The Measure Concentration of Convex Geometry in a Quasi Banach Spacetime behind the Supposedly Missing Dark Energy of the Cosmos

Mohamed S. El Naschie

doi:doi:10.11648/j.ajaa.20140206.13

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The Measure Concentration of Convex Geometry in a Quasi Banach Spacetime behind the Supposedly Missing Dark Energy of the Cosmos

Mohamed S. El Naschie

Published in American Journal of Astronomy and Astrophysics (Volume 2, Issue 6)

Received: 10 November 2014 Accepted: 24 November 2014 Published: 6 January 2015

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Abstract

Based on the Banach spaces motivated theory of convex geometry in high dimensionality we give a new confirmation of the derivation of the 95.5 per cent so called dark energy density of the cosmos. The result derives directly from the purely geometric-topological phenomenon of measure-mass concentration and gives an unqualified complete confirmation of our previous results including the hidden quantum nature of Einstein’s celebrated equation E = mc2. Thus the quantum dissection into ordinary energy of the quantum particle E(O) = mc2/22 and dark energy of the quantum wave E(D) = mc2(21/22) were validated by first a purely mathematical theorem of convex geometry and second by conservation of energy leading to E(O) + E(D) = mc2 as in Einstein’s special theory of relativity.

Published in	American Journal of Astronomy and Astrophysics (Volume 2, Issue 6)
DOI	10.11648/j.ajaa.20140206.13
Page(s)	72-77
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

Measure Concentration, Dvoretzky’s Theorem, High Dimensionality, Banach Spaces, E-Infinity Spectra, K-Theory, Dark Energy Cantorian-Fractal Spacetime, E Equals mc2 Divided by 22

References

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[27]	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.
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[29]	Mohamed S. El Naschie: Nash Embedding of Witten’s M-Theory and the Hawking-Hartle Quantum Wave of Dark Energy. Journal of Modern Physics, 4(10), 2013, pp. 1417-1428.
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[40]	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.
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Mohamed S. El Naschie. (2015). The Measure Concentration of Convex Geometry in a Quasi Banach Spacetime behind the Supposedly Missing Dark Energy of the Cosmos. American Journal of Astronomy and Astrophysics, 2(6), 72-77. https://doi.org/10.11648/j.ajaa.20140206.13

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Mohamed S. El Naschie. The Measure Concentration of Convex Geometry in a Quasi Banach Spacetime behind the Supposedly Missing Dark Energy of the Cosmos. Am. J. Astron. Astrophys. 2015, 2(6), 72-77. doi: 10.11648/j.ajaa.20140206.13

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AMA Style

Mohamed S. El Naschie. The Measure Concentration of Convex Geometry in a Quasi Banach Spacetime behind the Supposedly Missing Dark Energy of the Cosmos. Am J Astron Astrophys. 2015;2(6):72-77. doi: 10.11648/j.ajaa.20140206.13

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@article{10.11648/j.ajaa.20140206.13,
  author = {Mohamed S. El Naschie},
  title = {The Measure Concentration of Convex Geometry in a Quasi Banach Spacetime behind the Supposedly Missing Dark Energy of the Cosmos},
  journal = {American Journal of Astronomy and Astrophysics},
  volume = {2},
  number = {6},
  pages = {72-77},
  doi = {10.11648/j.ajaa.20140206.13},
  url = {https://doi.org/10.11648/j.ajaa.20140206.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajaa.20140206.13},
  abstract = {Based on the Banach spaces motivated theory of convex geometry in high dimensionality we give a new confirmation of the derivation of the 95.5 per cent so called dark energy density of the cosmos. The result derives directly from the purely geometric-topological phenomenon of measure-mass concentration and gives an unqualified complete confirmation of our previous results including the hidden quantum nature of Einstein’s celebrated equation E = mc2. Thus the quantum dissection into ordinary energy of the quantum particle E(O) = mc2/22 and dark energy of the quantum wave E(D) = mc2(21/22) were validated by first a purely mathematical theorem of convex geometry and second by conservation of energy leading to E(O) + E(D) = mc2 as in Einstein’s special theory of relativity.},
 year = {2015}
}

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TY  - JOUR
T1  - The Measure Concentration of Convex Geometry in a Quasi Banach Spacetime behind the Supposedly Missing Dark Energy of the Cosmos
AU  - Mohamed S. El Naschie
Y1  - 2015/01/06
PY  - 2015
N1  - https://doi.org/10.11648/j.ajaa.20140206.13
DO  - 10.11648/j.ajaa.20140206.13
T2  - American Journal of Astronomy and Astrophysics
JF  - American Journal of Astronomy and Astrophysics
JO  - American Journal of Astronomy and Astrophysics
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PB  - Science Publishing Group
SN  - 2376-4686
UR  - https://doi.org/10.11648/j.ajaa.20140206.13
AB  - Based on the Banach spaces motivated theory of convex geometry in high dimensionality we give a new confirmation of the derivation of the 95.5 per cent so called dark energy density of the cosmos. The result derives directly from the purely geometric-topological phenomenon of measure-mass concentration and gives an unqualified complete confirmation of our previous results including the hidden quantum nature of Einstein’s celebrated equation E = mc2. Thus the quantum dissection into ordinary energy of the quantum particle E(O) = mc2/22 and dark energy of the quantum wave E(D) = mc2(21/22) were validated by first a purely mathematical theorem of convex geometry and second by conservation of energy leading to E(O) + E(D) = mc2 as in Einstein’s special theory of relativity.
VL  - 2
IS  - 6
ER  -

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Author Information

Mohamed S. El Naschie

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

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Mohamed S. El Naschie. (2015). The Measure Concentration of Convex Geometry in a Quasi Banach Spacetime behind the Supposedly Missing Dark Energy of the Cosmos. American Journal of Astronomy and Astrophysics, 2(6), 72-77. https://doi.org/10.11648/j.ajaa.20140206.13

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ACS Style

Mohamed S. El Naschie. The Measure Concentration of Convex Geometry in a Quasi Banach Spacetime behind the Supposedly Missing Dark Energy of the Cosmos. Am. J. Astron. Astrophys. 2015, 2(6), 72-77. doi: 10.11648/j.ajaa.20140206.13

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AMA Style

Mohamed S. El Naschie. The Measure Concentration of Convex Geometry in a Quasi Banach Spacetime behind the Supposedly Missing Dark Energy of the Cosmos. Am J Astron Astrophys. 2015;2(6):72-77. doi: 10.11648/j.ajaa.20140206.13

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@article{10.11648/j.ajaa.20140206.13,
  author = {Mohamed S. El Naschie},
  title = {The Measure Concentration of Convex Geometry in a Quasi Banach Spacetime behind the Supposedly Missing Dark Energy of the Cosmos},
  journal = {American Journal of Astronomy and Astrophysics},
  volume = {2},
  number = {6},
  pages = {72-77},
  doi = {10.11648/j.ajaa.20140206.13},
  url = {https://doi.org/10.11648/j.ajaa.20140206.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajaa.20140206.13},
  abstract = {Based on the Banach spaces motivated theory of convex geometry in high dimensionality we give a new confirmation of the derivation of the 95.5 per cent so called dark energy density of the cosmos. The result derives directly from the purely geometric-topological phenomenon of measure-mass concentration and gives an unqualified complete confirmation of our previous results including the hidden quantum nature of Einstein’s celebrated equation E = mc2. Thus the quantum dissection into ordinary energy of the quantum particle E(O) = mc2/22 and dark energy of the quantum wave E(D) = mc2(21/22) were validated by first a purely mathematical theorem of convex geometry and second by conservation of energy leading to E(O) + E(D) = mc2 as in Einstein’s special theory of relativity.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - The Measure Concentration of Convex Geometry in a Quasi Banach Spacetime behind the Supposedly Missing Dark Energy of the Cosmos
AU  - Mohamed S. El Naschie
Y1  - 2015/01/06
PY  - 2015
N1  - https://doi.org/10.11648/j.ajaa.20140206.13
DO  - 10.11648/j.ajaa.20140206.13
T2  - American Journal of Astronomy and Astrophysics
JF  - American Journal of Astronomy and Astrophysics
JO  - American Journal of Astronomy and Astrophysics
SP  - 72
EP  - 77
PB  - Science Publishing Group
SN  - 2376-4686
UR  - https://doi.org/10.11648/j.ajaa.20140206.13
AB  - Based on the Banach spaces motivated theory of convex geometry in high dimensionality we give a new confirmation of the derivation of the 95.5 per cent so called dark energy density of the cosmos. The result derives directly from the purely geometric-topological phenomenon of measure-mass concentration and gives an unqualified complete confirmation of our previous results including the hidden quantum nature of Einstein’s celebrated equation E = mc2. Thus the quantum dissection into ordinary energy of the quantum particle E(O) = mc2/22 and dark energy of the quantum wave E(D) = mc2(21/22) were validated by first a purely mathematical theorem of convex geometry and second by conservation of energy leading to E(O) + E(D) = mc2 as in Einstein’s special theory of relativity.
VL  - 2
IS  - 6
ER  -

Copy | Download