24th March, 2011.
E-infinity Communication No. 85
Recent important papers on E-infinity
The following are some important papers on E-infinity which have just appeared in various international journals. Further details may be found from the internet.
1. M.S. El Naschie: Quantum collapse of wave interference pattern in the two-slit experiment. N.S.L.A., Vol. 2, No. 1 (2011), pp. 1-9.
2. Ciann-Dong Yang: Trajectory-based quantum chaos. N.S.L.B., (1), (2011), pp. 7-10.
3. L. Marek-Crnjac: The physics of empty sets and the quantum. N.S.L.B. (2011), pp. 13-14.
4. Lan Xu and Ting Zhong: Golden ratio in quantum mechanics. N.S.L.B., (1), (2011), pp. 25-26.
5. R. Murdzek, Daniela Magop and Roxana Stana: A fractal universe in Brane world scenario. N.S.L., (1), (2011), pp. 41-44.
6. Ji-Huan He, Tin Zhong, Lan Xu, L. Marek-Crnjac, Shokry Ibrahim Nada, Mohamed Atef Helal: The importance of the empty set and noncommutative geometry in underpinning the foundation of quantum physics. N.S.L.B., (1), (2011), pp. 15-24.
7. Ji-Huan He: The importance of the empty set underpinning the foundation of quantum physics (Editorial). N.S.L., (1), (2011), pp. 11-12.
8. M.S. El Naschie: Application of chaos and fractals in fundamental physics and set theoretical resolution of the two-slit experiment of the wave collapse. N.S.L.B., (1), (2011), pp. 1-3.
9. M.S. El Naschie: On the philosophy of being and nothingness in fundamental physics. N.S.L.B., (1), (2011), pp. 5-6.
In forthcoming communications we will give a brief discussion of the above mentioned papers as well as more helpful references and literature.
23rd March, 2011.
E-infinity Communication No. 84
Quantum scale, small world and nanotechnology
The macro world is abound with an incredible diversity of shapes, chemical and physical properties of living and inanimate material forms each distinct from the other in almost infinite ways at least on the phenomenological level. However as our observational scale becomes tinier and we descend to the micro and quantum scale, this diversity becomes highly restricted. At the level of the smallest building blocks of nature, namely the so called elementary particles the only diversity left is that of mass, spin and electrical charge. At ultra high energy we are left in theory with nothing more than numbers of state-like particles or the dimension of global symmetries. For instance in one of the presently most popular theories of everything, the so called superstring theory, all that we know is that we have 496 massless indistinguishable gauge bosons.
The problems thrown up by quantum physics of the micro world are solved traditionally using classical lattices (you may think of the finite difference or finite element method used in engineering and called in physics Regge calculus). However a relatively recently deciphered phenomena in social sciences called small world introduced a new kind of random transfinite lattice similar to the E-infinity Cantorian spacetime proposed by Mohamed El Naschie. In fact a small world network is behind the incredible connectedness which we witnessed in social networks such as Facebook and Twitter. It is for instance shown in this theory that for a population as large as that of the earth we only need 24 friends for each chosen two people to reduce the entire population to one compact net. In such a net only two randomly chosen persons are connected through 6 people at most. This is what lies behind the by now very famous phrase of only six degrees of separation. Note that 2 + 24 = 26 and that this is the dimension of the bosonic string theory which is supposed to be a theory of nearly everything. Note also that the exact value of El Naschie’s transfinite version of string theory is 26.18033989 and 6.18033989.
In future communications we will dwell on the connection between nanotechnology, high energy physics and small world networks. It is argued that Nano drugs delivery could benefit from understanding the body as a small world so that side effects are drawn into the healing processes. The same applies to social problems and the breakdown of the social fabric in a political uprising for instance.
It is conjectured that singularity theory (catastrophe theory), deterministic chaos and transfinite small world networks could be used under the auspices of nanotechnology to change the world and solve problems hitherto thought to be unsolvable such as stock market crash, material complex hair cracks propagation, fluid fully developed turbulence, earthquake predictions and climate disasters forecast.
For literature on the subject the reader may consult the Prof. El Naschie’s homes pages at: http://www.msel-naschie.com and/or http://www.el-naschie.net.
22nd March, 2011.
E-infinity Communication No. 83
On El Naschie’s small world of infinite dimensions
In the following we give a number of observations, interpretations and comments on the relationship between E-infinity theory and the theory of small world. The copyrights of the material published here, some for the first time should be respected by quoting the source, namely E-Infinity Communication Publications. We have not attempted to mention each of the sources of the information given here which is largely due to the papers as well as formal and informal talks and lectures by Prof. Mohamed El Naschie, Prof. Ji-Huan He, Prof. G. Ord, Prof. L. Marek-Crnjac and Prof. G. Iovane.
1. Ergodicity or global chaos as well as complete order may be assigned both the same zero complexity indexes. Both complete order and complete chaos are consequently structurally unstable in some vague topological sense. By contrast a KAM system which encompasses both chaos as well as order on all scales may be seen as relatively structurally stable and robust. This property of robustness to perturbation is shared by small world networks. In a sense robustness to perturbation is a substitute for friction in dissipative systems. Hamiltonian systems have no physical friction. However the irrationality of the winding number is what replaces physical friction in Hamiltonian systems such as quantum physics according to KAM theorem. That is how the golden mean comes in as being the most irrational number. From this view point E-infinity and small world theory seem to have common roots if not much more than that.
2. E-infinity’s quasi manifold is probably one of the most amazing geometrical and topological constructions which unite the un-unitable. It is infinite dimensional yet it has a resolution dependent finite expectation value for all its topological invariants including dimensions. It is infinitely large yet it is in more than one sense compact and so is its holographic boundary. It is fuzzy but within this fuzziness everything is probabilistically exact. It is completely discrete but due to the transfiniteness of its geometry it resembles the continuum. It is infinitely large but because it reproduces itself latest after moving a maximal distance equal to the isomorphic length multiplied with an arbitrary radius, it is semi-finite and resembles a semi-small world.
3. There are clear applications of both small world theory and E-infinity theory to any transfinite network such as neurons in the brain as well as complex fracture systems such as seismic fault structures relevant to earth quakes. The application in sociology may be among the most profound applications to things which may be shaping the future right this minute.
4. With regard to high energy physics Mohamed El Naschie’s theory de facto proposed the replacement of the classical lattice of the large world with the transfinite Cantorian lattices of the small world theory.
5. It is frequently argued that the six-degrees separation does not apply to a set of people alive at different times. The classical example for that is that Alexander the Great is separated from Albert Einstein by more than six-degrees. However if we take the degree of a degree into account, i.e. we take the weight of a degree (or a dimension) into account then we could still end with 6 or less degrees of separation. For instance we know that Alexander was interested in the art of knode. On the other hand Lee Smolin showed that Stuart Kauffman’s knode theory is relevant to quantum gravity. That means it is relevant to gravity and this connects Alexander to Einstein albeit it is a very weak connection.
6. Between two random people we have 24 acquaintances according to an application of Erdös-Rényi theorem. Thus we have 24 + 2 = 26. Similarly we have a world string sheet with two dimensions and when we add the 24 instantons of a Kähler to it we can simulate 2 + 24 = 26 degrees of freedom corresponding to the 26 bosonic dimensions of string theory. This is of course an extremely loose argument for the obvious but mathematically still terse connection between stringy networks and small world networks.
20th March, 2011.
E-infinity Communication No. 82
The small world of ‘t Hooft-Susskind holographic boundary – An E-infinity view
The diffeomorphic kinship between the Penrose fractal tiling universe and the compactified Klein modular curve is well known from El Naschie’s work on the holographic boundary theory. Following this theory a fundamental equation was established stating that the total numbers of state-like particles or massless gauge bosons may be taken to be the dimension of E8E8, namely 496 and that this number must be equal to certain isometries and dimensions pertinent to all elementary particles living on the holographic surface of the 496 dimensional bulk as well as pure gravity and finally electromagnetism. Since in four dimensional Einstein gravity as well as eight dimensional pure gravity the number of the corresponding independent components of the Riemannian tensor and the number of isometries is the same, namely 20, then it follows that 496 must be equal to 20 plus electromagnetism plus particle physics. Following E-infinity theory the number of particles on the holographic boundary are equal to the number of isometries of the classical Klein modular curve, namely 336 plus the compactification effect taking the boundary to infinity as in projective hyperbolic geometry, namely 3. Thus the total number of particle-like isometries is 336 + 3 = 339. Using the equation the inverse coupling of electromagnetism 137 is found exactly and given a topological meaning, namely a dimension of an electromagnetic manifold determined by the fundamental equation 496 – 20 – 339 = 137.
There is something even more astonishing about this holographic boundary which relates it to the theory of small world in an unexpected way which upon reflection should have been expected. The so called isometric length of E-infinity theory applied to the holographic boundary is given by half of the E-infinity core Hausdorff dimension which is half of the famous value 4.2360679, that is to say 4 plus the golden mean to the power of 3. Half of that is exactly 2.118033989. Now there is an approximate value to the Hausdorff dimension found using the classical continuous gamma distribution which was given long ago by El Naschie as well as S. Al Athel, namely 2 divided by the natural logarithm of the inverse golden mean which leads to 4.156173841. Dividing this by two we find an approximation to the isometric length, namely the (inverse) natural logarithm of 1.618033989 which means the isometric length is equal to the inverse of the natural logarithm of the inverse golden mean. There are two important points which we have to consider at this point. First the isometric length is the distance which we have to maximally travel in order to find our surroundings replicated almost exactly as if we had not moved at all. That means that our compactified holographic boundary which describes an infinite universe in all directions is still a finite and in fact small world-like universe. Let us call it small world-like holographic and Penrose universe. Second a small world non-transfinite ordinary network is typically characterized by a distance given also by a logarithmic value. Nor N nodes the distance between the two randomly chosen nodes is proportional to the logarithm of N, namely Log N. This logarithmic relation is behind the relation between social networks like Facebook and Twitter and the transfinite neural network behind quantum mechanics such as E-infinity transfinite networks as proposed for the first time by Mohamed El Naschie and his student Dr. Mahrous Ahmed as well as several other members of the E-infinity Group.
14th March, 2011.
E-infinity communication No. 81
One road to quantum gravity and E-infinity as a transfinite social network
Lee Smolin wrote a nice little book some time ago entitled Three Roads to Quantum Gravity. We discussed this book in an earlier communication where Smolin touched upon and really only touched upon fractal spacetime.
In the present very short communication we propose to reduce the number 3 of Smolin to only 1. In our opinion there is only one road to quantum gravity. This road is based upon the skeleton of a very old idea namely that of a network. Such a network may be for all we know the same network of a small world or even Lee Smolin’s favorite approach of loop quantum gravity. However to be the one and only road such a network must be a self similar grid. In addition this grid must have an element of randomness. When the reader ponders these basic requirements he or she will immediately realize the equivalence of E-infinity theory of Mohamed El Naschie with that of a transfinite social network. Incidentally this is not a new insight. It is only a neglected relatively old insight of El Naschie about which he wrote a paper or two in Prof. Ji-Huan He’s journal. Thus we may recall the following article which the reader may find quite useful: M.S. El Naschie: Transfinite electrical networks, spinoral varieties and gravity Q bits. Int. J. of Nonlinear Sci. & Numerical Simulation, 5(3), (2004), pp. 191-197.
In conclusion it should be noted that the American engineering scientist A.H. Zemanian seems t be the first to propose transfinite networks in electrical engineering and wrote many excellent papers on the subject. In fact Zemanian was in direct contact with El Naschie discussing this exceedingly interesting subject and in view of the events in the Middle East revolutions is also timely because of the role played by social networks such as Facebook and Twitter.
13th March, 2011.
E-infinity Communication No. 80
Small world E-infinity spacetime, Facebook and who wrote more papers, Mohamed El Naschie or Paul Erdös?
Maybe rightly or wrongly the uprisings sweeping the Arab countries and the Middle East including Mohamed El Naschie’s beloved homeland Egypt is attributed to social network sites such as Facebook and Twitter. We were not really fully aware of the possible connections between E-infinity, small world social networks and even less that Mohamed El Naschie had written any papers on this subject. Quite honestly we were mildly surprised when we became aware of several articles which he wrote on the subject in his daily column in the semi official Egyptian newspaper Rose Al Yusuf. Upon translating these articles into English we realized that he and some of his students published several papers in Chaos, Solitons & Fractals and elsewhere on the small world theory and its connection to super string theory and his E-infinity Cantorian spacetime. For more details the reader is referred to two papers:
1. N. Ahmed: Cantorian small world, Mach’s principle and the universal mass network. Chaos, Solitons & Fractals, 21 (2004), pp. 773-782.
2. M.S. El Naschie: Small world network, E-infinity topology and the mass spectrum of high energy particle physics. Chaos, Solitons & Fractals, 19 (2004), pp. 689-697.
The fact that although we worked rather closely with Mohamed El Naschie and are part of his group and yet were unaware about his paper prompted some of us to ask how many papers did El Naschie author and on how many subjects? The honest answer is that we still do not know and when we asked him it was clear that he does not know either and furthermore, does not care. A wild guess is that it is in the region of one thousand and some of us recall having seen that written by someone. Initially we thought that given his age, this must be a world record. However it was not long before we realized that among real scientists of international status in mathematics and physics, the record holder is a man admired by El Naschie, namely Paul Erdös with more than one thousand four hundred papers mostly with co-authors. Needless to say the number of papers nor the number of pages of written papers is no indication of any quality or excellence. It is ridiculous that some agencies use such trivial indexes to evaluate scientists.
Let us conclude this short communication by mentioning the most important common thing between small world and El Naschie’s Cantorian world. Similar to all quantum network approaches to quantum physics both theories are based on a network. However in E-infinity it is a self similar network on all scales and is thus a transfinite network. Second a true small world network is neither orderly nor disorderly. It is in between. This is exactly the KAM deterministic chaotic geometry of El Naschie’s E-infinity theory.