Cosserat-Cartan Modification of Einstein-Riemann Relativity and Cosmic Dark Energy Density

Mohamed S. El Naschie

doi:doi:10.11648/j.ajmp.20140302.17

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Cosserat-Cartan Modification of Einstein-Riemann Relativity and Cosmic Dark Energy Density

Mohamed S. El Naschie

Published in American Journal of Modern Physics (Volume 3, Issue 2)

Received: 7 March 2014 Accepted: 8 April 2014 Published: 10 April 2014

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Abstract

Based on pioneering works by Sciama and Kibble to extend Einstein-Cartan theory of gravity we give a new derivation for the cosmic energy density. It is argued that the ‘t Hooft-Veltman and Wilson method of renormalization implies the relativity of fractal spacetime at the quantum scale and a dark energy density of E(D) = 95.5 percent. It is further revealed that similar conclusions could be made using A.C. Eringen’s nonlocal elasticity. Finally the wider philosophical implication of the theory is discussed.

Published in	American Journal of Modern Physics (Volume 3, Issue 2)
DOI	10.11648/j.ajmp.20140302.17
Page(s)	82-87
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

Kibble Gravity, ‘t Hooft Fractal Spacetime, Dimensional Regularization, Wilson Renormalization, Cosmic Dark Energy, Sciama-Kibble gravity, Cantorian Spacetime, nonlocal elasticity, Cantorian philosophy of science

References

[1]	E.V. Linder, Resource Letter: Dark energy and accelerating universe. arXiv: 0705.4102V1[astro-ph]28May 2007.
[2]	S. Perlmutter and B. Schmidt, Measuring cosmology with supernova. arXiv: astro-ph/0303428V1 18 Mar 2003.
[3]	E.V. Linder, Einstein’s other gravity and the acceleration of the universe. arXiv: 1005.3039V2[astro-hy.co] 26 August 2010.
[4]	M.S. El Naschie, A resolution of cosmic dark energy via a quantum entanglement relativity theory. J. Quantum Info. Sci., Vol. 3(1), 2013, pp. 23-26.
[5]	M.S. El Naschie, Quantum gravity and dark energy via a new Planck scale. Fractal Spacetime & Noncommutative Geometry in Quantum & High Energy Phys., Vol. 3(2), 2013, pp. 106-119.
[6]	M.S. El Naschie, Dark energy via a quantum field theory in curved spacetime. J. Mod. Phys. & Appli., Vol. 1, 2014, pp. 1-7.
[7]	M.S. El Naschie, From Yang-Mills photon in curved spacetime to dark energy density. J. Quantum Info. Sci., Vol. 3(4), 2013, pp. 121-126.
[8]	L. Marek-Crnjac et al, Chaotic fractal tiling for the missing dark energy and Veneziano model. Appl. Math., Vol. 4(11B), 2013, pp. 22-29.
[9]	M.S. El Naschie, A Rindler-KAM spacetime geometry and scaling the Planck scale solves quantum relativity and explains dark energy. Int. J. of Astronomy and Astrophysics, Vol. 3(4), 2013, pp. 483-493.
[10]	M.S. El Naschie, Experimentally based theoretical arguments that Unruh’s temperature, Hawking’s vacuum fluctuation and Rindler’s wedge are physically real. American J. Mod. Phys., Vol. 2(6), 2013, pp. 357-361.
[11]	L. Marek-Crnjac and Ji-Huan He, An invitation to El Naschie’s theory of Cantorian spacetime and dark energy. Int. J. of Astron. & Astrophys., Vol. 3, 2013, pp. 464-471.
[12]	L. Marek-Crnjac. and M.S. El Naschie, Quantum gravity and dark energy using fractal Planck scaling. J. Mod. Phys., Vol. 4(11A), 2013, pp. 31-38.
[13]	T.W.B. Kibble, Lorentz invariance and the gravitational field. J. Math. Phys., Vol.2, 212 1961, pp. 212-221.
[14]	F. Hehl, Space-Time as Generalized Cosserat Coninuum. In “Mechanics of Generalized Continua”. Editor E. Kronev., Springer Verlag, Berlin 1968. pp. 347-349.
[15]	A. Einstein, Auf die Riemann-Metrik und den Fern-Parallelismus gegründete einheitliche Feldtheorie. Mathematische Annalen, Vol. 102, 1930, pp. 685-697.
[16]	E. Cartan, Notice historique sur la notion de parallelism absolu. Mathematische Annalen, Vol. 102, 1930, pp. 698-706.
[17]	E. Cosserat, and F. Cosserat, Théorie des corps déformables. Hermann, Paris 1909.
[18]	M. Blagojevic and M. Vasilic, Asymptotic symmetry and conserved quantities in the Poincaré gauge theory of gravity. Classical & Quantum Gravity, Vol. 5, 1988, pp. 1241-1257.
[19]	J. Burnett, Olga Chervova and Dmitri Vassiliev, Dirac equation as a special case of Cosserat elasticity. arXiv: 0812.3948V1[gr-qc]22 December 2008.
[20]	M.S. El Naschie, Nash embedding of Witten’s M-theory and the Hawking-Hartle quantum wave of dark energy. J. Mod. Phys., Vol. 4, 2013, pp. 1417-1428.
[21]	M.S. El Naschie, Ji-Huan He, S. Nada, L. Marek-Crnjac and M.A. Helal, Golden mean computer for high energy physics, Fractal Spacetime and Noncommutative Geometry in High Energy Phys., Vol. 2(2), 2012, pp. 80-92.
[22]	Ji-Huan He, Transfinite Physics. A collection of publications on E-infinity Cantorian spacetime theory. China Scientific & Cultural Publishing. ISBN 988-9 8846-5-8 2005.
[23]	M.J. Duff: M.J.: The World in Eleven Dimensions. Inst. of Phys. Publications, Bristol 1999.
[24]	E. Witten, 2 + 1 dimensional gravity as an exactly soluble system. Nucl. Phys. B. Vol. 311(1), 1988, pp. 46-78.
[25]	D. Kutasov and N. Seiberg, Number of degrees of freedom, density of states and tachyons in string theory and CFT. Nucl. Phys. B, Vol. 358(3), 1991, pp. 600-618.
[26]	M.S. El Naschie, On two new fuzzy Kähler manifolds, Klein modular space and ‘t Hooft holographic principles. Chaos, Solitons & Fractals, Vol. 29(4), 2006, pp. 876-881.
[27]	G. ‘t Hooft, A Confrontation With Infinity. In ‘Frontiers of Fundamental Physics’ 4. Editors B. Sidharth and M. Altaisky. Kluwer-Plenum, New York 2001, pp. 1-12.
[28]	M.S. El Naschie, ‘t Hooft’s dimensional regularization implies transfinite Heterotic string theory and dimensional transmutation. In ‘Frontiers of Fundamental Physics’ 4. Editors B. Sidharth and M. Altaisky. Kluwer-Plenum, New York 2001, pp. 81-86.
[29]	K.G. Wilson, Critical phenomena in 3.99 dimensions. Physica, Vol. 73, 1974, pp. 119-128.
[30]	K.G. Wilson, The renormalization group and the expansion. Phs. Reports, Vol. 12(2), 1974, pp. 75-200.
[31]	M.S. El Naschie, COBE satellite measurement, hyperspheres, super strings and the dimension of spacetime. Chaos, Solitons & Fractals, Vol. 9(8), 1998, pp. 1445-1471 .
[32]	M. Kaku, Introduction to Superstrings and M-Theory. Springer, New York 1999.
[33]	M.S. El Naschie et al: On the need for fractal logic in high energy quantum physics. Int. J. Mod. Nonlinear Theory & Application. Vol. 1(3), 2012, pp. 84-92.
[34]	Challamel, N., Wang, C.M. and Elishakoff, I.: Discrete systems behave as nonlocal structural elements; bending buckling and vibration analysis. Euro. J. Mech. A/Solids, Vol. 44, 2014, pp. 125-135.
[35]	El Naschie, M.S.: Stress, Stability and Chaos in Structural Engineering: An Energy Approach. McGraw Hill Int. Edi tions Civil Eng. Series., London, Tokyo (1990).
[36]	Wifi, A.S., El Naschie, M.S., Al Athel, S., Wu, C.W. and Obeid, K.: Coluterized stress and stability analysis of engi neering structures. King Abdulaziz City for Science and Tech. Publishing, Saudi Arabia, No. 21. (96 pages with Arabic translation of summary).
[37]	Eringen, A.C. and Edelen, D.G.: On nonlocal elasticity. Int. J. Eng. Sci., Vol. 10(3), 1972, pp. 233-248.
[38]	El Naschie, M.S.: Cosmic dark energy density from classical mechanics and seemingly redundant Riemannian infitely many tensor components of Einstein’s general relativity. World J. Mech. 2014. In press.
[39]	El Naschie, M.S.: Pinched material Einstein spacetime pro duces accelerated cosmic expansion. Int. J. Astron. & Astrophys. Vol. 4(1), 2014 pp. 80-90.
[40]	El Naschie, M.S. and Helal, A.: Dark energy explained via the Hawking-Hartle quantum wave and the topology of cosmic crystallography. Int. J. Astronomy & Astrophys., Vol. 3(3), 2013, pp. 318-343.
[41]	El Naschie, M.S.: Cosmic dark energy from ‘t Hooft’s di mensional regularization and Witten’s topological quantum field pure gravity. J. of Qant. Info. Sci., 2014. In press.
[42]	El Naschie, M.S.: Why E is not equal to mc2. J. of Modern Phys. In press. (2014).
[43]	El Naschie, M.S., Marek-Crnjac, L., Hela, M.A. and He, Ji-Huan: A topological Magueijo-Smolin varying speed of light theory, the accelerated cosmic expansion and the dark energy of pure gravity. Appl. Math. 2014. In Press.
[44]	El Naschie, M.S.: The meta energy of dark energy. Open J. of Philosophy, (2014). In press.
[45]	El Naschie, M.S.: Einstein’s general relativity and pure grav ity in a Cosserat and de Sitter-Witten spacetime setting as the explanation of dark energy and cosmic accelerated ex pansion. Int. J. Astron. & Astrophys. 2014. In press.
[46]	Heisenberg, W.: Der Teil und das Ganze. Piper, Munich (1969).
[47]	El Naschie, M.S.: A review of E-infinity and the mass spec trum of high energy particle physics. Chaos, Solitons & Fractals, Vol. 19(1), 2004, pp. 209-236.

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Mohamed S. El Naschie. (2014). Cosserat-Cartan Modification of Einstein-Riemann Relativity and Cosmic Dark Energy Density. American Journal of Modern Physics, 3(2), 82-87. https://doi.org/10.11648/j.ajmp.20140302.17

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ACS Style

Mohamed S. El Naschie. Cosserat-Cartan Modification of Einstein-Riemann Relativity and Cosmic Dark Energy Density. Am. J. Mod. Phys. 2014, 3(2), 82-87. doi: 10.11648/j.ajmp.20140302.17

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AMA Style

Mohamed S. El Naschie. Cosserat-Cartan Modification of Einstein-Riemann Relativity and Cosmic Dark Energy Density. Am J Mod Phys. 2014;3(2):82-87. doi: 10.11648/j.ajmp.20140302.17

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@article{10.11648/j.ajmp.20140302.17,
  author = {Mohamed S. El Naschie},
  title = {Cosserat-Cartan Modification of Einstein-Riemann Relativity and Cosmic Dark Energy Density},
  journal = {American Journal of Modern Physics},
  volume = {3},
  number = {2},
  pages = {82-87},
  doi = {10.11648/j.ajmp.20140302.17},
  url = {https://doi.org/10.11648/j.ajmp.20140302.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20140302.17},
  abstract = {Based on pioneering works by Sciama and Kibble to extend Einstein-Cartan theory of gravity we give a new derivation for the cosmic energy density.  It is argued that the ‘t Hooft-Veltman and Wilson method of renormalization implies the relativity of fractal spacetime at the quantum scale and a dark energy density of E(D) = 95.5 percent. It is further revealed that similar conclusions could be made using A.C. Eringen’s nonlocal elasticity.  Finally the wider philosophical implication of the theory is discussed.},
 year = {2014}
}

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TY  - JOUR
T1  - Cosserat-Cartan Modification of Einstein-Riemann Relativity and Cosmic Dark Energy Density
AU  - Mohamed S. El Naschie
Y1  - 2014/04/10
PY  - 2014
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DO  - 10.11648/j.ajmp.20140302.17
T2  - American Journal of Modern Physics
JF  - American Journal of Modern Physics
JO  - American Journal of Modern Physics
SP  - 82
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PB  - Science Publishing Group
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UR  - https://doi.org/10.11648/j.ajmp.20140302.17
AB  - Based on pioneering works by Sciama and Kibble to extend Einstein-Cartan theory of gravity we give a new derivation for the cosmic energy density.  It is argued that the ‘t Hooft-Veltman and Wilson method of renormalization implies the relativity of fractal spacetime at the quantum scale and a dark energy density of E(D) = 95.5 percent. It is further revealed that similar conclusions could be made using A.C. Eringen’s nonlocal elasticity.  Finally the wider philosophical implication of the theory is discussed.
VL  - 3
IS  - 2
ER  -

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Author Information

Mohamed S. El Naschie

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

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Mohamed S. El Naschie. (2014). Cosserat-Cartan Modification of Einstein-Riemann Relativity and Cosmic Dark Energy Density. American Journal of Modern Physics, 3(2), 82-87. https://doi.org/10.11648/j.ajmp.20140302.17

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ACS Style

Mohamed S. El Naschie. Cosserat-Cartan Modification of Einstein-Riemann Relativity and Cosmic Dark Energy Density. Am. J. Mod. Phys. 2014, 3(2), 82-87. doi: 10.11648/j.ajmp.20140302.17

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AMA Style

Mohamed S. El Naschie. Cosserat-Cartan Modification of Einstein-Riemann Relativity and Cosmic Dark Energy Density. Am J Mod Phys. 2014;3(2):82-87. doi: 10.11648/j.ajmp.20140302.17

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@article{10.11648/j.ajmp.20140302.17,
  author = {Mohamed S. El Naschie},
  title = {Cosserat-Cartan Modification of Einstein-Riemann Relativity and Cosmic Dark Energy Density},
  journal = {American Journal of Modern Physics},
  volume = {3},
  number = {2},
  pages = {82-87},
  doi = {10.11648/j.ajmp.20140302.17},
  url = {https://doi.org/10.11648/j.ajmp.20140302.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20140302.17},
  abstract = {Based on pioneering works by Sciama and Kibble to extend Einstein-Cartan theory of gravity we give a new derivation for the cosmic energy density.  It is argued that the ‘t Hooft-Veltman and Wilson method of renormalization implies the relativity of fractal spacetime at the quantum scale and a dark energy density of E(D) = 95.5 percent. It is further revealed that similar conclusions could be made using A.C. Eringen’s nonlocal elasticity.  Finally the wider philosophical implication of the theory is discussed.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Cosserat-Cartan Modification of Einstein-Riemann Relativity and Cosmic Dark Energy Density
AU  - Mohamed S. El Naschie
Y1  - 2014/04/10
PY  - 2014
N1  - https://doi.org/10.11648/j.ajmp.20140302.17
DO  - 10.11648/j.ajmp.20140302.17
T2  - American Journal of Modern Physics
JF  - American Journal of Modern Physics
JO  - American Journal of Modern Physics
SP  - 82
EP  - 87
PB  - Science Publishing Group
SN  - 2326-8891
UR  - https://doi.org/10.11648/j.ajmp.20140302.17
AB  - Based on pioneering works by Sciama and Kibble to extend Einstein-Cartan theory of gravity we give a new derivation for the cosmic energy density.  It is argued that the ‘t Hooft-Veltman and Wilson method of renormalization implies the relativity of fractal spacetime at the quantum scale and a dark energy density of E(D) = 95.5 percent. It is further revealed that similar conclusions could be made using A.C. Eringen’s nonlocal elasticity.  Finally the wider philosophical implication of the theory is discussed.
VL  - 3
IS  - 2
ER  -

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