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Elements of a New Set Theory Based Quantum Mechanics with Applications in High Energy Quantum Physics and Cosmology

Received: 5 November 2017     Accepted: 16 November 2017     Published: 24 November 2017
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Abstract

We outline the quintessence of a fairly new quantum theory based on transfinite set theory representing a synthesis of the work of J. von Neumann’s pointless continuous geometry, A. Connes’ noncommutative quantum geometry, Menger-Urysohn dimensional theory, Sir R. Penrose’s fractal tiling universe, ‘tHooft’s renormalon as well as D. Shectman quasi crystals and Einstein-Kaluza-Klein spacetime theories. We conclude that the Aether is a real non-materialistic material and that is essentially what we commonly call spacetime which can be accurately described as the empty five dimensional set in a Penrose quasi crystal universe. Seen in the light of the above, empty spacetime can be the source of infinite clean energy.

Published in International Journal of High Energy Physics (Volume 4, Issue 6)
DOI 10.11648/j.ijhep.20170406.11
Page(s) 65-74
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), 2017. Published by Science Publishing Group

Keywords

Quantum Mechanics, Von Neumann Continuous Geometry, Noncommutative Geometry, Quasi Crystals, Einstein Spacetime, Kaluza-Klein Spacetime, Golden Mean Number System, Bijection Formula, Menger-Urysohn Dimensional Theory, The Empty Set, The Zero Set, Nothingness, E-Infinity, El Naschie’s Cantorian Spacetime

References
[1] Ji-Huan He and M. S. El Naschie: A collection of publications on E-infinity Cantorian spacetime theory. Transfinite Physics. China Culture & Science, Shanghai, 2005. Publishing, 2005. ISBN 988-98846-5-8.
[2] P. Weibel, G. Ord, O. Rössler (Editors): Spacetime Physics and Fractality. Festschrift in honour of Mohamed El Naschie on the occasion of his 60th birthday. Springer, Vienna-New York (2005).
[3] Ji-Huan He, E. Goldfain, L. D. Sigalotti and A. Mejias and M. S. El naschie: Beyond the 2006 Physics Nobel Prize for COBE. An introduction to E-infinity spacetime theory. China Sci. & Culture Publishing, Shanghai. (2006). ISBN: 98807681-9.4/0.4.
[4] G. Ord (Guest Editor): Transfinite Physics–Treading the path of Cantor and Einstein. Chaos, Solitons & Fractals, 25(4), 2005.
[5] Mohamed S. El Naschie, L. Nottale, S. Al Athel and G. Ord: Fractal space-time and Cantorian geometry in quantum mechanics. Chaos, Solitons & Fractals, 7(6), 1996.
[6] M. S. El Naschie, O. E. Rössler and G. Ord: Chaos, information and diffusion in quantum physics. Chaos, Solitons & Fractals, 7(5), 1996.
[7] M. S. El Naschie, O. E. Rössler and I. Prigogine Editors): Quantum Mechanics, Diffusion and Chaotic Fractals. Pergamon Press/Elsevier, Oxford, 1995.
[8] M. S. El Naschie: Quantum two-slit gedanken experiment revisited. In “Einstein in Alexandria”. Editor, W. Witten. Bibliotheca Alexandrina Publishing, Alexandria, Egypt, 2008, pp. 141-153. ISBN 977-6163-49-1.
[9] M. S. El Naschie: Gödel, Cantor and Modern Nonlinear Dynamics: In ‘First International Symposium on Gödel‘s Theorem’s’, Editor Z. W. Wolkowski. World Scientific, Singapore, 1993, pp. 95-106.
[10] M. S. El Naschie: On a general theory for quantum gravity. In ‘Science of the Interface. Editor H. Diebner, T. Druckrey and P. Weibel. Genista Verlag, Tübingen, Germany, 2001, pp. 875-880.
[11] M. S. El Naschie: Deterministic quantum mechanics versus classical mechanical indeterminism and nonlinear dynamics. In “Frontiers of Fundamental Physics” Editors: B. Sidharth, A. Alfonso-Faus and Marius J. Fullana I Alfonso. American Institute of Physics, AIP Conference Proceedings No. 905, New York, 2007, pp. 56-66.
[12] M. S. El Naschie: Complexity theory interpretation of high energy physics and elementary particle mass spectrum. In “Frontiers of Fundamental Physics” Editors: B. Sidharth. University Press, Hyderabad, India, Vol. 3, New York, 2007, pp. 1-32. ISBN: 9788173715778.
[13] M. S. El Naschie: ‘tHooft dimensional regularization implies transfinite heterotic string theory and dimensional transmutation. In “Frontiers of Fundamental Physics” Editors: B. Sidharth and M. V. Altaisky, Kluwer Academic/Plenium Publisher, New York, USA, Vol. 4, 2001, pp. 81-86.
[14] M. S. El Naschie: The Cantorian gravity coupling constant is αgs(max)=1/26.18033989. In “Frontiers of Fundamental Physics” Editors: B. Sidharth and M. V. Altaisky, Kluwer Academic/Plenium Publisher, New York, USA, Vol. 4, 2001, pp. 87-95.
[15] A. Connes: Noncommutative Geometry. Academic Press, San Diego, USA, 1994.
[16] F. Scheck, H. Upmeier and W. Werner (Editors): Noncommutative Geometry and The Standard Model of Elementary Particle Physics. Springer, Berlin, Germany, 1996.
[17] G. Landi: An Introduction to Noncommutative Spaces and Their Geometrics. Springer, Berlin, 1997.
[18] A. Connes and M. Marcolli: Noncommutative Geometry, Quantum Fields and Motives. American Mathematical Society, Rhode Island, USA, 2008.
[19] Shahn Majid (Editor): On space and time. Cambridge Press, Cambridge, UK, 2008.
[20] J-Pierre Changeux and Alain Connes: Conversations on Mind, Matter and Mathematics. (Editor and translated by M. B. Debevoise). Princeton University Press, Princeton, New Jersey, USA, 1989.
[21] HRH The Prince of Wales, Tony Juniper and Ian Skelly: Harmony: A New Way of Looking At Our World. Harper Collins Publications, London, UK. 2010. (see in particular page 113).
[22] A. Connes, A. Lichnerowicz and M. P. Schützenberger: Triangle of Thought. American Mathematical Society, Providence, Rhode Island, USA, 2001.
[23] M. Waldschmidt, P. Moussa, J. M. Luck and C. Itzykson (Editors): From Number Theory to Physics. Springer Verlag, Berlin, Germany, 1992.
[24] J. von Neumann: Continuous Geometry, Vol. 25. Princeton University Press, Princeton, New Jersey, USA, 1988.
[25] V. Kodiyalam and V. S. Sunder: Topological Quantum Field Theories From Subfactors. Chapman & Hall/CRC, London, UK, 2001.
[26] M. S. El Naschie: Superstrings, knots and noncommutative geometry in E-infinity space. International Journal of Theoretical Physics, 37(12), 1998, pp. 2935-2951.
[27] J. Madore: An Introduction to Noncommutative Differential Geometry and Its Physical Applications. Cambridge University Press, Cambridge, UK, 1999.
[28] L. Marek-Crnjac: Generalized quantum entanglement family in connection to black holes and nanotechnology. Chapter in “Quantum Gravity”, Edited by B. Mitchell. Nova Publishers, New York, USA. 2017, pp. 33-48.
[29] L. Marek-Crnjac: Cantorian Space-Time Theory: The Physics of Empty Sets in Connection With Quantum Entanglement and Dark Energy. Lambert Academic Publishing, Saarbrucken, Germany, 2013. ISBN: 978-3-659-12876-9.
[30] Y. Manin: Topics in Noncommutative Geometry. Princeton University Press, Princeton, USA. 2014.
[31] M. S. El Naschie: Penrose universe and Cantorian spacetime as a model for noncommutative quantum geometry. Chaos, Solitons & Fractals, 9(6), 1998, p. 931-933.
[32] M. S. El Naschie: von Neumann geometry and E-infinity quantum spacetime. Chaos, Solitons & Fractals, 9(12), 1998, pp. 2023-2030.
[33] M. S. El Naschie: Nuclear spacetime theories, superstrings, monster group and applications, Chaos, Solitons & Fractals, 10(2-3), 1999, pp. 567-580.
[34] M. S. El Naschie: Einstein’s dream and fractal gravity. Chaos, Solitons & Fractals, 24(1), 2005, pp. 1-5.
[35] Mohamed S. El Naschie: The Quantum Gravity Immirzi Parameter–A General Physical and Topological Interpretation. Gravity and Cosmology, 19(3), 2013, 151-153.
[36] 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.
[37] M. S. El Naschie: On the uncertainty of Cantorian geometry and the two-slit experiment. Chaos, Solitons & Fractals, 19(3), 1998, pp. 517-529.
[38] Mohamed S El Naschie: The self similarity equivalence relation connecting Newton’s energy with Einstein’s energy and dark energy. International Journal of Innovation in Science and Mathematics, 4(1), 2016, pp. 42-57.
[39] Mohamed S. El Naschie: The Aether of spacetime physics is the empty set of pure mathematics. Natural Science, 9(9), 2017, pp. 289-292.
[40] Mohamed S. El Naschie: Spacetime as a new frontier advanced material with applications in physics, engineering, chemistry and cosmology. Advanced Material Physics and Chemistry, 7(9), 2017, pp. 347-352.
[41] Mohamed S El Naschie: From a dual Einstein-Kaluza spacetime to ‘tHooft renormalon and the reality of accelerated cosmic expansion. Journal of Modern Physics, 8(8), 2017, pp. 1319-1329.
[42] Mohamed S. El Naschie: Spacetime from Zitterbewegung. Open Journal of Modelling and Simulation, 5(3), 2017, pp. 169-173.
[43] Mohamed S. El Naschie: Einstein-Kaluza combined spacetime as the optimal and simplest framework to compute and understand dark matter, pure dark energy and measurable ordinary energy. Natural Science, 9(8), 2017, pp. 241-244. Letter to the Editor.
[44] Mohamed S. El Naschie: A combined Heterotic string and Kähler manifold elucidation of ordinary energy, dark matter, Olbers’s paradox and pure dark energy density of the cosmos. Journal of Modern Physics, 8(7), 2017, pp. 1101-1118.
[45] Mohamed S. El Naschie: The looped light of the triple-slit real experiment as a confirmation for the extra dimensions of quantum spacetime and the reality of dark energy. Optical and Photonic Journal, 7(2), 2017, pp. 19-26.
[46] Mohamed S. El Naschie: On a fractal version of Witten’s M-theory. Journal of Astronomy & Astrophysics, 6(2), 2016, pp. 135-144.
[47] 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.
[48] Mohamed S. El Naschie: The emergence of spacetime from the quantum in three steps. Advances in Pure Mathematics, 6(6), 2016, pp. 446-454.
[49] Mohamed S. El Naschie: Looped light on dark energy. Journal of Quantum Information Science, 7(2), 2017, pp. 43-47.
[50] Mohamed S. El Naschie and Scott Olsen: The universe as a golden super computer. YouTube: https://www.youtube.com/watch?v=3GiyWK_JQxg. 1 October 2017.
[51] F. Wliczek and L. Krauss: Materiality of a vacuum (YouTube - https://www.youtube.com/Watch?V=BBXDrNn6PVg). 24 February 2017.
[52] Dan Monroe: Nobel Prize–Discovery of Quasi Crystals Physics–October 7, 2011. Physics Review Focus 28, 14. https://physics.aps.org/story/V28/st14.
[53] R. Penrose: The Road to Reality. J. Cape, London, UK. 2004.
[54] Mohamed 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.
[55] Mohamed S. El Naschie: Three quantum particles Hardy entanglement from the topology of Cantorian-fractal spacetime and the Casimir effect as dark energy–A great opportunity for nanotechnology. American Journal of Nano Research and Applications, 2015, 3(1), pp. 1-5.
[56] Mohamed S. El Naschie: A resolution of cosmic dark energy via quantum entanglement relativity theory. Journal of Quantum Information Science, 2013, 3, pp. 23-26.
[57] 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.
[58] 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, pp. 78-88.
[59] 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.
[60] 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.
[61] Mohamed S. El Naschie: The Gap Labelling Integrated Density of States For a Quasi Crystal Universe Is Identical to The Observed 4.5 Percent Ordinary Energy Density of The Cosmos. Natural Science, 6, 2014, 1259-1265.
[62] G. Iovane: 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.
[63] P. Forman: Weimar Culture, Causality and Quantum Theory. Historical Studies in Physical Sciences, University of California Press, California, USA, 3, 1971, pp. 1-115.
[64] P. A. M. Dirac: Quotation taken from the Introduction of Prof. J. Madore’s book of Ref. 52 based on citation in The Mathematical Intelligence, 11, 1989, pp. 58.
[65] M. S. El Naschie: An outline for a quantum golden field theory. Chaos, Solitons & Fractals, 37(2), 2008, pp. 317-323.
[66] M. S. El Naschie: Quantum golden field theory–Ten theorems and various conjectures. Chaos, Solitons & Fractals, 36, 2008, pp. 1121-1125.
[67] M. S. El Naschie: Forbidden symmetries, Cantor sets and hypothetical graphite. Chaos, Solitons & Fractals, 4(12), 1994, pp. 2269-2272.
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  • APA Style

    Mohamed S. El Naschie. (2017). 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(6), 65-74. https://doi.org/10.11648/j.ijhep.20170406.11

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    Mohamed S. El Naschie. Elements of a New Set Theory Based Quantum Mechanics with Applications in High Energy Quantum Physics and Cosmology. Int. J. High Energy Phys. 2017, 4(6), 65-74. doi: 10.11648/j.ijhep.20170406.11

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    AMA Style

    Mohamed S. El Naschie. Elements of a New Set Theory Based Quantum Mechanics with Applications in High Energy Quantum Physics and Cosmology. Int J High Energy Phys. 2017;4(6):65-74. doi: 10.11648/j.ijhep.20170406.11

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  • @article{10.11648/j.ijhep.20170406.11,
      author = {Mohamed S. El Naschie},
      title = {Elements of a New Set Theory Based Quantum Mechanics with Applications in High Energy Quantum Physics and Cosmology},
      journal = {International Journal of High Energy Physics},
      volume = {4},
      number = {6},
      pages = {65-74},
      doi = {10.11648/j.ijhep.20170406.11},
      url = {https://doi.org/10.11648/j.ijhep.20170406.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijhep.20170406.11},
      abstract = {We outline the quintessence of a fairly new quantum theory based on transfinite set theory representing a synthesis of the work of J. von Neumann’s pointless continuous geometry, A. Connes’ noncommutative quantum geometry, Menger-Urysohn dimensional theory, Sir R. Penrose’s fractal tiling universe, ‘tHooft’s renormalon as well as D. Shectman quasi crystals and Einstein-Kaluza-Klein spacetime theories. We conclude that the Aether is a real non-materialistic material and that is essentially what we commonly call spacetime which can be accurately described as the empty five dimensional set in a Penrose quasi crystal universe. Seen in the light of the above, empty spacetime can be the source of infinite clean energy.},
     year = {2017}
    }
    

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    AB  - We outline the quintessence of a fairly new quantum theory based on transfinite set theory representing a synthesis of the work of J. von Neumann’s pointless continuous geometry, A. Connes’ noncommutative quantum geometry, Menger-Urysohn dimensional theory, Sir R. Penrose’s fractal tiling universe, ‘tHooft’s renormalon as well as D. Shectman quasi crystals and Einstein-Kaluza-Klein spacetime theories. We conclude that the Aether is a real non-materialistic material and that is essentially what we commonly call spacetime which can be accurately described as the empty five dimensional set in a Penrose quasi crystal universe. Seen in the light of the above, empty spacetime can be the source of infinite clean energy.
    VL  - 4
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Author Information
  • Distinguished Professor, Department of Physics, Faculty of Science, University of Alexandria, Alexandria, Egypt

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