Recordemos, las supercuerdas convencionales (las únicas de la que voy a hablar) se formulan en 10 dimensiones. Cómo el universo observado tiene la indecencia de no dar signo evidente de más de 4 hay que hacer algo para obtenerlo. Cómo bien explica el amigo Green lo que se hace es explotar la vieja teoría de Kalua-Klein de compactificar las dimensiones. Además uno saca la ventaja de que las isometrías del espacio compactificado se traducen en simetrías gauge. Las cuerdas tienen varias peculiaridades en las compactificaciones respecto a las teorías de campos puntuales, pero comparten una característica que es crucial. Resulta que cómo la compactificación se hace "a mano" no hay nada, en los casos más simples, que fije algunas características del espacio compactificado. En el caso más sencillo en que una sola dimensión se compactifica en un círculo la caracterísitica esencial es el radio. No hay nada uqe fije el tamaño del radio, es un parámetro libre. Y el problema es que algunas de las características del universo observado si dependen del valor exacto del radio. Si no lo podemos fijar teóricamente tenemos que las cuerdas ya tiene más parámetros libres y dejan de ser una teoría tan unificada (recuérdese que las cuerdas en principio sólo tiene un parámetro libre, la tensión de la cuerda).
La generalización más obvia de la compactificación en un n-toro, o sea, el producto de n-círculos. Aquí ya tenemos más estructura, y voy a analizar el caso del 2-toro para ejemplificar algunas cosillas útiles luego. No todos los toros son iguales, se distinguen unos de otros por la relación de tamaños de los radios. Esa relación nos describe familias de tornos no equivalentes bajo transformaciones conformes. Ese parámetro es lo que se conoce como móduli (luego daré una definición matemática más general, y como se calculan los móduli, el otro móduli del toro sería el tamaño de uno de los radios). Un aspecto que he mencionado, pero no he explicado, es que nada fija el valor del móduli. Pero ¿como debería fijarse ese valor? Bien, el moduli es un concepto geométrico, pero puede verificarse que en la toeria de cuerdas su valor siempre va a corresponder al valor esperado en el vacio (vev) de un campo escalar que aparece en la compactificación. El vev es básicamente el mínimo del potencial del campo. El problema es que los lagrangianos que describen la compactificacion no nos dejan ningún término de potencial para esos campos asociados a los móduli. Por eso permanecen indeterminados. Por poner un ejemplo sencillo, en el caso de compactificación en un círculo el campo asociado sería el (famoso en el mundillo) dilatón.
Bien, un círculo no vale como compactificación, que no nos da las dimensiones correctas, un 6-toro nos da las dimensiones correctas, pero deja demasiada simetría y no reproduce el modelo estándar ni de casualidad. Hay que ir a construcciones más complejas. Para poder entender bien algunas características esenciales luego explicaré ahora lo siguiente más sencillo que se puede hacer, compactificar en un orbifold. Un orbifold es lo que se conoce matemáticamente cómo conjunto cociente de un espacio topológico por al acción de un grupo finito. EL caso más simple puede verse como la acción de Z2 en el círculo. Esta puede verse que equivale a una identificación de las dos mitades de un círculo (respecto a un diámetro cualquiera), o sea, un segmento. El problema es que los dos extremos del diámetro son invariantes de la acción. Eso hace que el orbifold no sea un espacio suave, un manifold (o variedad, en español). Los puntos extremos son singularidades.
Llegados a este punto hay dos caminos, relativamente equivalentes. De un lado se puede comprobar que cierto tipo de estados, llamados twisted states, de la cuerda se propagan sin problemas en esas geometrías. Por otro lado se pueden eliminar esas singularidades mediante un proceso de "blowin-up" (o hinchado). El resultado del blowin up de un orbifold resulta ser un Calabi-Yau, de los que ahora hablaré. En ese blowin-up, la cuerda se propaga normalmente sin necesidad de estados twisteados (nada que ver con los twistors de Penrose pese al nombre) y tenemos dos descripciones matemáticas del mismo asunto.
Bien, vamos a los Calabi-Yaus. Las condiciones que se requieren alas cuerdas en 4 dimensiones es que tenga solo una carga supersimétrica (hay argumentos muy generales que indican que teorías con más de una supersimetría en 4 dimensiones no pueden ser consistentes). Aparte se pide que tengan algo llamado "holonomía SU(3)" y que sean Ricci flat, es decir, que su tensor de curvatura de Ricci sea nulo. Bien, el caos es que tenemos un espacio de 6 dimensiones reales con unas características precisas. Los matemáticos habían estudiado ya ese tipo de objetos, pero vistos como espacios complejos de dimensión (compleja) 3, y en particular de un tipo específico conocido como Khaler manifolds. Cómo curiosidad decir que la manera más sencilla d obtener calabi-Yaus es partir de espacios proyectivos complejos y hacer subespacios de los mismos definidos por polinomios homogéneos en variable compleja. La homogeneidad es requerida par ajustarse a que el espacio sea proyectivo. Reacuérdese que el plano proyectivo consiste en identificar todos los puntos de una recta, eso implica que sólo los polinomios homogéneos están bien definidos en el plano proyectivo.
Bien, el caso es que tenemos compactificaciones en Calabi-Yaus que nos dan aproximaciones muy buenas al modelo Standard si partimos de la cuerda heterótica. Esto esta bien, pero hay varias cosas que faltan. Un dato muy conocido de quien lea divulgación es que el número de generaciones de partículas se corresponde con un invariante topológico del Calabi-Yau, su característica de Euler. Hay otros aspectos de la física en 4 dimensiones que dependen de características topológicas, pero no todas, algunas, e importantes, dependen de la métrica del Calabi-Yau. Pues bien, en la época del libro, y de hecho hasta como quien dice antes de ayer, no se sabe calcular la métrica de un Calabi-Yau. Hoy día, quitando unos poquitos casos, las que se saben se obtienen, y con mucho trabajo, con métodos numéricos. ahí ya tenemos un avance.
Pero a ver, sigamos. Había dicho que necesitábamos saber el móduli space del Calabi-Yau. Para hacer eso lo que se hace es considerar la métrica del Calabi-Yau, no importa que no la sepamos, y variarla. Se impone que la nueva métrica siga siendo Ricci flat. Esto resulta en unas ecuaciones diferenciales.El número de soluciones de esas ecuaciones van a contar el número de modos independientes (en el sentido de dar las mismas topologías y supersimetrías) de modificar el Calabi-Yau. Los coeficientes de esas soluciones van a ser los modulis. En realidad los modulis no van por libre y definen ellos mismos un espacio geométrico. En ese espacio geométrico se puede dar una métrica. En algunos casos esos moduli spaces van a ser así mismo espacios de Khlaler. Normalmente se va a tener que le moduli consta de dos partes, una que nos da "la forma" (la relación de radios en el caso del toro) y otra que nos da el tamaño (el tamaño de uno cualquiera de los radios en el toro).
Espero que más o menos se me siga hasta aquí. Es que normalmente se pasa muy por encima en el tema este de la compactificación y es muy importante entenderlo medianamente bien para muchos aspectos importantes hoy día. Voy a ahora con algo que había omitido hasta ahora. Los Calabi-Yaus van a ser soluciones clásicas de la cuerda. Pero efectos perturbativos, y algunos no perturbativos, pueden cambiar eso. Uno de los efectos no perturbativos es la consideración de las D-branas. Resulta que la presencia de las D-branas esta relacionada con un aspecto que uno no esperaría en un Calabi-Yau. Algunos tipos de Calabi-Yaus, no compactos, tiene singularidades. En realidad es más preciso hablar de un conifold que de un Calabi-Yau en estos casos. Puede parecer que esto es muy técnico, y no se ajusta a nada "físico". Pero en realidad no es así. Estas peculiaridades son relevantes en dos aspectos. Uno el hecho de poder describir un
agujero negro mediante d-branaas enrolladas alrededor de cierto tipo de subvariedades del Calabi-Yau, conocidas cómo subvariedades de Lagrange (en realidad se puede calcular la entropía del black hole enrollando las branas en cosas más sencillas, como toros, pero el trabajo inicial usaba los Calabis). Otro aspecto, quizás más importante, es que esas singularidades del Calabi-yau, el conifold, permite que las cuerdas puedan realizar transiciones entre espacios con distintas topologias (obviamente en los puntos regularidades del Calabi-yau no se puede.
De todos modos con todas estas complejidades los Calabis, por si solos, no bastan. En un Calabi seguimos sin tener un potencial para el moduli. Hay que darle potencial a los modulis. La solución es peculiar. En los Calabis tenemos geometrías en que todos los campos de la cuerda, excepto la métrica, se anulan. Queremos considerar compactificaciones en que algunos campos de la cuerda, los supersimétricos que se pueden corresponder como campos gauge tomen valores no nulos. Esto es lo que se conoce como flux compactificacions, o compactificaciones de flujo. Se puede probar que en tales compactificaciones si se van a tener potenciales para los campos que determinan los valores de los moduli. Entonces ¿por que no se habían usado antes estas compactificaiones? de un lado porque se había demostrado que "eran imposibles". Pero se había demostrado antes de el descubrimiento de las d-branas. El truco esta en que algunos de estos campos gauge antisimétricos de los que hablo no pueden estar cargados respecto a al cuerda. Tiene que estar cargados respecto a D-Branas. Por tanto era imposible que se hubieran considerado estas compactificaciones antes del descubrimiento de las D-branas.
Otro aspecto muy interesante de estas compactificaciones de flujo es que son compatibles con compactificaciones "warped" (no sabría com traducirlo exactamente). En estas el espacio no va a ser ya un producto del espacio de Minkowky por el espacio interno, sino que estarán mezclados por un factor de warping, una exponencial decreciente de las coordenadas internas.
El hecho de que las compactificacioens de flujo permitan estas geometrías warped es lo que inspiro, como algo compatible con las cuerdas, los universos tipo Randal-Sundrum. En realidad ahí hay una dimensión de tamaño no planckiano (las compactificaciones tiene el orden del tamaño de Planck). Eso esta relacionado con que no se consideran solo compactificaicones de las teorías de cuerdas en 10 dimensiones. Se sabe que hay duales de las teorías de cuerdas que no son propiamente teorías de cuerdas, por ejemplo la teoria M. Otra de esas teorías es la teoría F (si la teoría M es dual de las supercuerdas tipo II A la teoría F es dual de la supercuerda tipo II B). Cierto tipo de compactificaciones de la teoría tipo II-B, que es dual a una compactificación de la teoria F, puede realizar, en la teoría de cuerdas, el modelo fenomenológico de Randall-Sundrum. Lo relevante es que la teoría M tiene 11 dimensiones, una más que la supercuerda. La teoría F, formulada como una libración elíptica de la cuerda tipo IIB, también (en otro formalismo tiene 12 dimensiones, pero una de esas dos dimensiones extra, respecto a la cuerda, es tipo tiempo, es decir, que hay dos dimensiones temporales). Lo peculiar es que esa dimensiones extra, respecto a las teorías de cuerdas, no tiene porque ser del tamaño de Planck de hecho no debería serlo.
Voy a cortar aquí, que si no nadie se va atrever con el post. Simplemente comentar que los modelos de Randall-Sundrum permiten cosas muy interesantes. Por ejemplo en ellos el gravitón se descompone en uno en 4 dimensiones, gravedad normal, y uno que puede moverse en la dimensión extra, el bulk, dando una modificación a la gravedad normal, y que hace que para distancias cortas la gravedad sea más fuerte. Eso posibilitaría (pero es improbable) que se formen agujeros negros en el CERN. Otra característica es que la energía de los modos masivos de la teoría de cuerdas, que normalmente serían del orden de la masa de Planck, tengan en realidad una masa que podría ser del orden de la energía del LCH (1 Tev). Esto abre la posibilidad de observar estados totalmente "cuerdistas" en el LHC (igualmente es muy improbable, y deberían distinguirse por sus productos de decay, no directamente). En fin, los warped universes son un submundo entero dentro de las cuerdas Aunque mucho de su estudio se puede hacer mediante modelos "fenomonologicos", o sea usando gravedad de Einstein + teorias de campos. Las cuerdas serían un motivante (y aparte permiten calcular algunos aspectos de los mismos, como el warp factor).
Wednesday, October 17, 2007
Tuesday, October 16, 2007
Mental illness and scientific thought
Fist of all to advise the possible readers that despite the name of the entry this post will, at least partially, be kept on the topic of quantum gravity related arena to which this blog is devoted, concretelly to the problem of the colapse of the wave function and some purposed solutions, including "quantum conscence" theories. I certainly could write about many other non "quantum gravity" topics, in physic, science in general, or other areas of knowledge (nor to say "everyday life" topics) but I think that the eventual readers will feel better if they have a clear "editorial line" and knows what to expect.
But previously to speak about the central topic I´ll make a few disquisitions about the "crankpot" issue, partially because it is somewhat related to the sustainer of some atipic ideas, and partially because it is somewhat interesting in itself.
First let´s state some possible aceptions of the "cranckpot" term. The proper definiton of mental illnes would correspond to a professional of psicology. But as i´ll briefly discuss the acceptance of their definitions would imply that psicology would have a firm scientific status and curiously the term "cranckpot" is beeing used sometimes for people whose level of rigour is a few orders of magnitude upper to the one used ofthen in psicology, so "houston, houston, we have got a problem" ;-). For the shake of simplicity I´ll use some commonly accepted notions in psicology and some "common language" aceptions also, with the apropiate explanations when necessary. I´ll make a first broad distintion which will be, i hope, very helpfull. I´ll diferentiate "social related" mental illnes from "science" related ones.
In the field of "sociall related" mental insane scientifics we have some very famous ones. For example Kürt Göedel had some paranoic behaviours(in the commonly used sense of the term). He used to think that people wanted to put poisson in her foods, to international conspirations and similar things. Other, even more famous nowadays due to the book, and posterior film "a beateafull mind", is Jonh Nash. I have not readed the book and I am not sure if an aspect of the filmm is true or not, but I want to rescue it because I find it very interesting for the notion of a proper definition of "mentall illness". He, in the film, had alucinatory episodes where he saw (and heared) people who driven him to behave in a totally unaceptable social way. Concretelly the made him to belive that he was working for an inteligence goverment department. When the circunstances made him to realize that some particular persons that he saw were not "real" he clearly knew that he had a very serious problem. I guess that in reality He had a medical tratement with meds who made the alucintions to dissapear, but in the film (maybe in reality, it doesn´t matter for what I whant to wonder now) he relies in his logic to actually try to distinguish possilbe "alucinatory people" from real people (for example he says that one of the "ilusinary people", a girl, hadn´t grown for years which made clear for him that he couldn´t be real, even if his mind still madde him appear. Well, I find that this a very interesting question in itself. Science is, among other things, the aplication of logic to have fiable knowledge about the world. In this sense he was apliying it´s formation as a scientific to bypass a "bad work" of his perception. I have known personally people who have been prescribed mental disfunctions (maybe apropiatelly, maybe not) but who, despite it´s unusuall behaviour sometimes were very logical in it´s reasoning. Even if they considered very utipical, and scientific, ideas (an aspect unrelated to the problmatic social behaviour) such like considering the possible of telekinesis as real were able to accept that withouth a verificable under scientifics standards proofs of it that belief in t.k would be discarded. On the contrarie another person, whose social behaviour was never questioned as pathologic (nor I perosnally see why it could b otherwise), and who was a psicologyst itself, had the beief that some martial art prastice could allow some physically imposilbe things, like, for example, to defeat an opponent without actually touching it throught the use of "chi". Well , in this case the social and the scientific criteria (of respecting logic and it´s relation to proved, and verificable everywhere data) clearly gave a diferent answer to discern who was crazy and who not. If we go a litle bit far in this question we go into the problem of religions and in general "mistics" beliefs. In hiss book Time scape" the physicst and science ficition writer Gregory Benford rise the same question. From a purely scientific perspective the widelyy accepted religious beliefs are crazyness. He also stated that more "exotic" beliefs (evil possesions, communication with death people, etc) are commmon in a lot of people which otherwise were very conventinal in the social relations. What to think about ten?. I would even add that there is also a large amount of people who have a conventinal social behaviour, that don´t have any particular exotic belief but whose capabilitie to go into logical and scientific reasoning is null. People who are unable to do theminimally mental complex reasing and whose acceptance of "rational" ideas seems more due to the cassualities of their education that to any capability to discern by themselves sane from insane ideas. How to consider them.
I am going to add a las historic example, more for their interest in iself that for their importance in the rest of the post. I am talking about Newton in person. He joined in his person many of the previously asked questions. He had a very ugly social behaviour (sme modern spicologists analizing his biographys hipotesizes that he could have what is known as "Asperger symdrome"). He also had very deep religous beliefs (more of the 80% of his writes are reigious). Besides of his known scientific apportations he had worked in "alchemy", understood more in it´s magic implicatinos that in ther pre-chemical ones. Also in his pure scientific carrer he had made some risked experiments (he was near to end blind on one of his eyes becuase some atipical optical experiments. Well, said all this I think that I must add that it would not be just to totally judge his acts from a modern viewpoint. Before him sicence as we know it simply didn´t exist (It wouldn´t be exagerate to say thathe invented it). But that baby science didn´t explain a lot of things in the everyday life. I guess that it is not untill the achievement of the modern quantum mechanics (with the Schroedinger equation and inmediate developments) and it´s explanations of the chemics implied in everyday life that almost every earth commonly observed fact has (or hopfully has, despite it´s math complexity) an explanation under science. I think that it is more acceptable for a person in an almost totally unscientific world where almost every thing was far from a proper explanation to have magic, as well as religious beliefs. Althought on the other side Newton was a rationalist, or at leas that is relfected in another writng form Gregory Benford, wherewe see a modern physicist go to "ell" and finding there Newton who in all the years gone from it´s dead is tritying to made a "science" addecuate for hell, which can´t be an strictly rationalism science (becuase of the observable behaviour of hell).
Sic, I see that this historic remarks are very temptative and I have writen a lot withouth actually going into modern physics and it´s "crackpots". First I need a definiton of a "scientific crackpot". I mostly agree with the famouse one proposed By Jonh Baez. But I need to make a few comments. One of the examples proposed by Baez is Myron Evans. I had a knowledge of the Evans case prior to the knowledge of Baez. One friend of me has made his (brilliant, crowned with an article in nature) doctoral thesis in something called "topological electromagnetism". Basically it consists in a change of variables from the E and B fields to another ones which are apropiate to be used for an topolocial annalisis of the solutions. In particular if you do the usual compactification of R 3 by the point at infinite you get that his frontier S2. Well, you can see that the solutions of the Maxwell equations can be classifed by a topological quantitie related to the topological index (in the sense of the ides of Millnor)of the electric and magenetic fields viewed as funtions from S2 to S2. For a brief time I collaborated with my friend in a try to extend this ideas to Yang-Mills case, but it has passed a while from them and maybe I have explained bad some details (J.L, if you are reading this I invoke you to crrect possilbe mistakes ;-)). Well, the thing is that Myron Evans was interested in his works in order to publish a review of them in a forthcoming book publisehd by Elsevier devoted to Evans own ideas and related ones (like this of topological electromagnetism). We brieflly discused about the particular. But I think that it is out of place to say any more about this because of discreption (anyway, nothing offensive was said if someone worries about it). As a rsoult I tried to learn the work of Evans the problem was that none of the papers I coulr read for that time presented a complete description of them and referenced unavailable works. Well, that´is preciselly some of the cliams of Baez against Evans, I don´t know how actually the question is, but I wouldn´t want to centrate the question in Evans. He is only one well known exponent of uncommon scientific behaviour. Another name with an slighly similar problem is Podkeltnov. He claimed that a device, desgned for a diferent purpose that the one which mae it famous, with superconductors had "antigravitatory" behaviour. But he denied to give the precise configuration of the device because it could "give clouds" to other people who could thief his ideas. The last time I readed about it the NASA had repeated the experiment with a simplifeid desing without antigravitation (or to say properly,gravity shieldin). In this line also is the "Allais effect" of atipical behaviour of gravity while solar eclipses(Allais is a nobel prize in economy who has a formation as physicist). Similarly the last time I wondered about it the NASA was analizing a most precise version of his expermient. I think that the main reason these experiments are beeing considered by the NASA is because of the problem that the own NASA has with some of it´s satellites (I don´t just now remember the name, but it is a very famous open problem of unexplained gravitational anomalies).
Well, afther an enumeration of examples the definitin. A "scientific crackpot" would
be someone who defends an idea (that he belives very important) whose reliability is very unlikely and who, ofthem, refuse to give all the aspects of it because of being scared of "intelectual apropiation". I would distinguish here two cases. People without academic formation and people with it. I think it is not the same case somone whose maths doesn´t go, in the best of cases of basic calculus, from people who have a PhD in physicst, or maybe they are enigners. Those last people have (almost certainly) proved that at least in some part of his life had a proper knowledge of science. I guess that if they insist in presenting slopy ideas as fundamental advances, against the commmon belief, they are more suspectous of triying to gain more scientific recognition of what they deserve that really beliving "crazy" ideas. But this is not the end of the history. Not allways things are "black or white". There are some famouse cases where unlikely and marginated ideas in the end proved to be truth some years later (for example the theory of continental derive) so it is not just that easy to say for sure who is "scientifically" crazy or not. Even the lack of a math rigour is not always a criteria. The most famous case is Faraday, who is known but it´s famous law in electromagnetism. But it is less known that he had not mathformation and that he was guided mainly by intuition. Ok, nowadays a case just as Faraday is very unlikely, but apropiate translations of it coud happen i guess. And, of course, it would be unapropiate to relate "scientiic" to "social" crankpoptism.
Well, le´ts go, at last, with quantum mechanist. The most discused aspect of it is the problem of wavefuntion reduction. The most accepted viewpoint is the traditional, positivst, one "it works, don´t fix it". The "many words" Everet viewpoint is mathematically consistent but unboservable in practice. Decoherence seems the most realistic path (for a very good description of it I recomend to search into the web of another science fiction writer, Greg Egan, I am unable to find it just now the exact link). But there are more proposals. These days I have readed (mainly in railway travels as "ligh readin") a book by Illya prigogyne titled "the laws of chaos". Prigogyne, a very prestigious nobel prize in chemistry, has been worried for a long time by the problem of the "arrow of time" (not joke intended). In this short book he present a formulation of classical mechanist in a probablistic fashion. He forgetes about classical orbits and uses a probablity of finding a particle in a certain trayectory. He makes this for classical mechanis justifiying the change in the "dterministic chaos". The keypoint is that afther the "liapunov time" (the inverse of the Liapunov exponen for a chaotic system, which has the meaing of the time the system need to "forget" his initial condtion with an 90%, or somthing similar, I don´t remember exactly, of accuracy). Later he proposes a similar formulation of quantum mechanics. But quantum mechanics is allready probabilistic. Well, the trick is that hw worries about the norm of the wave funtion, and not the wavefuntion itself, which is what has a clear probabilistic interpretation. He studies an equation for it and he finds tht it has the same structurre that the equation for the classical case. So he has a equal formlation for classical and quantum echanist. I will nt dive into the detaills now. Simply to add that he need to use spectral theory for operators with complex spectrum, and that he uses "rigged Hilbert Spaces" instead of commmon Hilbert Spaces. In fact this last thing is not new, The proper formulation of Q.M. requieres it. A rigged Hilber space is an space with contains L2 funtions together with distributions (in ths Schwartz sense,, i.. linear operators in the hilber space, speaking looselly) whose action in the test functions (an apropiate subset of the Hilber space, usually integrable and infintely derivable functions)is finite. As I say it it can sound reasonable (or at least I hope so), but when you read the book you find a lot of wordy statements whose realiztion is not too clear. It is a divulgation intended book (althought it has a lot of maths and may be it would be more acurate to call it an "essay"). Well, it´s last statement is that his formalisms gives a precise meaining to the arrow time. I wouldn´t like to discuse to somone who belongs to the status "I have writen more papers in peer to peer reviews that more sicentfics have readed". But on the other sied Prigoyne is not a physician (chemistry, maby be mathematician because of his works in complexity theory) but I don´t have any percpetion about that his works would have gained mayor attention (even thought the book is form the 98). At least I can say for sure that it is not of mayor concern for string theorists.
A diferent resolution of the problem of the waveefuntion colapse is the "conscence" viewpoint. If I am not wrong the idea can be backdated to Bohm. The idea is that the observer, who in earth in the last case is allways an human beeing, is the responsible of the collapse because of an act of conscience (I recomend to read a S.F book of the above mentioned author, Greg Egan, about this respect "quarentena", it´is not my favourite S.F. Book, but it plays a lot with this idea). A more recent propnent of this idea is the vry famouse physics and mathematician Roger Penrose. The firs exposition of his ideas can be readed in his book "the empirors new mind". There he tires to convence to the reader that that colapse is related to quantum gravityon one side and to human brain on the other. He states that a computer (touring machine) can´t work like a human mind and that the sacpe to this is that Human mind is not a computer because he can reduce the wave funtion. Well, beeing such a prominent figure he has had foundings to teste hemirically his ides (it is a googd thing that it would be empirically estable). I know that the firs experiments were not as he expected, but I didn´t read the second book about this line of reseach "the shadows of mind". And althougth I have readed some chapters of his most recent book "the road to realliy" I haven preaded the chapters about thisparticualr concern. Let´s say that I find it very unlikel, but of course it is just a personal opinion and may perfectly be wrong. But Penrose is not the only proponent of this idea. Other not so famouse physicist have similar ideas, and not having behind them te sucesffull trayectorie of Penrose they not allways are so well accepted. I think that based only in this criteria it is inapropiate to state someone as crackpoopt (at least not if you are not ready to say that Penrose is, and I guess none whoud dare, among other things, becuas I guess nobody thinks that Penrose could be nearly something similar).
To end up this long post I´ll say a few more things about the problem of wavefuntion reduction. Some time ago a friend asked me to try to do a "as serious as possible" background for the film "the buterrfly effect". That fil trates time travels an time paradox. Well, I was persuaded and I did some considerations (not intended never as something serious). I did a premise, wht if we go an step further with he probablistic meaning of the wavefuntion?. I played with the interpretation that the wavefuntion in addendum with th probalbitity of finding a prticle in a particular possition it gave the probablity of finding it in a given time. This, of course, meaned that you neded to search a reason of why you coudn´t be sure of the time you are. I did many reaonings, but the more funny was this, let´s supoose that we have a time machine. We pose somone in it in a manner in which he can´t see the enviroment. In a given time he sees a dinnosaur inside the time machine (behind a glass wall that protects him, of course). Later the dinnosaurs exits the time machine and at last observer exits also from the time machine back to ehre, and "when" he had entered in it. The question is did he travel to the past or somone bring the dinno to the present? It is, of course, a time orinted analogy of the Einstein elevtor whcih drived him to the equivalence principle. This proposal can be elaborated deeper, and I do so form time to time. But at least up to day it is just a funny entertaining. In fact the idea has grown a lot more that it´s intial purpose, and seems an interesting approach to the "problem of time 2in canonical quantum gravity. But be sure that if I would have some candidat to great development in a precise mathe formulation I would have tried to publish it in a peer to peer review. But that is not the case, at least untill now, and for certain that I wouldnt try to publish ideas about this paritcular "cronoquantum mechanics" withouh haveing published a some more conventional articles ìn well known and firmly stablisehed topics. It is not the enviroment for risked ideas, even if presented as modest proposals, be sure of that my eventual readers ;-).
But previously to speak about the central topic I´ll make a few disquisitions about the "crankpot" issue, partially because it is somewhat related to the sustainer of some atipic ideas, and partially because it is somewhat interesting in itself.
First let´s state some possible aceptions of the "cranckpot" term. The proper definiton of mental illnes would correspond to a professional of psicology. But as i´ll briefly discuss the acceptance of their definitions would imply that psicology would have a firm scientific status and curiously the term "cranckpot" is beeing used sometimes for people whose level of rigour is a few orders of magnitude upper to the one used ofthen in psicology, so "houston, houston, we have got a problem" ;-). For the shake of simplicity I´ll use some commonly accepted notions in psicology and some "common language" aceptions also, with the apropiate explanations when necessary. I´ll make a first broad distintion which will be, i hope, very helpfull. I´ll diferentiate "social related" mental illnes from "science" related ones.
In the field of "sociall related" mental insane scientifics we have some very famous ones. For example Kürt Göedel had some paranoic behaviours(in the commonly used sense of the term). He used to think that people wanted to put poisson in her foods, to international conspirations and similar things. Other, even more famous nowadays due to the book, and posterior film "a beateafull mind", is Jonh Nash. I have not readed the book and I am not sure if an aspect of the filmm is true or not, but I want to rescue it because I find it very interesting for the notion of a proper definition of "mentall illness". He, in the film, had alucinatory episodes where he saw (and heared) people who driven him to behave in a totally unaceptable social way. Concretelly the made him to belive that he was working for an inteligence goverment department. When the circunstances made him to realize that some particular persons that he saw were not "real" he clearly knew that he had a very serious problem. I guess that in reality He had a medical tratement with meds who made the alucintions to dissapear, but in the film (maybe in reality, it doesn´t matter for what I whant to wonder now) he relies in his logic to actually try to distinguish possilbe "alucinatory people" from real people (for example he says that one of the "ilusinary people", a girl, hadn´t grown for years which made clear for him that he couldn´t be real, even if his mind still madde him appear. Well, I find that this a very interesting question in itself. Science is, among other things, the aplication of logic to have fiable knowledge about the world. In this sense he was apliying it´s formation as a scientific to bypass a "bad work" of his perception. I have known personally people who have been prescribed mental disfunctions (maybe apropiatelly, maybe not) but who, despite it´s unusuall behaviour sometimes were very logical in it´s reasoning. Even if they considered very utipical, and scientific, ideas (an aspect unrelated to the problmatic social behaviour) such like considering the possible of telekinesis as real were able to accept that withouth a verificable under scientifics standards proofs of it that belief in t.k would be discarded. On the contrarie another person, whose social behaviour was never questioned as pathologic (nor I perosnally see why it could b otherwise), and who was a psicologyst itself, had the beief that some martial art prastice could allow some physically imposilbe things, like, for example, to defeat an opponent without actually touching it throught the use of "chi". Well , in this case the social and the scientific criteria (of respecting logic and it´s relation to proved, and verificable everywhere data) clearly gave a diferent answer to discern who was crazy and who not. If we go a litle bit far in this question we go into the problem of religions and in general "mistics" beliefs. In hiss book Time scape" the physicst and science ficition writer Gregory Benford rise the same question. From a purely scientific perspective the widelyy accepted religious beliefs are crazyness. He also stated that more "exotic" beliefs (evil possesions, communication with death people, etc) are commmon in a lot of people which otherwise were very conventinal in the social relations. What to think about ten?. I would even add that there is also a large amount of people who have a conventinal social behaviour, that don´t have any particular exotic belief but whose capabilitie to go into logical and scientific reasoning is null. People who are unable to do theminimally mental complex reasing and whose acceptance of "rational" ideas seems more due to the cassualities of their education that to any capability to discern by themselves sane from insane ideas. How to consider them.
I am going to add a las historic example, more for their interest in iself that for their importance in the rest of the post. I am talking about Newton in person. He joined in his person many of the previously asked questions. He had a very ugly social behaviour (sme modern spicologists analizing his biographys hipotesizes that he could have what is known as "Asperger symdrome"). He also had very deep religous beliefs (more of the 80% of his writes are reigious). Besides of his known scientific apportations he had worked in "alchemy", understood more in it´s magic implicatinos that in ther pre-chemical ones. Also in his pure scientific carrer he had made some risked experiments (he was near to end blind on one of his eyes becuase some atipical optical experiments. Well, said all this I think that I must add that it would not be just to totally judge his acts from a modern viewpoint. Before him sicence as we know it simply didn´t exist (It wouldn´t be exagerate to say thathe invented it). But that baby science didn´t explain a lot of things in the everyday life. I guess that it is not untill the achievement of the modern quantum mechanics (with the Schroedinger equation and inmediate developments) and it´s explanations of the chemics implied in everyday life that almost every earth commonly observed fact has (or hopfully has, despite it´s math complexity) an explanation under science. I think that it is more acceptable for a person in an almost totally unscientific world where almost every thing was far from a proper explanation to have magic, as well as religious beliefs. Althought on the other side Newton was a rationalist, or at leas that is relfected in another writng form Gregory Benford, wherewe see a modern physicist go to "ell" and finding there Newton who in all the years gone from it´s dead is tritying to made a "science" addecuate for hell, which can´t be an strictly rationalism science (becuase of the observable behaviour of hell).
Sic, I see that this historic remarks are very temptative and I have writen a lot withouth actually going into modern physics and it´s "crackpots". First I need a definiton of a "scientific crackpot". I mostly agree with the famouse one proposed By Jonh Baez. But I need to make a few comments. One of the examples proposed by Baez is Myron Evans. I had a knowledge of the Evans case prior to the knowledge of Baez. One friend of me has made his (brilliant, crowned with an article in nature) doctoral thesis in something called "topological electromagnetism". Basically it consists in a change of variables from the E and B fields to another ones which are apropiate to be used for an topolocial annalisis of the solutions. In particular if you do the usual compactification of R 3 by the point at infinite you get that his frontier S2. Well, you can see that the solutions of the Maxwell equations can be classifed by a topological quantitie related to the topological index (in the sense of the ides of Millnor)of the electric and magenetic fields viewed as funtions from S2 to S2. For a brief time I collaborated with my friend in a try to extend this ideas to Yang-Mills case, but it has passed a while from them and maybe I have explained bad some details (J.L, if you are reading this I invoke you to crrect possilbe mistakes ;-)). Well, the thing is that Myron Evans was interested in his works in order to publish a review of them in a forthcoming book publisehd by Elsevier devoted to Evans own ideas and related ones (like this of topological electromagnetism). We brieflly discused about the particular. But I think that it is out of place to say any more about this because of discreption (anyway, nothing offensive was said if someone worries about it). As a rsoult I tried to learn the work of Evans the problem was that none of the papers I coulr read for that time presented a complete description of them and referenced unavailable works. Well, that´is preciselly some of the cliams of Baez against Evans, I don´t know how actually the question is, but I wouldn´t want to centrate the question in Evans. He is only one well known exponent of uncommon scientific behaviour. Another name with an slighly similar problem is Podkeltnov. He claimed that a device, desgned for a diferent purpose that the one which mae it famous, with superconductors had "antigravitatory" behaviour. But he denied to give the precise configuration of the device because it could "give clouds" to other people who could thief his ideas. The last time I readed about it the NASA had repeated the experiment with a simplifeid desing without antigravitation (or to say properly,gravity shieldin). In this line also is the "Allais effect" of atipical behaviour of gravity while solar eclipses(Allais is a nobel prize in economy who has a formation as physicist). Similarly the last time I wondered about it the NASA was analizing a most precise version of his expermient. I think that the main reason these experiments are beeing considered by the NASA is because of the problem that the own NASA has with some of it´s satellites (I don´t just now remember the name, but it is a very famous open problem of unexplained gravitational anomalies).
Well, afther an enumeration of examples the definitin. A "scientific crackpot" would
be someone who defends an idea (that he belives very important) whose reliability is very unlikely and who, ofthem, refuse to give all the aspects of it because of being scared of "intelectual apropiation". I would distinguish here two cases. People without academic formation and people with it. I think it is not the same case somone whose maths doesn´t go, in the best of cases of basic calculus, from people who have a PhD in physicst, or maybe they are enigners. Those last people have (almost certainly) proved that at least in some part of his life had a proper knowledge of science. I guess that if they insist in presenting slopy ideas as fundamental advances, against the commmon belief, they are more suspectous of triying to gain more scientific recognition of what they deserve that really beliving "crazy" ideas. But this is not the end of the history. Not allways things are "black or white". There are some famouse cases where unlikely and marginated ideas in the end proved to be truth some years later (for example the theory of continental derive) so it is not just that easy to say for sure who is "scientifically" crazy or not. Even the lack of a math rigour is not always a criteria. The most famous case is Faraday, who is known but it´s famous law in electromagnetism. But it is less known that he had not mathformation and that he was guided mainly by intuition. Ok, nowadays a case just as Faraday is very unlikely, but apropiate translations of it coud happen i guess. And, of course, it would be unapropiate to relate "scientiic" to "social" crankpoptism.
Well, le´ts go, at last, with quantum mechanist. The most discused aspect of it is the problem of wavefuntion reduction. The most accepted viewpoint is the traditional, positivst, one "it works, don´t fix it". The "many words" Everet viewpoint is mathematically consistent but unboservable in practice. Decoherence seems the most realistic path (for a very good description of it I recomend to search into the web of another science fiction writer, Greg Egan, I am unable to find it just now the exact link). But there are more proposals. These days I have readed (mainly in railway travels as "ligh readin") a book by Illya prigogyne titled "the laws of chaos". Prigogyne, a very prestigious nobel prize in chemistry, has been worried for a long time by the problem of the "arrow of time" (not joke intended). In this short book he present a formulation of classical mechanist in a probablistic fashion. He forgetes about classical orbits and uses a probablity of finding a particle in a certain trayectory. He makes this for classical mechanis justifiying the change in the "dterministic chaos". The keypoint is that afther the "liapunov time" (the inverse of the Liapunov exponen for a chaotic system, which has the meaing of the time the system need to "forget" his initial condtion with an 90%, or somthing similar, I don´t remember exactly, of accuracy). Later he proposes a similar formulation of quantum mechanics. But quantum mechanics is allready probabilistic. Well, the trick is that hw worries about the norm of the wave funtion, and not the wavefuntion itself, which is what has a clear probabilistic interpretation. He studies an equation for it and he finds tht it has the same structurre that the equation for the classical case. So he has a equal formlation for classical and quantum echanist. I will nt dive into the detaills now. Simply to add that he need to use spectral theory for operators with complex spectrum, and that he uses "rigged Hilbert Spaces" instead of commmon Hilbert Spaces. In fact this last thing is not new, The proper formulation of Q.M. requieres it. A rigged Hilber space is an space with contains L2 funtions together with distributions (in ths Schwartz sense,, i.. linear operators in the hilber space, speaking looselly) whose action in the test functions (an apropiate subset of the Hilber space, usually integrable and infintely derivable functions)is finite. As I say it it can sound reasonable (or at least I hope so), but when you read the book you find a lot of wordy statements whose realiztion is not too clear. It is a divulgation intended book (althought it has a lot of maths and may be it would be more acurate to call it an "essay"). Well, it´s last statement is that his formalisms gives a precise meaining to the arrow time. I wouldn´t like to discuse to somone who belongs to the status "I have writen more papers in peer to peer reviews that more sicentfics have readed". But on the other sied Prigoyne is not a physician (chemistry, maby be mathematician because of his works in complexity theory) but I don´t have any percpetion about that his works would have gained mayor attention (even thought the book is form the 98). At least I can say for sure that it is not of mayor concern for string theorists.
A diferent resolution of the problem of the waveefuntion colapse is the "conscence" viewpoint. If I am not wrong the idea can be backdated to Bohm. The idea is that the observer, who in earth in the last case is allways an human beeing, is the responsible of the collapse because of an act of conscience (I recomend to read a S.F book of the above mentioned author, Greg Egan, about this respect "quarentena", it´is not my favourite S.F. Book, but it plays a lot with this idea). A more recent propnent of this idea is the vry famouse physics and mathematician Roger Penrose. The firs exposition of his ideas can be readed in his book "the empirors new mind". There he tires to convence to the reader that that colapse is related to quantum gravityon one side and to human brain on the other. He states that a computer (touring machine) can´t work like a human mind and that the sacpe to this is that Human mind is not a computer because he can reduce the wave funtion. Well, beeing such a prominent figure he has had foundings to teste hemirically his ides (it is a googd thing that it would be empirically estable). I know that the firs experiments were not as he expected, but I didn´t read the second book about this line of reseach "the shadows of mind". And althougth I have readed some chapters of his most recent book "the road to realliy" I haven preaded the chapters about thisparticualr concern. Let´s say that I find it very unlikel, but of course it is just a personal opinion and may perfectly be wrong. But Penrose is not the only proponent of this idea. Other not so famouse physicist have similar ideas, and not having behind them te sucesffull trayectorie of Penrose they not allways are so well accepted. I think that based only in this criteria it is inapropiate to state someone as crackpoopt (at least not if you are not ready to say that Penrose is, and I guess none whoud dare, among other things, becuas I guess nobody thinks that Penrose could be nearly something similar).
To end up this long post I´ll say a few more things about the problem of wavefuntion reduction. Some time ago a friend asked me to try to do a "as serious as possible" background for the film "the buterrfly effect". That fil trates time travels an time paradox. Well, I was persuaded and I did some considerations (not intended never as something serious). I did a premise, wht if we go an step further with he probablistic meaning of the wavefuntion?. I played with the interpretation that the wavefuntion in addendum with th probalbitity of finding a prticle in a particular possition it gave the probablity of finding it in a given time. This, of course, meaned that you neded to search a reason of why you coudn´t be sure of the time you are. I did many reaonings, but the more funny was this, let´s supoose that we have a time machine. We pose somone in it in a manner in which he can´t see the enviroment. In a given time he sees a dinnosaur inside the time machine (behind a glass wall that protects him, of course). Later the dinnosaurs exits the time machine and at last observer exits also from the time machine back to ehre, and "when" he had entered in it. The question is did he travel to the past or somone bring the dinno to the present? It is, of course, a time orinted analogy of the Einstein elevtor whcih drived him to the equivalence principle. This proposal can be elaborated deeper, and I do so form time to time. But at least up to day it is just a funny entertaining. In fact the idea has grown a lot more that it´s intial purpose, and seems an interesting approach to the "problem of time 2in canonical quantum gravity. But be sure that if I would have some candidat to great development in a precise mathe formulation I would have tried to publish it in a peer to peer review. But that is not the case, at least untill now, and for certain that I wouldnt try to publish ideas about this paritcular "cronoquantum mechanics" withouh haveing published a some more conventional articles ìn well known and firmly stablisehed topics. It is not the enviroment for risked ideas, even if presented as modest proposals, be sure of that my eventual readers ;-).
Sunday, October 07, 2007
Topological geometrodynamics
While I orginize ideas to post about more conventional ideas in physics (or science in general)I am goint to post today about topological geometrodynamics.
Ther first time I got knowledge of these thoery was as a consecuence of seraching for p-adic numbers in the net. If I don´t remember bad I did that rsearch because I was triying to understand some chapters in that monument to abstract mathemathics writen by Jean Dieudenot which respond to the name "panoramic of pure mathemthics" (bac translation to english of the spanish title, maybe it is not quite exact).
At last I found a very good introduction to the subject of p-adic numbers in a physics report article about p-adic strings so I didn´t go too far with topological geometrodynamics. One reason for that was that the theory depends on mini-superspaces and in that time my knowledge on the Wheleer-de Witt equation was too limited to even do the try.
Well, nowadays the author of TGD, topolgoical geometrodynamics, Matti Pitkanen, is a blogger, you can read him here. I have some idea that somewhere in internet there is a listing about theories of quantum gravity and that TGD is included as a candidate. Well, in all those years a¡I never have found the time to read some of the papers of Pitkanen, at most I had readed some entries of his blog or some comments of him on another blogs. Now, while around 10 hours of studying string theory I decided to do a few breaks to try to get a bried idea about the basics of TGD. For that I followed the links in the Pitkanen blog and went here: http://www.helsinki.fi/~matpitka/powerpoint.html
Concretely I readed the three main pdf´s. Also I readed the brief presentation, kind of guided tour for very quick ideas for the 400 book on the subject presented here: http://www.helsinki.fi/~matpitka/tgdppt/tgdbiogeneralweb.mht!tgdbiogeneralweb_files/frame.htm
Well, be sure that with that background my knowledge of the subject is really poor, to say the best, but anyway I am going to tray to present a few concepts.
What is these TGD? Well, aparently in part it is a way to save the energy problem in general relativity. This problem consists in that there is not a good notion of the energy of an space time. You can give a definition of energy using pseudotensors (magnittudes which are tensors only under more restircted transformations thtat the genral diffeomorphism group), the most famous one bein the Landau one. Another thing that you can do is to define it for certain special space times with special conditions (basically poincaré invariance) at infninity. This is a definition for the global spacetime and not a local one. The most famous of this definitions is the ADM (arnowitz-desser-misner) mass. This problem is closely related to the lack of a hamiltonian formulation for general relativity. I have commented, in spanish, the problem while I introduced LQG. Anyway, the key point is that genralrelativity is a fully constrained system, that is the hamiltonian is all it constraints. In the no LQG canonical gravity the most important of this constraints is the above mentioned Wheler-de witt equation.
Hw does TGD afront the energy problem. Well, it represnt spacetime as a surface embeded in a higer dimensional space, concretely H=M4xCP2. M is the Minkowsky space time and CP2 goes for the comple projective plane (I guess). At this time of the presentation Pitkanen says a few things whose reason I don´t understand. for example it relates this choice to particle physics, or at least quantum numbers, well, be sure that I don´t see areaosn for it in that exposition.
Later he says:
"Simple topological considerations lead to the notion of manysheeted
space-time and general vision about quantum TGD. In particular,
already classical considerations strongly suggests fractality meaning infinite
hierarchy of copies of standard model physics in arbitrarily long length and
time scales"
I neither understand this. The "manyshheted" part maybe could be related to the fact that in canonical quantum gravity you must do foliation of spacetime. The "fractality", well, I supose it referes to the well known fractals discovered and popularized by Mandelbroit, but, what the hell do they here? I mean, he says infinite copies of the standar model at arbitrary length. Certianly that looks like a fractal (selfsimilarity), but How did we go to an statement about the solution of the energy problem going to an upper dimension spacetime to all of this?
The only thing with I see with a certian logic is the reference to the Wheelers superspace. A superspace is. lossely speaking, a selection of a restricted metrics addecuated for a particular problem in general relativity (mainly for cosmological problems). There is a deduction of the Wheler-de witt eqution as a WKB aproximation to the euclidean path integral aproach to quantum gravity, so this could be understood as semiclassical quantum gravity in an upper dimensional spacetime, But, where the standar modell appears in here?.
Later he speaks about p-adics and p-adics mass and imbeddings. P-adic numbers are a very curious concept. In the construction of real numbers from fractionary ones one uses Cauchy sequences. If one makes the same construction, but instedad of using the usual norm for the Cauchy sequence one uses a diferent one based on prime descompostions (very loosely speaking)by a certain prime number you get p-adic numbers. In fact the prime number p is arbitrary, so you have as many p-adic numbers as prime numbers. There is some completion of the primes by something called adelic numbers (I am studiying now algebraic geometry I try to keep number theory as far of me as I can, so don´t ask me the details, please xD).
Well, once agian, where did p-adic numbers appear?. In p-adic strings it is argued that in real experiments you never obtain as a resoult of a measure a "pure" real number, that is, you always get an enteire or a fractionary number. Maybe Pitkanen tries to argue something similar to this, but once agian in the order of preesentation of his pdf, concretely in here: http://www.helsinki.fi/~matpitka/tgdppt/absTGD.pdf this is the order wollowed, and I guess that the possible readers will agree that it is really hard to disguish a logic in the derivation of the asserted results.
Later he presents a second part of the theory where he claims that he uses three dimenional lighlike hypersurfaces which plays the role of (super)string theries, they reproduce super kac-moody algebras (in fact I would think that more representative of string theory would be virasoro algebras, but well, who knows?). To me this lightlike hypersurface stuff remember me twistor theory and not string theory, but for sure, once again, a 6 pdf paper is a very bad way toget a proper idea of a 400 hundred book . One thing that I must say here is if these hypersurfaces resemble string theory they must have associated states which could be identified with ordinary fields in minkowsky space and It would be here where I would expect to see the appearence of the standard model and ot in the embeding of ordinary spacetime in an upper spacetime.
Well, a lot of question undoubtly. I have made this post like an invitation to pitkanen to discuss a bit his theory if he is interested. I am tired to see his journal with almost no comments to posts where he speaks about scientific facts, and instead seeing entires of very well known physicians talking about topics more appropiate for "peopple magazine" or similars (i.e. absoluttely unrelated to science) full of comments so I try somehow to equilibrate that balance.
UPDATE: Matti Pitkanen has writen an updated introdution to TGD. He has given in a blog entry a brief review of it. You can read it here
Ther first time I got knowledge of these thoery was as a consecuence of seraching for p-adic numbers in the net. If I don´t remember bad I did that rsearch because I was triying to understand some chapters in that monument to abstract mathemathics writen by Jean Dieudenot which respond to the name "panoramic of pure mathemthics" (bac translation to english of the spanish title, maybe it is not quite exact).
At last I found a very good introduction to the subject of p-adic numbers in a physics report article about p-adic strings so I didn´t go too far with topological geometrodynamics. One reason for that was that the theory depends on mini-superspaces and in that time my knowledge on the Wheleer-de Witt equation was too limited to even do the try.
Well, nowadays the author of TGD, topolgoical geometrodynamics, Matti Pitkanen, is a blogger, you can read him here. I have some idea that somewhere in internet there is a listing about theories of quantum gravity and that TGD is included as a candidate. Well, in all those years a¡I never have found the time to read some of the papers of Pitkanen, at most I had readed some entries of his blog or some comments of him on another blogs. Now, while around 10 hours of studying string theory I decided to do a few breaks to try to get a bried idea about the basics of TGD. For that I followed the links in the Pitkanen blog and went here: http://www.helsinki.fi/~matpitka/powerpoint.html
Concretely I readed the three main pdf´s. Also I readed the brief presentation, kind of guided tour for very quick ideas for the 400 book on the subject presented here: http://www.helsinki.fi/~matpitka/tgdppt/tgdbiogeneralweb.mht!tgdbiogeneralweb_files/frame.htm
Well, be sure that with that background my knowledge of the subject is really poor, to say the best, but anyway I am going to tray to present a few concepts.
What is these TGD? Well, aparently in part it is a way to save the energy problem in general relativity. This problem consists in that there is not a good notion of the energy of an space time. You can give a definition of energy using pseudotensors (magnittudes which are tensors only under more restircted transformations thtat the genral diffeomorphism group), the most famous one bein the Landau one. Another thing that you can do is to define it for certain special space times with special conditions (basically poincaré invariance) at infninity. This is a definition for the global spacetime and not a local one. The most famous of this definitions is the ADM (arnowitz-desser-misner) mass. This problem is closely related to the lack of a hamiltonian formulation for general relativity. I have commented, in spanish, the problem while I introduced LQG. Anyway, the key point is that genralrelativity is a fully constrained system, that is the hamiltonian is all it constraints. In the no LQG canonical gravity the most important of this constraints is the above mentioned Wheler-de witt equation.
Hw does TGD afront the energy problem. Well, it represnt spacetime as a surface embeded in a higer dimensional space, concretely H=M4xCP2. M is the Minkowsky space time and CP2 goes for the comple projective plane (I guess). At this time of the presentation Pitkanen says a few things whose reason I don´t understand. for example it relates this choice to particle physics, or at least quantum numbers, well, be sure that I don´t see areaosn for it in that exposition.
Later he says:
"Simple topological considerations lead to the notion of manysheeted
space-time and general vision about quantum TGD. In particular,
already classical considerations strongly suggests fractality meaning infinite
hierarchy of copies of standard model physics in arbitrarily long length and
time scales"
I neither understand this. The "manyshheted" part maybe could be related to the fact that in canonical quantum gravity you must do foliation of spacetime. The "fractality", well, I supose it referes to the well known fractals discovered and popularized by Mandelbroit, but, what the hell do they here? I mean, he says infinite copies of the standar model at arbitrary length. Certianly that looks like a fractal (selfsimilarity), but How did we go to an statement about the solution of the energy problem going to an upper dimension spacetime to all of this?
The only thing with I see with a certian logic is the reference to the Wheelers superspace. A superspace is. lossely speaking, a selection of a restricted metrics addecuated for a particular problem in general relativity (mainly for cosmological problems). There is a deduction of the Wheler-de witt eqution as a WKB aproximation to the euclidean path integral aproach to quantum gravity, so this could be understood as semiclassical quantum gravity in an upper dimensional spacetime, But, where the standar modell appears in here?.
Later he speaks about p-adics and p-adics mass and imbeddings. P-adic numbers are a very curious concept. In the construction of real numbers from fractionary ones one uses Cauchy sequences. If one makes the same construction, but instedad of using the usual norm for the Cauchy sequence one uses a diferent one based on prime descompostions (very loosely speaking)by a certain prime number you get p-adic numbers. In fact the prime number p is arbitrary, so you have as many p-adic numbers as prime numbers. There is some completion of the primes by something called adelic numbers (I am studiying now algebraic geometry I try to keep number theory as far of me as I can, so don´t ask me the details, please xD).
Well, once agian, where did p-adic numbers appear?. In p-adic strings it is argued that in real experiments you never obtain as a resoult of a measure a "pure" real number, that is, you always get an enteire or a fractionary number. Maybe Pitkanen tries to argue something similar to this, but once agian in the order of preesentation of his pdf, concretely in here: http://www.helsinki.fi/~matpitka/tgdppt/absTGD.pdf this is the order wollowed, and I guess that the possible readers will agree that it is really hard to disguish a logic in the derivation of the asserted results.
Later he presents a second part of the theory where he claims that he uses three dimenional lighlike hypersurfaces which plays the role of (super)string theries, they reproduce super kac-moody algebras (in fact I would think that more representative of string theory would be virasoro algebras, but well, who knows?). To me this lightlike hypersurface stuff remember me twistor theory and not string theory, but for sure, once again, a 6 pdf paper is a very bad way toget a proper idea of a 400 hundred book . One thing that I must say here is if these hypersurfaces resemble string theory they must have associated states which could be identified with ordinary fields in minkowsky space and It would be here where I would expect to see the appearence of the standard model and ot in the embeding of ordinary spacetime in an upper spacetime.
Well, a lot of question undoubtly. I have made this post like an invitation to pitkanen to discuss a bit his theory if he is interested. I am tired to see his journal with almost no comments to posts where he speaks about scientific facts, and instead seeing entires of very well known physicians talking about topics more appropiate for "peopple magazine" or similars (i.e. absoluttely unrelated to science) full of comments so I try somehow to equilibrate that balance.
UPDATE: Matti Pitkanen has writen an updated introdution to TGD. He has given in a blog entry a brief review of it. You can read it here
Thursday, October 04, 2007
Why Loop quantum gravity?
I had a few entries in this blog wondering about some unnaturallness that i find in string theory.
On the other side I am aware about what some people in the string theory comunity think about LQG, so I have decided to make a post about why someone could worry about LQG nowaday (or why not).
One important thing is your academic enviroment. One of my teachers (probably the best in the field of string theory, in my facoulty, when I was studiying) played atention to LQG in his general reviews about quantum gravity. By LQG I mean a broad conception which included to explain the wheeler-de Witt equation and the Astekhar connection in paers previous to the actual form of canonical LQG. In newer papers he stills includes some information about LQG (altought his main interest is in strig theory). I never asked him personally about his opinions so maybe he was just beeing polite, but from his papers one would think that it is not crazy to study LQG. So judging from direct influence of your teachers it was a free way to study LQG.
For a brief (unhappilly too brief) time I beguined to study for a tessis in geometrical quantization (in the math faculty). When later I saw that geometrical quantization played a role in LQG I really enjoyed it because it somewhat meaned that the time I studied geometrical quantization was not lost time.
As I stated before in this blog for a time my knowledge of string theory came mainly from the two books of Michio Kaku and the Lüst-Theisen (and secondary in theh Hatfield book "quantum field theouy of point particles and strings"). While they cover fine the "first revolution" string theory I must say that the second KAku book (string theory and M-theory) althought readed a posteriory when you allready understand the topics, is correct I feel that it doesn´t makes a good job presenting the intuitive ideas of the second string revolution. It would need more space to trate the topics.
Another aspect is that in my faculty library always there has been a democratic representation of string and LQG. You get all the new books in string theory (nowadys you can get the Michel Dine and Becker-Becker Schwartz ones) as well as books by LGG people (for example the book o Baez "lopps, knots and gauge fields). Also you can have books in euclidean quantum gravity and other topics (A hurray for my faculty library).
Also I must say that previously to going hard into string theory I wanted to have an as strong as possible basic in general relativity and quantum field theory. The quantum field theory books usually contained an intro to string theory (kaku´s book on QFT). Pariticularly usefull I found the book "particle physics and cosmology" to understand some more advanced topics in QFT and physicis beyond the standard model. But more important than QFT was for me general relativity. My main source where the book by wald and a really extense book about black holes writen by Frolov & Novikov. Also I found very usefull the online website "living reviews on relativity". I think that I don´t need to say that a general relativity formation favours to apreciate LQG over string theory.
Well, all these means that there is no a priory pressure agianst LQG. This leads me to a famous paper in 2003 (or around that date) in which it is presented the new (for that time) canonical LQG, with the very interesting promise of a soon to come experiment (the one related to the MAGIC experiment that I bloged in the last entry). As a complement living reviews had a somewhat complementary introduction to canonical LQG. You can doubt about the goodness of he physics behind, but as an introduction/presentation both articles (specially the one by Thieman) are ver well writen.
With all these background to study LQG and not string theoy seemed a very good idea. Also an a priory netural forum, physics forums, was very pro LQG (by that time the forum in www.superstringtheory.com had been hacked).
Well, what came next? I guest that LQG has somewhat killed itself. Canonical quantum gravity seemed a very elegant and usefull reformulation of the old idea behind wheeler de witt equation (reached from canonical gravity, not euclidean quantum gravity) But very soon the atention was deviated to spin-foams, arguably because of "the problem of time". But spin foams are not so obviously related to gravity as canonical LQG. I mean, there one starts not from the general relativty lagrangian, that is what one, at least naively would expect but from lagrangians which hopfully, with some constraints, reproduce classical general relativiy. Worse still, it is not clear which of all them is favoured so people study many of them (ok, the Crane one´s is the most favoured, seemingly).
But the history doesn´t end there. It is adviced to study causal triangulations, and quantum groups. Not to say there is not a clear relation betwen all these aporaches (besides a like ofr discretized space-time). I must say that I studied spin foams, mainlly thanks to the review articles by Alejandro Perez, which I find very well writen, and which, IMHO present the physics ideas a lot better than the reviews by Jon Baez. What I couldn´t find the interest enoguht to read are the recomended literature about causal triangulations and the like (maybe because I never liked too much lattice QCD, but I guess that it was not that the ultimate cause).
Later I found Lubos Motl blog and it´s comments about some famous papers in LQG (as for example the one in the calculation of the graviton propagator), and well, I beguined to be aware abouth that fraticide strings wars and the "not even wrong" blog (whcih at first I thought it was a blog pro string theory, why else would someone would devote so atention to string theory afhter all? :P).
Most interesting that his attacks to LQG I found interesting in Lubos Motl the presentation of some intuitive ideas of string theory that were somewhat ausent in the literature I had readed.
Well, nowadays I don´t really follow too much LQG. I am aware about it´s developments while I am devoting time to update my string theory knowledges (I feel I am ending that task at last, at least in the main fields, and some not so mianstream aspects also). Would I give any advise against LQG?
Well, LQG people, at least someones, have a like for "Filosofing". I find entertaining reading the prose of their papers (I specially recomend one containing a discusion about the entropy of black holes and if some would count or not the "inner" degrees of freedom. I would recomend people to read also the introductory papers that I have cited, and maybe also some paper of Router about his claim that conventinal quantum gravity has a renormalization group fixed point. Later I would recomend that people to read some of the frequent blog entries on Lubos Motl blog critizazing LQG approachs. At that point it would be an individual decision of every one to go further on LQG or not. But I think that not devoting the relativelly few time that it requires to read the papers I mention(if somone is interested I could give him the exact references if he is not abble to find them himself) is not a good idea.
Well, I have been almost a mounth without any post. In this time I have been reading about some topics, that I hope that my eventual readers could find interesting.
On the other side I am aware about what some people in the string theory comunity think about LQG, so I have decided to make a post about why someone could worry about LQG nowaday (or why not).
One important thing is your academic enviroment. One of my teachers (probably the best in the field of string theory, in my facoulty, when I was studiying) played atention to LQG in his general reviews about quantum gravity. By LQG I mean a broad conception which included to explain the wheeler-de Witt equation and the Astekhar connection in paers previous to the actual form of canonical LQG. In newer papers he stills includes some information about LQG (altought his main interest is in strig theory). I never asked him personally about his opinions so maybe he was just beeing polite, but from his papers one would think that it is not crazy to study LQG. So judging from direct influence of your teachers it was a free way to study LQG.
For a brief (unhappilly too brief) time I beguined to study for a tessis in geometrical quantization (in the math faculty). When later I saw that geometrical quantization played a role in LQG I really enjoyed it because it somewhat meaned that the time I studied geometrical quantization was not lost time.
As I stated before in this blog for a time my knowledge of string theory came mainly from the two books of Michio Kaku and the Lüst-Theisen (and secondary in theh Hatfield book "quantum field theouy of point particles and strings"). While they cover fine the "first revolution" string theory I must say that the second KAku book (string theory and M-theory) althought readed a posteriory when you allready understand the topics, is correct I feel that it doesn´t makes a good job presenting the intuitive ideas of the second string revolution. It would need more space to trate the topics.
Another aspect is that in my faculty library always there has been a democratic representation of string and LQG. You get all the new books in string theory (nowadys you can get the Michel Dine and Becker-Becker Schwartz ones) as well as books by LGG people (for example the book o Baez "lopps, knots and gauge fields). Also you can have books in euclidean quantum gravity and other topics (A hurray for my faculty library).
Also I must say that previously to going hard into string theory I wanted to have an as strong as possible basic in general relativity and quantum field theory. The quantum field theory books usually contained an intro to string theory (kaku´s book on QFT). Pariticularly usefull I found the book "particle physics and cosmology" to understand some more advanced topics in QFT and physicis beyond the standard model. But more important than QFT was for me general relativity. My main source where the book by wald and a really extense book about black holes writen by Frolov & Novikov. Also I found very usefull the online website "living reviews on relativity". I think that I don´t need to say that a general relativity formation favours to apreciate LQG over string theory.
Well, all these means that there is no a priory pressure agianst LQG. This leads me to a famous paper in 2003 (or around that date) in which it is presented the new (for that time) canonical LQG, with the very interesting promise of a soon to come experiment (the one related to the MAGIC experiment that I bloged in the last entry). As a complement living reviews had a somewhat complementary introduction to canonical LQG. You can doubt about the goodness of he physics behind, but as an introduction/presentation both articles (specially the one by Thieman) are ver well writen.
With all these background to study LQG and not string theoy seemed a very good idea. Also an a priory netural forum, physics forums, was very pro LQG (by that time the forum in www.superstringtheory.com had been hacked).
Well, what came next? I guest that LQG has somewhat killed itself. Canonical quantum gravity seemed a very elegant and usefull reformulation of the old idea behind wheeler de witt equation (reached from canonical gravity, not euclidean quantum gravity) But very soon the atention was deviated to spin-foams, arguably because of "the problem of time". But spin foams are not so obviously related to gravity as canonical LQG. I mean, there one starts not from the general relativty lagrangian, that is what one, at least naively would expect but from lagrangians which hopfully, with some constraints, reproduce classical general relativiy. Worse still, it is not clear which of all them is favoured so people study many of them (ok, the Crane one´s is the most favoured, seemingly).
But the history doesn´t end there. It is adviced to study causal triangulations, and quantum groups. Not to say there is not a clear relation betwen all these aporaches (besides a like ofr discretized space-time). I must say that I studied spin foams, mainlly thanks to the review articles by Alejandro Perez, which I find very well writen, and which, IMHO present the physics ideas a lot better than the reviews by Jon Baez. What I couldn´t find the interest enoguht to read are the recomended literature about causal triangulations and the like (maybe because I never liked too much lattice QCD, but I guess that it was not that the ultimate cause).
Later I found Lubos Motl blog and it´s comments about some famous papers in LQG (as for example the one in the calculation of the graviton propagator), and well, I beguined to be aware abouth that fraticide strings wars and the "not even wrong" blog (whcih at first I thought it was a blog pro string theory, why else would someone would devote so atention to string theory afhter all? :P).
Most interesting that his attacks to LQG I found interesting in Lubos Motl the presentation of some intuitive ideas of string theory that were somewhat ausent in the literature I had readed.
Well, nowadays I don´t really follow too much LQG. I am aware about it´s developments while I am devoting time to update my string theory knowledges (I feel I am ending that task at last, at least in the main fields, and some not so mianstream aspects also). Would I give any advise against LQG?
Well, LQG people, at least someones, have a like for "Filosofing". I find entertaining reading the prose of their papers (I specially recomend one containing a discusion about the entropy of black holes and if some would count or not the "inner" degrees of freedom. I would recomend people to read also the introductory papers that I have cited, and maybe also some paper of Router about his claim that conventinal quantum gravity has a renormalization group fixed point. Later I would recomend that people to read some of the frequent blog entries on Lubos Motl blog critizazing LQG approachs. At that point it would be an individual decision of every one to go further on LQG or not. But I think that not devoting the relativelly few time that it requires to read the papers I mention(if somone is interested I could give him the exact references if he is not abble to find them himself) is not a good idea.
Well, I have been almost a mounth without any post. In this time I have been reading about some topics, that I hope that my eventual readers could find interesting.
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