E-infinity communication No. 16
Feynman El Naschie conjecture, fractal time, negative dimensions and some loose ends from previous communications.
First things first. There were some unintended omissions of truly exceptional contributions to E-infinity and fractal spacetime. Two names slipped our collective memory in the E-infinity group and this is disgraceful. First and second in no particular order is Karl Svozil from Austria in fact from Johann Strauss' city Vienna and the exceptionally versatile and gifted Indian physicist and mathematician B.G. Sidharth. Svozil is actually one of the pioneers of fractal spacetime and he is the first to connect the idea of the British Canadian Garnet Ord with quantum field theory. Svozil works closely with the famous experimentalist and connoisseur of classical quantum mechanics and macroscopic quantum objects Anton Zeilinger. Svozil's seminal paper is Quantum field theory on fractal spacetime: a new regularization method, J. Phys. A, Math. Gen, 20, 1987, p. 3861. He also wrote a marvelous book which helped our group quite a bit called Randomness & Undecidability in Physics, published by World Scientific, 1993. Sidharth on the other hand connected fractal spacetime with fuzzy sets and P-Adic quantum mechanics. He wrote a few very nice books of which I mention the following three: Frontiers of Fundamental Physics, Vol. 3 published by Universities Press 2007, The Universe of Fluctuations - The Architecture of Spacetime and the Universe under Fundamental Theories of Physics published by Springer, 2005 and Frontiers of Fundamental Physics 4 published by Kluwer Academic Publishers, 2001.
You probably do not know how these communications function. There are only a limited number of our members who have the time and are also capable of writing in reasonably good English. Very often somebody will write something and then it is circulated. Subsequently the English is edited by the handful of people who are really writing something different from pigeon English. We have no problem admitting our weaknesses and English is our greatest weakness. Zhang and Wu alerted us to a few serious and good questions. We apologize for the delayed reaction and answer. No disrespect is ever intended or implied. When something is not polite, it is our bad English.
The question came from if I am not mistaken, Tom and a lady scientist. I am sorry if we are mixing the names. The first thing is the question regarding the so called Feynman El Naschie conjecture. This is related to a book by Feynman about his secret love - general relativity. He wrote a marvelous little book called Lectures on Gravitation edited by B. Hatfield, published by Addison-Wesley, New York, 1995. I do not think Richard wrote anything. I taught him painting. Normally however his students collect his notes and lectures and make books out of them. The paper responsible for coining this expression is probably the short note by El Naschie A Note on Quantum Gravity and Cantorian Spacetime, CS&F, Vol. 8, No. 1, 1997, p. 131. Do not hold me responsible for every word but as I understood it, it is something like the following sketch. Feynman said there is some form of forces called van der Waal's forces. If the molecule of a chemical reaction was completely orderly, these forces sum to a zero. It is because disorder creates these forces as forces due to non-equilibrium. They are forces created by fluctuation so to speak. Feynman claims however fluctuation in what? Mohamed El Naschie takes it from there. Spacetime fluctuates. No. He said it a little bit more subtly. A little bit more like Fubini. He said when your speed increases near to the speed of light, your weight increases considerably towards infinity and the time slows down until it stops. If space is fractal, so time is also fractal. The fluctuation of the fractal time creates this juggling which we then perceive as gravity. This is an extremely crude way to put it. So please read about it further in the following two papers by El Naschie: Remarks on Superstrings, Fractal Gravity, Nagasawa's Diffusion and Cantorian Spacetime, CS&F, Vol. 8, No. 11, 1997, p. 1873 and Dimensional Symmetry Breaking and Gravity in Cantorian Space, CS&F, Vol. 8, No. 5, 1997, p. 753. We also read a comment by Tom about Bohr and his mad theory. I wish I could copy it and put it in an E-infinity communication. However there is something called copyright and morality so we ask here for permission from Tom first.
Finally somebody was talking about Hilbert space and E-infinity. We told you El Naschie was the first to find this connection interesting. In fact he also looked at Fock space of quantum field theory. Let me give you the most important papers by him in this respect which you can consult: Hilbert, Fock and Cantorian spaces in the quantum two-slit gedanken experiment, CS&F, 27, 2006, p. 39, Hilbert space, Poincare dodecahedron and golden mean transfiniteness, CS&F, 31, 2007, p. 787, Hilbert space, the number of Higgs particles and the quantum two-slit experiment, CS&F, 27, 2006, p. 9, How gravitational instanton could solve the mass problem of the standard model of high energy particle physics, CS&F 21, 2004, p. 249 and Gravitational instanton in Hilbert space and the mass of high energy elementary particles, CS&F, 20, 2004, p. 917. Some asked for a simple introduction to concepts and mathematics of E-infinity theory. I find them all of course simple but maybe the following are simpler The concepts of E-infinity: An elementary introduction to the Cantorian-fractal theory of quantum physics, CS&F, 22, 2004, p. 495 and A guide to the mathematics of E-infinity Cantorian spacetime theory, CS&F, 25, 2005, p. 955. The two-slit experiment is explained concisely and nicely in connection with negative dimensions and the golden mean in appendix F of the paper Time Symmetry breaking, duality and Cantorian spacetime, CS&F, Vol. 7, No. 4, p. 499. Two comprehensive papers on the two-slit experiment are the following: The Feynman Path Integral and E-Infinity from the Two-slit Gedanken Experiment, Int. J. of Nonlinear Sci. & Num. Simulation, 6(4), 2005, p. 335 and The idealized quantum two-slit gedanken experiment revisited - Criticism and reinterpretation, CS&F, 27, 2006, p. 843. A mathematical resolution may be found in Fredholm Operators and the Wave-Particle Duality in Cantorian Space, CS&F, Vol. 9, No. 6, 1998, p. 975.
We once asked El Naschie who the greatest theoretical physicist is of all time in his opinion. He said the trinity. We were surprised and asked what that is? He said Einstein, Heisenberg and Richard Feynman. He paused for a minute and then said depending on my mood or the problem I am solving. From Einstein he singles out simplicity, intuition and the idea of spacetime. From Heisenberg he found the idea of symmetry. From Richard Feynman it is his path integral. In fact in retrospect path integral is the main idea at least mathematically in E-infinity. The standard procedure of El Naschie's formulation of E-infinity is summing over dimensions. Infinitely many of them and each dimension is weighted. Later on El Naschie started summing over exceptional Lie groups. In fact in one of his last papers he was summing over crystal groups. 319 of them which gave him almost exactly a large number 8872. I am ignoring the transfinite tail. 8872 you may recall corresponds exactly to the 8064 of classical Heterotic strings. In E-infinity 8872 plays a similar role to 685 of E12 of Munroe. When you look at it attentively you find you are summing over 17 two and three Stein spaces. Einstein space being one stein space. I told you on a previous occasion this is something which exceeded the knowledge of a certain American mathematician who is only good for cracking jokes on the internet and who finds everything that he does not know a good reason for a good laugh but not about himself. Of course it is about other people that he likes to laugh. Then you have summing over 8 exceptional Lie groups of the E type and this gives you 548. You can then sum over combinatorics in 11 dimensions and this gives you the 528 of Ed Witten. Finally you have the double E8 which gives you 496. This is the smallest number of massless gauge bosons known to give unification. If you want to read a truly nonconventional paper with exceptionally important findings, and then have a look at the three pages long note by El Naschie called The crystallographic space groups and Heterotic string theory, CS&F, 41, 2009, p. 2282. In this paper he derives the exact N zero which is 8872.135956. Weyl scaling then gives you everything you want including holographic boundary, superstring theory and even Renate Loll and Jan Ambjorn's spectral dimension of spacetime, namely 4.02. In the next communication which will take a bit longer to write we will expand more on this and other subjects.
