to 10 TeV, i.e., higher than what the LHC Run 2 will achieve.

Efstathiou: Paper testing BICEP2 might already be submitted, but have to wait for arXiv submission in ~2 weeks to learn more. He also said “it is pretty easy to infer what the answer will be”. It’s Just Dust. The Story is Over((

Peter, a discussion between Freese, Tegmark and Gleiser on grand unified theories.

(although lot of the discussion was about origin of consciousness etc)

https://www.youtube.com/watch?v=hoTgId9inb8

The brief comment by Mochizuki. His comment about reverting the mindset of a novice sounds a lot like a call to “beginners mind.”(http://en.wikipedia.org/wiki/Shoshin).

Mochizuki is a family name associated with the samurai class and the samurai were among the patrons of Zen.

Not that this necessarily means much, other than to suggest Mochizuki is using a familiar cultural idiom to describe how he expects people to approach his work.

There is a 3-weeks seminar in March about IUTT at RIMS, talks by his students Yamashita and Hoshi and Minhyong Kim is there giving a talk aswell according to the program. In addition, Yamashita will publish a 200-300pages proof in the proceedings of the seminar, so i guess soon afterwards.

If the seminar and especially yamashita’s writeup is good, the situation could clear up much faster than your pessimistic thought of “a story that is going to go on for a long time…” – don’t you think so?

Andreas,

Maybe Yamashita will produce the kind of document needed, that seems the most likely way for this to happen in the near future. We’ll see.

I did note though that Mochizuki writes

“This led me to pose the following question to Hoshi: If one were to assign to the level of understanding of IUTeich that he achieved as a result of reading through the papers on IUTeich at least five times a score of “100”, then how would he rate the level of understanding of IUTeich that he achieved as a result of attending Yamashita’s seminar? The answer that he gave me was a score of roughly “10 to 15””.

and describes Yamashita as writing a “survey” of IUTeich (rather than a proof of abc). Yamashita on his website does label the document as “A proof of abc conjecture after Mochizuki” which is more promising.

Hi Peter, the conference in Israel was a few days, not a couple of weeks! The poster suggests that it was mainly focused on the history and philosophy of general relativity to commemorate the centenary, looks very interesting

http://www.vanleer.org.il/sites/files/SpaceTimeConf_3.pdf

I had hoped to go, but couldn’t really justify the trip as there was no session on cosmology. This was a bit disappointing from my partisan viewpoint; our group contend that Einstein’s cosmic models of 1917, 1931 and 1932 (and his abandoned steady-state model) offer quite a lot of insights into his thoughts on space-time. Ah well, another time…

Sorry Peter, I get it now. What you called a winter school on GR was actually the 29th Jerusalem winter school on theoretical physics – the conference I mentioned was a GR centenary conference in Jerusalem on Jan 5-8, that coincided with the winter school for a few days…which explains some of the talks you referred to!

Wonder if I can get an accumulator (combo bet) on no primordial gravitational waves observed, no SUSY particles observed and no proof of the abc conjecture observed for 2015

Bob,

Given the vast length of Mochizuki’s proof and the complexity of even the normal and understood machinery of algebraic geometry that he is building on, I think it’s fair to say that this is

notsomething proof assistants are likely to be able to handle any time soon. (Even if someone was willing to do the work of formalizing hundreds and hundreds of pages of proofs.)The same could be said for Wiles’ proof of FLT, Deligne’s of the Weil conjectures or Falting’s of the Mordell conjecture (which is what Mochizuki is comparing his work to) and these three cases are (and were at the time) a lot less weird than Mochizuki’s work. In fact, it isn’t even clear if Mochizuki is claiming to have a proof of abc in ZF, the foundational paper on IUTeich being littered with references to grothendieck universes.

Glad you’re back Peter with everything okay. If I’m not mistaken, you were in or around Paris at the time of the terror. Glad you were not involved.

Justin,

Thanks. Yes, I was in Paris during all of that. A very sad situation, but I was impressed by the way the French dealt with it.

Le Bruyn’s comment on his screenshot of Mochizuki’s note comes off as a bit of a cheap shot.

Had not noticed this page before.

I thought of comments Prof Woit has made here when I watched the season premier of PBS NOVA and they had a very good episode about the LHC and the Higgs,.and the restart.

But they had Jim Gates on to describe SUSY and he said that as a young man he found it to be very satisfying as a theory because it really could explain everything… then he looked wistful and said that after the restart they did find some evidence.. because he did not want to be sbown that he has wasted 20 years of his life on a completely flawed theory.. which actually explained nothing because nature did not work like that.

A sad but telling moment that string theorists will confront as they get older. Compare Higgs in his old age to.. Witten?

@Benard

Nature has already spoken, the electron EDM measurement of the ACME collaboration essentially rules out SUSY partner masses up to 10 TeV, i.e., higher than what the LHC Run 2 will achieve.

^

how solid is this result? what is a % confidence interval. Could a sufficiently sensitive EDM measurement of the ACME collaboration essentially rules out SUSY partner masses up to the planck scale, i.e lower bound for EDM measurement under 10^-38

@electron EDM:

The current upper bound is 8.7 × 10^(−29) e·cm with 90% confidence. Going all the way down to the Planck scale will be difficult because the SM has a nonzero electron EDM around 10^(-38) e·cm, from where you’ll be measuring against a nonzero background.

Bernd, the Planck scale is just 10^-33 cm, so there is good chance to achieve it in EDM measurements, whatever the noise at 10^-38 cm may be …

@Klaus:

Generically, new CP-violating terms couple to the electron EDM proportional to the inverse of the mass scale squared. Even the most drastic assumption of the dipole moment being proportional to the electroweak scale only gives you corrections from the Planck scale at a sensitivity of 10^(-53) e·cm, i.e., way below the SM value.

Bernd

are there experiments underway to lower that bound?

How about people stop picking on Mochizuki? If no one ever understands his theory, who gets hurt? He’s not hurting anyone, no matter how sane or insane he turns out to be. Give the guy a break, jeez.

@neo:

ACME is upgrading the experiment, expecting another order of magnitude improvement in sensitivity. The group of Ed Hinds at Imperial is working on laser cooling of YbF molecules that should give another order of magnitude, so we’re talking of probing a scale of 100 TeV here.

The discussion on string theory vs alternative theories by Gross, Rovelli, Arkani-Hamed and Polchinski was very revealing. The string camp arguments are: (1) string theory is the only extension of GR and QM which generalizes the graviton scattering amplitudes and (2) string teory is the only game in town. According to (1) we do not need to worry about the experimental discrepancies, like the absence of supersymmetric particles in LHC, while (2) explains why so many young people are still attracted to string theory. Rovelli was quite right to say that we should “listen to Nature”, because the statements like (1) are based on certain assumptions,

which we know that are true for a certain range of the length scale, but we have no idea what happens outside of this range. That is why we need a hint from an observation or from an experiment.

The second statement, emphasized by Gross, is referring to the fact that it is very difficult to extract the semi-classical results for LQG (the loop quantum cosmology results, strictly speaking, do not count, because loop QC is a truncation of the full theory). However, in the past four years have been made important advances as far as the semi-classical limit of the spin foam models is concerned. SF models can be considered as the lattice formulation of LQG, so that in the strict sense they are not the same as LQG, but it is expected that they will give LQG in the continuum limit. Anyway, by using the effective action approach from QFT, one can obtain the classical limit for a SF model and calculate the quantum corrections. The classical limit of the standard SF models is the area-Regge theory, which is almost, but not quite, the GR. If the Lorentz group of a SF model is replaced by a categorical generalization

(2-Poincare group) one obtains a spin-cube model, and those have the desired classical limit, which is the Regge formulation of GR.

@Noah Smith

He wouldn’t get the flak if he hadn’t claimed such a big result. source

Why not post something like “I have some original approaches to mathematics and I might be able to develop a proof of some long-standing conjectures in this new framework. They might not conform to the standard ZF axioms or such, but I think it’s an interesting new approach”

@bernd

based on the current ACME results, what is the % likelihood that SUSY will show up in LHC run 2? If SUSY does show up in LHC run 2, does this mean there is a problem with ACME?

@neo:

If the interpretation of the ACME result in terms of sufficiently heavy superpartners is correct, then the likelihood is certainly less than 10% for a detection during LHC Run 2. Probably much less, depending how large the mass scale that the LHC can probe is ultimately going to be (which is much less than 13 TeV).

In case the LHC should see something, this most likely means that there is some fine-tuning going on to make the electron EDM sufficiently small. I’m sure it’s possible to cook up a variant of SUSY that produces such a fine tuning, but in terms of probabilities you should use your own discretion how much credibility you want to attach to such a theory.

Hi,

From any of these two articles from PhysicsWorld,

1> “Measuring (almost) zero” by Chad Orzel, or

2>“Search for electron’s electric dipole moment narrows”

or simply from the Wikipedia entry on ‘Electron electric dipole moment’, and references therein like, ‘Order of Magnitude Smaller Limit on the Electric Dipole Moment of the Electron’- http://arxiv.org/abs/1310.7534

It maybe noted that –

1>Within the standard model of elementary particle physics, Electric Dipole Moment of the Electron is predicted to be non-zero but very small, at most 10−38 e•cm or about about 10–39 e•cm

2> Present experimental range for EDM covers less than or upto,- 8.7 × 10–29 e cm

As such the naïve question (for me at least going by the numbers) is-

Why couldn’t any super-symmetric particles or some modified version of Standard Model via SUSY be lurking in the gap, or in other words,

if EDM is found positive within the still unexplored range why can’t we consider it’s existence owing to Super-symmetric particles among other explanations?

Else can we say that if ACME results closes the gap with a negative result, and the nearer it is as such to the SM limit, the lesser is the probability of detecting a super-partner, till none, if the gap is fully closed with a null result?

Any pointers will be much appreciated.

Thank you.

@Bernd

“The current upper bound is 8.7 × 10^(−29) e·cm with 90% confidence”

doesn’t this upper bound already eliminate SUSY?

Supersymmetric models predict that |de| > 10−26 e·cm (ref below)

SUSY predicted effect on Electron electric dipole moment |de| > 10−26 e·cm is >> > 8.7 × 10^(−29) e·cm by 3 to 4 orders of magnitude

improving the upper bound to 10e-30 or -31 e·cm would only increase the % confidence.

not only will LHC2 run not see SUSY but no upgrade at any scale will, either.

ref: Arnowitt, R.; Dutta, B.; Santoso, Y. (2001). “Supersymmetric phases, the electron electric dipole moment and the muon magnetic moment”. Physical Review D 64 (11): 113010. arXiv:hep-ph/0106089