The spy who loved me (neither I ;-)

Où comment Lubos Motl nous montre qu'il aime la géométrie noncommutative lui non plus ;-)

It happens that Lubos went so far as writing two posts about noncommutative geometry last July. They were motivated by the writings of another blogger and scientist named Florin Moldoveanu whose current research on quantum theory lead to get interested in the spectral noncommutative geometrisation (SNcG) of physics. I have already made some comments about Lubos' posts on my blog here for the first post and there for the second one (I put some comments on his own blog too). 

Today I choose to offer a personal collection of Lubos thoughts with some new comments so the reader may form a possible picture of some failings of the spectral Standard Model. My digest may also appear as a voluntary malicious or involuntary just naïve interpretation of Lubos' philosophically emotional objections as mirrors of some shortcomings of a particular string theorist practitioner. 

Connes and collaborators claim to have something clearly different from the usual rules of quantum field theory (or string theory). The discovery of a new framework that would be "on par" with quantum field theory or string theory would surely be a huge one, just like the discovery of additional dimensions of the spacetime of any kind. Except that we have never been shown what the Connes' framework actually is, how to decide whether a paper describing a model of this kind belongs to Connes' framework or not. And we haven't been given any genuine evidence that the additional dimensions of Connes' type exist.

...they have made some truly extraordinary claims that have excited me as well. I can't imagine how could I be unexcited at least once; but I also can't imagine that I would preserve my excitement once I see that there's no defensible added value in those ideas...

In 2006, for example, Chamseddine, Connes, and Marcolli have released their standard model with neutrino mixing that boldly predicted the mass of the Higgs boson as well. The prediction was 170 GeV which is not right, as you know: the Higgs boson of mass 125 GeV was officially discovered in July 2012... 

But in August 2012, one month after the 125 GeV Higgs boson was discovered, Chamseddine and Connes wrote a preprint about the resilience of their spectral standard model. A "faux pas" would probably be more accurate but "resilience" sounded better... In that paper, they added some hocus pocus arguments claiming that because of some additional singlet scalar field σ that was previously neglected, the Higgs prediction is reduced from 170 GeV to 125 GeV.

I can't make sense of the technical details – and I am pretty sure that it's not just due to the lack of effort, listening, or intelligence. There are things that just don't make sense. Connes and his co-author claim that the new scalar field σ which they consider a part of their "standard model" is also responsible for the Majorana neutrino masses...

Now, this just sounds extremely implausible because the origin of the small neutrino masses is very likely to be in the phenomena that occur at some very high energy scale near the GUT scale – possibly grand unified physics itself. The seesaw mechanism produces good estimates for the neutrino masses $$m_{\nu }\approx \frac{m_h^2}{m_{GUT}}.$$

$$$$

So how could one count the scalar field responsible for these tiny masses to the "Standard Model" which is an effective theory for the energy scales close to the electroweak scale or the Higgs mass mh∼125GeV? If the Higgs mass and neutrino masses are calculable in Connes' theory, the theory wouldn't really be a standard model but a theory of everything and it should work near the GUT scale, too.

The claim that one may relate these parameters that seemingly boil down to very different physical phenomena – at very different energy scales – is an extraordinary statement that requires extraordinary evidence. If the statement were true or justifiable, it would be amazing by itself. But this is the problem with non-experts like Connes. He doesn't give any evidence because he doesn't even realize that his statement sounds extraordinary – it sounds (and probably is) incompatible with rather basic things that particle physicists know (or believe to know).  

I don't believe one can ever get correct predictions out of a similar framework, except for cases of good luck. But my skepticism about the proposal is much stronger than that. I don't really believe that there exists any new "framework" at all. 

What are Connes et al. actually doing when they are constructing new theories? They are rewriting some/all terms in a Lagrangian using some new algebraic symbols, like a "star-product" on a specific noncommutative geometry. But is it a legitimate way to classify quantum field theories? You know, a star-product is just a bookkeeping device. It's a method to write down classical theories of a particular type.

But the quantum theory at any nonzero couplings isn't really "fully given by the classical Lagrangian". It should have some independent definition. If you allow the quantum corrections, renormalization, subtleties with the renormalization schemes etc., I claim that you just can't say whether a particular theory is or is not a theory of the Connes' type. The statement "it is a theory of Connes' type" is only well-defined for classical field theories and probably not even for them...

There are many detailed questions that Connes can't quite answer that show that he doesn't really know what he's doing. One of these questions is really elementary: Is gravity supposed to be a part of his picture? Does his noncommutative compactification manifold explain the usual gravitational degrees of freedom, or just some polarizations of the graviton in the compact dimensions, or none? ...

Again, I want to mention the gap between the "physical beef" and "artefacts of formalism". The physical beef includes things like the global symmetries of a physical theories. The artefacts of formalism include things like "whether some classical Lagrangian may be written using some particular star-product". Connes et al. just seem to be extremely focused on the latter, the details of the formalism. They just don't think as physicists.

... even if the theories of Connes' type were a well-defined subset of quantum field theories, I think that it would be irrational to dramatically focus on them. It would seem just a little bit more natural to focus on this subset than to focus on quantum field theories whose all dimensions of representations are odd and the fine-structure constant (measured from the electron-electron low-energy scattering) is written using purely odd digits in the base-10 form. ;-) You may perhaps define this subset but why would you believe that belonging to this subset is a "virtue"?

I surely don't believe that "the ability to write something in Connes' form" is an equally motivated "virtue" as an "additional enhanced symmetry" of a theory.   

This discussion is a somewhat more specific example of the thinking about the "ultimate principles of physics". In quantum field theory, we sort of know what the principles are. We know what theories we like or consider and why. The quantum field theory principles are constructive. The principles we know in string theory – mostly consistency conditions, unitarity, incorporation of massless spin-two particles (gravitons) – are more bootstrapy and less constructive. We would like to know more constructive principles of string theory that make it more immediately clear why there are 6 maximally decompactified supersymmetric vacua of string/M-theory, and things like that. That's what the constantly tantalizing question "what is string theory" means.  

But whenever we describe some string theory vacua in a well-defined quantitative formalism, we basically return to the constructive principles of quantum field theory. Constrain the field/particle content and the symmetries. Some theories – mostly derivably from a Lagrangian and its quantization – obey the conditions. There are parameters you may derive. And some measure on these parameter spaces.

Connes basically wants to add principles such as "a theory may be written using a Lagrangian that may be written in a Connes form". I just don't believe that principles like that matter in Nature because they don't really constrain Nature Herself but only what Nature looks like in a formalism...

Even though some of my objections are technical while others are "philosophically emotional" in some way, I am pretty sure that most of the people who have thought about the conceptual questions deeply and successfully basically agree with me. This is also reflected by the fact that Connes' followers are a restricted group and I think that none of them really belongs to the cream of the theoretical high-energy physics community. Because the broader interested public should have some fair idea about what the experts actually think, it seems counterproductive for non-experts ... to write about topics they're not really intellectually prepared for.

Reality vs Connes' fantasies about physics on non-commutative spaces

Lubos Motl (Sunday, July 10, 2016)

This post is a perverse teaser to the one to come...