Florin Moldoveanu, an eclectic semi-anti-quantum zealot, hasn't write nearly Alain Connes' proposals to build a right theory of particle physics using the concepts of noncommutative geometry.
Now, Connes is a real interesting guy, great, creative, as well as playful mathematician, as well as he sure enough belongs alongside the most successful abstract mathematicians who direct hold worked difficult to larn particle physics. Except that the production just isn't plenty because the airplanes don't land. His as well as his collaborators' proposals are intriguing but they just don't piece of work as well as what the "new framework" is supposed to hold upwards isn't really well-defined at all.
The status quo inwards particle physics is that quantum plain theories – often interpreted as effective plain theories (theories useful for the description of all phenomena at distance scales longer than a cutoff) – as well as string theory are the solely known ways to arrive at realistic theories. Moreover, to a large extent, string theory inwards most explicit descriptions nosotros know also adopts the full general principles of quantum plain theory "without reservations".
The globe canvass description of perturbative string theory is a touchstone two-dimensional conformal (quantum) plain theory, Matrix theory as well as AdS/CFT pull vacua of string/M-theory but they're also quantum plain theories inwards some spaces (world volumes or AdS boundaries), as well as string theory vacua direct hold their effective plain theory descriptions just of the type that 1 expects inwards the formalism of effective plain theories (even though string theory itself isn't "quite" a regular quantum plain theory inwards the bulk).
When nosotros verbalize over quantum plain theories, nosotros create upwards one's heed nearly the dimension, qualitative plain content, as well as symmetries. Once nosotros practice so, we're obliged to consider all (anomaly-free, consistent, unitary) quantum plain theories with these weather condition as well as all values of the parameters. This also gives us an thought nearly which choices of the parameters are natural or unnatural.
Now, Connes as well as collaborators claim to direct hold something clearly different from the commons rules of quantum plain theory (or string theory). The regain of a novel framework that would hold upwards "on par" with quantum plain theory or string theory would sure enough hold upwards a huge one, just similar the regain of additional dimensions of the spacetime of any kind. Except that nosotros direct hold never been shown what the Connes' framework really is, how to create upwards one's heed whether a newspaper describing a model of this sort belongs to Connes' framework or not. And nosotros haven't been given whatsoever genuine evidence that the additional dimensions of Connes' type exist.
So all this Connes' piece of work is some hocus pocus experimentation with mixtures of mathematics of noncommutative spaces (which he understands real well) as well as particle physics (which he understands much less well) as well as inwards betwixt some mathematical analyses that are in all likelihood hugely careful as well as advanced, he often writes things that are known to hold upwards just featherbrained to almost every physics graduate student. And a real large fraction of his beliefs how noncommutative geometry may piece of work within physics just seems wrong.
How is it supposed to work?
In Kaluza-Klein theory (or string theory), at that topographic point is some compactification manifold which I volition telephone telephone \(CY_6\) because the Calabi-Yau three-fold is the most ofttimes mentioned, as well as sort of canonical, example. Fields may hold upwards expanded to modes – a generalization of Fourier serial – which are functions of the coordinates on \(CY_6\). And at that topographic point is a countably infinite number of these modes. Only a modest number of them are real low-cal but if you lot allow arbitrary masses, you lot direct hold a whole tower of increasingly heavy Kaluza-Klein modes.
Connes et al. desire to believe that at that topographic point are just finitely many fields inwards 3+1 dimensions, similar inwards the Standard Model. How tin plow over the axe nosotros acquire a finite number of Kaluza-Klein modes? We acquire them if the infinite is noncommutative. The result is similar as if the infinite were a finite number of points except that a noncommutative infinite isn't a finite laid of points.
Influenza A virus subtype H5N1 noncommutative infinite isn't a laid of points at all. For this reason, at that topographic point are no "open sets" as well as "neighborhoods" as well as the normal notions of topology as well as infinite dimension, either. Influenza A virus subtype H5N1 noncommutative infinite is a generalization of the "phase infinite inwards quantum mechanics". The stage infinite has coordinates \(x,p\) but they don't commute with each other – it's why it's called a "noncommutative space". Instead, nosotros have\[
xp-px=i\hbar.
\] Consequently, the dubiety regulation restricts how accurately \(x,p\) may hold upwards determined at the same moment. The stage infinite is effectively composed of cells of surface area \(2\pi\hbar\) (or its power, if nosotros direct hold many copies of the coordinates as well as momenta). And these cells acquit much similar "discrete points" when it comes to the counting of the degrees of liberty – except that they're non discretely separated at all. The boundaries betwixt them are unavoidably fuzzier than fifty-fifty those inwards regular commutative manifolds. If you lot consider a compactified (periodic \(x,p\) inwards some sense) versions of the stage infinite (e.g. fuzzy sphere as well as fuzzy torus), you lot may literally acquire a finite number of cells as well as hence a finite number of fields inwards 3+1 dimensions.
That's basically what Connes as well as pals do.
Now, they direct hold made some really extraordinary claims that direct hold excited me as well. I can't imagine how could I hold upwards unexcited at to the lowest degree once; but I also can't imagine that I would save my excitement 1 time I encounter that there's no defensible added value inwards those ideas. In 2006, for example, Chamseddine, Connes, as well as Marcolli direct hold 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 non right, as you lot know: the Higgs boson of mass \(125\GeV\) was officially discovered inwards July 2012.
But the fate of this prediction \(m_h=170\GeV\) was sort of funny. Two years later, inwards 2008, the Tevatron became able to say something nearly the Higgs mass for the commencement time. It ruled out the commencement narrow interval of Higgs masses. Amusingly enough, the commencement value of the Higgs mass that was killed was just Connes' \(170\GeV\). Oops. ;-)
There's a consensus inwards the literature of Connes' community that \(170\GeV\) is the prediction that the framework should plow over for the Higgs mass. But inwards August 2012, 1 calendar month after the \(125\GeV\) Higgs boson was discovered, Chamseddine as well as Connes wrote a preprint nearly the resilience of their spectral touchstone model. Influenza A virus subtype H5N1 "faux pas" would in all likelihood hold upwards to a greater extent than accurate but "resilience" sounded better.
In that paper, they added some hocus pocus arguments claiming that because of some additional singlet scalar plain \(\sigma\) that was previously neglected, the Higgs prediction is reduced from \(170\GeV\) to \(125\GeV\). Too bad they couldn't brand this prediction earlier Dec 2011 when the value of \(125\GeV\) emerged as the almost sure enough right one to the insiders alongside us.
I can't brand feel of the technical details – as well as I am pretty sure that it's non just due to the lack of effort, listening, or intelligence. There are things that just don't brand sense. Connes as well as his co-author claim that the novel scalar plain \(\sigma\) which they consider a component of their "standard model" is also responsible for the Majorana neutrino masses.
Now, this just sounds extremely implausible because the beginning of the modest neutrino masses is real probable to hold upwards inwards the phenomena that occur at some real high unloose energy scale close the GUT scale – perhaps grand unified physics itself. The seesaw machinery produces goodness estimates for the neutrino masses\[
m_\nu \approx \frac{m_{h}^2}{m_{GUT}}.
\] So how could 1 count the scalar plain responsible for these tiny masses to the "Standard Model" which is an effective theory for the unloose energy scales to a greater extent than or less the electroweak scale or the Higgs mass \(m_h\sim 125\GeV\)? If the Higgs mass as well as neutrino masses are calculable inwards Connes' theory, the theory wouldn't really hold upwards a touchstone model but a theory of everything as well as it should piece of work close the GUT scale, too.
The claim that 1 may relate these parameters that seemingly boil downwards to real dissimilar physical phenomena – at real dissimilar unloose energy scales – is an extraordinary declaration that requires extraordinary evidence. If the declaration were truthful or justifiable, it would hold upwards amazing past times itself. But this is the occupation with non-experts similar Connes. He doesn't plow over whatsoever evidence because he doesn't fifty-fifty realize that his declaration sounds extraordinary – it sounds (and in all likelihood is) incompatible with rather basic things that particle physicists know (or believe to know).
Connes' "fix" that reduced the prediction to \(125\GeV\) was largely ignored past times the later on pro-Connes literature that kept on insisting that \(170\GeV\) is indeed what the theory predicts.
So I don't believe 1 tin plow over the axe ever acquire right predictions out of a similar framework, except for cases of goodness luck. But my skepticism nearly the proposal is much stronger than that. I don't really believe that at that topographic point exists whatsoever novel "framework" at all.
What are Connes et al. really doing when they are constructing novel theories? They are rewriting some/all price inwards a Lagrangian using some novel algebraic symbols, similar a "star-product" on a specific noncommutative geometry. But is it a legitimate way to sort quantum plain theories? You know, a star-product is just a bookkeeping device. It's a method to write downwards classical theories of a particular type.
But the quantum theory at whatsoever nonzero couplings isn't really "fully given past times the classical Lagrangian". It should direct hold some independent definition. If you lot allow the quantum corrections, renormalization, subtleties with the renormalization schemes etc., I claim that you lot just can't say whether a particular theory is or is non a theory of the Connes' type. The declaration "it is a theory of Connes' type" is solely well-defined for classical plain theories as well as in all likelihood non fifty-fifty for them.
Influenza A virus subtype H5N1 generic interacting fully quantum plain theory just isn't equivalent to whatsoever star-product based classical Lagrangians!
There are many detailed questions that Connes can't quite reply that exhibit that he doesn't really know what he's doing. One of these questions is really elementary: Is gravity supposed to hold upwards a component of his picture? Does his noncommutative compactification manifold explicate the commons gravitational degrees of freedom, or just some polarizations of the graviton inwards the compact dimensions, or none? You tin plow over the axe regain contradictory answers to this inquiry inwards the Connes' paper.
Let me say what is the reply to the inquiry whether gravity is a component of the consistent decoupled plain theories on noncommutative spaces – i.e. those inwards string theory. The reply is just No. String theory allows you lot to pick a \(B\)-field as well as decouple the low-energy open-string dynamics (which is a gauge theory). The gauge theory is decoupled fifty-fifty if the infinite coordinates are noncommutative.
But it's ever just a gauge theory. There are never spin-two fields that would meaningfully locomote inwards the Lagrangian with the noncommutative star-product. Why? Because the noncommutativity comes from the \(B\)-field which may hold upwards laid to null past times a gauge invariance for the \(B\)-field, \(\delta B_{(2)} = d \lambda_{(1)}\). So the value of this plain is unphysical. This decision solely changes within a D-brane where \(B+F\) is the gauge-invariant combination. The noncommutativity-inducing \(B\)-field may really hold upwards interpreted as a magnetic \(F\) plain within the D-brane which is gauge-invariant. Its value matters. But inwards the decoupling limit, it solely matters for the D-brane degrees of liberty because the D-brane globe volume is where the magnetic plain \(F\) is confined.
In other words, the star-product-based theory solely decouples from the balance of string theory if the open-string scale is parameterically longer than the closed-string scale. And that's why the same star-product isn't relevent for the closed-string modes such as gravity. Or: if you lot tried to include some "gravitational price with the star product", you lot would bespeak to consider all objects with the string-scale energies as well as the infinite tower of the massive string states would hold upwards a component of the picture, too.
Whether you lot larn these lessons from the string theory examples or you lot derive them purely from "noncommutative plain theory consistency considerations", your conclusions volition contradict Connes' assumptions. One just cannot direct hold gravity inwards these decoupled theories. If your description has gravity, it must direct hold everything. At the end, you lot could relate this decision with the "weak gravity conjecture", too. Gravity is the weakest forcefulness as well as so 1 time your theory of simple edifice blocks of Nature starts to hold upwards sensitive to it, you lot must already hold upwards sensitive to everything else. Alternatively, you lot may say that gravity admits dark holes that evaporate as well as they may emit whatsoever particle as the Hawking radiations – whatsoever particle inwards whatsoever stage of a microscopic phenomenon that is allowed inwards Nature. So there's no way to decouple whatsoever subset of objects as well as phenomena.
When I read Connes' papers on these issues, he contradicts insights similar that – which seem self-evident to me as well as in all likelihood to most existent experts inwards this component of physics. You know, I would hold upwards extremely excited if a totally novel way to build theories or decouple subsets of the dynamics from string theory existed. Except that it doesn't seem to hold upwards the case.
In proper string/M-theory, when you lot really consistently decouple some subset of the dynamics, it's ever close some D-brane or singularity. The decoupling of the low-energy physics on D-branes (which may hold upwards a gauge theory on noncommutative spaces) was already mentioned. Cumrun Vafa's F-theory models of particle physics are some other related example: 1 decouples the non-gravitational particle physics close the singularities inwards the F-theory manifold, basically close the "tips of some cones".
But Connes et al. basically desire to direct hold a non-singular compactification without branes as well as they nonetheless desire to claim that they may decouple some ordinary standard-model-like physics from everything else – similar the excited strings or (even if you lot decided that those don't exist) the dark hole microstates which sure enough direct hold to exist. But that's almost certainly non possible. I don't direct hold a totally rock-solid proof but it seems to follow from what nosotros know from many lines of enquiry as well as it's a goodness plenty argue to ignore Connes' enquiry administration as a incorrect 1 unless he finds something that is really nontrivial, which he hasn't done yet.
Again, I desire to cite the gap betwixt the "physical beef" as well as "artefacts of formalism". The physical beef includes things similar the global symmetries of a physical theories. The artefacts of formalism include things similar "whether some classical Lagrangian may hold upwards written using some particular star-product". Connes et al. just seem to hold upwards extremely focused on the latter, the details of the formalism. They just don't recollect as physicists.
You know, as nosotros direct hold learned peculiarly inwards the recent 100 years, a physical theory may often hold upwards written inwards real many dissimilar ways that are ultimately equivalent. Quantum mechanics was commencement flora as Heisenberg's "matrix mechanics" which turned into the Heisenberg moving painting as well as later on as "wave mechanics" which became Schrödinger's picture. Dirac pointed out that a compromise, the interaction/Dirac picture, ever exists. Feynman added his path integral approach later, it's really some other picture. The equivalence of those pictures was proven soon.
For particular quantum plain theories as well as vacua of string/M-theory, people flora dualities, peculiarly inwards recent 25 years: string-string duality, IIA/M, heterotic/M, S-dualities, T-dualities, U-dualities, mirror symmetry, AdS/CFT, ER=EPR, as well as others. The indicate is that physics that is ultimately the same to the observers who alive inwards that universe may often hold upwards written inwards several or many seemingly real dissimilar ways. After all, fifty-fifty the gauge theories on noncommutative spaces are equivalent to gauge theories on commutative spaces – or noncommutative spaces inwards dissimilar dimensions, as well as and so on.
The broader lesson is that the precise formalism you lot pick just isn't fundamental. Connes' whole philosophy – as well as the philosophy of many people who focus on appearances as well as non the physical inwardness – is real different. At the end, I recollect that Connes would concur that he's just constructing something that may hold upwards rewritten as quantum plain theories. If there's whatsoever added value, he just claims to direct hold a gadget that produces the "right" construction of the relevant quantum plain theories.
But fifty-fifty if he had some well-defined criterion that divides the "right" as well as "wrong" Lagrangians of this kind, as well as I recollect he just doesn't direct hold 1 because at that topographic point can't hold upwards one, why would 1 really believe the Connes' subset? Influenza A virus subtype H5N1 theory could hold upwards special because it could hold upwards written inwards Connes' cast but is that a existent virtue or just an irrelevant curiosity? The theory is every bit consistent as well as has equal symmetries etc. as many other theories that cannot hold upwards written inwards the Connes form.
So fifty-fifty if the theories of Connes' type were a well-defined subset of quantum plain theories, I recollect that it would hold upwards irrational to dramatically focus on them. It would seem just a footling combat to a greater extent than natural to focus on this subset than to focus on quantum plain theories whose all dimensions of representations are strange as well as the fine-structure constant (measured from the electron-electron low-energy scattering) is written using purely strange digits inwards the base-10 form. ;-) You may perhaps define this subset but why would you lot believe that belonging to this subset is a "virtue"?
I sure enough don't believe that "the mightiness to write something inwards Connes' form" is an every bit motivated "virtue" as an "additional enhanced symmetry" of a theory.
This word is a somewhat to a greater extent than specific instance of the thinking nearly the "ultimate principles of physics". In quantum plain theory, nosotros sort of know what the principles are. We know what theories nosotros similar or consider as well as why. The quantum plain theory principles are constructive. The principles nosotros know inwards string theory – mostly consistency conditions, unitarity, incorporation of massless spin-two particles (gravitons) – are to a greater extent than bootstrapy as well as less constructive. We would similar to know to a greater extent than constructive principles of string theory that arrive to a greater extent than straight off clear why at that topographic point are vi maximally decompactified supersymmetric vacua of string/M-theory, as well as things similar that. That's what the constantly tantalizing inquiry "what is string theory" means.
But whenever nosotros pull some string theory vacua inwards a well-defined quantitative formalism, nosotros basically supply to the constructive principles of quantum plain theory. Constrain the field/particle content as well as the symmetries. Some theories – mostly derivably from a Lagrangian as well as its quantization – obey the conditions. There are parameters you lot may derive. And some mensurate on these parameter spaces.
Connes basically wants to add together principles such as "a theory may hold upwards written using a Lagrangian that may hold upwards written inwards a Connes form". I just don't believe that principles similar that affair inwards Nature because they don't really constrain Nature Herself but solely what Nature looks similar inwards a formalism. I just don't believe that a formalism may hold upwards this of import inwards the laws of physics. Nature abhors bureaucracy. She doesn't really assist nearly formalisms as well as what they facial expression similar to those who direct hold to piece of work with them. She doesn't really discriminate against 1 type of formalisms as well as She doesn't favor some other kind. If She constrains some theories, She has goodness reasons for that. To focus on a subclass of quantum plain theories because they are of the "Connes type" just isn't a goodness reason. There isn't whatsoever rational justification that the Connesness is an payoff rather than a disadvantage etc.
Even though some of my objections are technical patch others are "philosophically emotional" inwards some way, I am pretty sure that most of the people who direct hold thought nearly the conceptual questions deeply as well as successfully basically concur with me. This is also reflected past times the fact that Connes' followers are a restricted grouping as well as I recollect that none of them really belongs to the cream of the theoretical high-energy physics community. Because the broader interested world should direct hold some fair thought nearly what the experts really think, it seems counterproductive for non-experts similar Moldoveanu to write nearly topics they're non really intellectually prepared for.
Moldoveanu's spider web log postal service is an instance of a text that makes the readers believe that Connes has flora a framework that is nearly as important, meaningful, as well as settled as the conventional rules of the model edifice inwards quantum plain theory or string theory. Except that he hasn't as well as the thought that he has is based on depression standards as well as sloppiness. More generally, people are beingness constantly led to believe that "anything goes". But it's non truthful that anything goes. The amount of empirical information nosotros direct hold collected as well as the laws, principles, as well as patterns nosotros direct hold extracted from them is huge as well as the feasible theories as well as frameworks are extremely constrained. Almost nix works.
The principles producing theories that seem to piece of work should hold upwards taken real seriously.
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