In a rather ironical manner the first Higgs mass that is now excluded by the Tevatron latest results is precisely 170 GeV, namely the one that was favored in the NCG interpretation of the Standard Model, from the unification of the quartic Higgs self-coupling with the other gauge couplings and making the "big desert" hypothesis, which assumes that there is no new physics (besides the neutrino mixing) up to the unification scale. My first reaction is of course a profound discouragement, mixed with an enhanced curiosity about what new physics will be discovered at the LHC.
I'll end with these verses of Lucretius:
Suave, mari magno turbantibus aequora ventis,
e terra magnum alterius spectare laborem;
non quia vexari quemquamst jucunda voluptas,
sed quibus ipse malis careas quia cernere suave est.
[Pleasant it is, when over a great sea the winds trouble the waters, to gaze from shore upon another's tribulation: not because any man's troubles are a delectable joy, but because to perceive from what ills you are free yourself is pleasant.]
sed nil dulcius est bene quam munita tenere
edita doctrina sapientum templa serena,
Well, at least we know we are safe from the "malis" of 170 GeV. Lacking, as we lack, of some ingredients (generations, to name one), it had been even suspicius to hit the target in the first shot.
Still, the model has SU(5) unification without proton decay. And it has these intriguing dimension 10 mod 8, middle way between the Kaluza Klein theories for the standard model group (11 dimensions) and the completely broken limit (surviving SU(3)xU(1), thus 9 dimensions). Perhaps it need other interpretation instead of standard 4D running of the couplings.
'chapeau' for being the first to tell about a possible conflict between your theory and experiment.
but then, there's still a 5% chance...
if all fails, there's Lucretius going on (as in arivero's comment)
Sed nil dulcius est bene quam munita tenere
edita doctrina sapientum templa serena.
atb :: lieven.
Beautiful sentiments. Of course, we should be excited that new physics is definitely indicated!
Dear Prof Connes,
thanks for this amazing speed and integrity. I am sure it wouldn't be matched by any other author of unusual and unexpected predictions in physics I know of.
The choice of the number 170 GeV seems unfortunate enough for you to start to be careful about the asteroids, too. ;-)
I wonder whether you appreciate the special role of the value 170 GeV. It's the value for which the Higgs quartic self-interaction is high enough for the RG running to push it to a divergent value - the Landau pole - at an accessible energy scale, namely the GUT scale.
I think that this week, we have the rare opportunity to push you to grab all the normal particle physics. Many great scientist respond in this way to such unfortunate events. For example, once some Japanese people found a mistake in the Dine-Rajaraman (DR) paper claiming a Supergravity-MatrixTheory disagreement in 3-graviton scattering, they sat down and found a better way to organize the proof that both sides actually agree.
So what you have done in your framework, rationally speaking? You reformulated the Standard Model in a very abstract, fancy, perhaps spectacular language that is hard to read for physicists but that is physically equivalent to the Standard Model. This theory has certain couplings and they simply must be allowed to be any real number.
Only the requirement of enhanced symmetries or the absence of anomalies or divergences or ghosts at special points are legitimate reasons to pick preferred values of the masses and other parameters of the Standard Model in any quantum field (-like) theory.
So even if a particular language makes it harder (or impossible) to write the Standard Model with generic values of the couplings in your (or another) formalism, it can't be viewed as a trusted prediction because it is always numerology that depends on the "language" i.e. the particular NCG reformulation of the Standard Model.
So QFT itself can't answer such questions, e.g. the values of the couplings, not even when one rewrites it with new symbols.
But there's one more way to interpret your model - not as a QFT but as a truncation of a stringy vacuum.
The underlying NCG is really "identical" to the stringy compact dimensions, whatever degrees of freedom one has beyond the 4D, except that you must truncate the stringy spectrum to the massless modes.
Now, when you have a sufficient anti-NCG momentum this week, it may be a great idea for someone like me to ask you to learn the rest of the string/M massive tower that you have been neglecting so far and that is actually completely necessary both to 1) unify the three forces with gravity in a physical way, not just by words (one needs the local geometry to "rotate" the 4 large dimensions into the compact one, which is necessary for saying that these two types of geometry are really about the "same physics"), and 2) to predict anything about the spectrum and the parameters (because the internal nature of the particles and interactions must be seen, which requires one to go beyond QFT and see "internal physics" inside the particles and messengers).
So I would like to boldly use the opportunity to invite you to throw away a young-man's maverickness for a while, to learn string/M-theory this and next week (or month) - something that much less inherently clever people than you were able not only to learn but also to discover, and I am not necessarily talking only about Lenny :-) - and to solve all the remaining open problems of string theory by this Christmas, including a non-perturbative universal definition of the theory applicable across the configuration space (landscape), the vacuum selection problem, and the cosmological constant problem.
Thanks, you can surely do it. I admire you and I have met way too many smart people who admire you even qualitatively more than I do so all this stuff is surely realistic. I might just be the first person who has the idea to simply ask Alain Connes to find the theory of everything, using the full knowledge available to mankind in 2008, not just the knowledge built from the scratch by AC. ;-)
All the best
"I wonder whether you appreciate the special role of the value 170 GeV. It's the value for which the Higgs quartic self-interaction is high enough for the RG running to push it to a divergent value - the Landau pole - at an accessible energy scale, namely the GUT scale."
I am hesitant to wade into this, but I believe that's wrong. 170 GeV came out of an RG analysis, alright. But, rather than diverging at the GUT scale, the Higgs quartic self-coupling "unifies" with the gauge couplings at that scale (the precise formula is in their paper, or in my blog post).
There are plenty of problems with their scenario, but the Higgs self-coupling hitting its Landau pole at the GUT scale is not one of them.
Dear Jacques, thanks for the precise numbers - the Landau-pole bound is a tiny bit higher than 170 GeV, then - but I didn't ever write that the GUT-scale Landau pole was a problem.
It would be on the edge of being a problem in a theory valid up to the GUT scale, and I would actually find it "somewhat natural" for the theory to break down as soon as possible.
More natural than a unification of a quartic coupling with gauge couplings. ;-)
I have really no idea whether you agree even with these basic comments but the main problem of these predictions is that they're only justified by some compactness of some abstract mathematical ways to formulate them, which is simply different from the "conciseness" criteria that can possibly be relevant in *physics*.
Your article didn't help me to increase my belief that it should be possible to predict from a new, different, equivalent formulation of a field theory relationships that cannot be extracted from the old-fashioned definitions of the theory.
It shouldn't be really possible and I don't understand the point of your text about this issue, Jacques. I've observed similar things in the Lisi's case. In some sense, it looks like you are trying to write particular appendices to papers by Alain or Garrett in which you accept some things that are known in physics but "forget" others.
I don't understand your rules, Jacques, that you use to take into account some of them but not others.
E.g. in heterotic string theory, all these couplings come from some worldsheet correlators that share a "common ancestor". So there could perhaps be a "unification" of quartic couplings with gauge couplings at the string scale. But these things are not model-independent, not even in big classes of string vacua, so I don't believe that they could be universal in all "good" theories sharing the same low-energy SM limit.
The particularity of 170 GeV, as mentioned by Lubos, is best seen in the typical plot by Quigg, for instance in page 28, figure 12, of 0704.2232v2, to quote the most recent version.
About NCG and strings, there is a question of method: the NCG approach keeps trying to get most hints from the known, experimental HEP information, and build on these fundations. So it could be asked if the standard model still has some useful information we have not been able to incorporate, and if the mechanisms of string theory are of some guide for this incorporation.
Of course, we have generations. Very open issue, but at least we could try to exploit the fact of the difference between the top and the rest of quarks. I will spare you of hearing again my speculations on this topic.
More important perhaps, we have the issue of 10 dim 8. A point of string theory is that they have a net of dualities jumping mainly between dimensions 11, 10, 9, and 6. It could be expected that a theory using the standard model subgroups "a la Kaluza-Klein" could also reproduce these dimensions: 11 is the minimum for SU(3)xSU(2)xU(1) Kaluza Klein with 4 dim of usual space-time; 9 is the minimum for SU(3)xU(1), and 6 is the minimum for SU(2). Note that whe web of dualities does not link 9 to 6 directly.
Going back to HEP data, in some sense the higgs interpolates between 11 and 9, because if the effective theory had massless W and Z we should need dimension 11, and if it had infinitely massive W and Z we would find ourselves in the SU(3)xU(1) case, thus 9 dim.
In NCG, it could be interesting a setup where the KO-theoretical dimension of the spectral triple were changed up or down by one unit depending of the limits you take for the parameters of the higgs field.
"Your article didn't help me to increase my belief that it should be possible to predict from a new, different, equivalent formulation of a field theory relationships that cannot be extracted from the old-fashioned definitions of the theory."
I have no idea why you think I was attempting to convince you of that.
At low energies (E≪Λ), everything can be phrased in the language of an effective QFT.
What they have is something completely different from a local QFT, for energies above the GUT scale.
you wrote: "I have no idea why you think I was attempting to convince you of that."
But I didn't claim that you were attempting to convince me of that. On the other hand, you should have tried - because this is the only physically meaningful question that matters in the debate about these novel kinds of predictions in general.
So the fact you were attempting to explain something different about Alain's papers - something that was probably supposed not to be Alain's papers but something that I haven't understood - was the bulk of my disappointment.
All the best
"The particularity of 170 GeV, as mentioned by Lubos, is best seen in the typical plot by Quigg, for instance in page 28, figure 12, of 0704.2232v2, to quote the most recent version."
Since the location of the Landau pole is exponentially-sensitive to the value of the Higgs mass (see, e.g., equation (48) of that paper), this is not something you do by eyeballing some graph.
There is a huge difference, in this regard, between m_H=170 GeV and m_H=177 GeV.
Dear professor Connes:
I envy you Dr. Connes. I wish I can come up with a theory which can make such concrete, testable numbers. You're my hero.
Am I dreaming ? An unknown guy called "lumo" who happens to have signed a book (which he's likely to have written less than a half) called "L'équation Bogdanov" in France, aimed to support fraudsters and to promote the delusion that "Harvard" support them is now giving lessons to Alain Connes ?
Dear Dr. Connes,
It appears that someone is impersonating you at (comment #121):
Kind of amusing. :)
I want to point you to a few things. First, is this Lubos Motl work, which is extremely intriguing:
Also, a collection of Lubos’ greatest works from his very own blog:
It’s a good collection of his insults, as well as his racist and sexist remarks. Very interesting.
Are you really sure you want someone this controversial invading your blog with all his hateful baggage?
Dear Dr. Connes,
If you want to see what Lubos wrote about you and your theory, here it is:
Dear Dr. Connes,
I would like to point you to the following post from a PI researcher:
Be careful when you're interacting with Lubos online. Try not to disagree with him and make sure that, in your dealings with him, you satisfy the demands of his overly inflated ego and his delusional sense of grandeur and importance. If you follow these steps, then you MAY not have to write a post like the one linked to above. He continues to believe that his 'fall from grace' last year is the result of physicists conspiring against him and trying to silence him, and not the result of his own ridiculous behavior online, as the facts clearly show.
By the way, I suggest you read the comments (especially the last 8 or so).
It is to be expected the readers of this blog will go for math and physics, not for personalities.
A friend of me expressed this question of personality, in a very NCG like verse:
de ti a mí distancia:
entre tú y yo, nada."
The third line "tu" and "yo" are the English "You" and "I", not to be confused with the personalizations "yourself" and "myself". In a strict interpretation, the poem simply abstracts the difference between the verbal subject in a discourse, where I and You exchange freely, and the localized subjects, living somewhere in space (or space time, if you wish, but linguists could differ here). But it is a poem, and then its set of meanings is a fuzzy one.
It is very tempting to move from arguments in a discussion to arguments about who was the person proposing the arguments. It is fascinating that in the Internet it keeps happening, and even with pseudo anonymous nicknames. And it is perhaps useful in some ways (for instance it can attract attention upon Lubos papers, or upon a given thread, or even upon my own page), but this topic is closer to anthropology than to math phys.
In our local case, the complementary post of Lubos, quoted somewhere above, in his own blog, clearly tell that the concept of "trunctation" is not intended in a precise way, but in a general principle from the belief that any interpretation of the standard model will be a truncation of string theory.
It could be noted than it the idea of finding a string interpretation whose truncated version becomes the spectral action of the SM is not a new proposal, and indeed it appears in some of the papers and draft books referred in connes.org. But we do not have, as far as I known, a concrete program to implement it.
"It is to be expected the readers of this blog will go for math and physics, not for personalities."
At least most of them but not all as an anonymous shows above .
Of course both AC and LM are much farther than most of us and that's why I learn useful things from both .
Apart from the fact that it is usually unwise to comment physics results based on press releases, I wonder how solid are the two supposedly incompatible results.
I am not qualified to comment on the experimental side, and I am probably also not qualified for the theoretical part, but I will comment on it anyway.
Alain will certainly remember that in various incarnations of the model, starting from his work with Lott, and in particular before the spectral action, the mass of the Higgs went as far up as 250 GeV if I remember well, if not higher.
The spectral action has been consistent in favouring a more or less "light" Higgs, and some sort of desert. This is probably a consequence of the requirement of the unification of coupling constants, which makes the model akin to SU(5).
The latest version of the model of Chamseddine Connes and Marcolli (ACM)^2 is certainly the most powerful and coherent one, but it assumes an almost commutative geometry all the way to very high scale, and as a consequence that the renormalization group analysis can be done in the usual way. I still find astonishing the fact that a model comes up with an Higgs mass "in the right ball park" from purely geometric considerations.
As first thing we should judge how unchangeable is the Higgs mass prediction in the (ACM)^2 model. The model is complicated, and I cannot say I mastered all of its details, but I think it is fairly solid. It is its strenght, it may become its problem. So its enhancement cannot come from the inside. It probably requires a wider change. My personal bias is to think that probably already at scales which would lie in the big desert some effects of the fact that spacetime is not describable by ordinary geometry should show. Probably the fact that neutrino masses are so small hint at a different mechanism, beyond see-saw.
It would be interesting to have the opinion of colleagues on this issue, preferably people who have at least read the abstract of the article...
At this point, while we wait with enhanced curiosity for LHC (and I would add Planck as well) it may be a good idea to keep fiddling with the model in a non-almost commutative direction.
It has become tradition in this thread to end with verse. Here is Dante (Paradiso, canto 33):
Qual è ’l geomètra che tutto s’affige
per misurar lo cerchio, e non ritrova,
pensando, quel principio ond’ elli indige,
tal era io a quella vista nova:
veder voleva come si convenne
l’imago al cerchio e come vi s’indova;
As the geometrician, who endeavours
To square the circle, and discovers not,
By taking thought, the principle he wants,
Even such was I at that new apparition;
I wished to see how the image to the circle
Conformed itself, and how it there finds place;
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