Monthly Archives: February 2014

Computers in science

You may be using a computer… I am using one right now. It is a marvel of engineering, I have to say that. However, I am not a computer fan… I started looking at a Commodore 64 when I was 7 and I was pretty impressed by it at that time… By age of 15 I tried all possible games and now I don’t have a single game on my computer… (although from time to time I may look at an old web game, but “from time to time” 2 minutes every 6 months or so…) I dislike computer games all in all, although I programmed my own game when I was 16 and bored to hell during a summer… it was something very simple, a few rules for the movement of some objects and some deformations and some gravity but more or less that was it… I completely gave up computer languages and programming immediately after high school and I have no intention to return (except if starving or begging)… Why am I saying this? Well, my experience with formal languages is that they are incomplete and ill defined. Say, I believe there may exist a value of truth associated to a fact that cannot be proved in a specific set of axioms… I also believe that in some cases this value is not obtainable in a finite number of trivial computations as done today on those “pseudo-turing-machines”… I really don’t care about the fact that a truth characteristic is not provable in a finite set of operations. This is a very relative concept. First, it is not clear at all that we perform the same “operations” that we code into computers… Ever had an idea? I doubt you can explain operationally how you had it. Of course, if you work in programming most of your ideas are representable with a finite number of operations but that is selection bias. I had lots of ideas that connected different areas of knowledge that I wouldn’t be able to represent in any finite way in the sense of operations etc. However, this is not the main aspect… What I want to say here is that I dislike computers and programming and I am not even remotely interested in having anything to do with that. I also think that we should start focusing more on analytic solutions (whatever analytic may mean in 1000 years from now) instead of performing numerical, finite, perturbative and inexact computer calculations. At least at the level of research of nature…

The Pyramidal effect…

I don’t hate string theorists… I don’t hate string theory either… How could I? I don’t hate aether theories just because they are wrong… String theorists remind me of some presentations made by a funny company working on a pyramidal scheme… The advertisers of that company were honest persons really believing that what they were doing was “honest marketing” and that referring to the “higher hierarchy” was also rather OK when being asked uncomfortable questions… Details were overlooked and well… all the stuff of dishonest marketing was done with the belief that “that’s the way things work” and it is perfectly ok and no problem arises… Of course this was not so and nothing was legal in the way they operated… nor was it moral, honest etc. but the people doing it on the lower ranks believed they were doing a decent and honorable job… String theory is the same… Many people working on it live in the illusion that what they do is honest science… that you can just impose restrictions on reality based on inconsistencies in your theory. That in principle you can send supersymmetric partners to arbitrary high energies and masses without having any problems at all… etc. while having this as the “permanent job”… This is as if you worked for a fraudulent company having a “permanent job”… you might be ignorant and used/abused but still you don’t really do anything relevant except tricking people… Don’t get me wrong: you have to learn multidimensional analysis, algebraic geometry, topology, etc. too in order to do decent QFTs… you need to work with infinite dimensional algebras, etc. So, the basics used in string theory are useful nevertheless… The problem is that string theory “per se” is wrong… while the amount of valid science it incorporates is of course valid and OK… so, if you learn flux compactification you will certainly know how to work with multidimensional calculus in a decent way, which is ok… so, the underlying structures have to be learned… while keeping in mind that string theory is a naive and rather silly generalization to “string” objects that doesn’t solve any problem at all, even worse, it complicates problems and yes, string theory is not correctly quantified nor (as far as I suspect) quantifiable using the current techniques… So, string theory is not a good theory of quantum gravity because 1. It is not good, 2. it is not really quantum and 3. it doesn’t really give any results related to gravity except its existence… which, if I am not wrong, was rather known since ancient times… 

Do I know string theory?

Yes! I worked officially on it 2 years and unofficially another 5 years… I know it inside out and on most of its faces… I even know more about it than some string theorists specialized in, say, flux compactifications, which are in general ignoring other aspects, etc. The thing is, I am also asking some questions when someone tells me something… I generally don’t accept hand-waving arguments so I go home and think carefully about what has been said… sometimes hours, sometimes days, sometimes months… This is how I found out what algebraic topology says about some things related to string theory, this is how I found out how string theory is lacking all forms of unicity proofs… how assumptions are being made on no ground whatsoever… swiss cheese is the thing that resembles most to string theory as it is now… 

Is string theory “the new calculus”?

Well, no… it cannot be… the first calculus I know, defined by Newton and then refined by Leibnitz was rather cumbersome to work with but otherwise well defined… You cannot say the same thing about string theory. Its mathematical foundations are shaky at best and there are consistent imprecisions in the use of terms (to quote a few: flux compactification, compact spaces, string quantization, world sheet integral, perturbative expansion terms, topological series, closing conditions, etc.) In fact I am not sure there is anything well defined in string theory except the idea that there should be strings… While the basic idea of dimensional extension has found some very specific applications (see dimensional regularization, dimensional extension, retraction, etc.) I doubt quite a lot about the “mathematical consistency” of string theory whatsoever… 

The Third Law Of Thermodynamics

I think a good subject for today is the third law of thermodynamics in the context of condensed matter systems and AdS/CFT… 

I think it is widely known that the laws of thermodynamics have their origin in human frustration. That means, after years and years of trying to do something that appeared to be possible people realized it actually cannot be done, either because the scope was mistaken or the mere question being asked had no meaning at all… This is the same for the third law of thermodynamics. In principle it states that via continuous transformations of the state of the system you can get arbitrarily close to absolute 0 in temperature without ever crossing or reaching it. This means that by standard methods of decreasing the temperature you can get close to zero but as you go the difference in entropy becomes so small that you practically get very little decrease in temperature with very much effort… This also can be translated in the fact that at T->0 the difference in entropy goes to 0 or, otherwise stated, all systems condense into a specific state of entropy at absolute zero and that state cannot be reached by any practical means. Whatever the residual entropy is, you cannot reach it in a finite set of steps. For crystal-like objects the end value of the entropy is zero. For glasses it may not be zero but it still remains out of reach due to the difference in entropy being zero on any path going towards T=0

Why am I saying this now? Well, because in string theory the situation is drastically different. String condensates should be considered real and do reach the ground-state which represents a minimum in a set of lots of minima accessible to the system. The minimum of the system is not uniquely defined. In fact it is not defined at all as nobody knows a solution to the “dramatic” string-landscape problem of proliferation.
Now, don’t get me wrong, it’s a very good subject to do research on but the point is to correct the ideas behind string theory and to correct the way string theorists think about nature or about mathematics or both… it simply implies to correct the way string theorists think… but then again, for some unknown reason the situation is a bit the other way around: string theorists don’t really want to learn anything while they want to teach everyone a theory that doesn’t work… that’s a problem… So, stop thinking about string theory as the source of wisdom… it is more likely that non-string people are the source of wisdom for string theorists… it certainly was so in my case…

Holography

I said I am going to discuss today about why the holographic principle is wrong… then I started thinking about it and I observed this could become a rather interesting paper so I decided to keep it for me until it becomes public… ya’ know… being in business it’s not that everything should be public immediately and I do have this VERY bad habit to talk too much serious stuff… I have to train myself in saying nonsense so that a conversation can flow easily without saying anything too relevant… 

Anyways… 

The idea of holography has its origin in the physics of black holes (or at least in what is vaguely understood from the physics of black holes). There are several fundamental paradoxes that appear when putting together Hawking radiation and Einstein-Hilbert Black Holes… I use the name vaguely (you know Hawking and his radiation… maybe you don’t know Einstein and Hilbert but together they form the name for a pretty nice action functional you can write for gravity, although somehow out of fashion nowadays when only wormholes and black holes with alice and bob around are of any measurable sexyness)… However, the idea relates quantum field theories on one side, assumed to describe fields in space-time and to be compatible with special relativity (i.e. local lorentz invariance, LOCAL, ok?) and to derive the interactions between various particles and … no, not gravitation, or at least not directly… in fact it relates this with information, or entropy (lack of information, so to say). What means that? Essentially it means that QFT describes a system made up of some fictional fields that, after applying a specific formalism, can be used to calculate various cross sections and get measurable results… The fields in QFT are NOT observable, or not directly. What you observe in your detector is the result of an interaction of an outgoing particle with your detector… keep this in mind. So, what are the degrees of freedom of QFT? Well, infinity… we have fields… fields are continuous objects in space-time so they have a potentially infinite number of possible excitations… (but the quantum fields in QFT are NOT physical…) 

Now, let’s start exciting these fields and add energy in some region of space (I don’t care if the energy is in form of photons, electrons or whatever, as long as it is energy)… When you do this you may reach an energy in that region of space that ends up collapsing under its own gravity… if you continue exciting the quantum fields you get enough energy there so that a black hole appears… but, if Hawking is right, the entropy of the black hole scales like the area of its horizon. Area of horizon means R^2 and entropy means the logarithm of the number of microstates accessible to the system or the information “lost” or “unaccessible”… So, you get a horizon at the moment when you excite not all the possible states in a volume, but on an area that encompasses the region of space… First conclusion: the information is not encoded in the volume but on an area… 

Ok-ish… now, this is the “state of the art”, vaguely speaking… If you think now as I thought you to think you will see where the difficult spots are in this construction… I won’t say anything else…

 

 

Why is the holographic principle wrong?

Today I am a tiny bit more ambitious but with less time in the morning: Why is AdS/CFT wrong or at least incompatible with any practical situation I already explained… But what about the basics of it? The Holographic principle? Defended by almost all the “great physicists” today? The task of explaining this might look as impossible so I’ll have to take the whole evening today to do it… 🙂 

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…