Topological vacuum fluctuation and Dvoretzky‘s theorem – Mathematical proofs in the context of the dark energy density of the universe
Keywords:
Fractal spacetime, E-infinity theory, Quantum vacuum fluctuation, Platonic quantum set theory, Dvoretzky’s theorem, Golden mean number system, G. Ord, L. Nottale, Pointless Geometry, Penrose fractal tiling, von Neumann continuous geometry, G. ‘tHooft-Weltman-Wilson fractal spacetime, A. Connes noncommutative geometry, E-infinty bijection.
Abstract
Starting from the initial triality of physics, namely mathematical philosophy, transfinite set theory and number theory we drive the inevitability of a topological quantum vacuum fluctuation of spacetime resulting in the fundamental reality of pair creation and annihilation. Subsequently we give a simple but strong mathematical proof of Dvoretzky‘s marvellous theorem on measure concentration, thus making dark energy and accelerated cosmic expansion not only an astrophysical measurement and observational reality, but also a plausible topological-geometrical fact of a pointless Cantorian actual universe akin to the Penrose fractal tiling space. This space is described accurately via the von Neumann-Conne noncommutative geometry using their golden mean dimensional function and the corresponding bijection of E-infinity theory. The said theory was developed by the authors of the present paper and their group and is based on and starts from the pioneering efforts of the Canadian physicist G. Ord and the French astrophysicist L. Nottale.
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References
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[2] Mohamed S. El Naschie, On the Fractal Counterpart of C. Vafa‘s twelve-Dimensional F-theory and the A. Schoenberg Twelve-tone Music Implicit in the Standard Model of High Energy Elementary Particles. International
Journal of Innovation in Science and Mathematics. 7(5), 2019, pp. 222-230.
[3] L. Marek-Crnjac and M.S. El Naschie, From fractal-Cantorian classical music to the symphony of the standard model of high energy physics. Journal of Progressive Research in Mathematics, 15(3), 2019, pp. 2700-2710.
[4] M.S. El Naschie, Spinoza‘s God, Leibniz‘s Monadology And The Universal Music Of Einstein‘s Cantorian Nature, International Journal of Innovation in Science and Mathematics, 7(1), 2019, pp. 33-39.
[5] M.S. El Naschie, From Pythagorean mathematical music theory to the density of the dark energy sector of the cosmos and unification of art with science. International Journal of Engineering Innovation and Research, 8(6), 2019, pp. 249-261.
[6] El Naschie, Symmetria Massima of the fractal M-theory via the golden mean number system- A new language for a deep dialogue between man and nature. International Journal of Artificial Intelligence and
Mechatronics, 7(3), 2018, pp.11-14.
[7] Scott Olsen, L. Marek-Crnjac, Ji-Huan He and M.S. El Naschie, A grand unification of science, art and consciousness: Rediscovering the Pythagorean Plato golden mean number system. To appear in the Journal
of Progressive Research in Mathematics. 2020.
[8] M.S. El Naschie, Elements of a new set theory based quantum mechanics with applications in high energy quantum physics and cosmology. International Journal of High Energy Physics, 4, 2017, pp.65-74.
[9] M. S. El Naschie. and L Marek-Crnjac, Set theoretical foundation of quantum mechanics, NASA's EM drive technology and minimal surface interpretation of the state vector reduction of the quantum wave collapse. Chaos and Complexity Letters, 12(2), 2018, pp.85-100.
[10] M.S. El Naschie, High energy physics and cosmology as computation. American Journal of Computational Mathematics, 6(03), 2016, pp.185-199.
[11] M.S. El Naschie: A review of E-infinity and the mass spectrum of high energy particle physics. Chaos, Solitons & Fractals, 19(1), 2004, pp. 209-236.
[12] Mohamed S. El Naschie: Computational fractal logic for quantum physics and cosmology. American Journal of Astronomy and Astrophysics, 4(4), 2016, pp. 42-53.
[13] M.S. El Naschie, ‗tHooft renormalon and the reality of accelerated cosmic expansion. Science Federation Journal of Quantum Physics, 1(1), 2017, pp. 1-7.
[14] Carlos Castro Perelman, Note on the golden mean, nonlocality in quantum mechanics and fractal Cantorian spacetime. Academia.edu. 2019.
[15] 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.
[16] M.S. El Naschie: An up to date summary of the most important aspects of Prof. Mohamed El Naschie’s work in quantum physics and E-infinity theory. E-infinity – High Energy Communication Quantum Mechanics and
the Golden Mean in Theoretic Physics. Nos. 65. January 2011.
[17] M.S. El Naschie, S. Olsen, Ji-Huan He, S. Nada, L. Marek-Crnjac, and 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.
[18] M.S. El Naschie, Simulating the quantum Universe via the golden mean number expert-like -system, International Journal of Artificial Intelligence and Mechatronics, 7(4), 2019, pp.15-18.
[19] Mohamed S. El Naschie: Hardy's entanglement as the ultimate explanation for the observed cosmic dark energy and accelerated expansion. International Journal High Energy Physics, 1(2), 2014, pp. 13-17.
[20] M.S. El Naschie, A fundamentally fractal universe from Einstein, Kaluza-Klein, Witten and Vafa‘s spacetime. International Journal of Artificial Intelligence & Mechatronics, 8(2), 2019, pp. 1-11.
[21] M.S. El Naschie, Electromagnetic gravity and the quanta. International Journal of Applied Science & Mathematics, 6(4), 2019, pp. 131-138.
[22] M.S. El Naschie, Gravity looks like electromagnetism when seen through fractal logic glasses. International Journal of Innovation is Science & Mathematics, 7(4), 2019, pp. 180-185.
[23] Mohamed S. El Naschie, Massive gravity from a fractal-Cantorian spacetime perspective. International Journal of Innovations in Science & Mathematics, 8(2), 2020, pp. 82-89.
[24] Jose de Olivera Junior, Maria Federaldo Tocantins, Maria de Sousa, Nelly da Silva and Matheus Lobo, O Teorema de Banach-Tarski NA CircumFerencia, Revista Sergipana de Matematica e Educacao Metematia, 2, 2019, pp. 146-155. https://doi.org/10.34199/revisen.V412./0649.
[25] Ji-Huan He and Qura-Tol Ain, New promises and future challenges of fractal calculus from two-scale thermodynamics to fractal variational principles. Thermal Science, 20(2A), 2020, pp. 659-681.
[26] M.S. El Naschie, On the philosophy of being and nothingness in fundamental physics. Nonlinear Science Letters B, Chaos, Fractal and Synchronization, 1(1), 2011, pp.4-5.
[27] M.S. El Naschie, L. Marek-Crnjac, and J.H. He, On the Mathematical Philosophy of Being and Nothingness in Quantum Physics. Fractal Space-Time & Non-Commutative Geometry in Quantum and High Energy
Physics, 2(2), 2012, pp.103-106.
[28] Ji-Huan He (Editorial), Nonlinear dynamics and the Nobel Prize in physics. International Journal of Nonlinear Science & Numerical Simulation, 8(1), 2007, pp. 1-4.
[29] L. Marek-Crnjac, M.S. El Naschie and J.H. He, Chaotic fractals at the root of relativistic quantum physics and cosmology. International Journal of Modern Nonlinear Theory and Application, 2(1), 2013, pp.78-88.
[30] M.S. El Naschie, Banach-Tarski theorem and Cantorian spacetime. Chaos, Solitons & Fractals, 5(8), 1995, pp. 1503-1508.
[31] M.S. El Naschie, The quantum gravity Immirzi parameter—A general physical and topological interpretation. Gravitation and Cosmology, 19(3), 2013, pp.151-155.
[32] M.S. El Naschie: ―On certain ‗empty‘ Cantor sets and their dimensions.‖ Chaos, Solitons & Fractals, 4(2), 1994, pp. 293-296.
[33] M.S. El Naschie, Cosmic Dark Energy from ‘t Hooft’s Dimensional Regularization and Witten’s Topological Quantum Field Pure Gravity. Journal of Quantum Information Science, 4, 2014, pp.83-91.
[34] Mohamed S. El Naschie: From E = mc2 to E = mc2/22—A Short Account of the Most Famous Equation in Physics and Its Hidden Quantum Entanglement Origin. Journal of Quantum Information Science, 4(4), 2014, pp. 284-291.
[35] L. Marek-Crnjac, Ji-Huan He: An Invitation to El Naschie‘s Theory of Cantorian Space-Time and Dark Energy. International Journal of Astronomy and Astrophysics,3(4), 2013, pp. 464-471.
[36] L. Marek-Crnjac: On El Naschie‘s fractal-Cantorian spacetime and dark energy – A tutorial review. Natural Science, 7(13), 2015, pp. 581-598.
[37] Y. Hu and Ji-Huan He, On fractal spacetime and fractional calculus. Thermal Sciences, 20(3), 2016, pp. 773-777.
[38] M.S. El Naschie, Ji-Huan He‘s ten dimensional polytope and high energy particle physics. International Journal of Nonlinear Science, 8(4), 2007, pp. 475-476.
[39] C. Beck: Spatio-temporal chaos and vacuum fluctuation of quantized fields. World Scientific, Singapore (2002).
[40] M.S. El Naschie, Topological defects in the symplictic vacuum, anomalous positron production and the gravitational instanton. International Journal of Modern Physics E, 13(4), 2004, pp. 835-849.
[41] Mohamed S. El Naschie:Why E Is Not Equal to mc2. Journal of Modern Physics,5(9), 2014, pp. 743-750.
[42] M.S. El Naschie, On a fractal version of Witten's M-theory. International Journal of Astronomy and Astrophysics, 6, 2016, pp.135-144.
[43] J. Argyris, and C. Ciubotariu, On El Naschie's complex time and gravitation. Chaos, Solitons&Fractals, 8(5), 1997, pp.743-751.
[44] M.S. ElNaschie, M.S., 2007. Towards a quantum golden field theory. International Journal of Nonlinear Sciences and Numerical Simulation, 8(4), 2007, pp.477-482.
[45] M. S. El Naschie. An exact Mathematical picture of quantum spacetime. Advances in Pure Mathematics. 5(9), 2015. pp. 560-570.
[46] M.S. El Naschie, Experimentally based theoretical arguments that Unruh’s temperature, Hawking’s vacuum fluctuation and Rindler’s wedge are physically real. American Journal of Modern Physics, 2(6), 2013, pp.357-
361.
[47] M.S. El Naschie, Gödel universe, dualities and high energy particles in Einfinity. Chaos, Solitons & Fractals, 25(3), 2005, pp. 759-764.
[48] M.S. El Naschie, Transfinite harmonization by taking the dissonance out of the quantum field symphony. Chaos, Solitons & Fractals, 36(4), 2008, pp.781-786.
[49] M.S. El Naschie, Banach Spacetime-Like Dvoretzky Volume Concentration as Cosmic Holographic Dark Energy. International Journal of High Energy Physics, 2(1), 2015, pp.13-21.
[50] A.J. Babchin, and M.S. El Naschie, On the real Einstein beauty E= kmc2. World Journal of Condensed Matter Physics, 6(1), 2016, pp.1-6.
[51] M.S. El Naschie, From Nikolay Umov E= kmc2 via Albert Einstein's E= mc2 to the dark energy density of the cosmos E=(21/22) mc2. World Journal of Mechanics, 8, 2018, pp.73-81.
[52] M.S. El Naschie, Platonic quantum set theory proposal and fractal heterotic Kaluza-Klein space. Global Journal of Science Frontier Research A: Physics & Space Science, 20(3), 2020.
[53] M.S. El Naschie, Application of Dvoretzky's Theorem of Measure Concentration in Physics and Cosmology. Open Journal of Microphysics, 5, 2015, pp.11-15.
[54] Jack Sarfatti, Bohm pilot wave post-quantum theory. Sept. 21, 2017. Academia.edu.
[55] P.R. Holland, The quantum theory of motion: An account of the de Broglie- Bohm causal interpretation of quantum mechanics. Cambridge University Press, Cambridge, UK, 1993.
[56] Mohamed S. El Naschie: Elementary number theory in superstrings, loop quantum mechanics, twistors and E-infinity high energy physics. Chaos, Solitons & Fractals, 27(2), 2006, pp. 297-330.
[57] M. S. El Naschie, On twistors in Cantorian E-infinity space. Chaos, Solitons & Fractals, 12(4), 2001, pp. 741-746.
[58] M.S. El Naschie, Time symmetry breaking, duality and Cantorian spacetime. Chaos, Solitons & Fractals, 7(4), 1996, pp. 499-518.
[59] Ji-Huan He: The importance of the empty set underpinning the foundation of quantum physics. Nonlinear Science Letters B, 1(1), 2011, pp. 6-7.
[60] L. Marek-Crnjac: The physics of empty sets and the quantum. Nonlinear Science Letters B, 1(1), 2011, pp. 13-14.
[61] M.S. El Naschie, P-Adic unification of the fundamental forces and the standard model. Chaos, Solitons & Fractals, 38(4), 2008, pp.1011-1012.
[62] M.S. El Naschie, Quantum entanglement as a consequence of a Cantorian micro spacetime geometry. Journal of Quantum Information Science, 1(02), 2011, pp.50-53.
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Published
2020-07-04
How to Cite
El Naschie, M. S., He, J.-H., & Marek-Crnjac, L. (2020). Topological vacuum fluctuation and Dvoretzky‘s theorem – Mathematical proofs in the context of the dark energy density of the universe. Journal of Progressive Research in Mathematics, 16(3), 2969-2985. Retrieved from http://scitecresearch.com/journals/index.php/jprm/article/view/1873
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