AdS/CFT with no humor…

well, maybe not that humor-less… however, let’s start from the very beginning… well, starting from the very beginning will mean I will jump over several aspects but I hope not over the important ones. So, you know that in quantum mechanics you have to sum over all possible wavefunctions and square the result in absolute value to get the final probability density. Well, in the case of collisions between particles that may have some structure and may interact through specific interactions you have to sum (or integrate) over all inequivalent configurations (emphasis on inequivalent). The situation can be represented in the form of some diagrams called Feynman diagrams after the smart guy called in the same way that invented them. There you represent some lines for particles but also use some other lines for whatever happens “in between” and you don’t really observe… you also have to sum (integrate) over whatever is inside and you don’t see in order to get the right amplitude so in the end a feynman diagram represents some sort of integral (in momentum or position space). Now, the propagators (internal lines) you find by solving some form of field equations and in this way you get some expressions you put in the integral. Now, these equations are equations of motion. They are derived from Lagrangians (or, if you are unlucky and work in condensed matter from Hamiltonians…) Now, you observe that a change in the phase of your field (yeah, that damn thing) should not affect the results… this is a relatively fundamental principle (although in some cases the phase difference becomes relevant, see Berry phases, Bohm Aharonov experiment, etc. due to topological features…). The name of this principle is called “gauge invariance” and the global gauge invariance (you change the phase in the same way everywhere) is a symmetry that is associated to the “conserved electric charge” (see Noether theorem). Now, the situation becomes slightly more complicated if you allow local phase changes. The results should be invariant to that too but in order to have this condition imposed you need a “connection” in your space that allows you to define the change of a quantity from one point to the other. Surely, this won’t change your results but you still need the mathematical structure to impose this and in order to have that mathematical structure you need to have a new field (well, new… you knew it as the Maxwell field). Now, of course you will need some equations for this field too, and it will appear in the inner part of your Feynman diagram especially if you describe e.m. phenomena. Well, the thing is that this field also has some freedom (gauge freedom) and when you integrate over it you practically integrate over lots of equivalent situations. This can be easily solved by fixing “the gauge”… ok, thing done, you obtain a consistent Feynman diagram. However, when you put a loop into your diagram you start obtaining divergencies. These are simple divergencies, you remove them by renormalization (there are several types of renormalizations and methods to achieve them, Minimal subtraction, multiplicative, counter-term, etc.) This renormalization appears due to a bad behavior of your theory at very high momenta or very small distances… remember, it is a perturbative approach (oh, damn it, I forgot to tell you this, it is of course a damn perturbative approach all this…) Yeah, and there are of course IR divergencies but these are easily removed by either introducing some regularization or some massive terms. Ok, so we have a theory that is UV and IR renormalized and represented by a series of graphs… this is the situation when the gauge algebra (the algebra associated to the gauge group transformations of the interaction fields) is abelian. If it is non-abelian the situation becomes lightly more complicated. The commutator must be considered. Now, when we have a gauge group like SU(3) we may have fermionic fields in its fundamental representation (having an internal index) and some gauge fields living in its dual representation (adjoint) and having 2 indexes. This is important… Now, Gerard ‘t Hooft ‘s idea was to represent the feynman diagrams such that the indices i and j are represented by different lines according to how they are i>j, i=j or i<j as lines with arrows. Now, these diagrams can be organized such that the internal lines cover a surface. Now, you obtain a very ugly figure over the plane with some lines and some doubled lines with directions. Well, at this you can look in a direct way but also in a dual way, where the distance between the lines becomes “your object”… now, as SU(3) becomes SU(N) and N->infinity. In principle you have a surface with holes in it that can be classified according to N and the coupling at each vertex, call it g. Euler’s theorem in topology will give you some exponents for you factors and here we go, a topological classification of your surface. Now, when N is large you can make an expansion in 1/N and this gives you a series expansion of the kind you want (string sheet expansion). Now wait a bit, this is just a representation of a formal power series. You don’t have a SU(Infinity) group and the “dual” representation of the fillings instead of the lines doesn’t mean nature is made out of strings and branes… Actually ‘t Hooft said that pretty clear in his paper but … lokomotiv string theory doesn’t stop… however, I said I am serious around now… so, let’s assume you make this connection then AdS/CFT says in principle that what you have is a conformal field theory on the string world-sheet surface (don’t forget, you speak about a 2 dimensional surface, CFT is the preferate choice but you did not start with that in the first place, so the relation is “jumpy”). You obviously don’t have a good 1/N approximation because in QCD N=3 which is not known to be terribly large… well, 4 is certainly larger than 3… and by all means electrons in a solid are NOT QCD… well, never mind, the idea is that you look at this and you see that your CFT is in fact a theory on a boundary … what boundary? well, if you desperately search for something you can expand in a series you will need a weak coupling and that one you find if you consider the CFT on the boundary of an AdS_{5}xS^{5} space. In that case the intuition may suggest (but it is NOT clearly proved, only “verified” and I don’t agree with the verifications either) that your strongly coupled theory on the boundary (hard to compute as you know only series expansions in small couplings) is “dual” (whatever that may mean) to a gravity (supergravity) theory in the “bulk” space of AdS_{5}xS^{5}. Of course the quantum case of the bulk supergravity must in principle also be a quantized theory of gravity so you may end up having to integrate over non-equivalent geometries… whatever “nonequivalent” may mean in this case… Well, this is the place where all the craziness starts… you can start playing with your AdS space, transforming it into a general manifold M and see what happens, how you do quantization on that one, what else can you put instead of S^{5} and so on, and so on… you see however, that the whole thing is based on a CONJECTURE… and some alternative (dual space) representations… 

String theory is wrong

Sure, my last post was rather long and dealt not explicitly with string theory but rather with AdS/CFT duality which is again wrong in the sense of being a true duality of nature between a naturally realized quantum field theory and some gravitational dual at low interactions. I should try to discuss why string theory is wrong per se and not through some conjectures that are in fact not really connected to string theory. Why, you can make AdS/CFT type dualities as automorphisms in gauge theories so of course AdS/CFT is not really connected to string theory, even from the way it was constructed it is not… While one may think this “saves” string theory, in fact it doesn’t. It does simply show that “constructions” made by string theorists wether related or not to string theory (always or sometimes, partially or totally) tend to be based on faulty thinking. But, I am going away from the red path… String theory is in fact a dimensional generalization. It is an attempt to describe and quantize objects which are not points. Physically they should not exist if it were not for a quantization prescription but then what exactly are you quantizing? One should however not think in this way: quantization is a prescription needed by out limited mind.. in reality nature is quantum mechanical and we simply don’t see it that way because we are too stupid or too fixed in a classical way of thinking… This might be true, I have nothing to object, it could happen to be the case… However, if that is the case then there should be a fully quantum description of strings in terms of any quantization prescription and a go and back map that may not be one to one but should always give the measured outcomes. Is this the case in string theory? Nope… Thing is, string theory has not one single theory in it compatible with reality. None whatsoever. It is not even sure the construction is quantum or that the quantization prescription is the same or should be the same let apart for the arbitrarily chosen prescriptions that lie all over string theory… 

AdS/CFT conjecture is wrong

Depending on how much time I am willing to allow to this subject this might become rather long… It could be of the length of a book if it really wants to cover all the aspects in which string theory is plain wrong but I want to insist also on the way of thinking that brought us into working so long on an idea that is wrong. First, experiments… it is not a direct or trivial problem because models have parameters and various parameters can give different fits and different fits can fit for good or bad with various experimental data… Then, of course it is the corruption at the level of string theory research and the willingness to declare something utterly nonsensical as “well fitting to experiment”… This happens not only in string theory but because string theory is SO wrong it is certainly the place where you see it most. Then, there is the notion of “observability”. Not all objects are in all circumstances observable. You can speak of position for example as an observable and of course you can say a car is 2 meters away from a building. This sentence has some meaning associated to it. It is “well defined” in the context of classical mechanics and classical mathematics. However, the position of a quark in a nucleus is not a well defined statement. The lack of a “precise definition” has various origins. First, due to the generally accepted model of strong interactions a quark is not observable. That doesn’t mean it’s not physical. You can probe it in various ways but a single quark is not defined by itself. This means you hardly can talk about the position of a quark or even less about its speed. Nor can you talk about collective properties of quarks in the same way. For example in order to define viscosity of a quark fluid you may have to define other concepts that have a meaning and are observable. Using some models you can extract some data about whatever you choose to call “viscosity” in your new, extended dictionary. You see, there is a choice and it is not physical. It is a choice of your way of talking. The “way of talking” is essential in almost any formulation of any field of science, from quantum mechanics to general relativity or string theory. You can chose sections of fiber bundles and define adjoint representations etc. but you see, all is dependent on a choice and on a way of speaking. This is why people tend to say fashionable nonsense in scientific journals (targeting a broader audience)… They usually play on the card of having words that sound familiar but are not well defined in the context that is common knowledge… (I said this is going to become hard)… We all know in quantum mechanics are so called “incompatible observables”… what that means essentially is just that they are associated to operators that don’t commute and that means they do not have a common set of eigenvalues (they cannot be diagonalized simultaneously). This is the quantum mechanical way to tell us we must be careful when speaking about two such “observables” at the same time. They are in general non independent in any description. This is another method of tricking the audience. So, we see now that objects that are well defined in some context may have a non-trivial derivation in some other context. Now we can start talking about the first “experiments” trying to give some data that is in accordance to AdS/CFT duality. I spoke quite some time about the “holographic principle” and why “the universe is not a hologram” (not even remotely)… Scaling properties of the holographic principle are in general not obeyed by nothing. Mainly fermions disobey them, reason for which many “corrections” have been introduced… needless to point out how pointless they were… Anyhow, one of the applications of AdS/CFT was to something called the “superfluidity of quark gluon plasma”… In fact this was also an idea of mine, unfortunately never published, when I was in Troy, NY… I just thought loudly about “using AdS/CFT for superfluid layers”… the reaction was : “oh, why didn’t I think at that?” (lol)… never mind, the idea was funny but the results were obviously wrong… You can derive solutions for the strong coupling of a field theory describing quark-gluon plasma using some weakly coupled gravity duals and find out that the viscosity of the system is low… however, the same solutions can be found using other models for the interactions that appear at a “more fundamental” level… so, precisely because the viscosity is not a directly defined quantity you cannot in principle say which formulation is right. Now, however, there is another problem, namely that you can in principle say what is the behavior of some other quantities that are directly measured and AdS/CFT is giving predictions for that. Compared to the experiments these predictions are WRONG! There is absolutely NO WAY TO ARGUE WITH THIS DATA! THEY ARE GODDAMN WRONG! No matter how you change the parameters of the fit you simply don’t get anything like that from AdS/CFT, not even by playing god and giving up the rest of physics just so your model works out! NO! Maybe the best expression for this is given by Feynman : http://www.youtube.com/watch?v=b240PGCMwV0 Now, they can be wrong in several ways, one of which is of particular importance for me… and it has to do with something called “large N expansion”… N is the N in SU(N) and it essentially is a trick you use in order to make an expansion in a small parameter on the “other side” of your duality. N=3 is the case for QCD. Now, during my master presentation in paris I remember quite well I discussed about this problem with someone teaching string theory and after 3 hours of lecture which I understood better than he did (apparently) the conclusion was that N=3 is LARGE! Or, at least large enough such that only small corrections could affect the leading term. So, you may apply AdS/CFT in that form whenever 3=infinity… oookkk… no, I mean, as a young wanna be string theorist with lots of arrogance towards the establishment you may swallow that kind of things… the problem is that nature doesn’t and your series becomes at least odd when saying 3=infinity… This however is important in another way too… the large N expansion… I will enter here in some rather technical details… few of you will be able to follow but hey, some may… the N is related to the quark families… In fact if you take an D=4 SU(N) Yang Mills theory with N_{f} quarks and write the renormalization group equation for large N you can redefine the equation using the old yang mills coupling squared and the N above using a single letter and call this new letter your “beta function” … in this way the basic “flow” of your redefined coupling becomes independent of N. So, in large N limit we can use this new “coupling”. Then your fields live in the direct representation and gluons and some ghosts in the adjoint representation. Now, we can go to the so called “t’hooft” diagram. Take a specific scale and then rescale. You will get a factor 1/N for every quark or ghost propagator and a factor of N for every vertex. Every index loop gives a factor of N too… What you may observe is that you get the Euler number : chi=F-E+V factors of N. F= loops, E= edges, V=vortices. How did we end up with this? Well, first of all remember that we speak about gluons and quarks. Quarks live in the direct representation while gluons in the “adjoint” (say dual) representation (obtained by linearizing the action of the group). This means in principle that gluons carry two color indices (being in the dual representation they are obtained as linear combinations). Now, in this representation one splits the diagram such that the color indices associated to the lines are not “lines” but “bands”… and looks at them as if they were simplicial complexes that map a surface with a given topology. In this way we end up with a partition function that is in the form of a series expansion of topological genera. Where are the problems? Everywhere: while mathematically ok-ish one forgets completely what one wants to describe… namely some form of QCD… that’s where we started from. The separation of the dual representation of the algebra over the indices may give you a topological object but that object has no meaning in the sense of QCD… it is NOT ISOMORPHIC. It is at best a dimensional extension over indices of the lines which HAVE NO PHYSICAL MEANING AT ALL! In fact it ruins the original group structure and it gives a sense ONLY when N-> Infinity… Now, after smoking lots of… whatever… you end up believing that N=3 is infinity… case in which the expansion would still be inexact as even in this case there is no isomorphism between the two. Why, I can twist the bands… I can make lots of extra structure after modifying the “dimension” in this way… But that’s me speaking, let’s have the experiments talk… Image The obvious result is that experiment is WAY OFF any AdS/CFT prediction and that’s the way they should be… Now, caveat: here we are dealing with a theory that is QCD in nature… so, the place where all the AdS/CFT duals started … QCD has some features: it is a sort of extension of Yang Mills which is non-abelian, it has quarks and gluons and confinement (if any)… these features make QCD a GOOD candidate for testing AdS/CFT… anyhow, far better than any many electron system around… and it fails Now, let’s go further and see how AdS/CFT duals can help condensed matter theorists (rumors of condensed matter people feeling targeted, crowding at the borders in a desperate escape tentative)… The “help” of AdS/CFT people (although I bet nobody asked for it) is to identify gravity duals to conformal field theory problems in condensed matter… If you understand the words you already see they don’t sound well… dual mapping is coming with a great deal of baggage from the gluon self-energy diagrams… I mean GLUONS! There are no gluons in condensed matter… and why on earth should N-> infinity there? Ok, string theorists will tell you that the “holographic idea” is more than AdS/QCD… it is so fundamental that you couldn’t eat your breakfast without it or at least without a black hole in the dual bulk… fact is, however, that nature proved this as being rubbish… and this is the end…

The fairy tale era!

I am just thinking that one day, in 50 years from now, this period when physicists invented sparticles, extra dimensions, heterotic strings, magnetic monopoles, all the spectrum from stops to selectrons, axions, dark matter etc. will be called “the Fairy Tale era”. It is mainly because of a refusal of mathematics. Or a lack of acceptance for the fact that it must not always have to be some sort of “entity” that generates or explains some aspects related to nature. Not every phenomenon must have its explanation in a small gnome of fairy or “sparticle” that hides in never-never-land (high energy domain) and from time to time generates strong gravitational effects in the center of the galaxy…  Or a symmetry by that matter…

particle string dichotomy

I said some time ago that Quantum loop gravity and string theory are in some sense identical… This is true! They are in the same way wrong. As everyone knows how quantum loop gravity is wrong (and if not, I’ll insist on that in a future blog-post), some are not aware about the ways in which string theory is wrong. Now, as  said before, I won’t criticize, as Peter Woit does, the fact that string theory is a perturbative approach to something unknown… The technique is ok, the idea that I call topological re-summation makes perfect sense to me and people should work on that, etc. The way in which string theory is wrong relates to the fact that it creates a false dichotomy between point like particles and string-like “particles”… Why false? You would say you can certainly tell the difference between a point and a line and string theory considers all generalizations (branes, etc.). Well, this is not the point: nobody could ever say physical particles are mathematical points. This idea, no matter how widespread it may be is obviously wrong. There is no such thing as a mathematical point in nature. It is just a description. Saying that you end up with problems at the level of renormalizability etc. and yes, string theory deals with UV completion in a nice way. However, the fact that string theory gives you a fundamental object that stops UV-divergencies does NOT mean fundamental objects are strings. Making them “strings” just means you made a very naive extension, of the sort made by QLG people when saying their nonsense… You see, the main issue here is not if the “fundamental building block” is a particle or a string but what structure you can add on whatever the fundamental thing is… and if that structure depends on some other things there might, and just might, be a question whether your fundamental thing is really fundamental or if there can be a thing as fundamental as you expect it to be? I believe not! There are several ideas that I will publish sooner or later… the main point however is not to  confound the description of reality (which might be pleasant in some representations and rather unpleasant in others) and reality itself…

How many times can you discover something for the first time…

now, now, the title sounds strange as discovering something should imply doing it for the first time… right? Again, WRONG! 

Some years ago (maybe three) we were told in the same way that THE MAGNETIC MONOPOLE HAS BEEN DISCOVERED! Back in Romania we had jokes with “radio Erevan” usually discussing about soviet censorship and how a honest news was deformed by the censors in order to fit with the soviet doctrine… fortunately this is not the case now… now, it’s scientists that change news in order to fit to the doctrine of the funding body… so, Three years ago they discovered a magnetic monopole which was in fact not a magnetic monopole, in a free state which in fact was a atomic lattice in a natural environment which in fact was magnetic ice… now, the subject is interesting and deserves some remote analysis… While doing second quantization (you know, go to a Fourier representation, take the coefficients, impose on them commutation and anticommutation rules, introduce a Hilbert space and start playing with them in all sort of interacting environments) what you actually do is define a vacuum… and impose something called “normal ordering”. This “normal ordering” prescription tells you in principle that all the creator operators are at the left of all annihilator operators. It is only a rule but it has important effects on the value of the “vacuum energy”… Whenever no gravitational interactions are included (and spacetime is flat) you can do that. The choice is not unique but the fact that you “renormalize the vacuum” means essentially you assign to it a finite value. Beware however that normal ordering is not a linear operation and normal ordering of a function of operators is not always well defined… but now I’m going into too much depth… The thing is that we now have operators that create excitations on our “vacuum”… However, in condensed matter this vacuum is not “the vacuum” whatever that means, but the set of particles you have there in your background… the movement of an excitation through this system (a.k.a. a collective excitation) can be quantized and can produce collective “particles” known as “quasiparticles”. They behave AS IF they were particles but in fact are collections of particles. Ok, the magnetic monopole in this case is just a specific configuration of the field generated by the spin structure in that object when the alignment did not reach a equilibrium. A hedgehog structure emerges for some time and it’s “pictured” as a monopole. Anyhow, a few days ago I started looking on facebook and people made me be careful and watch how they “discovered” the monopole… and of course, I said: “what? again?”… well, yes, this time not in a spin ice system but in a bose-einstein condensate… oh dear! I am about to fall of my chair… well… maybe not… 

Magnetic monopoles however, the true ones, the ones coming from vacuum don’t exist in nature… magnetic lines are always closed… well, Dirac was of course right: you can quantize a theory with magnetic monopoles and there is no problem or contradiction in doing so but they are not realized in nature for some reasons (about which I won’t talk now and here, as they reflect my own personal research and that has to be published first). String theory loves magnetic monopoles… not the ones discovered now, but the real ones that should be… around 1 per universe… so, keep searching… funding is assured! 

 

Quantum mechanics…

I wrote several posts about this subject but I keep seeing nonsense around… so, here, another one… What is the connection between this evening and quantum mechanics… well, after reading two very interesting papers which I strongly recommend: this http://arxiv.org/pdf/0809.0305v2.pdf and reference [1] therein and I am thinking about writing a paper related to the subject myself as soon as I’ll have some time, I was bombarded on my facebook page with some nonsense involving the, by now ubiquitous “many world interpretation”… Now, you know, I get goosebumps whenever I hear about this “many worlds” nonsense… and I am absolutely not in the mood to explain here, again, and again, and again why the many world interpretation is equivalent to the Copenhagen interpretation and why it means essentially nothing, apart from the pointless media hype it always tends to get… On the other side, I strongly recommend the paper by Gukov and Witten and I also recommend you to read whatever you can find about geometric quantization. Also, the Kirillov quantization, also known as “orbit quantization” is pretty important and gives quite some insight into what quantization should be and what mathematical structures you need to understand before speaking about “quantization”… Let me tell you, quantization is a tricky thing to do… it is rather obvious if you know what you have to do, and this is the case in the 0 dimensional case… not that much in the 1 dimensional case (quantum field theory) and even less in the 2 dimensional case (string theory, sigma models, etc.). The basic prescription has many “holes” in it, places where arbitrariness is pretty important and places where a choice of a specific  structure may change results in a significant way. 

Unfortunately, most if not all “quantum fundamentalists” or “quantum computerists” nowadays have NO CLUE about all this “stuff” and keep doing things almost blindly. We see all the time some pointless nature and science papers saying they “teleported” whatever there might be, from a photon, a boson, an atom, energy, matter, me, you, him, her from here to there, where there is the table next to mine, the lab next door, the closest island, the closest satellite, the moon, etc. but NOTHING of any fundamental relevance… If you look at quantum chemists, which are at least 50 years behind the current knowledge you will be scared about how they calculate correlation… then you go to quantum computerists and fundamentalists who are at least 70 years behind and you will see they have even less contact to path integral quantization or quantum field theory than quantum chemists… what am I saying, they still debate about BELL STATES and CAT STATES! STONE AGE RE-ENACTED! 

mathematically impossible…

There is a phrase that I sometimes hear from string theorists saying that any other option is “mathematically impossible”… really? is it? And I go back to the discussion about “interactions” in mathematics… no kidding? Really impossible? Let me give you an example: in spectroscopy, a field that I find rather boring unless someone discovers the electron is an ellipsoid, there is something called “selection rule”. In principle it says that if the symmetry groups to which the various parts of a matrix element do not fit together (have no common irreducible representation) the matrix element is zero and there is no transition allowed… Well, this never happens in reality. There is NEVER in reality a situation in which the symmetry is exact or the selection rule is perfectly applied! Every student after he/she (or it) finishes the 1st year of physics knows that selection rules should be taken with a pitch of salt and pepper and that in principle corrections to perfect symmetries are always there: the operator in the middle has corrections, the wavefunctions are not perfect etc. Why am I giving now such a trivial example? I mean: spectroscopy??? Well, because the same thing happens in string theory: you cannot simply say you have a specific structure, say a monoid and whatever goes beyond that structure and is induced by who knows what “does not exist”… because that is NONSENSE!  

Holly crêpe!

Am I defending string theory? No way! This is why this will be a short post… Some people started saying that string theory “predicts” that gravity should be different at who knows what scales and because we measured gravity and it fits to what we know string theory is wrong! I am very short on this: THAT ARGUMENT IS TOTALLY WRONG!