tag:blogger.com,1999:blog-2497048322692604828.post1973780796486582032..comments2022-10-08T11:53:53.832-07:00Comments on The Golden Mean in Quantum Mechanics and High Energy Physics: The Golden Ratio and Understanding the UniverseMohammedhttp://www.blogger.com/profile/16988659862333776903noreply@blogger.comBlogger64125tag:blogger.com,1999:blog-2497048322692604828.post-62393935379708379672010-04-14T11:07:37.850-07:002010-04-14T11:07:37.850-07:00(25-3)
‘tHooft answered as follows: “We thought ...(25-3)<br /> ‘tHooft answered as follows: “We thought of such possibility. As far as the real world is concerned.............................................Weltman once thought there might be real physics in non integer dimensions but he never got anywhere with that............................................ I do know what negative dimensions mean................................it is anti-commuting coordinate.” Those in the know must be exhilarated to see how<br />far ahead of anybody E-Infinity group was. With all the due respect and it is a genuine respect we have for Gerard ‘tHooft, his statement could not remain unchallenged. Mohamed El Naschie derives the exact value of the Hausdorff dimension of quantum spacetime namely 4.23606799 from ‘tHooft’s dimensional regularization and he gets real physics out of it. We use the word real physics with large doses of salt. Talking about real physics in a simple way in the realm of quantum gravity can be the most misleading thing which one can do. We do not intend to dwell on the illusive nature of reality. However those who are philosophically inclined to use words like real physics should know about dozens of incidents where inclination to reality made reality disappear. The paper in question was entitled: On ‘tHooft dimensional regularization in E-Infinity space, Chaos, Solitons & Fractals 12 (2001) pp 851-858. This paper was preceded by another paper<br />which was entitled: “ ‘Thooft dimensional regularization implies Cantorian Space time.” The paper was presented at a conference which the great man ‘tHooft himself attended. We sincerely hope that this closes the subject which Oh! So many lesser mortals try to keep artificially alive again and again on certain blogs. When you multiply 4.23606799 by ten you get 42.3606.........and this is the non super symmetric inverse grand unification coupling. Let us discuss how this value as well as the super symmetric value namely 26.18..........could be obtained from the fundamental equation of unification. This is what we will do in part 2 of this communicationE-Infinity Communicationnoreply@blogger.comtag:blogger.com,1999:blog-2497048322692604828.post-21248946344119837102010-04-14T11:07:02.167-07:002010-04-14T11:07:02.167-07:00(25-2)
They wrote “Imagine our elation when the nu...(25-2)<br />They wrote “Imagine our elation when the number of<br />dimensions came out as 4 (more precisely as 4.02 plus minus 0.1.)It was the first time anyone had ever derived the observed number of dimensions from first principles. “ We in E-Infinity theory group can imagine their elation but we ask you at the same time to imagine our alienation when no reference whatsoever was made in this paper or any of similar papers published at the same time in Physics Review Letter and the Journal of the Institute of Physics to our work. The first derivation of the dimensionality of quantum space time from first principle was made as you can check yourselves at least 9 years earlier. In fact the value found by Ambjorn et al namely 4.02 was found to be a spectral dimension and obtainable using other methods. One of these methods is the Bose Einstein statistics of El Naschie was found approximately 16 years earlier. When you see the structure of the paper in Scientific American you see that the logic expressed in the<br />fractal figures on page 28 and 29 including the Menger Sponge and the Serpinski Gasket follow the same logic of El Naschie’s paper in Il Nuovo Cimento and the Journal of the Franklin Institute. Rediscovering things again and again was not uncommon in the past. We mean no disrespect to anybody when we point out these facts. What is important is how we react or others reacted to these facts. Something positive came out of this any case. Cantor sets are in quantum mechanics to stay. Random cantor sets with golden mean Hausdorff dimension are meantime an experimental fact. No amount of propaganda could possibly change these facts. Should we have unintentionally compromised anyone then we as a group apologize collectively as long as the issue of priority is restored. For science priority is unimportant. For scientists it is important. The Yang-‘tHooft know that better than anyone else. He wrote a great deal about something similar which happened to<br />him in connection with the strong interaction. This is the subject which we will discuss shortly. Before doing that however let us recall something extremely important in various respects which involves Nobel Laureate Gerard ‘tHooft. In an excellent book on quantum gravity, edited by Daniel Oriti published in Cambridge this year but dated 2009, Gerard ‘tHooft makes the following answers to questions on page 155. The question was by L. Crane about non integer Hausdorff dimension in quantum gravity.E-Infinity Communicationnoreply@blogger.comtag:blogger.com,1999:blog-2497048322692604828.post-83288194816983880162010-04-14T11:05:51.083-07:002010-04-14T11:05:51.083-07:00Communication No. 25 (Part 1) (1-1)
The Fundamenta...Communication No. 25 (Part 1) (1-1)<br />The Fundamental Equation of Unification of E-Infinity Theory as a harmonization of the corresponding renormalization group equation of classical high energy physics.<br />After considering many fundamental problems in non linear dynamics and its possible connection to quantum physics, a paper entitled: Complex Dynamic in a 4D Peano-Hilbert Space appeared in Il Nuovo Cimento in 1992. This was a famous journal where Einstein published some of his work but after a short period of stagnation the Journal was re-launched and renamed: The European Journal of Physics. The author of the paper is Mohamed El Naschie and he wrote it during his Cambridge time. It can be found in Vol. 107 B, N. 5 – Maggio 1992 pp.583-594. In this paper Mohamed El Naschie made an explicit connection though in general terms between quantum mechanics and fractals. Sub section 8, page 593 is titled: Quantum mechanics, Dirac’s vacuum and foam space-time. He was not accurate at that time by thinking that Wheeler’s foam space time is a proper fractal. Nevertheless the point was made. In fact he mentioned explicitly that lifting the Menger foam<br />to 4 dimensions leads to something very similar to our space time. He was clearly not yet aware of the fundamental role played by randomness and was still working with a deterministic cantor set. In a paper published at about the same time in the Journal of Franklin Institute, Mohamed El Naschie expanded the idea, discussed in more detail the Menger sponge and expressed his hope that fractal cantorian spacetime can easily resolve all the paradoxes associated with quantum mechanics. Mohamed El Naschie continued his effort until he determined the exact expectation value of the topological and Hausdorff dimension of quantum space time. He perfected the theory mathematically after discovering the relevance of Jones’ Invariant and quantum groups to his work. About 7 years after his the mentioned Nuovo Cimento paper, the mathematical basis and the connection to hyperbolic geometry and KAM theorem became crystal clear. Just as two examples for his work<br />in this period, I may quote the following two papers: 1. Jones’ Invariant, Cantorian Geometry and Quantum Space-time. 2. Quantum Groups and Hamiltonian Sets on a Nuclear Spacetime Cantorian Manifold. Both papers are published in the 1999 volume of Chaos, Solitons & Fractals. In other words latest by 1999 the following fundamental facts were proven by Mohamed El Naschie and elaborated upon extensively by J. Huan-He, Marek-Crnjac and Erwin Goldfain. First the building blocks of quantum spacetime are random cantor sets with a golden mean Hausdorff dimension. Second, the expectation value of the topological dimension of the space time core is exactly 4. On the other hand, the corresponding exact Hausdorff dimension is exactly 4 plus the golden mean to the power of 3. That is to say, it is 4.23606799.... In 2008 the paper by Jan Ambjorn, Jerry Jurkiewicz and Renate Loll appeared in Scientific American. The paper uses computer simulation extensively. Well<br />you could say it is not exactly computer simulation but computer computation of a Regg calculus approximation of a quantum gravity model. You could also view it as an improvement of Regg calculus using Ambjorn’s triangulation. Professor Jan Ambjorn from the Neils Bohr Institute in Copenhagen is a world authority on triangulation technique of this kind. Leaving details aside and to make a long story short, the main thrust and results of the paper are the following: Quantum space time is best modeled using cantor sets as building blocks. Second, assuming Prigogine’s arrow of time on the quantum level, things work out perfectly. Third and most importantly, a space time dimension of 4.02 was worked out from first principles for the first time. To see how much emphasis the authors put on this fact, let us quote verbatim what they wrote on page 29 of their July 2008 Scientific American Paper.E-Infinity Communicationnoreply@blogger.comtag:blogger.com,1999:blog-2497048322692604828.post-79873325919409388262010-04-14T10:55:31.195-07:002010-04-14T10:55:31.195-07:0023-3
To be able to complete the job, you have to f...23-3<br />To be able to complete the job, you have to free yourself of all prejudice and have no hiccups about fractals, transfiniteness and golden means. The result of this effort will be evident from the following equation of E-Infinity theory.In general the equation reads as following: the inverse unification coupling is equal to the<br />following sum: alpha bar 3 plus alpha bar 4 plus the natural logarithm of the ratio of the unification mass or energy divided by a reference mass or energy. This logarithm is multiplied by the factor which has to do with super symmetry. In the classical form this equation is not much different but it is clumsy and filled with numerical factors which a beginner could not make heads or tails of. It takes a long time to familiarize oneself with it. The E-Infinity theory version is by contrast perfect. Let me mention first that the discovery of the Logarithmic scaling decay was a major step in high energy physics. I forgot who discovered it first and I forgot a lot of things about its history which I read once upon a time. I do not remember where I read it but I did. We all would be very grateful for readers of these comments and I mean readers who are only interested in science could draw our attention to this logarithmic law and give us its background<br />and history.That would be very nice indeed and would save us a lot of work to dig in old papers and textbooks. E-Infinity took this logarithmic law and changed it de facto to a golden mean scaling of E-Infinity hierarchy. <br />In the next communication we will show you these things step by step. We hope also that you will notice that the inverse problem becomes tractable and lead to a simple solution of quarks confinement using E-Infinity modification of the original classical solution. Hopefully without wanting in any sense to sound pompous and give our enemies fuel to burn more wood, let me say that if we in E-Infinity could see so far then it was because we stood on the shoulders of giants. These giants are: Gerard ‘tHooft, David Gross, David Politzer and Frank Wilczek, to mention only a few of the key players in this field.E-Infinity Communicationnoreply@blogger.comtag:blogger.com,1999:blog-2497048322692604828.post-41879278906236488392010-04-14T10:54:57.722-07:002010-04-14T10:54:57.722-07:0023-2
We met this number frequently when we discuss...23-2<br />We met this number frequently when we discussed transfinite corrections. It is this technique of writing things in the most convenient form using the simplest and most efficient binary system that there is which allows E-Infinity to produce exact results with<br />simplicity which is difficult to comprehend when we use the old mentality of algebraic manipulation brute force, patching and approximating at different stages until things become approximately correct but truly ugly and cumbersome to handle. <br />I am too young to have been together with Heisenberg, Paul Dirac and Neils Bohr at the Tate Gallery in London when they visited it. Mohamed El Naschie told me however the following story which he again heard it from Heisenberg directly. The story is too beautiful not to be true even if it is true and just ingeniously invented by El Naschie to impress us. Paul Dirac loved perfection. When he presented a draft paper to Neils Bohr and the latter made his usual correction, Dirac becomes extremely sad. One day the three mean were in London. Paul suggested taking the opportunity to visit the Tate Gallery. I knew the old location of this gallery because Mohamed El Naschie took me there when I visited him in London. They were standing all in front of a large picture either by Turner or Claude Monet. I cannot remember. Dirac stood silent for a while then he moved forward and pointed to a spot at the bottom of the painting and said in his calm voice:”This point<br />is wrong”. I do not think I can say anymore. That must be one of the best signs of Paul Dirac’s conviction that it must be beautiful or it is not true or correct. If you look to the classical form of the renormalized equation of unification of fundamental action in high energy physics, you realize that it is extremely involved, clumsy and cannot be described as being beautiful. However it is approximately true. To use the same language of Dirac, there is a point there which is wrong. Not so with the same equation which E-Infinity produces. The equation of E-Infinity is perfection per excellence in this case. We will discuss it in detail. But I wanted to introduce the idea first. I know from El Naschie that he traveled to a country in Northern Europe known for its beautiful tulips, in order to introduce his equation to a man whose opinion he values above every other mortal. To make a long story short, the great man told Mohamed El Naschie:”Yes,<br />it is amazingly simple but there are too many things before that. Your equation comes from where? It just comes out of the blue”. I cannot reproduce the sense of disappointment which Mohamed El Naschie felt at this point. I could almost hear what is going in his mind. Of course there are many things before that. I thought you know that I know that. In fact how a great man like you could think that I could not know that. The problem is Mohamed El Naschie knew what the great man knows but the great man did not know what Mohamed El Naschie knows mainly fractals, chaos and complexity theory.You could write any simple equation if you can. If you are clever you can always guess the answer and idealize it. Next you ask yourself: What do I need to have? Normally a Lagrangian in order to get this result. This is the well known inverse problem. El Naschie worked on many problems in the calculus of variations. He knew from his classical engineering work<br />the power of the inverse problem as a method. The inverse problem is always more difficult. For instance, relative to multiplication division is more difficult. Similarly we have many opposed mathematical procedures where the inverse is always more difficult. It is not impossible to find whatever you want when so many clever people have worked so hard to give you a theory which is almost but not completely perfect. Classical quantum field theory is such theory. It is almost but not completely perfect. Those who have studied it carefully will be led to a simple solution of the inverse problem as will be explained later.E-Infinity Communicationnoreply@blogger.comtag:blogger.com,1999:blog-2497048322692604828.post-1664612601009854782010-04-14T10:53:29.668-07:002010-04-14T10:53:29.668-07:00Communication No. 23-1
The inverse problem of quan...Communication No. 23-1<br />The inverse problem of quantum field theory in E-Infinity theory and symplectic tiling<br /> <br />We mentioned few very good reasons why the golden mean should pop up at so many different places and so unexpectedly in quantum high energy physics. We reasoned that quadratic equation with golden mean roots is the simplest non trivial algebraic equation that there is. We mentioned the maximal irrationality of the golden mean and the role it plays in KAM theorem and the stability of dynamic systems. We alluded to wild topology and its connection to the simplest form of random cantor set which by a well known theorem due to American mathematician Mauldin and his student William will have a golden mean as a Hausdorff dimension. There are far more reasons than what we mentioned. The reasons are sometimes very subtle and none is so subtle and so important than the relation to Penrose Tiling. I remember vividly attending a lecture by Professor El Naschie in the Einstein Institute for Gravitation in the Max Planck Institute near Berlin, Germany. A very<br />imminent and famous German astrophysicist was present when El Naschie was talking about the Penrose Tiling and E-Infinity theory. The imminent German scientist became very agitated and said: “This is all a simple tiling, how could you scale things denying the existence of a natural scale and how could use that for high energy physics”? El Naschie was equally agitated but remained calm. Of course it was El Naschie’s mistake. He thought everyone has seen the wonderful example for non commutative geometry presented in the book of Alain Conne. El Naschie explained to the imminent astrophysicist that of course he should have said Penrose fractal tiling. El Naschie meant that every tile in Penrose Tiling could be tiled again using Penrose tiling and so on ad infinitum. The great German astrophysicist and he was definitely a great astrophysicist was not familiar with fractals. He belonged to a generation which worked decades before Andre Linde, the<br />Russian astrophysicist, moved to America and introduced fractals to the big bang. Talking to Mohamed El Naschie later on, the irony became even bigger. El Naschie learned much about fractal geometry in astrophysics and quantum mechanics from a remark in a paper published in the 60’s by the very same German astrophysicist. The remark concerned the famous paper of Carl Menger which he dedicated to Einstein at his birthday. Many of us and I am not an exception refer to papers without reading them attentively. Let us return to Penrose tiling. Without the golden mean, there is no Penrose tiling but why is it like that? El Naschie gave a naive example which I find very instructive. Being a structural civil engineer, his example comes yet again from engineering. Suppose you are building a wall. You are using bricks. Watch a master mason performing his job. He fits the bricks together. These are the integers in number theory. Now and then he takes a smaller<br />or a larger brick so that things fit a little bit better.These are the rationals. However no matter how clever our master bricklayer is, he will never get a smooth monolithic wall without resorting to mortar. The mortar between the bricks helps to produce a smooth monolithically connected wall. These are the irrationals of number theory. If you take the golden mean 0.6180339 you notice that it is almost equal to half i.e. 0.5 + 0.1180339. It is a rational plus an irrational tail which is easily expressed again in terms of the golden mean. In this case it is simply 1 + k all divided by 10. The k is the famous golden mean to the power of 3 multiplied by 1 minus the golden mean to the power of 3.E-Infinity Communicationnoreply@blogger.comtag:blogger.com,1999:blog-2497048322692604828.post-23361620518387588322010-04-10T11:38:42.568-07:002010-04-10T11:38:42.568-07:00(22-2)
2. The golden mean is the most irrational...(22-2)<br /> <br />2. The golden mean is the most irrational number. Its continued fraction expansion involves only unity. Consequently it is the backbone of the KAM theorem. There is no stability in a Hamiltonian system without a rational number. Since the golden mean is the most irrational, it is the threshold of the most stable periodic orbit in a dynamic system. The marriage between KAM and quantum mechanics resulted in Rene Thom’s VAK conjecture which has been re-generalized by El Naschie and used in high energy physics.<br />3. A random cantor set possesses a Hausdorff dimension equal to the golden mean. Of course there are many cantor sets which are random and have a Hausdorff dimension close to or different from the golden mean. However the most simple and generic random cantor set has the golden mean as a Hausdorff dimension. A wild topology always ramifies at infinity into a set of wild point, equivalent to a random cantor set. Generically this is equal to the golden mean. If you regard the final state and forget about the mechanism leading to it, then you have golden cantor sets geometry at ultra high energy corresponding to the wild topology. The basic mathematical work in this direction was done by an American topologist Alexander. The most famous examples are Alexander Horned spheres and Antoine Collier. Mohamed El Naschie merely carried these ideas to high energy physics and was probably inspired by S. Kaufmann in the U.S.A.<br />4. The fundamental theory of 4-manifold depends crucially on the Fibonacci and thus the golden mean. This has been considered at length in the corresponding mathematical literature. Many references to this work are given in El Naschie’s papers and elsewhere, for instance Crnjac’s work. <br />We must stress that the excellent work of T. N. Palmer depends crucially on an understanding of number theory. In fact classical quantum mechanics depends on number theory. You must always remember the trivial fact that without complex numbers, there is no classical quantum mechanics. We think enough for today as my hands are getting heavier and we hope to be back as soon as possible.E-Infinity Communicationnoreply@blogger.comtag:blogger.com,1999:blog-2497048322692604828.post-8577281089755919022010-04-10T11:38:10.069-07:002010-04-10T11:38:10.069-07:00Communication No. 22-1
Why does the golden mean po...Communication No. 22-1<br />Why does the golden mean pop up everywhere in mathematical physics?<br /><br />A true scientist aiming at scientific truth could not be afflicted by a worse malady other than prejudice. Some notable scientists who have done occasionally excellent work elude themselves in confusing prejudice with scientific skepticism. I am far too skeptical to believe anything easily, you will hear them say. Give him anything new and he will answer immediately: I do not need to read it. I waste my time on big names only. I know before I read that this is no good any case. Too many great people have tried before and failed. Who the hell could be this guy from Rumania to teach me a Caltech man about the quantum or anything at this level? When it comes to the golden mean things could be dozen of times worse. Ignorance is invariably covered up pure arrogance and never ever forget the witty jokes, the hallmark of a hole head. In what follows we would like to give well known elementary evidence that it is absolutely natural for the golden mean to be the foundation of quantum mechanics and high energy physics and much much more. Many of these evidences have been discussed at length by Mohamed El Naschie, Marek-Crnjac and their students. For convenience summary, we recommend a paper titled: A short history of fractal-Cantorian space-time by L. Marek-Crnjac, published in Chaos, Solitons & Fractals 41 (2009) 2697-2705. <br />1. The golden mean is the solution of a simple quadratic equation with appropriate sign. A quadratic equation is the simplest non linear equation we know of. Only a linear equation is simpler. Einstein said if everything would be linear nothing would affect nothing. Therefore, for things to affect things we need at least a quadratic equation to describe physics of a minimal complexity. The simplest vibrational set fulfilling Einstein’s requirement is a 2 degree of freedom linear oscillator. The characteristic equation for such set when normalizing all constants is a quadratic equation with a golden mean solution. This is discussed at length in a paper by Mohamed El Naschie titled: On a class of general theories for high energy physics, published in Chaos, Solitons & Fractals. 14 (2002) 649-668. The Slovenian mathematician Marek-Crnjac suggested that fusing infinitely many but hierarchical sets of this type leads to E-Infinity theory. The connection to the basic concepts of string theory is evident. It might be interesting for some to note that structural engineers habitually replace complex structures by systems of springs and masses. In some sense this is a finite element realization of a structure. In the same sense and taking a bird’s eye view this is the connection to Regg Calculus. No wonder that Mohamed El Naschie used this method when you remember he is a Structure Engineer and a past student of John Argyres, the inventor of finite elements who used it skillfully in the modern fuselage structure of airplanes at the dawn of the aerospace age.E-Infinity Communicationnoreply@blogger.comtag:blogger.com,1999:blog-2497048322692604828.post-65965061203562555422010-04-08T11:24:05.193-07:002010-04-08T11:24:05.193-07:00(21-2)
It was not always golden mean from the begi...(21-2)<br />It was not always golden mean from the beginning. El Naschie used initially deterministic fractals. He started initially by using the classical triadic cantor set with the Hausdorff dimension ln2 divided by ln3. You do not get golden mean for deterministic cantor sets. Paradoxically it is randomness which introduced golden mean harmony. You can see that from a paper published in Vistas in Astronomy. The author is Mohamed El Naschie. The title of the paper is: Quantum Mechanics, Cantorian Space-time and the Heisenberg Uncertainty Principle. This paper dated 1993, vol. 37, pp. 249-252, did not include the golden mean yet. Mohamed El Naschie rediscovered the average Hausdorff dimension of a quantum path. This is equal to 2. It is the individual Hausdorff dimension of a quantum path which is equal to the golden mean. The interplay between 2 and the golden mean produced the approximate value for the Hausdorff dimension of the core of quantum cantorian spacetime which is approximately equal to the exact value. To be specific, it is 2 divided by ln of the inverse golden mean which gives us an approximation to the exact value 4.23606799. There is a nice paper summarizing the application of the golden mean by El Naschie titled: The Golden Mean in Quantum Geometry, Knot Theory and Related Topics, Chaos, Solitons & Fractals, Vol. 10 No. 8 page 1303-1307 (1999). Another paper which seems to have strong influence on groups working in the Parameter Institute in Canada is El Naschie’s Quantum Groups and Hamiltonian Sets on a Nuclear Spacetime Cantorian Manifold, published in Chaos, Solitons and Fractals, vol. 10 no 7, pp. 1251-1256 (1999). The golden mean as such and its connection to E8 became fundamental in the work of Mohamed El Naschie after one of his students, Dr. Ahmed Mahrus from Newcastle, Department of Physics, UK, drew the attention of Mohamed El Naschie to the golden mean binary system. Academician and Nobel Prize nominee Alexei Stakhov expanded this system in a recent magnificent work published by World Scientific entitled: The Mathematics of Harmony. Mohamed El Naschie started his adventure with period doubling and renormalization relatively early. He was at the time Director of Projects and one of the main editors of a prestigious Middle Eastern Journal. Later on he published a paper on the subject titled: Order, Chaos and Generalized Bifurcation. The paper is published in the Journal of Engineering Sciences, King Saud University, vol. 14, no.2 (1988), pp 437-444. I did hear some good news for those who do not have easy access to expensive scientific Journals. I am told that a charity organization did put all the scientific papers of Mohamed El Naschie in a free access blog. I do not know where or when this was done, but those who will search will find it. I hope this will facilitate serious study of E-Infinity. Of course those who prefer other activities will not be deterred from following their natural inclinations. We hope however that the majority will follow their scientific inclination. We hope also this little contribution is helpful and we will be shortly returning with more.E-infinity Communicationnoreply@blogger.comtag:blogger.com,1999:blog-2497048322692604828.post-17732915244442602232010-04-08T11:22:11.114-07:002010-04-08T11:22:11.114-07:00Communication No. 21
The Golden Mean in High Energ...Communication No. 21<br />The Golden Mean in High Energy Physics before, during and after E-Infinity<br />We will have to leave it to the philosopher and historian of science to determine the complex history of the golden mean in high energy physics. As far as we are concerned, we feel that Mohamed El Naschie must be accredited with integrating the golden mean in high energy physics in a systematic way and on a grand scale. He did not do that intentionally. It just happened. The golden mean more or less manifested in the computation as fundamental for any minimal consistent and accurate quantum field theory formulation outside the rules of classical quantum field theory. Without any attempt to be historically correct we must draw attention to very important papers where the golden mean manifested itself. I must say that the authors which I am about to mention were initially not traditional mainstream. They are not renegades. They are somewhere in between. They are meantime part of the establishment but it was not always like that. The first is an exceptional Russian mathematician who worked initially in turbulence, A. Polyakov. The second is a superb solid state physicist, mathematician and hobby engineer, Subir Sachdev. If my memory serves me right, although this is slightly on the gossip side, I think Sachdev’s American wife is the daughter or the grandchild of Dwight Eisenhower, the great President of USA and the hero of D-Day in the Second World War. The paper of Polyakov is entitled: Feigenbaum universality in string theory, published in Journal of Theoretical Physics (JETP), vol. 77, No 6/March 2003, pp. 260-365. Polyakov found the period doubling of Feigenbaum in quantum field theory. Please read Mohamed El Naschie’s paper on the connection between the hyperbolic region of period doubling and the Hausdorff dimension of fractal spacetime. A critical value in the hyperbolic region is his famous 4.23606799. When you talk Feigenbaum, you talk golden mean renormalization groups. In fact it was Mitchell Feigenbaum, Otto Rossler, Julio Casati, Boris Cherekov and Itmar Proccaccia who initiated Mohamed El Naschie’s interest in nonlinear dynamics, KAM theorem, period doubling and thus the golden mean threshold. Mohamed El Naschie merely extended that to high energy physics. The second paper by Sachdev was published in Physics Letters B 309, 285(1993), Polylogarithm identities in a conformal field theory in three dimensions. You can find it free of charge published in arXiv: hep.th/93605131, 25 May 1993. An extremely instructive and neat summary of the application of the golden mean is a nice paper by the very versatile, Slovenian mathematician L. Marek-Crnjac. The paper is titled: The golden mean in the topology of four-manifolds, in conformal field theory, in the mathematical probability theory and in Cantorian space-time, published in Chaos, Solitons & Fractals 28(2006) 1113-1118. A wonderful paper by Professor Christian Beck from Queen Mary University, London and Muhammad Maher from the same department is: Chaotic quantization and the mass spectrum of fermions, published in Chaos, Solitons & Fractals, 37 (2008) 9-15. This paper was refereed and recommended for publication in Chaos, Solitons & Fractals by Professor, Dr. Dr. Werner Martienssen from the University of Frankfurt. In this paper you can see the influence of nonlinear dynamic and cantor sets in modern physics and determining the mass spectrum of elementary particles in a similar but not identical way to E-InfinityE-infinity Communicationnoreply@blogger.comtag:blogger.com,1999:blog-2497048322692604828.post-55408597877201782942010-04-03T11:16:22.193-07:002010-04-03T11:16:22.193-07:00(20-2)
Take the experimental value of alpha bar an...(20-2)<br />Take the experimental value of alpha bar and do the same. You will not get the correct value for the mass of the proton. You will get a good approximation but not the correct value. To understand that, you have to read El Naschie’s paper on the Mass Spectrum. However before this you have to depart from the naïve belief of reality physics and maths. You cannot take Newton nor Einstein as a paradigm in a naïve way. I may come to this point later on when we have the time. For the moment I would like to give a second example. In fact I would like to give many examples to refute the naïve belief of dividing physics from maths in a simplistic way. I said previously that the real negative dimension is the empty set. The best example I know is El Naschie SU(n) hierarchy. I will not give now details but I give it to you as given in the papers of El Naschie. It is minus 1, zero, 3, 8, 63 and then finally 3968. This is not ‘tHooft’s beloved Yang-Mill theory. It is the super Yang-Mill theory. If in any doubt, please see Kaku’s book:”Introduction to superstring and M theory, page 385. El Naschie’s hierarchy just stated is connected to n equal zero 1238 and 63 in the same order. I will explain that later on in detail. I just want to say that those who think this is numerology know nothing about numerology or physics and Beck calculation is a numerical confirmation for that. In fact the work of Renate Loll and Jon Ambjorn lies squarely on the side of El Naschie and Beck. They use with great skill the number crunching efficiency of a computer. El Naschie on the other hand does the same using a number system made extra for that. The Great Russian academician Alexey Stakhov said in his recent book which was acclaimed on the level of a Nobel Prize that missing the use of the golden mean binary system was a disaster and nothing less for the development of mathematical physics. I have made many claims here and I did not give you details. I owe you a few. I will do this as soon as we can piece things together for you. I also promise to show you that the theory presented for quarks confinement using E-Infinity is absolutely correct. We had our doubts initially but now there is no doubt whatsoever. That also will be addressed very soon.E-Infinity Communicationnoreply@blogger.comtag:blogger.com,1999:blog-2497048322692604828.post-49612235496954031142010-04-03T11:15:42.465-07:002010-04-03T11:15:42.465-07:00Communication No. 20
Miscellaneous comments, some ...Communication No. 20<br />Miscellaneous comments, some corrections and continuation of Part 3 of Communication No. 17<br /><br />Let me start with a minor correction. We said that Christian Beck in his famous book linking non linear dynamics to high energy physics: “Spatio-Temporal Chaos and Vacuum Fluctuations of Quantized Fields” has calculated the probability of an element of numerology and found it to be absurdly small. We quoted a number. The correct number is even far absurdly small than our memory had it at the time. The number quoted on page 247 by Beck is ten to the power of minus 60. Let me repeat. This is 1 divided by ten and another 59 zeros beside it. You have to be incorrigible fanatic to talk of any numerology in the work of Beck who worked directly with a computer as well as the work of El Naschie who knowingly or unknowingly was working with the golden mean binary system which can match any computer.<br />We all know that super string depends crucially on a number well known from number theory namely 496. Is this numerology? Not even the greatest enemy of string theory could make such claim. We know that loop quantum mechanic would not work at all unless we multiply everything with a mysterious numerical factor, the Imerze-barbiro number. I probably spelt the name wrongly but never mind is loop quantum mechanic numerology? I don’t think our Nobel Laureate Gerard ‘tHooft would like that at all, he believes reasonably well in loop quantum mechanic because it does not have extra dimensions. Why? Because extra dimensions cannot be seen. Is this prejudiced? I don’t think he believes it is prejudiced. Forgive me for being confused at this point. Did anybody see an instanton? Did anybody see the unification monopole of Polyakov and ‘tHooft? Don’t get me wrong, I believe they will be found or something similar will be found. However it is clear that beauty is in the eye of the beholder. Funding is a problem. Some say “Cherchez la femme.” In our community it is more the case that we should “cherchez la monnaie”. Continuing in the same vein, what about this quadratic equation which Mohamed El Naschie has given? The equation was expressed in terms of alpha bar. It reads alpha bar square minus 140 alpha bar plus 400 equal zero. It has of course two solutions: the first is alpha bar is 137 plus k0. This is 137.082039325. Note it is the theoretical value of E-Infinity. It is not the experimental value. The second value is 3 minus k0. This is a scaling of one of the dimensions of spacetime. Now take the mass of the proton. According to E-Infinity it has to be alpha bar square divided by 20. That way you get the real experimental value of the proton.E-Infity Communicationnoreply@blogger.comtag:blogger.com,1999:blog-2497048322692604828.post-66871566371840119292010-04-03T11:13:16.688-07:002010-04-03T11:13:16.688-07:00(19-3)
He put it in the most eloquent way we know ...(19-3)<br />He put it in the most eloquent way we know of. Far more eloquent than anything which Ord, Nottale or Mohamed have written. It is eloquent because it is short, sweet and simple. He said quantum mechanics is blind to fractals. This is the main problem. That is why wild topology is important. At this level philosophy is not decoration. At this level philosophy is part and parcel of the physical shebang. <br />What I wanted to clarify in this communication was initially the question of unification, Weyl scaling and the rest. Inevitably diversion took place. We have to stop and start again in another communication. I will call it if I am the one to write it: an equation searching for a Lagrangian. Or was it six characters searching for an author. If Barandello is correct then they have to be six equations searching again for a Lagrangian. For the time being, I bid you goodbye for I have to take the plane or was it the train to San Fernando. A last minute note, you need some literature for wild topology. I cannot recommend strongly enough the classical book of John Hocking and Gail Young “Topology.” It is republished in Dover, copyright 1961. Another Russian book on set theory is by N.J. Wilenkin. It is called Set theory for Entertainment. Finally there is a marvelous book by Christian Beck, an English Professor of Physics at Queen Mary College called: Spatio-Temporal Chaos and Vacuum Fluctuations of Quantized Fields. It is published in World Scientific, copyright 2002. Beck reproduced everything that Mohamed El Naschie has found but using a computer. The work is recommended to anyone who is deluded to think that El Naschie’s work is numerology. Beck calculated the possibility that this is numerology and found that the possibility is 10 to the power of minus 38. <br />Goodbye for now but not for long.E-Infinity Communicationnoreply@blogger.comtag:blogger.com,1999:blog-2497048322692604828.post-74314761884235083372010-04-03T11:12:42.579-07:002010-04-03T11:12:42.579-07:00(19-2)
Gerard ‘tHooft. There is no doubt of the a...(19-2)<br /> Gerard ‘tHooft. There is no doubt of the admiration of Mohamed El Naschie to Gerard ‘tHooft but the latter would be the first to acknowledge that a Nobel Prize is not a passé partout. It is a great pity that this great man hasn’t fully taken in the fact that a random cantor set has a golden mean Hausdorff dimension and that a random cantor set is the end state and by duality it is the very very beginning. As such you are started with a golden mean binary system. You have now a chance to solve things with unheard of simplicity similar to what John Wheeler has always proclaimed. At such level it is absolutely misguided to take the theories of Newton or even Einstein as a guiding light. It is totally wrong at this level to differentiate between physics and maths. It is completely naïve to think that there is really a distinction between reality as we think we know it and ir-reality whatever we mean by this word in our so called real world where our labs exist and measurements are taken. There are those religious fundamentalists. We regard them as fatal and misguided apart from being non scientific. But there are equally inclined fundamentalists who think that everything is only measurable in the laboratory. These things must be expressed in lengthy complicated equations. We call them scientific fundamentalists. They are just as misguided. Dawker continuous onslaught using political means on religion and anything resembling it is but one symptom of this narrow minded fundamentalism. One question these fundamentalists never ask themselves: why are they so fanatic about denying anything they don’t see including God, whatever this is? A fastly more rational way is to analyze the brains of these people as well as the brains of the oppositely inclined people to find what all the fuss is about. A look into the mirror, a chat with a beautiful woman, or reminiscing about past time may help fundamentalists to know the real reason for why they are insisting on whatever they are insisting on particularly when we could not know the answer. E-Infinity starts where George Cantor started. It will be surprising that those who believe in chairs and tables as chairs and tables and we jolly good will build some could swallow E-Infinity immediately. But I think I may be wrong here. If you really understand fractals, and if you really did not just learn it by heart from a text book because others have accepted it, then you will understand E-Infinity. The wonder of E-Infinity is the wonder of fractals and the empty set. Gerard ‘tHooft once said: “I understand what negative dimension is, it is a Grassmanian variable”. That is fine but it is not fundamental. The fundamental thing is to say a negative dimension is the dimension of the empty set. In fact the empty sets. All empty sets are fractal like. The totally empty set is the incarnation of nothingness. For traditional physicists with or without the highest decorations, this is a difficult part to swallow. Tim Palmer understood part of the dilemma.E-Infinity Communicationnoreply@blogger.comtag:blogger.com,1999:blog-2497048322692604828.post-82841097350265630122010-04-03T11:11:24.303-07:002010-04-03T11:11:24.303-07:00E-Infinity 19-1
Part 2 of Communication No. 17
Not...E-Infinity 19-1<br />Part 2 of Communication No. 17<br />Not only Confucius is advising restraint when faced with the awesome power of irrational hatred or the poisonous device of twisting facts. Aristotle finds no way to face the artificial wit of those who have nothing in their heads apart of comic strips and slapsticks except to fortify yourself in continuing serious discussion. That is what we will do here.<br />There is nothing called weird topology. Of course you can call it what you want but there is no such expression in use. The correct expression is wild topology. The only person who could be very upset about that in a professional way that is must be John Baez. In his n-Category café he made a meal out of wild topology only to find that he is of course wrong. That is what happened to you when you spend too much in cracking jokes, writing silly articles with ha-ha-ha instead of reading seriously to expand your horizon. So many people calling themselves anonymous spend unreasonable amount of time on worthless blogs achieving nothing except maybe getting rid of their internal frustrations with themselves. John Baez of Riverside University proclaimed loudly that there is no 8 exceptional Lie group. Of course he was wrong and his victim was right. We have E8 with 248 generators. Then we have E7 with 133 and then we have E6 with 78. That is not where it stops. Because most people know F4 with 52 and G2 with 14. But these last two are not E line. The correct E5 is somewhat surprisingly SO(10) with 45 generators. Then we have E4 and this is a counterpart of SO(10) namely, SU5 with 24 generators and you can go on that way until you exhaust the E Line. The sum was found by El Naschie to be 548 to the nearest integer. Next blunder of John Baez was regarding 2 and 3 Stein spaces. He never heard of them. What a blog master does not know about does not exist by definition. It is replaced systematically by silly jokes and ha-ha-ha. That is what Charlie Chaplin would call modern times, or theoretical physics a la blogs with café au lait. We could go on indefinitely like that but this will violate the rules laid down by Prof. Mohamed El Naschie about refraining from personal remarks and jokes that have nothing to do with science. Wild topology is a very important part of general topology. It is connected also to knot theory. The Russian literature is abounding with such examples. In particular, a Great Russian mathematician living in France made this connection and that is where Mohamed El Naschie learned his stuff about the connection between knot theory and cantor sets. He added a trick to that which he learned from Nicholas Hoff. Do not ask me who is Nicholas Hoff? However I know from Mohamed El Naschie that he is one of his teachers. He used to be the Head of Aeronautical and Astro-nautical Department in USA. When faced with big nonlinear problems, Hoff chopped the thing into two parts. He ignored the nonlinear terms and solved the linear part. That is mathematically acceptable. But then he did something unconventional based on intuition. He chops the linear part and somehow regards only the nonlinear end state. That is a bit unusual to say the least. It is unusual for pure mathematicians although I am not one. Hoff did not carry the ballast and regarded only in state. When he reached the top with a ladder, he kicked the ladder and onlookers wondered how he reached the top. Mohamed El Naschie did not follow the intricate knot doubling of an entanglement. He took only the end state. He took the limit set. This limit set is the Cantor set. Something similar was done though not quantitatively by Tim Palmer. Before them something similar was done by Michael Berry. People working in nonlinear dynamics have an engineering sense. This is a world apart from the algebraic computational approach of a great man like Nobel LaureateE-Infinity Communicationnoreply@blogger.comtag:blogger.com,1999:blog-2497048322692604828.post-592469340858379032010-03-29T12:42:36.673-07:002010-03-29T12:42:36.673-07:00(18-3)
‘tHooft writes “In this theory the only thi...(18-3)<br />‘tHooft writes “In this theory the only thing relevant is the number and kind of knots<br />linking the loops………..Accidentally Knot Theory is one of the most difficult branches of modern mathematics”. In E-Infinity we beg to differ profoundly. It is a prejudice to think knot theory is difficult. Knot theory is simple. You can do experimental with the rope and nothing more. Most of the knots are in 3D and they become unknots in 4. There is of course more complex knots in 4 which become unknot in 5. Mohamed El Nastier used Knot Theory skillfully to point a connection between knots, Feigenbaum scenario and ramification at a Cantor set. In one of his very readable papers titled: Fuzzy muti-instanton knots in the fabric of space-time and Dirac’s vacuum fluctuation, El Naschie discussed ‘tHooft’s work in detail and points out how he can obtain ‘tHooft instanton as a volume of a symmetry group. This is a trivial consequence of E-Infinity theory. You see the special orthogonal group SO3 has a volume equal to 8 Pie square. Mohamed El<br />Naschie gave the exact value in transfinite form as well as many other interesting points. You see this way, the instanton becomes more physical as a knot which has volume and becomes nearer to a particle like state or a collection of 16 particle like states. The schism between string theory calculation of the 8064 and the holographic calculation of the same disappear. In a certain way, it was ‘tHooft who pointed out to Mohamed El Naschie that he has a new theory. It was however a lost opportunity to combine forces and pull in the same direction rather than sit on the fence and have to bear what Shakespeare called: the slings and arrows of outrageous fortune. However at E-Infinity we are ready to follow Shakespeare as well. We will take arms against a sea of trouble and by opposing we will end them. And it is nobler in the heart to suffer. <br />E-InfinityE-Infinity Communicationnoreply@blogger.comtag:blogger.com,1999:blog-2497048322692604828.post-13135550078176096062010-03-29T12:41:44.000-07:002010-03-29T12:41:44.000-07:00(18-2)
For instance one of the past students of We...(18-2)<br />For instance one of the past students of Weinberg and a leading string theoretician and a colleague of<br />Weinberg in the meantime is Joseph Polchinski. In volume 2 of his book String Theory, he calculates the same value and comes to the result that the inverse unification coupling constant must be something near to 25. In fact on page 347 of Polchinksi’s said book, two values are given for the unification by virtue of equation (18.312).The first value is the unification energy of about 10 to the power of 16 Gev. The second value is the inverse unification of 25. Of course Polchinski says it is for grand unification.However and as we reasoned earlier since super symmetry is involved, it is for complete unification including gravity. Now how did we notice so quickly. The reason is that we have at our disposal, a set of very simple principles and even simpler sets of equations which leads us directly to the correct result. In detail we should say the following: We know the exact theoretical value of the four fundamental couplings of the electro weak<br />theory which we need to reconstruct the exact theoretical value of the inverse electromagnetic fine structure constant namely 137.082039325. The value needed for that is Alpha bar 1 equal to 60, alpha bar 2 equal 30 and alpha bar 3 equal 9. In addition, we have the Planck coupling 1. Using the well known reconstruction of E-Infinity we obtain 137.082039325. As anticipated by E-Infinity theory the exact theoretical value 60, 30, and 9 are extremely close to the nearest integer approximation to the experimental value found in the literature. It is a very elementary business to find by averaging a value for the unification inverse constant. You simply take the geometrical mean of the 3 said values. In other words you take the third root of the multiplication of 60, 30 and 9 + 10. You could of course take 9 instead of 10. If you take the 9 you get 25.3 as an approximation. If you take the 10 you get 26.2 as an approximation. An E-Infinity exact<br />analysis will give you of course the exact transfinite value namely 26.18033989. This is nothing but the inverse golden mean to the power of 2 and taken 10 times. It is interesting to note that the value of approximately 17 refers only to partial unification. This partial unification is easily obtained by averaging. You just take the square root of 30 multiplied by 10 and get 17.3. This is unification of strong force with electro weak alone without considering electromagnetism. You see how easily we can do calculations because the golden mean binary system makes cumbersome computations elementary. But this is also not all. We have conceptual simplicity. We know the building blocks of spacetime. They are the random Cantor set of the golden mean Hausdorff dimension. The great Dutch scientist Nobel Laureate Gerard ‘tHooft made the search for the building blocks of Nature and the title of his beautiful popular book: In search of the ultimate building<br />blocks published by Cambridge University Press 1997. That brings us to the next example of a missed opportunity. In his book on page 2 in figure 1, Gerardus ‘tHooft plays with a wonderful idea namely making smaller and smaller kites from a sheet of paper. Miraculously and as if an invisible hand is moving ‘tHooft’s hand, he designed in figure 1 a logarithmic spiral connected to the golden mean without saying so. For practical considerations, which are totally justified, ‘tHooft stopped before making the ultimate theoretical conclusion that he is reaching an element of a wild topology with a Cantor set ramification which harbors the golden mean. Then on page 174 ‘tHooft finds at long last a unification theory which he could praise since he does not like string theory. This theory not surprisingly is Loop Quantum Mechanics of Lee Smolin and Rovelli.E-Infinity Communicationnoreply@blogger.comtag:blogger.com,1999:blog-2497048322692604828.post-86306385712320275532010-03-29T12:39:58.224-07:002010-03-29T12:39:58.224-07:00E-Infinity Communication no. 18-1
Some lost opport...E-Infinity Communication no. 18-1<br />Some lost opportunities <br /> <br />What we have to say in this communication might seem at the first instance to be a diversion. Believe me it is not and I just ask you to bear with me a little. I will give two examples where E-Infinity could have been of a great help but it was not utilized and not even considered. We are all no matter how liberal and open minded we think of ourselves subject to prejudice which is deep rooted. Try as much as we want, we cannot escape from two things: The noise of our upbringing and the noise in our brain. Nobody is saved from this “condition humane, to use a term of John Paul Sartre. The two examples we will give are related to the work of two towering figures of the 20th century theoretical physics who are still with us and are still working and contributing vigorously to the literature. The two are Nobel Laureates Steven Weinberg and Nobel Laureate Gerard ‘tHooft. Let me start with a much simpler example of Weinberg. I don’t think there is a<br />single person who has anything to do with theoretical physics who wouldn’t know the great man Steven Weinberg who has written the Definitive Treatise on Quantum Field Theory in three volumes published by Cambridge Press. In addition Steven is a great intellectual personality and his influence goes far beyond physics. For instance in his book facing up he presented in a courageous and logical way the point view of Zionism. This is of course a ticklish issue particularly nowadays and with regards to the Middle East and the rise of the Muslim religion in political form. But Weinberg’s Zionism has an undeniable human and logical face. He is right to warn from the rise of any religious discrimination. He is also right to warn from repetition of the holocaust in any form or guise. Some years ago I was told that the great man was invited to a Conference dedicated to transfinite physics. Weinberg did not hear this expression before. He declined the<br />invitation politely being a responsible and courteous person. What a pity that he wasn’t there. Gaining such mega brain to transfinite physics would have completed the revolution which started with Richard Feynman and continued with the work of Garnett Ord, Laurent Nottale , Mohamed El Naschie, Goldfain and dozens of other scientists including Sidharth, Svotzel, Otto Rossler and yes Renate Loll, Jan Ambjorn and of course Fay Dawker in England who followed a slightly different line initiated by David Finkelstein in America and Heinrich Saller in Germany. Let me be now specific. Consider volume 3 of Steven Weinberg’s book on quantum field theory. Volume 3 is dedicated to super symmetry and the book was published by Cambridge in the year 2000. On page 188 to 192 of the book, Weinberg considers super symmetric unification of the strong and electro weak. He calculates the inv unification coupling constant and finds it by virtue of equation (28.219) to be<br />1 divided by 17.5. In other words the inverse coupling constant of unification is simply 17.5. Now to us working in E-Infinity we recognize immediately this result as wrong. We do not need to make many calculations to realize that somewhere a misfortune and probably trivial computational error was introduced to Weinberg’s analysis. Let me explain why: First, if you are dealing with super symmetric unification, then you are implying gravitational force whether it is explicit or not. Consequently, Weinberg’s analysis is not simply a grand unification but complete unification of all fundamental forces namely electro magnetism, weak force, strong force and gravity. Now we know for sure that the exact value approximated to the nearest integer of the inverse coupling in such case must be 26. The 17 and half is too far for 26 to be even remotely correct.E-Infinity Communicationnoreply@blogger.comtag:blogger.com,1999:blog-2497048322692604828.post-80602543033409285812010-03-29T12:39:51.083-07:002010-03-29T12:39:51.083-07:00E-Infinity Communication no. 18-1
Some lost opport...E-Infinity Communication no. 18-1<br />Some lost opportunities <br /> <br />What we have to say in this communication might seem at the first instance to be a diversion. Believe me it is not and I just ask you to bear with me a little. I will give two examples where E-Infinity could have been of a great help but it was not utilized and not even considered. We are all no matter how liberal and open minded we think of ourselves subject to prejudice which is deep rooted. Try as much as we want, we cannot escape from two things: The noise of our upbringing and the noise in our brain. Nobody is saved from this “condition humane, to use a term of John Paul Sartre. The two examples we will give are related to the work of two towering figures of the 20th century theoretical physics who are still with us and are still working and contributing vigorously to the literature. The two are Nobel Laureates Steven Weinberg and Nobel Laureate Gerard ‘tHooft. Let me start with a much simpler example of Weinberg. I don’t think there is a<br />single person who has anything to do with theoretical physics who wouldn’t know the great man Steven Weinberg who has written the Definitive Treatise on Quantum Field Theory in three volumes published by Cambridge Press. In addition Steven is a great intellectual personality and his influence goes far beyond physics. For instance in his book facing up he presented in a courageous and logical way the point view of Zionism. This is of course a ticklish issue particularly nowadays and with regards to the Middle East and the rise of the Muslim religion in political form. But Weinberg’s Zionism has an undeniable human and logical face. He is right to warn from the rise of any religious discrimination. He is also right to warn from repetition of the holocaust in any form or guise. Some years ago I was told that the great man was invited to a Conference dedicated to transfinite physics. Weinberg did not hear this expression before. He declined the<br />invitation politely being a responsible and courteous person. What a pity that he wasn’t there. Gaining such mega brain to transfinite physics would have completed the revolution which started with Richard Feynman and continued with the work of Garnett Ord, Laurent Nottale , Mohamed El Naschie, Goldfain and dozens of other scientists including Sidharth, Svotzel, Otto Rossler and yes Renate Loll, Jan Ambjorn and of course Fay Dawker in England who followed a slightly different line initiated by David Finkelstein in America and Heinrich Saller in Germany. Let me be now specific. Consider volume 3 of Steven Weinberg’s book on quantum field theory. Volume 3 is dedicated to super symmetry and the book was published by Cambridge in the year 2000. On page 188 to 192 of the book, Weinberg considers super symmetric unification of the strong and electro weak. He calculates the inv unification coupling constant and finds it by virtue of equation (28.219) to be<br />1 divided by 17.5. In other words the inverse coupling constant of unification is simply 17.5. Now to us working in E-Infinity we recognize immediately this result as wrong. We do not need to make many calculations to realize that somewhere a misfortune and probably trivial computational error was introduced to Weinberg’s analysis. Let me explain why: First, if you are dealing with super symmetric unification, then you are implying gravitational force whether it is explicit or not. Consequently, Weinberg’s analysis is not simply a grand unification but complete unification of all fundamental forces namely electro magnetism, weak force, strong force and gravity. Now we know for sure that the exact value approximated to the nearest integer of the inverse coupling in such case must be 26. The 17 and half is too far for 26 to be even remotely correct.E-Infinity Communicationnoreply@blogger.comtag:blogger.com,1999:blog-2497048322692604828.post-20490293519722252952010-03-29T12:36:05.419-07:002010-03-29T12:36:05.419-07:00(17-2)
If you want to be sophisticated you just ad...(17-2)<br />If you want to be sophisticated you just add that since the speed of light is the maximum speed in spacetime, then gravity’s effect cannot travel between two gravitating masses instantly and must travel at a maximum with the speed of light. We do not notice the curvature because it is noticeable only on very large scales. When you say all that everybody is happy. Why are things different in E-infinity? Why, despite so many explanations do people want to understand in a simple way what this E-infinity is? Here is a simple way. While classical spacetime is smooth and Euclidean at intermediate distance and curved at very large distance it is not smooth and not continuous at very short distance. That is all folks. To model the large scale geometry we use Riemannian geometry. The curvature tensor is the driving force behind Einstein’s equation. Similarly to model quantum spacetime at these very short distances we use fractal geometry in its simplest form. The simplest form of a fractal is a Cantor set. We take infinite numbers of Cantor sets to do the job. How on earth could anyone draw a conclusion from that that Cantorian spacetime is infinite. No it can be finite and have infinite dimensions. Even from elementary school mathematics we know that we can sum an infinite series and find a finite answer. That is the whole point behind fractals. When you hold a piece of fractal in your hand, you are de facto holding infinity in your hand. E-infinity theory is very similar to the no boundary proposal of Hawking. It is all extremely simple. Sometimes I am reminded with the heavy weight lifters who are used to carry this 300 kilos and go to lift something which is very light although it does not look it and in doing so, he hurts himself because he was not expecting it to be so light. It is similar to Sonny Liston when he directed a blow to Muhammad Ali’s head but Ali shuffled sideways and Sonny tore the muscle in his right arm. People are expecting E-infinity to be difficult. That is why they find it difficult. Just relax and have faith. It is far simpler than you think. I will not answer any question unless the concerned person gives me his word of honor that he has read at least one single review paper written by an expert on E-infinity theory. In the next communication I will go into slightly more detail and talk about the missed opportunities of ‘tHooft and Weinberg, two people for whom we have the highest possible regard a scientist can have for another scientist as far as science is concerned.E-infinity communicationnoreply@blogger.comtag:blogger.com,1999:blog-2497048322692604828.post-59669871378162693222010-03-29T12:35:10.143-07:002010-03-29T12:35:10.143-07:00E-infinity communication No. 17-1
Summing over pa...E-infinity communication No. 17-1<br /><br />Summing over paths, dimensions, exceptional Lie groups and knots in E-infinity and tidying some loose ends from previous communications. Part I<br /><br />I am taking over from my colleague and will start by apologizing for various gaps in the presentation. The number of states which are of interest are 496 for superstrings, 528 for the 5-Brane model, 548 for summing over 8 exceptional Ei Lie groups, 685 for summing over 17 two and three Stein spaces and the same sum for 12 exceptional Lie groups some of which are not from the Ei family. Finally and most importantly 8872 for 219 three dimensional crystalographic group. The knowledgeable reader will remember that the 17 two dimensional crystalographic group, that is to say the 17 Alhambra Andalusian tiling corresponds to 230 three dimensional group. This is an error and a common one. The 17 correspond to 230 minus 11 making 219. These are the 3D crystalographic group which truly corresponds to the 17 two dimensional crystalographic group. This is all explained in details in the literature and the papers mentioned in the previous communication. The connection between Heterotic string theory and the 219 crystalographic group is truly remarkable. As far as I know it is Mohamed El Naschie who drew attention to this fundamental fact for the first time. Before I finish remind me to tell you about two missed opportunities. The first is connected to Nobel laureate Gerard ‘tHooft and the second is connected to Nobel laureate Steve Weinberg. It is not only an anecdote I will quote paragraph and verse hoping this will at least make you trust E-infinity a little because unless a certain amount of trust is assumed at the beginning, you cannot made headway easily.<br /><br />Let me explain the last two lines in come details. When you explain Einstein’s special theory of relativity, what do you say? You simply say that you no longer think of our space as being 3 plus 1 space and time but as a fused four dimensional spacetime. You would also say that the simultaneousity is not possible because every point has four different coordinates in this spacetime. Finally you add that the speed of light cannot be exceeded. When you want to be more sophisticated you say that these conditions are not independent of each other as is obvious from the Lawrence transformation which preceded Einstein’s work. To give the impression of historical sophistication one would probably add that Poincare knew all of that long before Einstein and that in his work he spelt out indirectly that E is equal to m multiplied with C squared, where C is the speed of light. The general relativity is much easier to explain because you only say that in the very, very large spacetime is curved. This geometrical curvature is what we perceive as gravity.E-infinity communicationnoreply@blogger.comtag:blogger.com,1999:blog-2497048322692604828.post-76659646627142539482010-03-27T11:48:53.855-07:002010-03-27T11:48:53.855-07:00(15-2)
The quotient manifold is given by a dimensi...(15-2)<br />The quotient manifold is given by a dimension which is the quotient of the dimension of the sub manifolds. That way you find the elementary fact that the dimension of a manifold which can sustain the preceding set theoretical conditions is nothing else but the infinite dimensional Hilbert cube which is not identical but very similar in many aspects to the space studied by Ji-Huan He. It is the same space which you obtain from putting a four dimensional cube into another four dimensional cube and so on ad infinitum. Again I am probably going to fast now but everything you know from string theory and high energy physics can be obtained as a deformation of this infinite dimensional Hilbert cube which has a Hausdorff dimension four plus the golden mean to the power of three, a topological expectation value of exactly 4 and a formal dimension of infinity. It is infinity in a hierarchal sense. It is infinity because you are taking infinitely many concentric four dimensional cubes to reach this result. Do not forget, Ruelle’s theorem. A classical system is necessarily chaotic when the dimensionality is infinity, even when it is hierarchal. In a sense you are holding infinity in the palm of your hand as in the famous poem of William Blake. For a geometrical visualization and easy access to the connection to string theory, I strongly recommend that you carefully study the excellent paper entitled Twenty-six dimensional polytope and high energy spacetime physics by Ji-Huan He, Lan Xu, Li-Na Zhang and Xu-Hong Wu, CS&F, 33, 1, 2007, p.5-13. In addition we cannot stress enough the importance of reading the work by the exceptionally gifted young Italian professor of applied mathematics, Gerardo Iovane. One of Gerardo’s computer graphics representations of fuzzy K3 Kähler manifold of E-infinity was entitled ‘E-infinity Cantorian Universe: A fractal manifestation of love’. Many of Gerardo’s papers can be obtained free of charge either directly from Elsevier’s science direct who do not always charge for every paper when you come to it through Google Scholar or can be found on certain pirate blogs claiming to belong to E-infinity members which is not always true. <br /><br />Mohamed El Naschie is a walking encyclopedia when it comes to certain anecdotes of famous people with whom he had the privilege of talking. Again I hope this remark is not taken as cult. He said quoting Sir Prof. Herman Bondi that a fool can ask more questions than a wise man can answer’. However he hastened to say following Weizsaker who was again quoting Heisenberg ‘one has to learn, sometimes the hard way, that asking the right question is normally half of the answer’. We are frequently perplexed because the questions we are asking are imprecise or meaningless or undecidable. Undecidability is not the work of the devil. In fact undecidability in the sense of Gödel implies chaos and chaos implies fractals and fractals imply E-infinity theory. Very frequently when one does not understand something, one should not try too hard. There are very frequently mental blockages caused by our very selves. It is best to go and sleep and not to try too hard. During sleep the subconscious work and it is frequently according to surrealistic artists far more intelligent than consciousness. That is at least the theory of the sleep walkers advocated by Koestler. Accordingly I am now going to sleep. It is one o’clock after midnight local time. (24.3.10)E-infinity Communicationnoreply@blogger.comtag:blogger.com,1999:blog-2497048322692604828.post-16392250278588299062010-03-27T11:48:17.604-07:002010-03-27T11:48:17.604-07:00E-infinity Communication No. 15-1
Set language an...E-infinity Communication No. 15-1<br /><br />Set language and probability language dictionary of E-infinity as a two-slit experiment with quantum particles<br /><br />A philosophically inclined cleric in England invented diagrams which are quite useful to use to move from one language to another in E-infinity theory. I mean set theoretical language and the language of probability theory or events. This was important for El Naschie in developing E-infinity and may be helpful for some in understanding this part which is crucial. The classical language of events or probability language speaks of probability space, events, impossible events, not d or the opposite of d, either/or or both, both, mutually exclusive and if then. In set theoretical language and in the same order you could say universal set, subset, empty set, compliment of d, the union operation, intersection operation, operation of intersection for a totally disjoined set and a set being a subset of another set. The set notations are different from one author to another but are well known. El Naschie studied mathematics in Germany under Kaluza. The anecdote connected to examining a rebellious though peaceful member of the extra-parliamentary opposition is laid down in his reminiscence of his student years written on the occasion of his 60th birthday, A tale of two Kleins unified in strings and E-infinity theory, CS&F, 26, 2005, p. 247. I hope referring to these things is not interpreted draconically as cult which is way over the top to say the least. Everyone has his own style of writing. Some like these anecdotes as a welcome distraction from the boredom of too much formality. It is immodest to recommend one’s own taste but it is hypocritical to recommend somebody else’s taste. If we must we would rather be something, we would rather be immodest than hypocritical, so if our kind friends would bear with us and consider that we are doing all that for fun and free of charge to the benefit of everybody else, then at least be so tolerant to leave everyone express himself in the way he likes. If you do not like something, do not read it. We are not offensive to anyone and mentioning the outstanding achievements of people like Richard Feynman, Nottale, Ord, Rössler and Tim Palmer should not be provocative to anyone. We would like that the young people have the right examples to follow at least if they are serious about science.<br /><br />Now let us suppose you are on the unit interval of which a Cantor set was made. The dimension of the interval before digging so many holes in it is unity. This is the same for the Hausdorff dimension as well as the topological Menger-Urysohn. If you are a member of the Cantor set then the dimension attached to you would be zero for Menger-Urysohn and the golden mean for Hausdorff. If you are not then you are definitely in the empty set. The corresponding dimension would then be minus 1 and the golden mean to the power of square. These simple facts follow from Connes’ formulation of Penrose universe. This is just another formalism of the bijection formula with a slightly different mental picture. You can have whatever mental picture you want as long as this helps you to have this mystical feeling of understanding. Now you have two basic operations from the set theoretical point of view, union and intersection from which you get two dimensions for two elementary manifolds.E-infinity Communicationnoreply@blogger.comtag:blogger.com,1999:blog-2497048322692604828.post-78870280935303334462010-03-27T11:44:43.263-07:002010-03-27T11:44:43.263-07:00(14-3)
The Cantor set also has a dimension and fro...(14-3)<br />The Cantor set also has a dimension and from a well known theorem by Mauldin and Williams a random Cantor set of the triadic type also has a dimension when you assume uniform probability which is the simplest assumption you could possibly make and this Hausdorff dimension is equal to the golden mean. Now we can define a topological probability so to speak. Such quotient would be made of the dimension of the Cantor set divided by the dimension of the line. This is the golden mean divided by 1 which is equal to the golden mean. At long last we have at least something with which we can do some computation. If the simplicity of the solution confuses you and if the question you pose to yourself confuses you even further, do not despair. The great Poincare himself managed to confuse himself in an exam for mathematics and failed. He took the examination once more, succeeded and then invented topology. When he became so famous he failed once more. This time he did not realize that he was wrong. He failed to recognize the work of Cantor. He considered Cantor’s geometry a gallery of monsters. He agreed to a certain extent with Kronecker that Cantor’s ideas are maladies which inflicted mathematics and he was sure that mathematics would soon recover from it. You would rightly say nowadays that you could take all this nonsense from anybody, including Kronecker the arch enemy of the non-finite but for God’s sake, not Poincare. However we cannot rewrite history. Poincare did not recognize his three body problem. The geometry of non-integrability is the geometry of chaos and the limit set of chaos and the backbone of any chaotic system is as James Yorke taught us, a Cantor set. God invented the integer. Everything else is the work of man. This is of course total nonsense, typical for Kronecker on this subject. We have now so many infinities and hierarchies of cardinalities beyond Kronecker’s and even Cantor’s imagination. They are sufficient to make Kronecker turn in his grave, infinitely many times. I hope you got the right taste for the thing to come next to resolve the two-slit experiment which is the basis for the Cantorian proposal for quantum spacetime. And yes, a point, whatever we mean with this word can exist at two different locations at the same time in the infinite dimensional topology of Cantorian spacetime and similar spaces. One of the nicest people one could ever meet anywhere at any time is an English/Canadian physicist whose name is Garnet Ord. Ord is the man who coined the word fractal spacetime. He corresponded and discussed many things with Richard Feynman. Einstein is great but Feynman is something else altogether. Ord intuitively knew about the power of fractals and Cantor sets but if you see Ord and El Naschie discussing things regarding Kronecker and Cantor you would think these two extremely close friends are in two totally opposed sides as far as finite and infinite are concerned. I will keep many anecdotes about El Naschie and Ord for the next communication but I advise you for the time being to familiarize yourself with the greatest mathematical genius of all time, Georg Cantor by reading the wonderful book of Joseph Warren Dauben entitled Georg Cantor, His Mathematics and Philosophy of the Infinite, Princeton University Press, 1979. All the best. (23.3.10).E-infinity Communicationnoreply@blogger.comtag:blogger.com,1999:blog-2497048322692604828.post-87764205109254437432010-03-27T11:44:14.285-07:002010-03-27T11:44:14.285-07:00(14-2)
This all would convince you that Cantor set...(14-2)<br />This all would convince you that Cantor sets have nothing to do with reality and consequently it should have no place in physics. I call now to the witness stand Prof. Friedrich Pfeiffer from the University of Munich. This professor is probably one of the world’s most prominent professors of mechanical engineering. He was not only the Head of the Department of a Centre of Excellence, namely the University of Munich, Germany but also he was the Editor in Chief of the German Journal Ingenieur Archv. If you published a paper in this journal then you reached the promise land in Germany. The professor’s specialty is chaotic research of mechanical systems applicable directly in the industry. Before joining university again, the famous professor worked for an even more famous car producer in Bavaria, BMW. Some of his contributions were to take unnecessary noise from the motor and the clutch and let a BMW car be as silent as a Rolls Royce. No wonder BMW bought Rolls Royce. In a manner of speaking the famous professor was taking the Cantor set causing chaotic noise out of the BMW car. Cantor set, esoteric or not for physicists, are as real as hell for engineers and many other professions. It is strange that of all people high energy scientists and quantum physics theoreticians who deal with things which nobody has ever seen or experienced firsthand should consider Cantor sets esoteric and resist its integration into quantum physics as a basis of new micro spacetime geometry. There are of course many exceptions which we mentioned earlier, David Finkelstein, Heinrich Saller, Parisi, Ord, Nottale and many others. However the typical theoretical physicist neither appreciates nor most of the time knows anything about Cantor sets. Now let us return to our subject properly. When the combinatorial method fails this is no surprise. We have the geometrical method. You know in the darts game you also have infinitely many points but then you define probability geometrically by the quotient of different areas. Great. However calamity struck. A Cantor set has no measure. So we have no length. We are dealing with an esoteric phenomena measured zero. The geometrical method and geometrical probability goes out of the window. Of course there are sophisticated methods based on measured theory. Mark Kac described probability theory as a measure theory with a soul. We would like to keep this soul and remain in probability theory as much as we can. When all things fail, you rub Aladdin’s wonder lamp and ask the genie to bring you in some topology. A line, thin as it may be has a dimension 1.E-infinity Communicationnoreply@blogger.com