In the spirit of the work of Ramanujan’s infinite Cesaro sum and the formalization of his work by G. Hardy, we propose that quantum physics and cosmology are governed by fractal logic rather than ordinary classical logic. Various general considerations as well as specific examples are given to illustrate and support our thesis leading to a revision of the standard model of elementary particles as well as relativity. These examples range from the practical aspect to almost esoteric considerations but at the end, everything converges towards a unity of theory and computation presented in the form of modern fractal logic and transfinite quantum field theory in a Cantorian spacetime. We conclude that the universe is akin to a transfinite Turing machine, or a Transfinite Infinite capacity of 'tHooft Automaton.
| Published in | American Journal of Astronomy and Astrophysics (Volume 4, Issue 4) |
| DOI | 10.11648/j.ajaa.20160404.12 |
| Page(s) | 42-53 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2016. Published by Science Publishing Group |
Fractal Logic, E-infinity, Cantorian Spacetime, P. Erdos, Transfinite Turing Machine, Non-commutative Geometry, Von Neumann Geometry, Golden Computer, Pointless Geometry, Fuzzy Logic
| [1] | M. Waldschmidt, P. Moussa, J. Luck and C. Itzykson: From Number Theory to Physics. Springer-Verlag, Berlin, Germany, 1992. |
| [2] | G. H. Hardy and E. M. Wright: An Introduction to The Theory of Numbers. Clarendon Press, Oxford, UK, 1979. |
| [3] | Hector Zenil (Editor): A Computable Universe. World Scientific, Singapore, 2013. |
| [4] | M. Tegmark: Our Mathematical Universe. Allen Lane-Penguin Books, London, UK, 2014. |
| [5] | Seth Lloyd: Programming The Universe. Jonathan Cape, London, 2005. |
| [6] | C. A. Pickover: Computers, Patterns Chaos and Beauty. St. Martin’s Press, New York, USA, 1990. |
| [7] | A. H. Beiler: Recreations in The Theory of Numbers. Dover Publications, New York, USA, 1966. |
| [8] | R. Dedekind: Essays on The Theory of Numbers. Dover Publications, New York, USA, 1963. |
| [9] | B. Artman: The Concept of Numbers. Ellis Horwood Ltd. -John Wiley, New York, USA, 1988. |
| [10] | D. Deutsch: The Beginning of Infinity. Allen Lane-Penguin Books, London, US, 2011. |
| [11] | A. S. Posamentier and Ingmar Lehmann: The Fabulous Fibonacci Numbers. Prometheus Books, New York, USA, 2007. |
| [12] | Alexey Stakhov: The Mathematics of Harmony, World Scientific, Singapore, 2009. |
| [13] | J-Pierre Changeux and Alain Connes: Conversations on Mind, Matter and Mathematics. Princeton University Press, Princeton, New Jersey, USA, 1989. |
| [14] | Paul Rendell: Turing Machine in Conway Game of Life. In ‘Designing Beauty: The Art of Cellular Automata. Springer, Heidelberg, Germany, 2016. (See pages 149-154). |
| [15] | D. Deutsch: Quantum Theory, The Church-Turing Principle and The Universal Computer. Proceedings of the Royal Society, Mathematical, Physical and Engineering Sciences, Series Vol. 400, No. 1818, 1985, pp. 97-117. |
| [16] | A. M. Turing: Computing machinery and intelligence. Mind, 59 (236), 1950, pp. 433-460. |
| [17] | L. Babai, C. Pomerance and P. Vertesi: The mathematics of Paul Erdos. Notices of the American Mathematical Society, 45 (1), 1998, pp. 19-31. |
| [18] | P. Hoffman: The Man Who Loved Only Numbers, Hepron, New York, USA, 1998. |
| [19] | R. Kanigel: The Man Who Knew Infinity. Scribners, New York, USA, 1991. |
| [20] | S. Ramanujan: Collected Papers of Ramanujan. Cambridge University Press, Cambridge, UK, 2015. |
| [21] | M. S. El Naschie: Physics-like mathematical model for chaos and ergodic criticality in four dimensions. Thirteenth Canadian Congress of Applied Mechanics (CANCAM 91), 1991. Paper No. A90. 19. |
| [22] | M. S. El Naschie: Mathematical model for chaos and ergodic criticality in four dimensions. Mathematical and Computer Modelling, 15 (12), 1991, pp. 77-80. |
| [23] | M. S. El Naschie: Complex dynamics in a 4D Peano-Hilbert space. Il Nuovo Cimento, 107B (N5), 1992, pp. 583-594. |
| [24] | M. S. El Naschie: Multi-dimensional Cantor-like sets and ergodic behaviour. Speculations in Science & Technology, 15 (2), 1992, pp. 138-142. |
| [25] | M. S. El Naschie: On universal behaviour and statistical mechanics of multi-dimensional triadic Cantor sets. SAMS, Vol. II, 1993, pp. 217-225. Published by Gordon and Breach Science Publishers, S. A. |
| [26] | M. S. El Naschie: On turbulence and complex dynamics in a four dimensional Peano-Hilbert space. Journal of The Franklin Institute, 330, 1993, pp. 183-198. |
| [27] | M. S. El Naschie: Statistical geometry of a Cantor discretum and semi conductors. Computer Math & Applications, 29 (12), 1995, pp. 103-110. |
| [28] | A. Connes: Non-commutative Geometry. Academic Press, San Diego, USA, 1994. |
| [29] | J. von Neumann: Continuous Geometry, Vol. 25. Princeton University Press, Princeton, New Jersey, USA, 1960. |
| [30] | J. Kappraff: Connections. McGraw-Hill Inc., New York, USA, 1991. |
| [31] | M. S. El Naschie: A review of E-infinity theory and the mass spectrum of high energy particle physics. Chaos, Solitons & Fractals, 19 (1), 2004, pp. 209-236. |
| [32] | M. S. El Naschie: A guide to the mathematics of E-infinity Cantorian spacetime theory. Chaos, Solitons & Fractals, 25 (5), 2005, pp. 955-964. |
| [33] | M. S. El Naschie: The concepts of E-infinity: An elementary introduction to the Cantorian-fractal theory of quantum physics. Chaos, Solitons & Fractals, 22, 2004, pp. 495-511. |
| [34] | M. S. El Naschie: Elementary prerequisites for E-infinity (Recommended background readings in nonlinear dynamics, geometry and topology). Chaos, Solitons & Fractals, 30, 2006, pp. 579-605. |
| [35] | M. S. El Naschie: A review of application and results of E-infinity. International Journal of Nonlinear Science & Numerical Simulation, 2007, 8 (1), pp. 11-20. |
| [36] | M. S. El Naschie: The theory of Cantorian spacetime and high energy particle physics (An informal review). Chaos, Solitons & Fractals, 41 (5), 2009, pp. 2635-2646. |
| [37] | M. S. El Naschie: On an eleven dimensional E-infinity fractal spacetime theory. Int. J. Nonlinear Sci. & Numerical Simulation, Vol. 7, No. 4, 2006, pp. 407-409. |
| [38] | M. S. El Naschie: Quantum entanglement as a consequence of a Cantorian micro spacetime geometry. Journal of Quantum Information Science, 1 (2), 2011, pp. 50-53. |
| [39] | M. S. El Naschie: Feigenbaum scenario for turbulence and Cantorian E-infinity theory of high energy particle physics. Chaos, Solitons & Fractals, 32 (3), 2007, pp. 911-915. |
| [40] | M. S. El Naschie: On a fuzzy Kähler-like manifold which is consistent with the two slit experiment. International Journal of Nonlinear Sciences and Numerical Simulation. 6 (2), 2005, pp. 95-98. |
| [41] | M. S. El Naschie: On the topological ground state of E-infinity spacetime and the super string connection. Chaos, Solitons & Fractals, 32, 2007, pp. 468-470. |
| [42] | M. S. El Naschie: On the cohomology and instantons number in E-infinity Cantorian spacetime. Chaos, Solitons & Fractals, 26 (1), 2005, pp. 13-17. |
| [43] | M. S. El Naschie: Advanced prerequisites for E-infinity theory. Chaos, Solitons & Fractals, 30 (12), 2006, pp. 636-641. |
| [44] | M. S. El Naschie: Topics in the mathematical physics of E-infinity theory. Chaos, Solitons & Fractals, 30 (3), 2006, pp. 656-663. |
| [45] | M. S. El Naschie: The two-slit experiment as the foundation of E-infinity of high energy physics. Chaos, Solitons & Fractals, 25, 2005, pp. 509-514. |
| [46] | M. S. El Naschie: Holographic dimensional reduction: Center manifold theorem and E-infinity. Chaos, Solitons & Fractals, 29 (4), 2006, pp. 816-822. |
| [47] | M. S. El Naschie: Fuzzy dodecahedron topology and E-infinity spacetime as a model for quantum physics. Chaos, Solitons & Fractals, 30 (5), 2006, pp. 1025-1033. |
| [48] | M. S. El Naschie: Elementary number theory in superstring loop quantum mechanics, twistors and E-infinity high energy physics. Chaos, Solitons & Fractals, 27 (2), 2006, pp. 297-330. |
| [49] | M. S. El Naschie: Hilbert, Fock and Cantorian spaces in the quantum two-slit gedanken experiment. Chaos, Solitons & Fractals, 27 (1), 2006, pp. 39-42. |
| [50] | M. S. El Naschie: From experimental quantum optics to quantum gravity via a fuzzy Kähler manifold. Chaos, Solitons & Fractals, 25 (5), 2005, pp. 969-977. |
| [51] | M. S. El Naschie: Symmetry group prerequisite for E-infinity in high energy physics. Chaos, Solitons & Fractals, 35 (1), 2008, pp. 202-211. |
| [52] | M. S. El Naschie: Intermediate prerequisites for E-infinity theory. Chaos, Solitons & Fractals, 30, 2006, pp. 622-628. |
| [53] | M. S. El Naschie: Superstrings, entropy and the elementary particles content of the standard model. Chaos, Solitons & Fractals, 29 (1), 2006, pp. 48-54. |
| [54] | M. S. El Naschie: Hilbert space, the number of Higgs particles and the quantum two-slip experiment. Chaos, Solitons & Fractals, 28 (1) 2006, pp. 9-13. |
| [55] | M. S. El Naschie: On two new fuzzy Kähler manifolds, Klein modular space and ‘tHooft’s holographic principles. Chaos, Solitons & Fractals, 29 (4), 2006, pp. 876-881. |
| [56] | M. S. El Naschie: The idealized quantum two-slit gedanken experiment revisited – Criticism and reinterpretation. Chaos, Solitons & Fractals, 27 (4), 2006, pp. 843-849. |
| [57] | M. S. El Naschie: Modular groups in Cantorian E-infinity high energy physics. Chaos, Solitons & Fractals, 2003, 16, pp. 353-366. |
| [58] | M. S. El Naschie: E (infinity) Cantorian space-time and its consequences in cosmology. Chaos, Solitons & Fractals, 2003, 25 (4), pp. 775-779. |
| [59] | M. Helal, L. Marek-Crnjac and Ji-Huan He: The three page guide to the most important results of M. S. El Naschie’s research in E-infinity quantum physics. Open Journal of Microphysics, 2013, 3, pp. 141-145. |
| [60] | M. S. El Naschie: The brain and E-infinity. International Journal of Nonlinear Science & Numerical Simulation, 7 (2), 2006, pp. 129-132. |
| [61] | M. S. El Naschie: E-infinity – Some recent results and new interpretations. Chaos, Solitons & Fractals, 29, 2006, pp. 845-853. |
| [62] | M. S. El Naschie: The symplictic vacuum, exotic quasi particles and gravitational instanton. Chaos, Solitons & Fractals, 22 (1), 2004, pp. 1-11. |
| [63] | M. S. El Naschie: The VAK of vacuum fluctuation, spontaneous self organization and complexity theory interpretation of high energy particle physics and the mass spectrum. Chaos, Solitons & Fractals, 18 (2), 2003, pp. 579-605. |
| [64] | M. S. El Naschie: Quasi exceptional E12 Lie symmetry group with 685 dimensions, KAC-Moody algebra and E-infinity Cantorian spacetime. Chaos, Solitons & Fractals, Vol. 38, No. 4, 2008, pp. 990-992. |
| [65] | G. Iovane and E. Benedetto: El Naschie E-infinity Cantorian spacetime and length scales in cosmology. International Journal of Nonlinear Sciences and Numerical Simulation, 7 (2), 2006, pp. 155-162. |
| [66] | Ji-Huan He: Application of E-infinity theory to biology. Chaos, Solitons & Fractals, 28 (2), 2006, pp. 285-289. |
| [67] | M. S. El Naschie: Non-linear dynamics and infinite dimensional topology in high energy particle physics. Chaos, Solitons & Fractals, 17 (2-3), 2003, pp. 2635-2646. |
| [68] | M. S. El Naschie: Deterministic quantum mechanics versus classical mechanical indeterminism. International Journal of Nonlinear Science & Numerical Simulation, 8 (1), 2007, pp. 1-10. |
| [69] | M. S. El Naschie: Quantum gravity, Clifford algebras, fuzzy set theory and the fundamental constants of nature. Chaos, Solitons & Fractals, 20 (3), 2004, pp. 437-450. |
| [70] | M. S. El Naschie: On Penrose view of transfinite sets and computability and the fractal character of E-infinity spacetime. Chaos, Solitons & Fractals, 25 (3), 2005, pp. 531-533. |
| [71] | G. Iovane and P. Giordano: Wavelets and multiresolution analysis: Nature of E-infinity Cantorian spacetime. Chaos, Solitons & Fractals, 32 (3), 2007, pp. 896-910. |
| [72] | L. D. G. Sigalotti and A. Mejias: On El Naschie’s conjugate complex, time, fractal E-infinity spacetime and faster than light. International Journal of Nonlinear Science & Numerical Simulation, 7 (4), 2006, pp. 467-472. |
| [73] | M. S. El Naschie: Kleinian groups in E-infinity and their connection to particle physics and cosmology. Chaos, Solitons & Fractals, 2003, 16, pp. 637-649. |
| [74] | M. S. El Naschie: Is gravity less fundamental than elementary particles theory? Critical remarks on holography and E-infinity theory. Chaos, Solitons & Fractals, 2006, 29 (4), pp. 803-807. |
| [75] | M. S. El Naschie: A unified Newtonian-relativistic quantum resolution of supposedly missing dark energy of the cosmos and the constancy of the speed of light. International Journal of Modern Nonlinear Theory & Application, 2013, 2, pp. 43-54. |
| [76] | M. S. El Naschie: On a class of fuzzy Kähler-like manifolds. Chaos, Solitons & Fractals, 26, 2005, pp. 477-481. |
| [77] | M. S. El Naschie: A cold fusion-Casimir energy nano reactor proposal. World Journal of Nano Science and Engineering, 5, 2015, pp. 49-56. M. S. El Naschie: Fractal black holes and information. Chaos, Solitons & Fractals, 29 (1), 2006, pp. 23-35. |
| [78] | M. S. El Naschie: Fractal black holes and information. Chaos, Solitons & Fractals, 29 (1), 2006, pp. 23-35. |
| [79] | M. S. El Naschie: A few hints and some theorems about Witten’s M-theory and T-duality. Chaos, Solitons & Fractals, 25 (3), 2005, pp. 545-548. |
| [80] | L. Marek-Crnjac and Ji-Huan He: An invitation to El Naschie’s theory of Cantorian spacetime and dark energy. International Journal of Astronomy and Astrophysics, 2013, 3, pp. 464-471. |
| [81] | G. Iovane: El Naschie E-infinity Cantorian spacetime and length scales in cosmology. International Journal of Nonlinear Sciences and Numerical Similation, 7 (2), 2006, pp. 155-162. |
| [82] | M. S. El Naschie: The Fibonacci code behind superstrings and P-Branes. An answer to M. Kaku’s fundamental question. Chaos, Solitons & Fractals, 31 (3), 2007, pp. 537-547. |
| [83] | L. Marek-Crnjac, Mohamed S. El Naschie: Ji-Huan He: Chaotic fractals at the root of relativistic quantum physics and cosmology. International Journal of Modern Nonlinear Theory and Application, 2 (1A), 2013. |
| [84] | Mohamed S. El Naschie: Towards a quantum golden field theory. International Journal of Nonlinear Sciences and Numerical Simulation, 8 (4), 2007, pp. 477-482. |
| [85] | M. S. El Naschie: The cosmic Da Vinci code for the big bang – a mathematical toy model. International Journal of Nonlinear Sciences and Numerical Simulation, 8 (2), 2007, pp. 191-194. |
| [86] | M. S. El Naschie: Superstrings, knots and noncommutative geometry in E-infinity space. International Journal of Theoretical Physics, 37 (12), 1998, pp. 2935-2951. |
| [87] | M. S. El Naschie: Transfinite electrical networks, spinoral varieties and gravity Q bits. Int. Journal of Nonlinear Sciences and Numerical Simulation. 5 (3), 2004, pp. 191-198. |
| [88] | G. Iovane, E. Laserra, F. S. Tortoriello: Stochastic self similar and fractal universe. Chaos, Solitons & Fractals, 3 (4), 2004, pp. 415-426. |
| [89] | M. S. El Naschie: On the universality class of all universality classes and E-infinity spacetime physics. Chaos, Solitons & Fractals, 32 (3), 2007, pp. 927-936. |
| [90] | Ji-Huan He, Y. Liu, L. Xu and J. Y. Yu: Micro sphere with nanoporosity by electrospinning. Chaos, Solitons & Fractals, 32 (3), 2007, pp. 1096-1100. |
| [91] | M. S. El Naschie: Superstring theory: What it cannot do but E-infinity could. Chaos, Solitons & Fractals, 29 (1), 2006, pp. 65-68. |
| [92] | M. S. El Naschie: Cosmic dark energy from ‘thooft’s dimesnionl regularization and Witten’s topological quantum field pure gravity. Journal of Quantum Information Science, vol. 4 (2), 2014, pp. 83-91. |
| [93] | M. S. El Naschie: Kerr black hole geometry leading to dark matter and dark energy via E-infinity theory and the possibility of nano spacetime singularity reactor. Natural Science, 7 (4), 2015, pp. 210-225. |
| [94] | M. S. El Naschie: From E = mc2 to E = mc2/22 – A short account of the most famous equation in physics and its hidden quantum entangled origin. Journal of Quantum Information Science, 4, 2014, pp. 284-291. |
| [95] | Mohamed S. El Naschie: Pinched material Einstein space-time produces accelerated cosmic expansion. International Journal of Astronomy and Astrophysics. 4 (1), 2014, pp. 80-90. |
| [96] | Mohamed S. El Naschie: On a new elementary particle from the disintegration of the symplectic 't Hooft-Veltman-Wilson fractal spacetime. World Journal of Nuclear Science and Technology, 4 (4), 2014, pp. 216-221. |
| [97] | Mohamed S. El Naschie: The measure concentration of convex geometry in a quasi Banach spacetime behind the supposedly missing dark energy of the cosmos. American Journal of Astronomy & Astrophysics, 2014, 2 (6), pp. 72-77. |
| [98] | Ji-Huan He: A tutorial review on fractal spacetime and fractional calculus. International Journal of Theoretical Physics, 53 (11), 2014, pp. 3698-3718. |
| [99] | Mohamed S. El Naschie: Electromagnetic—Pure Gravity Connection via Hardy’s Quantum Entanglement Journal of Electromagnetic Analysis and Applications, 6 (9), 2014, pp. 233-237. |
| [100] | Mohamed S. El Naschie: An exact mathematical picture of quantum spacetime. Advances in Pure Mathematics, 2015, 5, pp. 560-570. |
| [101] | Mohamed S. El Naschie: A resolution of the black hole information paradox via transfinite set theory. World Journal of Condensed Matter Physics, 5, 2015, pp. 249-260. |
| [102] | W. Tang et al: From nonlocal elasticity to nonlocal spacetime and nanoscience. Bubbfil Nano Technology, 1 (1), 2014, pp. 3-12. |
| [103] | M. S. El Naschie: To dark energy theory from a Cosserat-like model of spacetime. Problems of Nonlinear Analysis in Engineering Systems, vol. 20 (1-41), 2014, pp. 79-98. |
| [104] | M. S. El Naschie: The Cantorian monadic plasma behind the zero point vacuum spacetime energy. American Journal of Nano Research & Application. 3, 2015, pp. 66-70. |
| [105] | M. S. El Naschie: The Casimir topological effect and a proposal for a Casimir-dark energy nano reactor. World Journal of Nano Science & Engineering, 5 (1), 2015, pp. 26-33. |
| [106] | Mohamed S. El Naschie: Calculating the Exact Experimental Density of the Dark Energy in the Cosmos Assuming a Fractal Speed of Light. International Journal of Modern Nonlinear Theory and Application, 3 (1), 2014, pp. 1-5. |
| [107] | Mohamed Salah El Naschie, Leila Marek-Crnjac, Mohamed Atef Helal, Ji-Huan He: A Topological Magueijo-Smolin Varying Speed of Light Theory, the Accelerated Cosmic Expansion and the Dark Energy of Pure Gravity. Applied Mathematics, 5 (12), 2014, pp. 1780-1790. |
| [108] | Mohamed S. El Naschie: On a non-perturbative quantum relativity theory leading to a Casimir-dark energy nanotech reactor proposal. Open Journal of Applied Science, 5 (7), 2015, pp. 313-324. |
| [109] | Mohamed S. El Naschie: From Chern-Simon, Holography and Scale Relativity to Dark Energy. Journal of Applied Mathematics and Physics, 2 (7), 2014, pp. 634-638. |
| [110] | Mohamed S. El Naschie: Why E Is Not Equal to mc2. Journal of Modern Physics, 5 (9), 2014, pp. 743-750. |
| [111] | Mohamed S. El Naschie: Capillary Surface Energy Elucidation of the Cosmic Dark Energy—Ordinary Energy Duality Open Journal of Fluid Dynamics, 4 (1), 2014, pp. 15-17. |
| [112] | Mohamed S. El Naschie: Cosmic Dark Energy Density from Classical Mechanics and Seemingly Redundant Riemannian Finitely Many Tensor Components of Einstein’s General Relativity World Journal of Mechanics, 4 (6), 2014, pp. 153-156. |
| [113] | Mohamed S. El Naschie: Dark energy and its cosmic density from Einstein’s relativity and gauge fields renormalization leading to the possibility of a new ‘tHooft quasi particle. The Open Journal of Astronomy. 8, 2015, pp. 1-17. |
| [114] | Mohamed S. El Naschie: If quantum “wave” of the universe then quantum “particle” of the universe: A resolution of the dark energy question and the black hole information paradox. International Journal of Astronomy & Astrophysics, 5, 2015, pp. 243-247. |
| [115] | Mohamed S. El Naschie: From modified Newtonian gravity to dark energy via quantum entanglement. Journal of Applied Mathematics and Physics, 2 (8), 2014, pp. 803-806. |
| [116] | Mohamed S. El Naschie: From highly structured E-infinity rings and transfinite maximally symmetric manifolds to the dark energy density of the cosmos. Advances in Pure Mathematics, 4 (12), 2014, 641-648. |
| [117] | Mohamed S. El Naschie: Entanglement of E8E8 exceptional Lie symmetry group dark energy, Einstein’s maximal total energy and the Hartle-Hawking no boundary proposal as the explanation for dark energy. World Journal of Condensed Matter Physics, 4 (2), 2014, pp. 74-77. |
| [118] | Mohamed S. El Naschie: From fusion algebra to cold fusion or from pure reason to pragmatism. Open Journal of Philosophy, 5 (6), 2015, pp. 319-326. |
| [119] | Mohamed S. El Naschie: Einstein-Rosen bridge (ER), Einstein-Podolski-Rosen experiment (EPR) and zero measure Rindler KAM Cantorian spacetime geometry (ZMG) are conceptually equivalent. Journal of Quantum Information Science, 6, 2016, pp. 1-9 |
| [120] | Mohamed S. El Naschie: A Casimir-dark energy nano reactor design – Phase I. Natural Science, 7, 2015, pp. 287-298. |
| [121] | Mohamed S. El Naschie: Einstein’s General Relativity and Pure Gravity in a Cosserat and De Sitter-Witten Spacetime Setting as the Explanation of Dark Energy and Cosmic Accelerated Expansion International Journal of Astronomy and Astrophysics, 4 (2), 2014, p. 332-339. |
| [122] | Mohamed S. El Naschie: Application of Dvoretzky’s theorem of measure concentration in physics and cosmology. Open Journal of Microphysics, 5, 2015, pp. 11-15. |
| [123] | Mohamed S. El Naschie: Quantum fractals and the Casimir-dark energy duality – The road to a clean quantum energy nano reactor. Journal of Modern Physics, 6, 2015, pp. 1321-1333. |
| [124] | Mae-Wan Ho, M. S. El Naschie and MW Giuseppe Vitello: Is spacetime fractal and quantum coherent in the golden mean? Global Journal of Science Frontier Research, 15 (1), 2015, pp. 61-80. |
| [125] | Leila Marek-Crnjac: On El Naschie’s Fractal-Cantorian Space-Time and Dark Energy—A Tutorial Review. Natural Science, 7 (13), 2015, pp. 581-598. |
| [126] | Mohamed S. El Naschie: Hubble scale dark energy meets nano scale Casimir energy and the rational of their T-duality and mirror symmetry equivalence. World Journal of Nano Science and Engineering, 5, 2015, pp. 57-67. |
| [127] | M. S. El Naschie: The Casimir effect as a pure topological phenomenon and the possibility of a Casimir nano reactor – A preliminary design. American Journal of Nano Research and Application, 3 (3), 2015, pp. 33-40. |
| [128] | Mohamed S. El Naschie: On a fractal version of Witten’s M-theory. Journal of Astronomy & Astrophysics, 6 (2), 2016, pp. 135-144. |
| [129] | Mohamed S. El Naschie: Rindler space derivation of dark energy. Journal of Modern Physics Applications. 6, 2014, pp. 1-10. |
| [130] | Mohamed S. El Naschie: From Kantian-Reinen Vernunft to the real dark energy density of the cosmos via the measure concentration of convex geometry in quasi Banach spacetime. Open Journal of Philosophy, 5, 2015, pp. 123-130. |
| [131] | Mohamed S. El Naschie: From Witten’s 462 supercharges of 5-D Branes in eleven dimensions to the 95. 5 percent cosmic dark energy density behind the accelerated expansion of the universe. Journal of Quantum Information Science, 6 (2), 2016, pp. 57-61. |
| [132] | Mohamed S. El Naschie: Quantum dark energy from the hyperbolic transfinite Cantorian geometry of the cosmos. Natural Science, 8, 2016, pp. 152-159. |
| [133] |
Mohamed S. El Naschie: On a quantum gravity fractal spacetime equation: QRG  HD + FG and its application to dark energy – accelerated cosmic expansion. Journal of Modern Physics, 7, 2016, pp. 729-736.
|
| [134] | Mohamed S. El Naschie: The emergence of spacetime from the quantum in three steps. Advances in Pure Mathematics, 6 (6), 2016, pp. 446-454. |
| [135] | Mohamed S. El Naschie: Negative norms in quantized strings as dark energy density of the cosmos. World Journal of Condensed Matter Physics, 6, 2016, pp. 63-67. |
| [136] | Mohamed S. El Naschie: On the stringy ghosts which we call the missing dark energy of the cosmos. Journal of Applied Mathematics and Physics, 4 (6), 2016, pp. 979-987. |
| [137] | Mohamed S. El Naschie: Einstein’s dark energy via similarity equivalence, ‘tHooft dimensional regularization and Lie symmetry groups. International Journal of Astronomy & Astrophysics, 6, 2016, pp. 56-81. |
| [138] | E. Ott: Chaos in Dynamical Systems. Cambridge University Press, Cambridge, UK, 1993. |
| [139] | P. S. Addison: Fractals and Chaos: An Illustrated Course. Institute of Physics Publishing, Bristol, UK, 1997. |
| [140] | D. Ruelle: Chance and Chaos, Princeton University Press, New Jersey, USA, 1991. |
| [141] | F. Diacu and P. Holmes: Celestial Encounters. Princeton University Press, Princeton, New Jersey, USA, 1996. |
| [142] | T. Kapitaniak: Chaotic Oscillators – Theory and Applications. World Scientific, Singapore, 1992. |
| [143] | M. S. El Naschie: The average (n) sphere spans a four dimensional manifold. Chaos, Solitons & Fractals, 9 (10), 1998, pp. 1789-1792. |
| [144] | M. S. El Naschie: COBE satellite measurement, hyper spheres, superstrings and the dimension of spacetime. Chaos, Solitons & Fractals, 1998, 9 (8), pp. 1445-1471. |
| [145] | Ji-Huan He: Transfinite Physics. China Culture & Science Publishing, 2005. ISBN 988-98846-5-8. |
| [146] | M. S. El Naschie: The mean sphere < s > as a three manifold in R4. Chaos, Solitons & Fractals, 9 (9), 1998, pp. 1631-1635. |
| [147] | J. H. Conway and N. J. Sloane: Sphere Packings, Lattices and Groups. Springer, New York, USA, 1999. |
| [148] | Mohamed S. El Naschie: Dark Energy from Kaluza-Klein Spacetime and Noether’s Theorem via Lagrangian Multiplier Method. Journal of Modern Physics, 4 (6), 2013, pp. 757-760. |
| [149] | M. S. El Naschie: Kaluza-Klein unification – some possible extensions. Chaos, Solitons & Fractals, 37 (1), 2008, pp. 16-22. |
| [150] | M. S. El Naschie: Electromagnetic and gravitational origin of dark energy in Kaluza-Klein D= 5 spacetime. Piers Proceedings, Stockholm, Sweden, August 12-15, 2013, pp. 94-97. |
| [151] | J. Polchinski: String Theory Vol. I: Cambridge University Press, Cambridge, 1998. (See in particular pp. 22, equation (1. 3. 33)). |
| [152] | M. S. El Naschie, S. Olsen, J. H. He, S. Nada, L. Marek-Crnjac, A. Helal: On the Need for Fractal Logic in High Energy Quantum Physics International Journal of Modern Nonlinear Theory and Application, 1 (3), 2012, pp. 84-92. |
| [153] | M. S. El Naschie: Physics-like mathematics of chaos and ergodicity in four dimensions. 13th World Congress on Computation and Applied Mathematics, Trinity College, Dublin, Ireland. Proceedings Vol. 2, 1991, pp. 851-852. |
| [154] | M. S. El Naschie: von Neumann geometry and E-infinity quantum spacetime. Chaos, Solitons & Fractals, 9 (12), 1998, pp. 2023-2030. |
| [155] | M. S. El Naschie: Small world network, E-infinity topology and the mass spectrum of high energy particle physics. Chaos, Solitons & Fractals, 19 (3), 2004, pp. 689-697. |
| [156] | G. ‘tHooft: The cellular automaton interpretation of quantum mechanics. arXiv: 1405. 1548 [quant-ph], May 7, 204. |
APA Style
Mohamed S. El Naschie. (2016). Computational Fractal Logic for Quantum Physics and Cosmology. American Journal of Astronomy and Astrophysics, 4(4), 42-53. https://doi.org/10.11648/j.ajaa.20160404.12
ACS Style
Mohamed S. El Naschie. Computational Fractal Logic for Quantum Physics and Cosmology. Am. J. Astron. Astrophys. 2016, 4(4), 42-53. doi: 10.11648/j.ajaa.20160404.12
AMA Style
Mohamed S. El Naschie. Computational Fractal Logic for Quantum Physics and Cosmology. Am J Astron Astrophys. 2016;4(4):42-53. doi: 10.11648/j.ajaa.20160404.12
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Download@article{10.11648/j.ajaa.20160404.12,
author = {Mohamed S. El Naschie},
title = {Computational Fractal Logic for Quantum Physics and Cosmology},
journal = {American Journal of Astronomy and Astrophysics},
volume = {4},
number = {4},
pages = {42-53},
doi = {10.11648/j.ajaa.20160404.12},
url = {https://doi.org/10.11648/j.ajaa.20160404.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajaa.20160404.12},
abstract = {In the spirit of the work of Ramanujan’s infinite Cesaro sum and the formalization of his work by G. Hardy, we propose that quantum physics and cosmology are governed by fractal logic rather than ordinary classical logic. Various general considerations as well as specific examples are given to illustrate and support our thesis leading to a revision of the standard model of elementary particles as well as relativity. These examples range from the practical aspect to almost esoteric considerations but at the end, everything converges towards a unity of theory and computation presented in the form of modern fractal logic and transfinite quantum field theory in a Cantorian spacetime. We conclude that the universe is akin to a transfinite Turing machine, or a Transfinite Infinite capacity of 'tHooft Automaton.},
year = {2016}
}
TY - JOUR T1 - Computational Fractal Logic for Quantum Physics and Cosmology AU - Mohamed S. El Naschie Y1 - 2016/08/06 PY - 2016 N1 - https://doi.org/10.11648/j.ajaa.20160404.12 DO - 10.11648/j.ajaa.20160404.12 T2 - American Journal of Astronomy and Astrophysics JF - American Journal of Astronomy and Astrophysics JO - American Journal of Astronomy and Astrophysics SP - 42 EP - 53 PB - Science Publishing Group SN - 2376-4686 UR - https://doi.org/10.11648/j.ajaa.20160404.12 AB - In the spirit of the work of Ramanujan’s infinite Cesaro sum and the formalization of his work by G. Hardy, we propose that quantum physics and cosmology are governed by fractal logic rather than ordinary classical logic. Various general considerations as well as specific examples are given to illustrate and support our thesis leading to a revision of the standard model of elementary particles as well as relativity. These examples range from the practical aspect to almost esoteric considerations but at the end, everything converges towards a unity of theory and computation presented in the form of modern fractal logic and transfinite quantum field theory in a Cantorian spacetime. We conclude that the universe is akin to a transfinite Turing machine, or a Transfinite Infinite capacity of 'tHooft Automaton. VL - 4 IS - 4 ER -
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