Trantor is a ficticial planet presented in the Isaac Asimov series of books about the foundation. It is the centrer of a galactic imperia.
In that universe the king of sciences is psicohistory. By that name is referred a mathemathical model of human societies with detailed qualitative predictive power. Physics has become an obsolete discipline that had dead of success long time ago. Supposedly it had answered all the basic questions and no new important discovery had been made for hundreds of years.
But still there were some physicists. The problem with them is that the lack of new experimental results had resulted in a vicious system where the quality of one particular physicist depended on the knowledge of the achievements and, maybe, his ability to reinterpret them in new, basically irrelevant, ways that didn't lead to new discovering.
Well, that is fictional. But sometimes actual physics somewhat resemblances that trantorian physicists. Lot of people like to culprit string theory for that, but I don't agree at all, it is a problem common to all the alternatives.
I mean, what actual observable predictions make alternative theories?
LQG great achievement was the frequency depending speed of light. In fact Liouville strings also predicted that Well, FERMI/GLAST has almost ruled that possibility (although there is some discrepancy on the interpretation of results depending of who
writes about it, for example Lubos Motl and Sabine Hossenfander disagree, as always).
Horava's gravity, being as a classical theory slightly different from Einstein's gravity makes predictions not too hard to measure. But after the initial explosion of papers it is somewhat stopped now due to some papers that posed serious doubt about is goodness as a quantum theory despite being power counting renormalizable. It would have been nice to see how it was received in the actually developing strings 2009 conference, but this year there is no live broadcast nor, at least until now, none bloging about it.
Nonconmutative theories are also almost dead, despite they had some time of glory (although today, afther many months, there is a paper in arxiv in the subject http://arxiv.org/abs/0906.4727). There are two types of NCT theories, field theoretic ones, and geometric ones. The fist are inspired in string theory. The last ones re mainly geometric and were promoted by the mathemathician Alain Connes. They mde a firm prediction, a value for the Higgs mass, that was ruled out (at lest in the original way, I am not sure whether some modifications have been suggested) last year by measures of the tevatron.
So, basically, we have that despite many theoretical efforts in many different approaches to basic physic (i.e., particle physics) we have no new experimentally confirmed since the formulation of the standard model, in the last sixties and former seventies of the past century. The only new result was the confirmation that neutrinos have an small mass. The other experimental news come from cosmology, and, as I said in previous posts, are not so firm as laboratory experiments.
Is this a problem of theoretical physicists. I hardly think so. String theory is a very rich framework. Different aspects of them actually are promising candidates for phenomenology. For example the mesoscopic extra dimensions suggested by Arkani-Hammed et all in the last nineties was a very original idea, that has led to cheap experiments that had put new bounds on the size of that dimensions. LQG, as said did a good prediction (shared by most Lorentz violating theories) and LQC is trying to do observable predictions about cosmology, maybe not rigorous ones, but if the were observed none would care too much about it ;).
The big problem I see is not related to theory but to experiments. And, specially, to collider experiments. USA cancelled founds for a new linear accelerator in the nineties. The LCH schedule has seen almost five years of delay (that is, if finally beguines to operate in September, as expected). The tevatron has made it's bests, going beyond the expectations. It has showed that QCD at high temperatures behaves not as a quantum gas (as expected) but as a quantum liquid.That doesn't means new basic physics, but at least it gives clouds about the properties of QCD that are very hard to study mathematically and computationaly. And, hey, it has ruled out NCG ;-). Even there are some possibilities that a careful analysis of the collected data would find the Higss bosson. Not that bad for a recicled collider.
If there is no serious money inverted in experiments researchers are going to spend time in increasingly twisted theories. Internal coherence is a good guide, but it is not clear that that alleged coherence is so free of doubts as some people try to present it. That goes for LQG and for string theory (and the alternatives). Again that is not a reason to go again string theory (or the alternatives, well, some of the alternatives are theorethically unlikely, but still). The ultimate justification of the theoretical developments is that they re made searching for compatibility with known physics and also guessing new phenomenology. What is seriously need is that experiments would be made. The LHC is, hopefully, next to operate, but there s no serious project for the post LHC.
Maybe some people could think that there is no good reason to expend a lot of money in that expensive experiments. Specially not in the current economic crisis. In my opinion that is a narrow minded vision. Certainly other areas of physics are giving interesting results (solid state/condensed mater and the wide area know as nanotechnology) but they are based on very all basic physics. It is necessary to pursue the development of new physics. For example, one very important problem that the society need to face is the energy supply. There are discrepancies about how many fossil combustibles (specially at cheap prices) remain. In fact that depends heavily on the growth of demand. But sooner or later (and most likely sooner) they will extinct. The "ecological" alternatives (solar energy, wind, etc) are mostly propagandistic solutions. Nuclear energy has better chances, but it depends on a limited resource,uranium. Certainly there are proposals for fast breed reactors that could create fissible elements. But they are somewhat experimental. It is an open question where they will operate as expected. The other alternative, nuclear fusion is fine. But again governments are not spending enough money on it (as the fate of ITTER clearly shows).
The thing is that when we are looking for energy sources the best thing we can is understand how the universe behaves at high energies. If one looks at the way on how "energy sources" work one sees a common pattern. One has a two energy state system separated by a barrier where the difference of energy between the two states is greater than the energy of the barrier. If one supply the system with energy enough to go over the barrier when the system goes to the lower energy state it returns more energy than the employed one. That is the way chemical combustibles work. And also the way nuclear fission and fusion works. Nuclear process involve higher energies and so they return more energy also (well, in fact it could be otherwise, but it would be very unnatural).
Well, if we go to higher energies one expects that, somewhere, there will be some systems that share that property (a good name for it would be metastability).For example in some supersymmetric models there is, if R-symmetry is present, a lightest supersymmetric partner, LSP, which is stable, and a candidate for dark matter. And also there is the possibility of a NLSP (next to light supersymetric partner) that would be metastable. Well, that is the kind of thing we like. One would expect that there is a big energy difference among them. If they are found and it is discovered a way to force the decay of the NLSP into the LSP we would have an energy source. Moreover, dark matter represent the, 75%, 90%? of the mass of the universe. That could men that there is a lot of it out there. One could argue that if we are not able to do nuclear fusion, using known elements we badly could develop a technology to extract energy from something that is still hypothetical. But the truth is that we don't know. Maybe it is a lot easier to extract energy form dark matter (let it be (N)LSP, WIMPS or whatever) that from known sources.
Still there are other possibilities. There is an small possibility that if the LHC creates black holes it could also create wormholes. Wormholes (lorentzian ones) have received a lot of attention in SF as a tool for interstellar travel or even as time machines. But there are other interesting uses for them if they would actually exist. If one mouth of the wormhole is posed in a very energetic environment it could drive that energy onto the other mouth by a direct way. For example one could put one mouth deep inside the earth and the other in the surface. That would be a good way to extract geotermic energy. Of course one could think that is a lot more likely to use more conventional ways to get that energy, but still it could be not. Other very energetic environment would be the sun. It is not totally clear how much energy requires to create a wormhole, but one would expect that if the outer distance between the mounts growth the same applies to the required energy. But it could again not to be so. Still there is a problem in using the sun, the gravitational interaction. The gravitational field of the sun would be transferred together with light and it could alter the earth orbit.
There is a more interesting possibility for wormholes (or maybe we would call them warmholes, or not, depending on how one would worry about double meanings of words xD). If they are created at the LHC that would probably mean that the reason behind it is that mesoscopic extra dimensions exist. In string theory there are various ways to realize that sceneries. A common feature of many of them is that the would mean that we leave in a three dimensional (or effectively three dimensional) brane. But it is possible the existence of additional branes. It could be that some of them would have a high background energy. And it also could be that they would bee not too far away into that additional dimensions. Actually they could be so near that it wouldn't be improbable that a wormhole could be created with one mouth inside that hot brane and the other in ours. Still better, the sceneries with mesoscopic extra dimensions offer good possibilities for wormholes becoming stable. That would rise the possibilit to use that wormholes to extract energy from that hot branes. Depending on the details they could be a mean to solve all the energy requirements of the human kind at a level that exceeds all the actual xpectations.
All the hipothethical energy sources that I have presented are related to string theory likely situations. Alternative theories maybe also would offer options. For example black holes in alternative theories could not evaporate completely and one could use the remanents to extract energy from them in Penrose lie process. A serious problem with it is that without mesoscopic dimensions there is no way to create black holes in the LHC so we woudn't have remanents either.
By the way, black hole physics is a very good example of trantorian physisic. Specially the black holes inners. The gravity/LQG community has a, widely accepted, viewpoint of them where the radius behaves as a time coordinate. Well, in string theory there are very different proposals, none of them too friendly with that LQG viewpoint. Also the string theory strongly supports the complementary principle. Well, some people in LQG don'even know of it's existence (or at least not until they published a paper that was incompatible with that principle). My problem with this is that we don't have a near black hole to do experimental tests. In fact even if we would create them into the LHC it is not clear that we could make experimental tests about black hole inners. Neither is too clear how that black hole inners have any consequence into the behaviour of the event horizon. Well, if naked singularities are allowed the thing would improve, but then they wouldn't be black holes ;-).
Well, certainly in this post, apart of some sociological consideratins, I have presented very speculative ideas with two few details about them. Maybe that is what top notch physicist do in trantor. Not being there I hope to present more earth based physic in next entries ;-).
By the way, if one is absolutely serious about it many proposal for alternative "ecological" energy sources are actually less unlikely to be good alternatives to oil that the ones I have proposed here. They look otherwise because they are based in things that laymen think that they understand, but if one goes into the details of the implied physics one really hope that wormholes actually exists xD.
Friday, June 26, 2009
Thursday, June 04, 2009
String theory is good for...phenomenology of particle physics
Yesterday the number of visits to this blog had a major increase. Most of the traffic came from this post in Miguis web/blog.
The post was a translation to Spanish of an article in new scientist about the good points of string theory. I had seen a discussion of that article in Lubos blog, concretely here.
Well, that article comes to say that string theory is nowadays a good theory because it´s math structure, through the AdS/CFT correspondence is useful in QCD and condensed matter physics. Well, I don't know too much about that applications but if the experts in that subjects say so is a good sign.
But, actually, I don't think that that image is quite right nowadays. Readers of this blog know that I have played attention to many alternative theories. Some of the proponents of that theories make claims against string theory. Others, who don't actually offer any theory, that is, Peter Woit, claims that string theory "makes no predictions". In his blog he usually bring attention mostly to the most speculative articles written by string theorists.
Well, I am following, as much as I can, the actual F-theory minirevolution. Doing so I have become very surprised, and impressed, by how close string theory has become of actual physics. Before going into it I must say that I somewhat understand the sceptics in string theory. If one reads the books on the subject one certainly gets the impression that actual predictions are far away. For example the 1999 (that is, not too old) book of Michio Kaku Introduction to superstrings and M-theory in its chapters about phenonenology show the results of heterotic compactifications. In that results the best one could get were the standard model plus some additional U(1) factors. Also it was stated that to achieve the right number of generations , given by n=1/2X(Cy), that is, one half of the Euler characteristic of the Calabi-Yau mainfold, was difficoult (if not almost impossible).
Other books, as Polchinsky´s two volumes book and the Clifford Jones "D-branes" don't say too much about realistic compactifications. There are good reasons for that. The books are mostly concerned about the D-brane revolutions and its consequences, the black hole entropy calculation and the AdS/CFT conjecture. The most recent book of Becker-Becker-Schwartz makes more in deep cover of compactifications. But , with a good criteria, somewhat cares more about technical issues such as the moduli space of the compactification, mirror symmetries among type II A and type II B, and flux compactifications, which are relevants for the very important issue of moduli stabilization and the KKLT like models (related to the landscape). And , of course, the all make introductions to dualities, M theory, and , to a least extent, F-theory.
In fact all that are important technical aspects, and it requires time to learn them (one must read some articles if he really wants to properly understand some aspects). But one gets the impression that everything is still to far from LHC phsyics and cosmology testable predictions. In fact there is a very recent book, by a Michel Dine which goes into phenomenology title "supersymmetry and superstrings". I must say that I find that book somewhat failed. It is to brief covering subjects that even with some previous knowledge are hard to appreciate properly.
Well, in definitive, a lot of text books and no a clear signal of actual testable physics. Certainly discouraging. Divulgative books are not too different. That, certainly, can explain why some people has the impression that string theory is far from it's objectives. Blogs from string theorists try to say, to whoever listen them, that string theory is "the only game in town". In fact there are not many blogs in string theory with a decent publication rate. However I had also the idea that string theory was far of phenomenology, and I had not purchased too mcuh that topic.
F-theory minirevolution has changed that. I have read at last the two big pioneer papers of Vafa (arXiv:0802.3391v1 and arXiv:0806.0102v1), and almost completed the reading of the F-theory Guts cosmology (arXiv:0812.3155v1). Also I have made partial readings of some subsequent papers, and a few previous papers needed to understand the formalism developed.
Certainly are hard to understand papers. But once one gets familiar with them one sees what kind of physics is discussed. The first thing to say is one need to know the details of GUT's and symmetry (and supersymmetry) breaking. F-theory local models, with the right decoupling from gravity, can give an SU(5) model, without any exotics. They offer it's own way to break SU(5) into the MSSM, through an U(1) flux of hyperchrge, That mechanism avoids some of the problems presents in purely field theoretic models. In particular they can avoid problems with the observed lifetime of the proton. Ulterior papers get values in the CKM matrix that are good to get the observed asymetry oof baryons in universe. They offer ways to advoid the singlet-tripplet spliting problem of GUT's (That is, requiring the existence of Higgs doublets (1, 2)±1/2 leads necessarily also to color triplets. However, there exist rather uncomfortable lower bounds on the mass of these triplets). They offer a natural way to get small neutrino masses. In cosmology, trough a late decay of the saxion (whose lifetimem is predicted, that is, properly bounded, by the theory), they can avoid some of the problems that symmetry breaking bring to cosmology (the gravitino problem) and gives a righ way to obtain reheating after an inflactionary phase and some extra things that I haven't finished to read.
As you can see these models are quite near the cutting edge phenomenology. They offer solutions to problems not available by other approaches. And F-theory is not alone. Seemingly M-theory is going also into the local models + gravity decoupling business, see for example the paper Hitchin’s Equations and M-Theory Phenomenology by Tony Pantev and Martijn Wijnholt.
As I said I hadn't followed previously phenomenology with too much attention. But, in fact, more traditional approaches also had made some advances. For example this 2008 short review article of heterotic compactifications, From strings to the MSSM also cares about some of the previously mentioned aspects.
Another very recent paper, Towards Realistic String Vacua From Branes At Singularities, by Joseph P. Conlon, Anshuman Maharana, Fernando Quevedo, use the D-brane approach to phenomenology, not related to the gravity decoupling approach. They offer the bonus of moduli stabilization (something more habitual in cosmological models). In the abstract the conclude saying: "We propose that such a gauge boson could be responsible for the ghost muon anomaly recently found at the Tevatron’s CDF detector". Well, there some serious doubts about the real existence of that anomalies (see the tomasso dorigo´s blog, linked in this web site, and search for discussion of that topic).
Well, certainly there are a few bunch of models inspired by string theory, and not all of them (if any) can be truth at once. Also not all models make firm predictions. But the point is that they are actually reproducing the MSSM, GUT´s supersymmetric models, and mechanism to enhance the purely particle physics models. Also , in cosmology there are many different points where string is enhancing purely field theoretic models.
But, such as I see it, string theory is actually dictating the construction of (at least some of) the models that are going to be checked in the near future. Also one must not forget about the RS models, inspired by string theory, where one could get black holes in the LHC (that models possibly are not compatible with F-theory GUTs).
With all of this I think that string theory is doing exactly what one would expect from a traditional fundamental theory of physics such it has been made traditionally. Certainly I am talking about very, very, recent developments, most of them from this year and the previous one. But, anyway, it looks like if string theory is definitively "landing" into experimental physics, that is what it was expected from it. And, still, it is doing progress into clarifying it`s theoretical aspects, and the description of black holes (a topic not too easy to study in laboratory, except if LCH produce black holes, that is).
I am not at all a radical and I understand if some people wants to keep doing alternative approaches. The point of this post is to say that, as far as I see, the "not even wrong" criticism of string theory doesn't make too much sense nowadays.
And please, remember that I am not in a faculty position getting money from doing research in string theory. I have no economic, doctrinal or political reason to favour one theory or another. It is just that, according to what I know just now, string theory seems a perfectly good theory for doing high energy physics, and I have tried to explain why.
The post was a translation to Spanish of an article in new scientist about the good points of string theory. I had seen a discussion of that article in Lubos blog, concretely here.
Well, that article comes to say that string theory is nowadays a good theory because it´s math structure, through the AdS/CFT correspondence is useful in QCD and condensed matter physics. Well, I don't know too much about that applications but if the experts in that subjects say so is a good sign.
But, actually, I don't think that that image is quite right nowadays. Readers of this blog know that I have played attention to many alternative theories. Some of the proponents of that theories make claims against string theory. Others, who don't actually offer any theory, that is, Peter Woit, claims that string theory "makes no predictions". In his blog he usually bring attention mostly to the most speculative articles written by string theorists.
Well, I am following, as much as I can, the actual F-theory minirevolution. Doing so I have become very surprised, and impressed, by how close string theory has become of actual physics. Before going into it I must say that I somewhat understand the sceptics in string theory. If one reads the books on the subject one certainly gets the impression that actual predictions are far away. For example the 1999 (that is, not too old) book of Michio Kaku Introduction to superstrings and M-theory in its chapters about phenonenology show the results of heterotic compactifications. In that results the best one could get were the standard model plus some additional U(1) factors. Also it was stated that to achieve the right number of generations , given by n=1/2X(Cy), that is, one half of the Euler characteristic of the Calabi-Yau mainfold, was difficoult (if not almost impossible).
Other books, as Polchinsky´s two volumes book and the Clifford Jones "D-branes" don't say too much about realistic compactifications. There are good reasons for that. The books are mostly concerned about the D-brane revolutions and its consequences, the black hole entropy calculation and the AdS/CFT conjecture. The most recent book of Becker-Becker-Schwartz makes more in deep cover of compactifications. But , with a good criteria, somewhat cares more about technical issues such as the moduli space of the compactification, mirror symmetries among type II A and type II B, and flux compactifications, which are relevants for the very important issue of moduli stabilization and the KKLT like models (related to the landscape). And , of course, the all make introductions to dualities, M theory, and , to a least extent, F-theory.
In fact all that are important technical aspects, and it requires time to learn them (one must read some articles if he really wants to properly understand some aspects). But one gets the impression that everything is still to far from LHC phsyics and cosmology testable predictions. In fact there is a very recent book, by a Michel Dine which goes into phenomenology title "supersymmetry and superstrings". I must say that I find that book somewhat failed. It is to brief covering subjects that even with some previous knowledge are hard to appreciate properly.
Well, in definitive, a lot of text books and no a clear signal of actual testable physics. Certainly discouraging. Divulgative books are not too different. That, certainly, can explain why some people has the impression that string theory is far from it's objectives. Blogs from string theorists try to say, to whoever listen them, that string theory is "the only game in town". In fact there are not many blogs in string theory with a decent publication rate. However I had also the idea that string theory was far of phenomenology, and I had not purchased too mcuh that topic.
F-theory minirevolution has changed that. I have read at last the two big pioneer papers of Vafa (arXiv:0802.3391v1 and arXiv:0806.0102v1), and almost completed the reading of the F-theory Guts cosmology (arXiv:0812.3155v1). Also I have made partial readings of some subsequent papers, and a few previous papers needed to understand the formalism developed.
Certainly are hard to understand papers. But once one gets familiar with them one sees what kind of physics is discussed. The first thing to say is one need to know the details of GUT's and symmetry (and supersymmetry) breaking. F-theory local models, with the right decoupling from gravity, can give an SU(5) model, without any exotics. They offer it's own way to break SU(5) into the MSSM, through an U(1) flux of hyperchrge, That mechanism avoids some of the problems presents in purely field theoretic models. In particular they can avoid problems with the observed lifetime of the proton. Ulterior papers get values in the CKM matrix that are good to get the observed asymetry oof baryons in universe. They offer ways to advoid the singlet-tripplet spliting problem of GUT's (That is, requiring the existence of Higgs doublets (1, 2)±1/2 leads necessarily also to color triplets. However, there exist rather uncomfortable lower bounds on the mass of these triplets). They offer a natural way to get small neutrino masses. In cosmology, trough a late decay of the saxion (whose lifetimem is predicted, that is, properly bounded, by the theory), they can avoid some of the problems that symmetry breaking bring to cosmology (the gravitino problem) and gives a righ way to obtain reheating after an inflactionary phase and some extra things that I haven't finished to read.
As you can see these models are quite near the cutting edge phenomenology. They offer solutions to problems not available by other approaches. And F-theory is not alone. Seemingly M-theory is going also into the local models + gravity decoupling business, see for example the paper Hitchin’s Equations and M-Theory Phenomenology by Tony Pantev and Martijn Wijnholt.
As I said I hadn't followed previously phenomenology with too much attention. But, in fact, more traditional approaches also had made some advances. For example this 2008 short review article of heterotic compactifications, From strings to the MSSM also cares about some of the previously mentioned aspects.
Another very recent paper, Towards Realistic String Vacua From Branes At Singularities, by Joseph P. Conlon, Anshuman Maharana, Fernando Quevedo, use the D-brane approach to phenomenology, not related to the gravity decoupling approach. They offer the bonus of moduli stabilization (something more habitual in cosmological models). In the abstract the conclude saying: "We propose that such a gauge boson could be responsible for the ghost muon anomaly recently found at the Tevatron’s CDF detector". Well, there some serious doubts about the real existence of that anomalies (see the tomasso dorigo´s blog, linked in this web site, and search for discussion of that topic).
Well, certainly there are a few bunch of models inspired by string theory, and not all of them (if any) can be truth at once. Also not all models make firm predictions. But the point is that they are actually reproducing the MSSM, GUT´s supersymmetric models, and mechanism to enhance the purely particle physics models. Also , in cosmology there are many different points where string is enhancing purely field theoretic models.
But, such as I see it, string theory is actually dictating the construction of (at least some of) the models that are going to be checked in the near future. Also one must not forget about the RS models, inspired by string theory, where one could get black holes in the LHC (that models possibly are not compatible with F-theory GUTs).
With all of this I think that string theory is doing exactly what one would expect from a traditional fundamental theory of physics such it has been made traditionally. Certainly I am talking about very, very, recent developments, most of them from this year and the previous one. But, anyway, it looks like if string theory is definitively "landing" into experimental physics, that is what it was expected from it. And, still, it is doing progress into clarifying it`s theoretical aspects, and the description of black holes (a topic not too easy to study in laboratory, except if LCH produce black holes, that is).
I am not at all a radical and I understand if some people wants to keep doing alternative approaches. The point of this post is to say that, as far as I see, the "not even wrong" criticism of string theory doesn't make too much sense nowadays.
And please, remember that I am not in a faculty position getting money from doing research in string theory. I have no economic, doctrinal or political reason to favour one theory or another. It is just that, according to what I know just now, string theory seems a perfectly good theory for doing high energy physics, and I have tried to explain why.
Monday, June 01, 2009
Quick ideas to become a cosmology atheist
As I said in the other post, and not for the first time, I don't take cosmology too seriously. I find that there are many uncertainties in the observed data and also in the interpretations. Because of that I hadn't bothered to think too much about that questions.
In the last post Kea sugested me to read the Louise Riofrio theory, which resulted to be a version of the VSL (variable speeds of light) cosmologies. I have partially readed some of their statements, and also made the usual googling abbout the topic. The first thing that one finds is a mention of Von Riemman space. Well, I have no idea of what that is supposed to be. of course that could be because iI am not spetialist in the field so I googled for it and Ireached a physiscs forum's thread where other people also agreed that they didn't know it. Well, there som other points in her papers whose motivation I don't see clear. Beeing so I can't say too much else about the general theory
Another apect where she seems to see a point, independent of the general model, favouring her theory of a VSL is the following argument. In some epoch ths sun , according the standard model o solar evolutions, radiates a 75% of the energy that it radiates now. Ok, according to that she claims that earth should be a ice ball contradicitng the fact that there was life in it. The VSl solves the problem because someway the VSl implies tht the sun luminosity should be corrected to the right factor.
Without going into the detaill I must say that I find very unlikely that conventinal astronomy wouldn't have considered that possibbility before. Also there is another consideration. Earth is hot by itself. The friction energy that leaded to it's formation is accumulted inside it. In the XIX there was a controversy among the geologists and a prominent physics I don't remember for sure but I think that it was kelvin). The geological observations dated the antiquitie of earth in a number of years that was imcompatible with its temperature. Using the heat equation and the conventional data for earth materials one could see that earth would have frozen long time sooner that the age estimated bby the geologists. Later Somerfeld said that the reconciliation of the two viewpoints was the prsence of radiactive materials inside earth. Beeing sommerfeld such a well qualified physicist the argument was accepted as valid withouth criticism.
Well, in fact if one does the actual calculationsit can be shown that the radiactive materials are not enought to achieve the hotting of earth,. The reaosn earth is still hot (inthe outside) is that the heat equation used by Kelvin was not right. One needs to consider also trasnport phenomena, that is, convection. Doing so
it canbe shown that earth is hot bbecause of it's inner hot adquired within it's formatioin.
Beeing so I am not sure of how much of the riofrio argument makes too much sense. Also I find that history interesting because it whos explicitly how cautous one must be with arguments not based in observations made inlaboratory controlled conditions. Simply there are too many uncertaintiees.
Well, It has coincided that this mount the spanish edition of scientific american has an article where the cosmological arguments leading to the cosmological constant where revised. Being a divulgative article, that is, easy to read, I did so (it didn't take too mcuh time) The idea is that the observational reason why we belive univserse is expanding aceleratedly is that we see that far supernovaes light arrives to us with less intensity that what it would be expected from it's red shift it the univserse would be under a decelerating FRW (Friedman-Robertson-Walker) expansion. In the article they offert an alternative explanation. They say that it we would be in a particularly empty region of space-time the local decelartion of the universe would be slowest here that in distant points (for example the points near the observed supernovae. It contraicts the copernican principle that says that we are not in a particular place in space time. But tht can be circunvated in a natural way. If in the early universe there would e a random distribution of density inhomogenities that respected that principle the evolution would make that the less dense parts would increase it's size bby a factor ggreater than the more dense ones. In that way it would be mor probable that we would be in a relatively empty region of the universe. The last part of the argument is very similar to the nucleation mechanism that susskind used to explain the cosmological constant (but there are also diferences, of course).
Well, afther reading all that I wondered if I myself could ideate a mechanism to go agains the conventional big bang + inflaction scenary. Well, indeed I could.
The firs thing I did is to think about how fiabble is the red shit factor. Certainly the usual idea, that the expansion of universe generatees red shit is reaonable. And things like the BBN (big ang nucleosinthesys) respald that oservation. But the thing is that maybe there are aditional contributions to red shift. I have not had time to thnk for detailed mechanims. One of the first things that I have thought is that photons have mass. To be more explicit they have energy, and energy is a source of gravitation. One traditional way to put maths on that idea is to asign a mass to the photon MUhV whre v is it's frecuency. Themetiric corresponding to that mas is the Aichelbburg-Sexl solution (basically a Lorentz boost to v=c of the Schwarschild solution). Once one realizes that photons can radiate (and that they indded should radiate) one can think that it must llose energy. That loose would mean an aditional red shift. Ok, one could do the calculation for four dimensions, but that's not the whole history. If one thinks of a Randal-Sundrum like scnary one could expec that there is aditionanl radiation of energy to the one corrspoonding to four dimensions, that is, some energy would be radiated to the bulk. The RS scenary means that there are a range of possible values to the radiated energy that could be used to fit observations (that is, the aditioal red shiths would mean that the univser could have n smaller size that the expected oneand so advoid the problem of thermaliztion of causally disconected zones, usually solved by inflation, or, in other non-sntandrd scenaries, bby VSL). It also has another point. The warp factor could be variating in time. That could mean that the radiated energy could have been greater in the past and that would explain the cosmological constant. This is a particlar mechanis for aditional distant depending red shift, but surely one could guess many others I think.
Well, surelly there are drawacks in the argument.But I have used around an hour to think about the question. I think that for the inverted time I have got a well sounding arguments (certainly there are many imprecisions on the exposed arguments, don't look at them as definitive serious proposals). I have also imaginated another possibility, but it sounds less convincing. Well, don't take the idea too seriously (althought I don't totally dislike it as an a priory total crap one). But the point is that if in so short time ihave ideated an alternative to the standard scenary, even if it is false, possibly there are ther many more options.
Update:
1)Not too surprisingly my idea about additional redshift for photons was not new. It dates back to as soon as 1929 made by Fritz Zwicky. See the entry Tired Light in wikipedia for additional details. To be honest my idea has some differences with that proposals. To beguine with I didn't intend to create an alternative to the BBT but to modify it by a small amount. ON the other hand the kind of ways I had thought for the tired light phenomena where very different to what is exposed in wikipedia. The main objection I have read there is that there is no observed redshift for photons within our galaxy and any tired light mechanism would operate in it, and not only in the light from distant galaxies. Maybe I'll make some additional thinking about this topic, to see if the diferences in my proposals save something, but the proposal very probably will dimmer without success.
Anyway, it was only a quick idea. It is not bad to see that it has been considered before by important people. Also it means that the BBT is solid enough to resist elementary attacks. Still the arguments of the scientific american article keep making some sense. Also applies to the uncertainties in the nature of CMB anisotropy explained in the previous entry.
2) For VSL theories you can see this recent post (not the first one he does) about the toic on Lubos blog
In the last post Kea sugested me to read the Louise Riofrio theory, which resulted to be a version of the VSL (variable speeds of light) cosmologies. I have partially readed some of their statements, and also made the usual googling abbout the topic. The first thing that one finds is a mention of Von Riemman space. Well, I have no idea of what that is supposed to be. of course that could be because iI am not spetialist in the field so I googled for it and Ireached a physiscs forum's thread where other people also agreed that they didn't know it. Well, there som other points in her papers whose motivation I don't see clear. Beeing so I can't say too much else about the general theory
Another apect where she seems to see a point, independent of the general model, favouring her theory of a VSL is the following argument. In some epoch ths sun , according the standard model o solar evolutions, radiates a 75% of the energy that it radiates now. Ok, according to that she claims that earth should be a ice ball contradicitng the fact that there was life in it. The VSl solves the problem because someway the VSl implies tht the sun luminosity should be corrected to the right factor.
Without going into the detaill I must say that I find very unlikely that conventinal astronomy wouldn't have considered that possibbility before. Also there is another consideration. Earth is hot by itself. The friction energy that leaded to it's formation is accumulted inside it. In the XIX there was a controversy among the geologists and a prominent physics I don't remember for sure but I think that it was kelvin). The geological observations dated the antiquitie of earth in a number of years that was imcompatible with its temperature. Using the heat equation and the conventional data for earth materials one could see that earth would have frozen long time sooner that the age estimated bby the geologists. Later Somerfeld said that the reconciliation of the two viewpoints was the prsence of radiactive materials inside earth. Beeing sommerfeld such a well qualified physicist the argument was accepted as valid withouth criticism.
Well, in fact if one does the actual calculationsit can be shown that the radiactive materials are not enought to achieve the hotting of earth,. The reaosn earth is still hot (inthe outside) is that the heat equation used by Kelvin was not right. One needs to consider also trasnport phenomena, that is, convection. Doing so
it canbe shown that earth is hot bbecause of it's inner hot adquired within it's formatioin.
Beeing so I am not sure of how much of the riofrio argument makes too much sense. Also I find that history interesting because it whos explicitly how cautous one must be with arguments not based in observations made inlaboratory controlled conditions. Simply there are too many uncertaintiees.
Well, It has coincided that this mount the spanish edition of scientific american has an article where the cosmological arguments leading to the cosmological constant where revised. Being a divulgative article, that is, easy to read, I did so (it didn't take too mcuh time) The idea is that the observational reason why we belive univserse is expanding aceleratedly is that we see that far supernovaes light arrives to us with less intensity that what it would be expected from it's red shift it the univserse would be under a decelerating FRW (Friedman-Robertson-Walker) expansion. In the article they offert an alternative explanation. They say that it we would be in a particularly empty region of space-time the local decelartion of the universe would be slowest here that in distant points (for example the points near the observed supernovae. It contraicts the copernican principle that says that we are not in a particular place in space time. But tht can be circunvated in a natural way. If in the early universe there would e a random distribution of density inhomogenities that respected that principle the evolution would make that the less dense parts would increase it's size bby a factor ggreater than the more dense ones. In that way it would be mor probable that we would be in a relatively empty region of the universe. The last part of the argument is very similar to the nucleation mechanism that susskind used to explain the cosmological constant (but there are also diferences, of course).
Well, afther reading all that I wondered if I myself could ideate a mechanism to go agains the conventional big bang + inflaction scenary. Well, indeed I could.
The firs thing I did is to think about how fiabble is the red shit factor. Certainly the usual idea, that the expansion of universe generatees red shit is reaonable. And things like the BBN (big ang nucleosinthesys) respald that oservation. But the thing is that maybe there are aditional contributions to red shift. I have not had time to thnk for detailed mechanims. One of the first things that I have thought is that photons have mass. To be more explicit they have energy, and energy is a source of gravitation. One traditional way to put maths on that idea is to asign a mass to the photon MUhV whre v is it's frecuency. Themetiric corresponding to that mas is the Aichelbburg-Sexl solution (basically a Lorentz boost to v=c of the Schwarschild solution). Once one realizes that photons can radiate (and that they indded should radiate) one can think that it must llose energy. That loose would mean an aditional red shift. Ok, one could do the calculation for four dimensions, but that's not the whole history. If one thinks of a Randal-Sundrum like scnary one could expec that there is aditionanl radiation of energy to the one corrspoonding to four dimensions, that is, some energy would be radiated to the bulk. The RS scenary means that there are a range of possible values to the radiated energy that could be used to fit observations (that is, the aditioal red shiths would mean that the univser could have n smaller size that the expected oneand so advoid the problem of thermaliztion of causally disconected zones, usually solved by inflation, or, in other non-sntandrd scenaries, bby VSL). It also has another point. The warp factor could be variating in time. That could mean that the radiated energy could have been greater in the past and that would explain the cosmological constant. This is a particlar mechanis for aditional distant depending red shift, but surely one could guess many others I think.
Well, surelly there are drawacks in the argument.But I have used around an hour to think about the question. I think that for the inverted time I have got a well sounding arguments (certainly there are many imprecisions on the exposed arguments, don't look at them as definitive serious proposals). I have also imaginated another possibility, but it sounds less convincing. Well, don't take the idea too seriously (althought I don't totally dislike it as an a priory total crap one). But the point is that if in so short time ihave ideated an alternative to the standard scenary, even if it is false, possibly there are ther many more options.
Update:
1)Not too surprisingly my idea about additional redshift for photons was not new. It dates back to as soon as 1929 made by Fritz Zwicky. See the entry Tired Light in wikipedia for additional details. To be honest my idea has some differences with that proposals. To beguine with I didn't intend to create an alternative to the BBT but to modify it by a small amount. ON the other hand the kind of ways I had thought for the tired light phenomena where very different to what is exposed in wikipedia. The main objection I have read there is that there is no observed redshift for photons within our galaxy and any tired light mechanism would operate in it, and not only in the light from distant galaxies. Maybe I'll make some additional thinking about this topic, to see if the diferences in my proposals save something, but the proposal very probably will dimmer without success.
Anyway, it was only a quick idea. It is not bad to see that it has been considered before by important people. Also it means that the BBT is solid enough to resist elementary attacks. Still the arguments of the scientific american article keep making some sense. Also applies to the uncertainties in the nature of CMB anisotropy explained in the previous entry.
2) For VSL theories you can see this recent post (not the first one he does) about the toic on Lubos blog
Monday, May 25, 2009
The danger with cosmological arguments
I had said it before, but a new article, well, in fact two of them, almost consecutives, in arxiv, commented in the arxiv blog, brings again alive the question.
My point was to state that although cosmology is a legitimate topic, and that it has seen a fructiferous interplay with particle physic(in, for example, the BBN-big bang nucleosynthesis) cosmological observations are subject to many uncertainties. In my opinion that implies that one shouldn't sacrify the coherence and "physic common sense" of a theory it if not match some particular cosmological observation.
In particular I find that the problem of the cosmological constant is not enough reason to go into the landscape/anthropic scenery.
In the article Giant Lens May Be Distorting Echo of the Big Bang, based in the arsiv paper A Heliosheath Model for the Origin of the CMB Quadrupole Moment is stated that the analysis of the data send by the sputnik satellites when the left the solar system reveals that possibly the observed anisotropies in the CMB observed by COBE and WMAP could have an astrophysical origin, in the out shells of the solar system, and they don´t reflect a real cosmological anisotropy. that is certainly very important because the recently launched PLANCK and HERSCHELL satellites are supposed to make a better measure of that polarizations. Supossedly the sensitivity of that measures would allow to tests some models of inflation. But if the measured quantities are of astrophysical origin the utility of the whole busines would change radically.
Today other article claim to have a model for the accelerated cosmological expansion baed on five foreces actin in long ranges (but in not shor ones). Certainly it is not the first, and it will not be the last, article who proposes an alternative to the cosmological constant. For example, as far as I know models based in "quintaessence" are not ruled out. I personally find unnecessary to go into the landscape when it is reasonable to expect better explanations for the observed expansion of the universe. And, well, as the previous article clearly shows it is a good idea to be cautious about the accuracy and veracity of cosmological data.
My point was to state that although cosmology is a legitimate topic, and that it has seen a fructiferous interplay with particle physic(in, for example, the BBN-big bang nucleosynthesis) cosmological observations are subject to many uncertainties. In my opinion that implies that one shouldn't sacrify the coherence and "physic common sense" of a theory it if not match some particular cosmological observation.
In particular I find that the problem of the cosmological constant is not enough reason to go into the landscape/anthropic scenery.
In the article Giant Lens May Be Distorting Echo of the Big Bang, based in the arsiv paper A Heliosheath Model for the Origin of the CMB Quadrupole Moment is stated that the analysis of the data send by the sputnik satellites when the left the solar system reveals that possibly the observed anisotropies in the CMB observed by COBE and WMAP could have an astrophysical origin, in the out shells of the solar system, and they don´t reflect a real cosmological anisotropy. that is certainly very important because the recently launched PLANCK and HERSCHELL satellites are supposed to make a better measure of that polarizations. Supossedly the sensitivity of that measures would allow to tests some models of inflation. But if the measured quantities are of astrophysical origin the utility of the whole busines would change radically.
Today other article claim to have a model for the accelerated cosmological expansion baed on five foreces actin in long ranges (but in not shor ones). Certainly it is not the first, and it will not be the last, article who proposes an alternative to the cosmological constant. For example, as far as I know models based in "quintaessence" are not ruled out. I personally find unnecessary to go into the landscape when it is reasonable to expect better explanations for the observed expansion of the universe. And, well, as the previous article clearly shows it is a good idea to be cautious about the accuracy and veracity of cosmological data.
Thursday, May 14, 2009
Prehistory of the F-theory GUTs (mini?)- revolution
After an intensive training in algebraic geometry and the reading of the use of type II-B/F-theory in cosmology (KKLT, moduli stabilization and all that) I tried to do a direct attack to the two papers that initiated the F-theory revolution.
I had read generic aspects of them in the Lubos and Distler's blogs (well, Distler is actually disappeared and only put an entry about the first paper, this). I also found useful an entry in U-duality blog linking a paper of Schwartzabout the status of superstring theory, this entry
Well, my attack flailed miserably. I remotely understood some of the statements but I didn´t understand where they come from. I needed to go to the bibliography of the Vafa et all papers. I also have found clarifying some hints in follow up papers.
The first thing that I needed to understand properly is what a local model is. The proposal of local models seems to be born in a paper by (mostly) Spanish string theorist´s: G. Aldazabal1, L. E. Ib´a˜nez2, F. Quevedo3 and A. M. Uranga in the paper D-Branes at Singularities : A Bottom-Up Approach to the String Embedding of the Standard Model
The idea is to do instead of a top-down approach, that is, choose a compactification, study the resulting physic and see how well it matches the MSSM (minimal supersymmetric standard model) or something resembling the known physic one does a bottom up approach. It consists of two steps (I cite form the paper):
i) Look for local configurations of D-branes with worldvolume theories resembling
the SM as much as possible. In particular we should search for a gauge group SU(3) ×
SU(2) × U(1) but also for the presence of three chiral quark-lepton generations. Asking
also for D = 4 N = 1 unbroken supersymmetry may be optional, depending on what
our assumptions about what solves the hierarchy problem are. At this level the theory
needs no compactification and the D-branes may be embedded in the full 10-dimensional
Minkowski space. On the other hand, gravity still remains ten-dimensional, and hence
this cannot be the whole story.
ii) The above local D-brane configuration may in general be part of a larger global
model. In particular, if the six transverse dimensions are now compactified, one can in
general obtain appropriate four-dimensional gravity with Planck mass proportional to the
compactification radii.
In that paper the fields come form D-bran physics, i.e. open strings ending on the branes. They consider the branes suited at singularities of an orbifold. In F-Theory (and also M-theory) that approach takes a much more difficult form, but the idea is the same.
By the way, the idea of local models has had some development outside of the F-theory revolution, see for example Building the Standard Model on a D3-brane, by the Verlinde brothers. In general that attempts were influenced by the paradigm of D-brane intersections (of which I don´t know too much neither).
Almost at the same time that the now famous Vafa papers it appeared in arxiv another paper on model building with F-theory by Ron Donagi and Martijn Wijnholt (arXiv:0802.2969v2). I find that paper very illuminating. It explains in a very accessible way many facts of F-theory. For example the difference of the 7-brane of F-theory, which is not necessarily an D-brane but instead is a brane where a (p,q) string can end. It also clarifies the geometric idea behind the local model approach and gives intuitions on how gauge matter can appears, based in considerations of the supersymetry limit of F-theory.
I still haven't read all the paper. But in some point it talks about some of the other hard to follow questions of the F-theory revolution, the subject of ADE groups and it's relation to algebraic geometry and, in particular, the Kodaira classification of singularities.
That topic is covered in some early (mid nineties) papers of Vafa, for example Geometric Singularities and Enhanced Gauge Symmetries or Matter From Geometry
I am still trying to catch many aspects of how that works, but I believe that the essence of the argument is that F-theory and M-theory are related by dualities. Compactifiying F-theory in K3 surfaces (complex two dimensional Calabi-Yaus) is equivalent to compactify M-theory in a torus. The spectra of M-theory is easy to obtain and, by duality, one gets an idea of the particle spectra in F-theory and how it relates to the structure of the singularities. actually it is more complicated that that, and one must see how the idea holds in realistic compactifications. By the way, that work was previous to the local model engineering approach.
In this approach of F-theory the local model idea morphs into what is known as gravity decoupling. It is perfectly explained in the U-duality blog entry whcich I cite:
The criterion is that it should be possible to make the dimensions transverse to the 4-cycles wrapped by the 7-branes arbitrarily large. Equivalently, it should be possible to contract the 4-cycles to points while holding the six-dimensional volume fixed. Such contractible 4-cycles must be positive curvature Kahler manifolds. These are fully classified and are given by manifolds called del Pezzo manifolds (or del Pezzo surfaces), which are denoted dP_n. The integer n takes the values 0 ≤ n ≤ 8.9 The del Pezzos have a close relationship with the exceptional Lie algebras E_n. The basic idea is that they contain 2-cycles whose intersections are characterized by the E_n Dynkin diagram. By this type of F-theory construction, one can construct an SU(5) or SO(10) SUSY-GUT model. Constructions that involve 7-branes of various types are much more subtle – and also more interesting than ones that only involve D7-branes. D7-branes are mutually local. A stack of N of them gives U(N) gauge symmetry. Matter fields at intersections (due to stretched open strings) are bifundamental. However, different kinds of 7-branes are mutually nonlocal. As a result, there are stacks (corresponding to the ADE classification of singularities) that can give U(N), SO(2N) or even E_N gauge symmetry."
Well, this is just the beginning of the history. One must consider how the GUT groups are broken, this is achieved by means of hypercharge U(1) fluxes. I still must understand many points so I will stop here before misguiding to the possible readers.
I am finding very usefull this papers: F-theory Compactifications for Supersymmetric GUTs by Joseph Marsano, Natalia Saulina and Sakura Sch¨afer-Nameki and E ffective Field Theories for Local Models in F-Theory and M-Theory by Jacob L. Bourjaily.
This last one explains that, actually, the technology of the F-theory revolution also applies to M-theory. In fact both theories seem to have shared part of the development as is seem in the paper Chiral Fermions from Manifolds Of G2 Holonomy by Bobby Acharya and Edward Witten.
By the way, in the improbable case the reader wouldn't know what Vafa papers I am talking about here are the links: First paper and second paper
When I would gain a better understanding of the subject I'll try to do more posts on the subject, but certainly it would a good idea for my readers to see the Lubos blog entries on the same subject (and the Distler ones if he returns to the blogosphere). Well, surely there are more people out there who also could do a fine work bloging about those topics, certainly better than what can be reasonably expected form me .
By the way, a last note. This works are getting string theory very, very near of the phenomenology of LHC particle physics and cosmology testable effects. In fact it gets many pieces of actual physic by separate. Seemingly it "only" remains to join them. For example it must be addressed in deep the relevance of gin from local to global and the role that moduli stabilization plays there. Some work is on the way, but I will not give the links now. After all I wouldn´t like to fall in the category of "linker not thinker" ;-).
I had read generic aspects of them in the Lubos and Distler's blogs (well, Distler is actually disappeared and only put an entry about the first paper, this). I also found useful an entry in U-duality blog linking a paper of Schwartzabout the status of superstring theory, this entry
Well, my attack flailed miserably. I remotely understood some of the statements but I didn´t understand where they come from. I needed to go to the bibliography of the Vafa et all papers. I also have found clarifying some hints in follow up papers.
The first thing that I needed to understand properly is what a local model is. The proposal of local models seems to be born in a paper by (mostly) Spanish string theorist´s: G. Aldazabal1, L. E. Ib´a˜nez2, F. Quevedo3 and A. M. Uranga in the paper D-Branes at Singularities : A Bottom-Up Approach to the String Embedding of the Standard Model
The idea is to do instead of a top-down approach, that is, choose a compactification, study the resulting physic and see how well it matches the MSSM (minimal supersymmetric standard model) or something resembling the known physic one does a bottom up approach. It consists of two steps (I cite form the paper):
i) Look for local configurations of D-branes with worldvolume theories resembling
the SM as much as possible. In particular we should search for a gauge group SU(3) ×
SU(2) × U(1) but also for the presence of three chiral quark-lepton generations. Asking
also for D = 4 N = 1 unbroken supersymmetry may be optional, depending on what
our assumptions about what solves the hierarchy problem are. At this level the theory
needs no compactification and the D-branes may be embedded in the full 10-dimensional
Minkowski space. On the other hand, gravity still remains ten-dimensional, and hence
this cannot be the whole story.
ii) The above local D-brane configuration may in general be part of a larger global
model. In particular, if the six transverse dimensions are now compactified, one can in
general obtain appropriate four-dimensional gravity with Planck mass proportional to the
compactification radii.
In that paper the fields come form D-bran physics, i.e. open strings ending on the branes. They consider the branes suited at singularities of an orbifold. In F-Theory (and also M-theory) that approach takes a much more difficult form, but the idea is the same.
By the way, the idea of local models has had some development outside of the F-theory revolution, see for example Building the Standard Model on a D3-brane, by the Verlinde brothers. In general that attempts were influenced by the paradigm of D-brane intersections (of which I don´t know too much neither).
Almost at the same time that the now famous Vafa papers it appeared in arxiv another paper on model building with F-theory by Ron Donagi and Martijn Wijnholt (arXiv:0802.2969v2). I find that paper very illuminating. It explains in a very accessible way many facts of F-theory. For example the difference of the 7-brane of F-theory, which is not necessarily an D-brane but instead is a brane where a (p,q) string can end. It also clarifies the geometric idea behind the local model approach and gives intuitions on how gauge matter can appears, based in considerations of the supersymetry limit of F-theory.
I still haven't read all the paper. But in some point it talks about some of the other hard to follow questions of the F-theory revolution, the subject of ADE groups and it's relation to algebraic geometry and, in particular, the Kodaira classification of singularities.
That topic is covered in some early (mid nineties) papers of Vafa, for example Geometric Singularities and Enhanced Gauge Symmetries or Matter From Geometry
I am still trying to catch many aspects of how that works, but I believe that the essence of the argument is that F-theory and M-theory are related by dualities. Compactifiying F-theory in K3 surfaces (complex two dimensional Calabi-Yaus) is equivalent to compactify M-theory in a torus. The spectra of M-theory is easy to obtain and, by duality, one gets an idea of the particle spectra in F-theory and how it relates to the structure of the singularities. actually it is more complicated that that, and one must see how the idea holds in realistic compactifications. By the way, that work was previous to the local model engineering approach.
In this approach of F-theory the local model idea morphs into what is known as gravity decoupling. It is perfectly explained in the U-duality blog entry whcich I cite:
The criterion is that it should be possible to make the dimensions transverse to the 4-cycles wrapped by the 7-branes arbitrarily large. Equivalently, it should be possible to contract the 4-cycles to points while holding the six-dimensional volume fixed. Such contractible 4-cycles must be positive curvature Kahler manifolds. These are fully classified and are given by manifolds called del Pezzo manifolds (or del Pezzo surfaces), which are denoted dP_n. The integer n takes the values 0 ≤ n ≤ 8.9 The del Pezzos have a close relationship with the exceptional Lie algebras E_n. The basic idea is that they contain 2-cycles whose intersections are characterized by the E_n Dynkin diagram. By this type of F-theory construction, one can construct an SU(5) or SO(10) SUSY-GUT model. Constructions that involve 7-branes of various types are much more subtle – and also more interesting than ones that only involve D7-branes. D7-branes are mutually local. A stack of N of them gives U(N) gauge symmetry. Matter fields at intersections (due to stretched open strings) are bifundamental. However, different kinds of 7-branes are mutually nonlocal. As a result, there are stacks (corresponding to the ADE classification of singularities) that can give U(N), SO(2N) or even E_N gauge symmetry."
Well, this is just the beginning of the history. One must consider how the GUT groups are broken, this is achieved by means of hypercharge U(1) fluxes. I still must understand many points so I will stop here before misguiding to the possible readers.
I am finding very usefull this papers: F-theory Compactifications for Supersymmetric GUTs by Joseph Marsano, Natalia Saulina and Sakura Sch¨afer-Nameki and E ffective Field Theories for Local Models in F-Theory and M-Theory by Jacob L. Bourjaily.
This last one explains that, actually, the technology of the F-theory revolution also applies to M-theory. In fact both theories seem to have shared part of the development as is seem in the paper Chiral Fermions from Manifolds Of G2 Holonomy by Bobby Acharya and Edward Witten.
By the way, in the improbable case the reader wouldn't know what Vafa papers I am talking about here are the links: First paper and second paper
When I would gain a better understanding of the subject I'll try to do more posts on the subject, but certainly it would a good idea for my readers to see the Lubos blog entries on the same subject (and the Distler ones if he returns to the blogosphere). Well, surely there are more people out there who also could do a fine work bloging about those topics, certainly better than what can be reasonably expected form me .
By the way, a last note. This works are getting string theory very, very near of the phenomenology of LHC particle physics and cosmology testable effects. In fact it gets many pieces of actual physic by separate. Seemingly it "only" remains to join them. For example it must be addressed in deep the relevance of gin from local to global and the role that moduli stabilization plays there. Some work is on the way, but I will not give the links now. After all I wouldn´t like to fall in the category of "linker not thinker" ;-).
Sunday, April 26, 2009
New Einstein, new Galois, new Margalef...
Firs a clarification about the title. Most people know who Einstein or Galois are, but maybe not so many will know Margalef. He is an Spanish ecologist who begun his career as a self educated amateur and ended up with a tenure. I choose him because I needed a somewhat Spanish equivalent of the other two personalities.
All those people share a common point. They were brilliant scientifcs (Einstein and Galois simply top notch genius) who did at least part of it´s work outside academia.
The posts, as some can have supposed, is related to the famous "new Einstein" issue initiated by Lee Smollin. For those who don't know this affair simply to say that Lee Smollin published an article entitled "why no new Einstein" where he asked for somewhat who would revolutionize the nowadays physic in a similar way to what Einstein did in its time. Smollin was particularly interested in the philosophical nature of the Einstein contributions.
Well, I think that Einstein had a great intuition and that he presented his ideas in a very elegant way. But I don't think that to consider them Philosophy would make them any justice.
Possibly most interesting was his other consideration about Einstein. He did part of his work (the work in his "anni mirabilis") outside academy, you know, when he was in the patent office. In this respect Einstein was not alone. Before him many well known names had a similar role. Galois never had an academic position (possibly because he was killed before his work was broadly known). Lagrange was a self educated guy. Faraday made significant contributions to physics without a formal academic formation. The list is long and includes a large amount of well known scientifics in the ninety century. Also in the twenty century there are some names beyond Einstein (I am not totally sure but I guess that Banach was one of them).
But the truth is hat nowadays seemingly there are not too many examples (if any) of them. Maybe Perelman is the nearest example. He proved the Poincares conjecture which deserved him the corresponding Claymath prize. Also he was honoured with Fields medal, but he rejected it. He declined his academic position and now works in his home (or his mother home). But it is not the exact situation because as fr as I know he , until them, has followed a conventional way in academy.
Well, Smollin stated that he expected that the revolution of physic would come from out of the academy and was very interested in searching the "new Einstein".
I will say some comments about this particular. There is a difference between Einstein and previous times to nowadays. The scientific knowledge has growth a lot and it is necessary much more time to get the right preparation to be in conditions to publish important and revolutionary things. For example the gap between graduate studies and cutting edge physics is a lot greater now that in Einstein times (I would say that in Einstein times were around two or three years and now is 40 years). that means that an intelligent guy who has ended his undergraduate studies in physics and elaborates creatively with them has very few possibilities to create something valuable.
Another aspect is that in Einstein times there were no computers (nor financial markets). It is very easy that the "should be new Einstein" would end programming in an anonymous software company or doing "econophysic" in the financial markets.
I would add other thing. The goodbeeing state doesn't aim people to make a big effort to make big contributions that would give them fame, and, consequently money if they can live reasonably well without them. Anyone with the intelligent to be a "should be Einstein" surely knows hot to make some money without too much effort so creating something terribly special that would make him famous is not a priority.
Said that, is impossible a "new Einstein"?. I totally agree with Lubos that the most probable place to find him is inside academy. I totally recommend to anyone interested in purchasing a research position to care his expedient and all that. Certainly academy has is dark points (Lubos apparently is out of it because he doesn't like them) but it is not that bad.
Still there is a point about the new Einstein issue that is interesting. To become famous and doing great contributions being inside academy is "easy" (haha). But if you are a real genius it is possible that you would think precisely that, that is too easy and that the good point is to do your great work outside academy. Only the "minor minds" need to depend on good teachers and all the facilities that a first class university offers. Certainly it sound more "fashion", but I wouldn't recommend none to do that way.
And no, I am not at all trying to, subtlety, qualify myself as a "new Einstein" candidate. The main point of this post is to clarify th issue of the gap between undergraduate (or graduate, I always get lost with the correspondence between the Spanish word "licenciatura" and the corresponding English equivalent)and the cutting edge physic. If someone dreams about doing valuable work outside academy after finishing his studies he would be aware that he would need at least five years of intensive study to become near the frontier of knowledge. He would consider seriously if his economic/personal positions would allow him to do that, specially in this incoming years of economic crisis. I think that in that sense the claims of Smollin, and in fact not inly him, are dangerous because in a certain sense they make look glamorous a path that is mainly destined to fail.
All those people share a common point. They were brilliant scientifcs (Einstein and Galois simply top notch genius) who did at least part of it´s work outside academia.
The posts, as some can have supposed, is related to the famous "new Einstein" issue initiated by Lee Smollin. For those who don't know this affair simply to say that Lee Smollin published an article entitled "why no new Einstein" where he asked for somewhat who would revolutionize the nowadays physic in a similar way to what Einstein did in its time. Smollin was particularly interested in the philosophical nature of the Einstein contributions.
Well, I think that Einstein had a great intuition and that he presented his ideas in a very elegant way. But I don't think that to consider them Philosophy would make them any justice.
Possibly most interesting was his other consideration about Einstein. He did part of his work (the work in his "anni mirabilis") outside academy, you know, when he was in the patent office. In this respect Einstein was not alone. Before him many well known names had a similar role. Galois never had an academic position (possibly because he was killed before his work was broadly known). Lagrange was a self educated guy. Faraday made significant contributions to physics without a formal academic formation. The list is long and includes a large amount of well known scientifics in the ninety century. Also in the twenty century there are some names beyond Einstein (I am not totally sure but I guess that Banach was one of them).
But the truth is hat nowadays seemingly there are not too many examples (if any) of them. Maybe Perelman is the nearest example. He proved the Poincares conjecture which deserved him the corresponding Claymath prize. Also he was honoured with Fields medal, but he rejected it. He declined his academic position and now works in his home (or his mother home). But it is not the exact situation because as fr as I know he , until them, has followed a conventional way in academy.
Well, Smollin stated that he expected that the revolution of physic would come from out of the academy and was very interested in searching the "new Einstein".
I will say some comments about this particular. There is a difference between Einstein and previous times to nowadays. The scientific knowledge has growth a lot and it is necessary much more time to get the right preparation to be in conditions to publish important and revolutionary things. For example the gap between graduate studies and cutting edge physics is a lot greater now that in Einstein times (I would say that in Einstein times were around two or three years and now is 40 years). that means that an intelligent guy who has ended his undergraduate studies in physics and elaborates creatively with them has very few possibilities to create something valuable.
Another aspect is that in Einstein times there were no computers (nor financial markets). It is very easy that the "should be new Einstein" would end programming in an anonymous software company or doing "econophysic" in the financial markets.
I would add other thing. The goodbeeing state doesn't aim people to make a big effort to make big contributions that would give them fame, and, consequently money if they can live reasonably well without them. Anyone with the intelligent to be a "should be Einstein" surely knows hot to make some money without too much effort so creating something terribly special that would make him famous is not a priority.
Said that, is impossible a "new Einstein"?. I totally agree with Lubos that the most probable place to find him is inside academy. I totally recommend to anyone interested in purchasing a research position to care his expedient and all that. Certainly academy has is dark points (Lubos apparently is out of it because he doesn't like them) but it is not that bad.
Still there is a point about the new Einstein issue that is interesting. To become famous and doing great contributions being inside academy is "easy" (haha). But if you are a real genius it is possible that you would think precisely that, that is too easy and that the good point is to do your great work outside academy. Only the "minor minds" need to depend on good teachers and all the facilities that a first class university offers. Certainly it sound more "fashion", but I wouldn't recommend none to do that way.
And no, I am not at all trying to, subtlety, qualify myself as a "new Einstein" candidate. The main point of this post is to clarify th issue of the gap between undergraduate (or graduate, I always get lost with the correspondence between the Spanish word "licenciatura" and the corresponding English equivalent)and the cutting edge physic. If someone dreams about doing valuable work outside academy after finishing his studies he would be aware that he would need at least five years of intensive study to become near the frontier of knowledge. He would consider seriously if his economic/personal positions would allow him to do that, specially in this incoming years of economic crisis. I think that in that sense the claims of Smollin, and in fact not inly him, are dangerous because in a certain sense they make look glamorous a path that is mainly destined to fail.
Wednesday, April 22, 2009
Naked singularities
This month, April 2009, the Spanish edition of Scientific American(investigación y ciencia)has an article about naked singularities (the English version was dated on February).
The author, Pankaj S. Joshi, seems to be an total expert in the subject (a common issue in Scientific American)and has a recent book- from 2008- about the particular,
Gravitational Collapse and Spacetime Singularities.
I didn´t read the book, but I found the article interesting so I searched in wikipedia and some of the papers linked there. I´ll try to explain some of the aspects now.
In general relativity there are two well known places where singularities appear, black holes and cosmology. The most naive way of thinking/defining singularities is to characterise them as points where the metric (or curvature) of space-time becomes infinite. According to that the event horizon of a Schwarschild black hole would be a singularity. It was realized that that infinity was due to a bad choice of coordinates. In that solution the centrer of the black hole, the R=0 point, also get an infinity value and this can´t be overcome by any other choice of coordinates so it is a genuine singularity.
As far as we like to have coordinate free definitions there is more technical definition, a singularity is defined to be one which contains geodesics which cannot be extended in a smooth manner. The end of such a geodesic is considered to be the singularity. That definition is useful to probe theorems (as did Penrose and Hawkings in the 70´s) about how singularities can´t be avoided in classical general relativity in cosmological sceneries. It also permit to make a diferentiation about coordinate singularities, the ones I talked before, related to black holes, and what are known as conical singularities, related to things such as cosmic strings. A conical singularity occurs when there is a point where the limit of every diffeomorphism invariant quantity is finite. In which case, spacetime is not smooth at the point of the limit itself. Thus, spacetime looks like a cone around this point, where the singularity is located at the tip of the cone. The metric can be finite everywhere if a suitable coordinate system is used.
The S.A article treats about singularities associated to gravitational collapse. There exists what is known like the cosmic censorship conjecture (or hypothesis) , own to Roger Penrose, which states that there are not naked singularities. That is, every singularity must be hidden behind an event horizon and cant be seen from the outside. It has the status of conjecture because it hasn´t be proved in a rigorous way under physically reasonable assumptions. In fact it hasn´t even stated in a mathemathical rigorous way.
The article, obviously, try to answer the conjecture in the negative. Before describing it's arguments I´ll talk about an aspect closely related to the CCC. If one examines the solutions for rotating black holes (Kerr solution) one sees that if is allowed that J, the angular momentum is greater than the mass M of the black hole, that is J/M>1 a naked singularity (a ringed shaped one) appears. A similar thing goes for charged (electric of whatever associated to U(1) gauge symmetry)black hole solutions (Reissner-Nordstom black holes) where a naked singularity appears if the charge, Q, is greater than the mass of the b-h, i.e., Q/M>1. It is commonly assumed that the CCC holds and the case where the equality would arise are called extremal black holes. The possibility of a reverse, negative, sign in the above expressions is not even contemplated in most theoretical considerations.
That´s a reason why I was somewhat surprised when I read the article and saw that in fact when one makes actual calculations, in classical general relativity, of how gravitational collapse behaves when some oversimplifying assumptions about the state of the star are neglected naked singularities actually are shown to be possible.
If the star is perfectly spherically symmetric and of uniform density everything is o.k and the black hole is formed. But relaxing one of the assumptions separately(or both at once) it can be shown that naked singularities actually appear.
Intuitively the reason is, for the case of non uniform density, that it can happen that the rate of accretion into the centre is never fast enough to actually form an even horizon and a central, unique, singularity appears. In the case of non sphericity it is shown that the collapse is neither spheric so the mass is concentrated in two points that become singularities at the end of the collapse avoiding the formation of the event horizon because of the oblong shape of the infalling matter that forbids the concentration of enough mass inside the Schwarschild radius.
Once that this facts are established one can wonder about how realistic and stable are. After all they mean that a large amount of the mass of a big star is concentrated in a point. The precise nature of what a singularity actually is usually is thought to be a question related to quantum gravity. But for regions relatively close (but not too much) to the singularity classical relativity still holds and it is expected that neighbouring matter would be attracted to the singularity. The inexistence of the event horizon means that there is the possibility of going arbitrarily near the singularity and returning to the original point (well, if tide forces don´t kill you and such that). In particular light can go near the singularity and scape to a distant observer so we can see what happens there. But even thought some matter in certain trajectories could scape I think that it is reasonable that most of the matter would be trapped in the singularity. Intuitively one would think that that increases the mass of the singularity and that it sooner or later it will become a black hole. Possibly that is a too naive way of think and that is one of the particularities of the singularity (but I am not sure about it).
Anyway, if singularities re shown to be possible (at least for a certain time) one could try to consider if they are distinguishable from black holes. The answer is in the positive. Even one could try a little bit further and consider the possibility that an existing black hole could break and leave behind the singularity. The most natural case would be kerr black hole which is led to rotate faster than it´s extremal limit. Because astrophysical black holes are usually believed to be Kerr ones one immediately can answer for particular observable signatures of this breaking. ONe arxiv article where one can read the details is this: Magnification relations for Kerr lensing and testing Cosmic Censorship. There are described some mathematical details of calculations made on the pna (post Newtonian approximation)of some optical effects. The author claim that the differences in behaviour among black holes and naked singularities could be observed with the incoming new generation of available technology.
From the viewpoint of an string theorist 4 dimensions are very restrictive, what about the influence of additional dimensions? You can read a paper about the particular: Spherical gravitational collapse in N-dimensions. It is co-authored by Joshi and the answer is mildly positive. I recommend to read the considerations that he makes in the conclusions.
A later thing I am going to discuss is the role of quantum gravity. If naked singularities actually exist they are a window to do observations of quantum gravitational effects (or at least one so expects). But before going there one could answer if quantum gravity considerations modify the classical predictions of formation of naked singularities. I don´t know the "asscendence" of Joshi, tat is, if he is an string theoretic oriented or an LQG oriented researcher. Being an specialist in general relativity one, maybe, would expect him being an LQG researcher, but reading his papers I guess that a better fir would be to consider him a "naked singularity phenomenologist". Anyway, LQG is easier to learn that string theory and is accepted by a plausible quantum gravity by hundreds of people with a tenures/investigation positions in universities so it is reasonable to expect some paper using LQG to investigate the question. And, effectively, there is such paper: Quantum evaporation of a naked singularity.
This papers point in a different direction that the classical results. Using a toy model with an scalar field (in a way similar to loop quantum cosmology calculations) it is shown that near the should be singularity gravity becomes a repulsive force and the naked singularity isn't formed. I guess that one must understand that this calculations make sense in the case where the classical equations point to the formation of the singularity. That is, classically one expect the formation of the naked singularity, but looking at quantum phenomena one sees that actually the singularity is avoided. I must clarify that this calculations are not claimed to be fully quantum by the authors and they still believe that in full quantum sceneries the naked singularity would easily reappear.
Still this last scenery could have relevant observational consequences in the form of powerful gamma ray bursts that result in the evaporation of the should be singularity. The precise signature of that bursts depend in some free factors of the theory, and, in particular, the claim that can be used to estimate a value of LQG, j, the value of the representation of (complex) SU(2) used.
Well, certainly I don´t believe that string theory people would take too seriously this considerations, but claiming possible near future experimental results I believe it well deserves to say something about the subject.
In fact actually there are some results in string theory about singularities, particularly the enhanchon mechanism, but it is related to "educated" singularities inside a black hole who are prudent enough to not show themselves naked. Abut black holes in string theory I hope to write a post soon.
To end this post to leave a link to a self claimed naked singularity who is kind enough have a blog (in Spanish), that links to this: La Singularidad Desnuda.
The author, Pankaj S. Joshi, seems to be an total expert in the subject (a common issue in Scientific American)and has a recent book- from 2008- about the particular,
Gravitational Collapse and Spacetime Singularities.
I didn´t read the book, but I found the article interesting so I searched in wikipedia and some of the papers linked there. I´ll try to explain some of the aspects now.
In general relativity there are two well known places where singularities appear, black holes and cosmology. The most naive way of thinking/defining singularities is to characterise them as points where the metric (or curvature) of space-time becomes infinite. According to that the event horizon of a Schwarschild black hole would be a singularity. It was realized that that infinity was due to a bad choice of coordinates. In that solution the centrer of the black hole, the R=0 point, also get an infinity value and this can´t be overcome by any other choice of coordinates so it is a genuine singularity.
As far as we like to have coordinate free definitions there is more technical definition, a singularity is defined to be one which contains geodesics which cannot be extended in a smooth manner. The end of such a geodesic is considered to be the singularity. That definition is useful to probe theorems (as did Penrose and Hawkings in the 70´s) about how singularities can´t be avoided in classical general relativity in cosmological sceneries. It also permit to make a diferentiation about coordinate singularities, the ones I talked before, related to black holes, and what are known as conical singularities, related to things such as cosmic strings. A conical singularity occurs when there is a point where the limit of every diffeomorphism invariant quantity is finite. In which case, spacetime is not smooth at the point of the limit itself. Thus, spacetime looks like a cone around this point, where the singularity is located at the tip of the cone. The metric can be finite everywhere if a suitable coordinate system is used.
The S.A article treats about singularities associated to gravitational collapse. There exists what is known like the cosmic censorship conjecture (or hypothesis) , own to Roger Penrose, which states that there are not naked singularities. That is, every singularity must be hidden behind an event horizon and cant be seen from the outside. It has the status of conjecture because it hasn´t be proved in a rigorous way under physically reasonable assumptions. In fact it hasn´t even stated in a mathemathical rigorous way.
The article, obviously, try to answer the conjecture in the negative. Before describing it's arguments I´ll talk about an aspect closely related to the CCC. If one examines the solutions for rotating black holes (Kerr solution) one sees that if is allowed that J, the angular momentum is greater than the mass M of the black hole, that is J/M>1 a naked singularity (a ringed shaped one) appears. A similar thing goes for charged (electric of whatever associated to U(1) gauge symmetry)black hole solutions (Reissner-Nordstom black holes) where a naked singularity appears if the charge, Q, is greater than the mass of the b-h, i.e., Q/M>1. It is commonly assumed that the CCC holds and the case where the equality would arise are called extremal black holes. The possibility of a reverse, negative, sign in the above expressions is not even contemplated in most theoretical considerations.
That´s a reason why I was somewhat surprised when I read the article and saw that in fact when one makes actual calculations, in classical general relativity, of how gravitational collapse behaves when some oversimplifying assumptions about the state of the star are neglected naked singularities actually are shown to be possible.
If the star is perfectly spherically symmetric and of uniform density everything is o.k and the black hole is formed. But relaxing one of the assumptions separately(or both at once) it can be shown that naked singularities actually appear.
Intuitively the reason is, for the case of non uniform density, that it can happen that the rate of accretion into the centre is never fast enough to actually form an even horizon and a central, unique, singularity appears. In the case of non sphericity it is shown that the collapse is neither spheric so the mass is concentrated in two points that become singularities at the end of the collapse avoiding the formation of the event horizon because of the oblong shape of the infalling matter that forbids the concentration of enough mass inside the Schwarschild radius.
Once that this facts are established one can wonder about how realistic and stable are. After all they mean that a large amount of the mass of a big star is concentrated in a point. The precise nature of what a singularity actually is usually is thought to be a question related to quantum gravity. But for regions relatively close (but not too much) to the singularity classical relativity still holds and it is expected that neighbouring matter would be attracted to the singularity. The inexistence of the event horizon means that there is the possibility of going arbitrarily near the singularity and returning to the original point (well, if tide forces don´t kill you and such that). In particular light can go near the singularity and scape to a distant observer so we can see what happens there. But even thought some matter in certain trajectories could scape I think that it is reasonable that most of the matter would be trapped in the singularity. Intuitively one would think that that increases the mass of the singularity and that it sooner or later it will become a black hole. Possibly that is a too naive way of think and that is one of the particularities of the singularity (but I am not sure about it).
Anyway, if singularities re shown to be possible (at least for a certain time) one could try to consider if they are distinguishable from black holes. The answer is in the positive. Even one could try a little bit further and consider the possibility that an existing black hole could break and leave behind the singularity. The most natural case would be kerr black hole which is led to rotate faster than it´s extremal limit. Because astrophysical black holes are usually believed to be Kerr ones one immediately can answer for particular observable signatures of this breaking. ONe arxiv article where one can read the details is this: Magnification relations for Kerr lensing and testing Cosmic Censorship. There are described some mathematical details of calculations made on the pna (post Newtonian approximation)of some optical effects. The author claim that the differences in behaviour among black holes and naked singularities could be observed with the incoming new generation of available technology.
From the viewpoint of an string theorist 4 dimensions are very restrictive, what about the influence of additional dimensions? You can read a paper about the particular: Spherical gravitational collapse in N-dimensions. It is co-authored by Joshi and the answer is mildly positive. I recommend to read the considerations that he makes in the conclusions.
A later thing I am going to discuss is the role of quantum gravity. If naked singularities actually exist they are a window to do observations of quantum gravitational effects (or at least one so expects). But before going there one could answer if quantum gravity considerations modify the classical predictions of formation of naked singularities. I don´t know the "asscendence" of Joshi, tat is, if he is an string theoretic oriented or an LQG oriented researcher. Being an specialist in general relativity one, maybe, would expect him being an LQG researcher, but reading his papers I guess that a better fir would be to consider him a "naked singularity phenomenologist". Anyway, LQG is easier to learn that string theory and is accepted by a plausible quantum gravity by hundreds of people with a tenures/investigation positions in universities so it is reasonable to expect some paper using LQG to investigate the question. And, effectively, there is such paper: Quantum evaporation of a naked singularity.
This papers point in a different direction that the classical results. Using a toy model with an scalar field (in a way similar to loop quantum cosmology calculations) it is shown that near the should be singularity gravity becomes a repulsive force and the naked singularity isn't formed. I guess that one must understand that this calculations make sense in the case where the classical equations point to the formation of the singularity. That is, classically one expect the formation of the naked singularity, but looking at quantum phenomena one sees that actually the singularity is avoided. I must clarify that this calculations are not claimed to be fully quantum by the authors and they still believe that in full quantum sceneries the naked singularity would easily reappear.
Still this last scenery could have relevant observational consequences in the form of powerful gamma ray bursts that result in the evaporation of the should be singularity. The precise signature of that bursts depend in some free factors of the theory, and, in particular, the claim that can be used to estimate a value of LQG, j, the value of the representation of (complex) SU(2) used.
Well, certainly I don´t believe that string theory people would take too seriously this considerations, but claiming possible near future experimental results I believe it well deserves to say something about the subject.
In fact actually there are some results in string theory about singularities, particularly the enhanchon mechanism, but it is related to "educated" singularities inside a black hole who are prudent enough to not show themselves naked. Abut black holes in string theory I hope to write a post soon.
To end this post to leave a link to a self claimed naked singularity who is kind enough have a blog (in Spanish), that links to this: La Singularidad Desnuda.
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