Please send your scientific comments and evaluation. They are urgently needed.
he concludes. In number 60, El Naschie reformulates his controversial assertion about Witten's lack of a physics degree. Indignant readers took him to the woodshed over that in E-infinity communication number 52.
14th December, 2010.
E-infinity communication No. 58
You call it numerology, I call you mathematical illiteratology
Let us take one really obvious example for what we would like to illustrate here, namely how intricate the role played by number theory in physics could be and how hasty judgment could put one in an embarrassing situation. Academics in general are judgmental but mathematical physicists should not be no matter how senior they are because at a certain very deep level mostly connected to quantum mechanics rather than general relativity there is no real difference between ‘pure mathematics’ and ‘pure physics’. At this deep level as Prof. El Naschie stressed in one of his lectures, one should not relay on ‘common sense’ which he calls ‘the logic of savages’ following Lord B. Russler. The only thing one can rely on is the most stringent form of logic as in transfinite set theory and K-theory or inspiration from God or such higher instance. Such inspiration is hard to come by and cannot be depended upon in a regular way. The example we will give here is taken from Table No. 6, page 658 of the paper “On a class of general theories for high energy particle physics”, published in CS&F, (2006), pp. 649-668 by M.S. El Naschie. The table is labeled “The number 42 in mathematics and physics – A short survey”.
The importance of 42 is that it is 10 times the expectation Hausdorff dimension of E-infinity spacetime when we take the integer part only and is also equal to the inverse coupling constant of non-super symmetric grand unification of all fundamental forces excluding gravity. The first number of the list is the third Bernoulli number. I remember that one notable scientist protested against such unmotivated connection and obvious numerology. Others went as far as calling on a French scientist very close to Mohamed El Naschie and becoming impolite about this playing with numbers. One in particular who is as self confident as he is ignorant called it ‘alchemy’ although modern physics has long shown that the dream of alchemists of changing copper into gold is in principle correct because the basic building blocks are the same, namely elementary particles. Deep mathematical contemplation coupled with a great deal of knowledge of mathematical and physical facts shows that a relation between all Bernoulli numbers and quantum mechanics is by no means outlandish nor numerology or number coincidence. For instance the function guessed initially by Max Planck for his black body radiation which marked the beginning of quantum theory was a complex function involving many hidden things such as the Bernoulli numbers. That is how Planck arrived at a constant which he later called h and which we know as the Planck constant in order to obtain dimensionless numbers from physical quantities with dimension. Even more general than that, we have to recall that the Bernoulli numbers originally come from the function of integers and are thus related to K-theory topics such as the Riemann-Roch index used by C. Castro and M.S. El Naschie in E-infinity theory as well as the Atiyeh-Singer index used in topological quantum field theory of Witten. Finally for this communication, they are related to the Gauss-Bonnet theorem which El Naschie was able to generalize for a fractal Cantorian geometry and find the curvature of spacetime as a topological invariant exactly equal to the square root of the sum of all two and three Stein spaces which is in turn exactly equal to (5) multiplied with the inverse of the electromagnetic fine structure constant 137. Taking the square root of 685.4101966 we find the said curvature, namely 26 + k = 26.18033989 which is the inverse coupling constant of the super symmetric unification of all fundamental forces including gravity. Consequently 685.4101966 may be seen as a numerical potential or a Lagrangian and using Weyl-Suslin scaling as a substitute for calculus, a great deal of information of physical relevance may be obtained with an unheard of simplicity and elegance.
So in the end, the joke is on those who think they are very witty and spend most of their time making silly jokes on other people instead of spending their time on something useful. For this reason, and although he can be very witty when he wants to be, El Naschie as well as most of his colleagues and friends keep a great distance from making fun of other people’s work or personality. Trying to be witty most of the time is a clear sign of poverty of intellect and personality.
1. Curvature, Lagrangian and holonomy of Cantorian-fractal spacetime, Chaos, Solitons & Fractals, Vol. 41(4), (2009), p. 2163-2167.
2. Deriving the largest expected number of elementary particles in the standard model from the maximal compact subgroup H of the exceptional Lie group E7(-5), Chaos, Solitons & Fractals, Vol. 38(4), (2008), p. 956-961.
3. Derivation of the Euler characteristic and the curvature of Cantorian-fractal spacetime using Nash Euclidean embedding and the universal Menger sponge, Chaos, Solitons & Fractals, Vol. 41(5), (2009), p. 2394-2398.
14th December, 2010.
E-infinity communication No. 59.
Super Yang-Mills, super gravity and super strings. Spectroscopy and the impossibility of number coincidence
If the reader is not very familiar with the theory of super strings, it would be advisable to have a text book to one side whilst reading this communication. For convenience we recommend M. Kaku’s book “Introduction to superstrings and M-theory”, Springer, New York (1999).
Let us look at the Heterotic string and consider its spectrum. For instance following pages 384 and 385 of Kaku’s book we have the following: For the left moving sector there are three distinct states. First 480 states equal in number to the kissing of two E8 and also equivalent to their roots number. In addition we have another 16 states. These make together the 496 of E8E8 dimension where each E8 has clearly 248 dimensions. Finally we have another 8 states so that the total number of the left moving section is 496 + 8 = 504. Note that this is exactly the sum of the dimensions of E8 plus E7 plus E6 plus E5 as found by M. El Naschie (248 + 133 + 78 + 45 = 504). Now we look at the right moving sector where we have only 16s states. Following the rule of Fock space of quantum field theory (where Fock space is the generalization of Hilbert space of quantum mechanics to quantum field), then the total number of all states is the multiplication of the left and right sectors. This gives us the famous number of the first level of massless particle-like states of the Heterotic string theory, namely No = (504)(16) = 8064. Now page 385 gives the number of states in a super Yang-Mills theory as 3968. These could be thought of as lifting E8E8 dimensions to super space by taking 8 copies of the 496 dimensions leading to (8)(496) = 3968. On the other hand we know from the spectrum of the theory of super gravity that we have 512 states. This could be thought of as raising the two dimensional average Hausdorff dimension of a quantum particle path to the ten dimensions of super strings. Using E-infinity bijection, this means we have 2 to the power of 10 minus 1. This is 2 to the power of 9 which is equal 512. This is only 16 more than 496 and 8 more than 504. Let us lift these 512 to super space like we did with super Yang-Mills. Proceeding in this way we find (512)(8) = 4096. The next step taken by Mohamed El Naschie is to consider No to be the sum of super Yang-Mills and a super-super gravity. That means Heterotic strings could be thought of as combing Yang-Mills and super gravity. In all events the spectrum indeed gives the correct result, namely 3968 + 4096 = 8064. In other words No = 8 (496 + 512) = 16 (248 + 256) = (16)(504).
At this point El Naschie makes the following argument: Why stop at E5 and the sum 504? It seems more natural to take the entire exceptional E-line of Lie symmetry groups. In other words we should add the dimensions of E4, E3, E2 and E1. In his extensive work on the exceptional Lie symmetry groups’ hierarchy, El Naschie shows that the sum is 548. Consequently 504 should be replaced with 548. However El Naschie also knows that the 548 is 4 times 137. This is the integer value of the inverse electromagnetic fine structure constant. The exact E-infinity value is however = 137.082039325. In addition El Naschie also knows that due to the main scaling sequence of this ( /2) we must have 16 + k rather than simply 16. This means 16 should be ‘corrected transfinitely’ to 16.18033989. The exact No value is thus No = (16.18033989)(548.3281573) = 8872.135956. This last value may be expressed differently as No = (16 + k) (4) ( ) = (64 + 4k)(137 + ko) where k = 0.18033989 and ko = 0.082039325 are all higher order values of the golden mean. Recalling that 64 is the number of different spin directions and 137 was shown to be the number of elementary particles in an extended standard model, then one could easily conjecture that a return to the classical No = 8064 of Green, Schwarz and Witten may be obtained by replacing 137 with the number of the conventional standard model, namely 126 and 64 + 4k by simply 64. Proceeding this way one finds No = (64)(126) = 8064. This is a delightful result showing the logical consistency of the entire theory.
Anyone suspecting any form of numerology in the intended bad sense of the word should remember that = 137.0820393 and all other transfinitely corrected values harmonize with each and every equation. If one makes a single error in the calculation it is impossible not to notice it immediately after two steps and never, ever more than six steps. It is the well known butterfly effect of chaos manifested in the most irrational number of all irrational numbers, namely the golden mean. The charge of numerology is the cheapest shot possible and comes mainly from those with not so well hidden agendas. These people are well known to all the E-infinity researchers and we need not name them here. They will also be eternalized as infamous in the history books for their non-scientific, disgraceful attacks on innocent people in their literally obscene blogs.
14th December, 2010.
E-infinity communication No. 60
Highly structured ring spectrum and the mathematical foundations of E-infinity theory
Mohamed El Naschie did not develop his theory starting from abstract mathematics. He could not even if he had wanted to because, as stressed by him on countless occasions, he is not a mathematician and does not hold a degree in mathematics nor in fact in physics. This is not usual but it is not that unusual either. For instance Prof. E. Witten who is a Field Medalist has studied neither mathematics nor physics as an under graduate. The great inventor of green functions was not even an academic and as everyone knows, the best study is self study. All the same a mathematical foundation for E-infinity was given by El Naschie many years ago after the initial geometrical picture of a Cantorian space was established. After realizing that E-infinity theory is a particularly simple and neat example of K-theory and Rene Thom (bordism) spectra El Naschie opted for the name E-infinity suggesting that all these subjects, including infinity-categories are united in a mathematical theory called “Highly structured ring spectrum” which deals with multiplicative processes similar to E-infinity and is usually designated in the mathematical literature by E-infinity rings and E-infinity loop algebra. Prof. El Naschie says that he is particularly indebted to Prof. Sir R. Penrose because his tiling was an eye opener for him. He is equally indebted to the work of Prof. A. Connes because it made him realize the large arsenal of mathematics behind noncommutative geometry and K-theory of which he actually never dreamed when he started working on his simple model of Cantorian-fractal spacetime.
A fairly mathematical paper dealing with the foundations of E-infinity as related to the Coxeter and reflection groups is the following note: ‘Mathematical foundations of E-infinity via Coxeter and reflection groups’, M.S. El Naschie, CS&F, Vol. 37 (2008), pp. 1267-1268. After becoming familiar with the dimensional theory of F. Hausdorff as distinct from that of K. Menger and P. Urysohn, El Naschie started his own mathematical program to introduce transfiniteness everywhere. In doing so he was far ahead of almost all mathematicians because he was of course using intuitive arguments without the essential mathematical rigor which mathematicians must subject themselves to. El Naschie followed two generalizations from integer to non-integer and even irrational values, namely the Hausdorff dimension and the factorial function. The Hausdorff dimension generalizes the usual topological integer dimension to a non-integer ‘fractal’ dimension. Similarly the gamma function generalizes the factorial function to non-integer function. El Naschie did not stop at that and generalized the integer dimension of a symmetry group to a non-integer dimension of a fractal symmetry semi-group. If you think about physics very deeply, like a mathematician of the caliber of A. Connes, then you will find that except in physics integer values are mostly empty mathematical concepts not applicable to the rest of the real world. The quantum Hall effect was discovered by Nobel Laureate K. von Klitzing and generalized to a fractional Hall effect by Nobel Laureate H. Stoermer. El Naschie’s theory predicts a fractal Hall effect as the final generalization of the previous two and he has written a few papers about that and all that remains is the experimental confirmation El Naschie’s fractal Hall effect.
Another mathematical generalization which was achieved within E-infinity theory is the curvature of a fractal-Cantorian point set. This is discussed in connection with the Gauss-Bonnet theorem in one of the most important papers of E-infinity: “On zero-dimensional points curvature in the dynamics of Cantorial-fractal spacetime setting and high energy particle physics”, M.S. El Naschie, CS&F, Vol. 41 (2009), pp. 2725-2732. The detailed discussion of this paper will be given in a forth coming communication.
15th December, 2010.
Important: E-infinity communication No. 61 – Latest News
Prof. Alain Connes’ new 2010 paper with Prof. Ali Chamseddine comes to the same fundamental conclusions and predictions of E-infinity, namely 9 new particles and a Higgs mass equal 170 Gev
Connes and Chamseddine published a brand new paper on 3rd April, 2010. The paper is entitled “Noncommutative geometry as a frame work for unification of all fundamental interactions including gravity. Part I is on arXiv: 1004.0464V1[hep-th], 3rd April, 2010. Researchers working in E-infinity will remember that the 2005 paper of Prof. Ji-Huan He entitled “In search of 9 hidden particles”, published in Int. J. of Nonlinear Sci. & Numerical Simulation, 6(2), (2005), pp. 93-94. Using Prof. El Naschie’s theory 9 new particles were predicted to exist in an extended and completed standard model. Prof. Alain Connes is the inventor of noncommutative geometry and one of the greatest living mathematicians of our time who was awarded the Field Medal in 1982. Prof. Ali Chamseddine is an outstanding mathematical physicist who previously worked intensively with Nobel Laureate Abdulsalam and who met Prof. El Naschie, the last time in Alexandria where they had a hearty conversation. For these reasons alone this work of the two outstanding achievers of the highest caliber should be taken very seriously by our group. On the other hand the paper is detailed and very easy to read and understand. In a nutshell they use a non-simple Lie symmetry group SU(2) SU(2)SU(4) which gives 3 + 3 + 15 = 21 massless gauge bosons. A symmetry breaking leading to the standard model with the well known standard model 12 gauge bosons shows that there are 21 – 12 = 9 particles missing. This is the start of the paper. The important result and conclusion could not be anything better than predicting the mass of the Higgs which they do. The result is identical to that found years ago by El Naschie, namely 170 Gev. This result of M.S. El Naschie can be found for instance in his paper “Experimental and theoretical arguments for the number and the mass of the Higgs particles”, CS&F, 23 (2005), pp. 1091-1098.
For additional reading we recommend the book of A. Connes as well as the following papers.
1. An elementary proof for the nine missing particles of the standard model Chaos, Solitons & Fractals, Vol. 28(5), (2006), p. 1136-1138.
2. L. Marek-Crnjac: Different Higgs models and the number of Higgs particles. CS&F, 27, (2006), pp. 575-579.
It should be remembered that both E-infinity theory and noncommutative geometry are K-theory based and both have Penrose fractal universe (Penrose tiling) as a prototype and generic example where the golden mean plays a crucial role in the dimension function.
Please send your scientific comments and evaluation. They are urgently needed.