Compactified Dimensions as Produced by Quantum Entanglement, the Four Dimensionality of Einstein’s Smooth Spacetime and ‘tHooft’s 4-ε Fractal Spacetime

Mohamed S. El Naschie

doi:doi:10.11648/j.ajaa.20140203.12

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Compactified Dimensions as Produced by Quantum Entanglement, the Four Dimensionality of Einstein’s Smooth Spacetime and ‘tHooft’s 4-ε Fractal Spacetime

Mohamed S. El Naschie

Published in American Journal of Astronomy and Astrophysics (Volume 2, Issue 3)

Received: 8 June 2014 Accepted: 28 July 2014 Published: 10 August 2014

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Abstract

We show how Einstein’s four dimensionality of spacetime arises via a Hardy quantum entanglement form of compactification acting on Veneziano bosonic strings space. In turn this quantum entanglement mechanism is directly connected to the transfinite version of Heterotic string’s dimensional hierarchy, i.e. 26, 16, 10, 6, 4 and leads directly to ‘tHooft-Veltman-Wilson fractal spacetime of dimensional renormalization from which the missing 95.5% dark energy density of the cosmos may be accurately determined. Furthermore we predict the existence of a quasi dimensional regularization quasi particle with a topological mass charge equal to twice that of Hardy's entanglement.

Published in	American Journal of Astronomy and Astrophysics (Volume 2, Issue 3)
DOI	10.11648/j.ajaa.20140203.12
Page(s)	34-37
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), 2024. Published by Science Publishing Group

Keywords

Quantum Entangled Dimensions, Einstein’s Smooth Space, ‘tHooft’s Fractal Spacetime, Cosmic Expansion, Dark Energy, Feigenbaum Turbulence, New Elementary Particle form Dimensional Regularization, Dimensional Renormalization

References

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[2]	M.S. El Naschie, Superstrings, knots and noncommutative geometry in E-infinity space. Int. Journal of Theoretical Physics, 37(12), 2000, pp. 2935-2951.
[3]	M.S. El Naschie, Ji-Huan He, L. Marek-Crnjac, Missing dark energy from Veneziano dual-resonance model. Journal of Fractal Spacetime, Noncommutative Geometry and Quantum High Energy Physics. 3(2), 2013, pp. 94-105.
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[5]	M.S. El Naschie, Quantum entanglement as a consequence of a Cantorian micro spacetime geometry. Journal of Quantum Information Science, 1, 2011, pp. 50-53.
[6]	M.S. El Naschie, A resolution of cosmic dark energy via a quantum entanglement relativity theory. Journal of Quantum Information Science, 3, 2013, pp. 23-26.
[7]	M.S. El Naschie, Cosmic dark energy from ‘tHooft’s dimensional regularization and Witten’s topological quantum field pure gravity. J of Quantum Information Science, 4, 2014, pp. 83-91.
[8]	M.S. El Naschie, Logarithmic running of ‘tHooft-Polyakov monopole to dark energy. Int. Journal of High Energy Physics, 1(1), 2014, pp. 1-5.
[9]	M.S. El Naschie, From classical gauge theory back to Weyl scaling via E-infinity spacetime. Chaos, Solitons & Fractals, 38(4), 2008, pp. 980-985.
[10]	M.A. Helal, L. Marek-Crnjac, Ji-Huan He, The three page guide to the most important results of M.S. El Naschie’s research in E-infinity quantum physics and cosmology. Open Journal of Microphysics, 3, 2013, pp. 141-145.
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[12]	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.
[13]	M.S. El Naschie, Elementary prerequisites for E-infinity (Recommended background readings in nonlinear dynamics, geometry and topology). Chaos, Solitons & Fractals, 30(3), 2006, pp. 579-605.
[14]	L. Marek-Crnjac, Modification of Einstein’s E = mc2 to E = (1/22) mc2. American Journal of Modern Physics, 2(5), 2013, pp. 255-263.
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[19]	M. S. El Naschie. Feigenbaum's scenario for turbulence and Cantorian E-Infinity Theory of high energy particle physics. CS&F. Vol. 32. May 2007, pp. 911-915.
[20]	M. S. El Naschie. Stress, Stability and Chaos in structural engineering. An Energy Approach. McGraw-Hill-London 1990.
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[22]	M. S. El Naschie et al. A Topological Magueijo-Smolin Varying speed of light theory, the accelerated cosmic expansion and he dark energy of pure gravity applied mathematics. Vol. 5 No. 12 (2014) pp. 1780-1790.
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[26]	M.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. Vol.4 No.2, June 2014. PP. 332-339.
[27]	M.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..
[28]	M.S. El Naschie. Deriving E = mc2 /22 of Einstein’s ordinary quantum relativity energy density from the Lie symmetry group SO(10) of grand unification of all fundamental forces and without quantum mechanics. American Journal of Mechanics and Applications. April 30, 2014.
[29]	M.S. El Naschie. Cosserat-Cartan modification of Einstein-Riemann relativity and cosmic dark energy density. American Journal of Modern Physics. April 10, 2014.

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Mohamed S. El Naschie. (2014). Compactified Dimensions as Produced by Quantum Entanglement, the Four Dimensionality of Einstein’s Smooth Spacetime and ‘tHooft’s 4-ε Fractal Spacetime. American Journal of Astronomy and Astrophysics, 2(3), 34-37. https://doi.org/10.11648/j.ajaa.20140203.12

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ACS Style

Mohamed S. El Naschie. Compactified Dimensions as Produced by Quantum Entanglement, the Four Dimensionality of Einstein’s Smooth Spacetime and ‘tHooft’s 4-ε Fractal Spacetime. Am. J. Astron. Astrophys. 2014, 2(3), 34-37. doi: 10.11648/j.ajaa.20140203.12

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AMA Style

Mohamed S. El Naschie. Compactified Dimensions as Produced by Quantum Entanglement, the Four Dimensionality of Einstein’s Smooth Spacetime and ‘tHooft’s 4-ε Fractal Spacetime. Am J Astron Astrophys. 2014;2(3):34-37. doi: 10.11648/j.ajaa.20140203.12

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@article{10.11648/j.ajaa.20140203.12,
  author = {Mohamed S. El Naschie},
  title = {Compactified Dimensions as Produced by Quantum Entanglement, the Four Dimensionality of Einstein’s Smooth Spacetime and ‘tHooft’s 4-ε Fractal Spacetime},
  journal = {American Journal of Astronomy and Astrophysics},
  volume = {2},
  number = {3},
  pages = {34-37},
  doi = {10.11648/j.ajaa.20140203.12},
  url = {https://doi.org/10.11648/j.ajaa.20140203.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajaa.20140203.12},
  abstract = {We show how Einstein’s four dimensionality of spacetime arises via a Hardy quantum entanglement form of compactification acting on Veneziano bosonic strings space. In turn this quantum entanglement mechanism is directly connected to the transfinite version of Heterotic string’s dimensional hierarchy, i.e. 26, 16, 10, 6, 4 and leads directly to ‘tHooft-Veltman-Wilson fractal spacetime of dimensional renormalization from which the missing 95.5% dark energy density of the cosmos may be accurately determined. Furthermore we predict the existence of a quasi dimensional regularization quasi particle with a topological mass charge equal to twice that of Hardy's entanglement.},
 year = {2014}
}

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TY  - JOUR
T1  - Compactified Dimensions as Produced by Quantum Entanglement, the Four Dimensionality of Einstein’s Smooth Spacetime and ‘tHooft’s 4-ε Fractal Spacetime
AU  - Mohamed S. El Naschie
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AB  - We show how Einstein’s four dimensionality of spacetime arises via a Hardy quantum entanglement form of compactification acting on Veneziano bosonic strings space. In turn this quantum entanglement mechanism is directly connected to the transfinite version of Heterotic string’s dimensional hierarchy, i.e. 26, 16, 10, 6, 4 and leads directly to ‘tHooft-Veltman-Wilson fractal spacetime of dimensional renormalization from which the missing 95.5% dark energy density of the cosmos may be accurately determined. Furthermore we predict the existence of a quasi dimensional regularization quasi particle with a topological mass charge equal to twice that of Hardy's entanglement.
VL  - 2
IS  - 3
ER  -

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Author Information

Mohamed S. El Naschie

Dept. of Physics, University of Alexandria, Alexandria, Egypt

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APA Style

Mohamed S. El Naschie. (2014). Compactified Dimensions as Produced by Quantum Entanglement, the Four Dimensionality of Einstein’s Smooth Spacetime and ‘tHooft’s 4-ε Fractal Spacetime. American Journal of Astronomy and Astrophysics, 2(3), 34-37. https://doi.org/10.11648/j.ajaa.20140203.12

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ACS Style

Mohamed S. El Naschie. Compactified Dimensions as Produced by Quantum Entanglement, the Four Dimensionality of Einstein’s Smooth Spacetime and ‘tHooft’s 4-ε Fractal Spacetime. Am. J. Astron. Astrophys. 2014, 2(3), 34-37. doi: 10.11648/j.ajaa.20140203.12

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AMA Style

Mohamed S. El Naschie. Compactified Dimensions as Produced by Quantum Entanglement, the Four Dimensionality of Einstein’s Smooth Spacetime and ‘tHooft’s 4-ε Fractal Spacetime. Am J Astron Astrophys. 2014;2(3):34-37. doi: 10.11648/j.ajaa.20140203.12

Copy | Download

@article{10.11648/j.ajaa.20140203.12,
  author = {Mohamed S. El Naschie},
  title = {Compactified Dimensions as Produced by Quantum Entanglement, the Four Dimensionality of Einstein’s Smooth Spacetime and ‘tHooft’s 4-ε Fractal Spacetime},
  journal = {American Journal of Astronomy and Astrophysics},
  volume = {2},
  number = {3},
  pages = {34-37},
  doi = {10.11648/j.ajaa.20140203.12},
  url = {https://doi.org/10.11648/j.ajaa.20140203.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajaa.20140203.12},
  abstract = {We show how Einstein’s four dimensionality of spacetime arises via a Hardy quantum entanglement form of compactification acting on Veneziano bosonic strings space. In turn this quantum entanglement mechanism is directly connected to the transfinite version of Heterotic string’s dimensional hierarchy, i.e. 26, 16, 10, 6, 4 and leads directly to ‘tHooft-Veltman-Wilson fractal spacetime of dimensional renormalization from which the missing 95.5% dark energy density of the cosmos may be accurately determined. Furthermore we predict the existence of a quasi dimensional regularization quasi particle with a topological mass charge equal to twice that of Hardy's entanglement.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Compactified Dimensions as Produced by Quantum Entanglement, the Four Dimensionality of Einstein’s Smooth Spacetime and ‘tHooft’s 4-ε Fractal Spacetime
AU  - Mohamed S. El Naschie
Y1  - 2014/08/10
PY  - 2014
N1  - https://doi.org/10.11648/j.ajaa.20140203.12
DO  - 10.11648/j.ajaa.20140203.12
T2  - American Journal of Astronomy and Astrophysics
JF  - American Journal of Astronomy and Astrophysics
JO  - American Journal of Astronomy and Astrophysics
SP  - 34
EP  - 37
PB  - Science Publishing Group
SN  - 2376-4686
UR  - https://doi.org/10.11648/j.ajaa.20140203.12
AB  - We show how Einstein’s four dimensionality of spacetime arises via a Hardy quantum entanglement form of compactification acting on Veneziano bosonic strings space. In turn this quantum entanglement mechanism is directly connected to the transfinite version of Heterotic string’s dimensional hierarchy, i.e. 26, 16, 10, 6, 4 and leads directly to ‘tHooft-Veltman-Wilson fractal spacetime of dimensional renormalization from which the missing 95.5% dark energy density of the cosmos may be accurately determined. Furthermore we predict the existence of a quasi dimensional regularization quasi particle with a topological mass charge equal to twice that of Hardy's entanglement.
VL  - 2
IS  - 3
ER  -

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