Three Quantum Particles Hardy Entanglement from the Topology of Cantorian-Fractal Spacetime and the Casimir Effect as Dark Energy – A Great Opportunity for Nanotechnology

Mohamed S. El Naschie

doi:doi:10.11648/j.nano.20150301.11

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Three Quantum Particles Hardy Entanglement from the Topology of Cantorian-Fractal Spacetime and the Casimir Effect as Dark Energy – A Great Opportunity for Nanotechnology

Mohamed S. El Naschie

Published in American Journal of Nano Research and Applications (Volume 3, Issue 1)

Received: 9 January 2015 Accepted: 28 January 2015 Published: 6 February 2015

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Abstract

The present work brings together three different fields which depend crucially upon nano hardware under the umbrella of E-infinity theoretical framework. We start by following E-infinity topological methodology by dividing Hardy’s entanglement into two parts, a global ‘counterfactual’ part given by Φ3 where Φ = 2/(1+ √5) and a ‘local’ part Φn where n is the number of quantum particles. For Hardy’s celebrated gedankenexperiment with two quantum particles, which was moreover experimentally confirmed with high accuracy, the quantum probability is found for n = 2 to be P(2) (Hardy) = Φ3+2= Φ5 exactly as calculated by Hardy using orthodox quantum mechanics. Applying the same topological E-infinity entanglement theory to three quantum particles give a maximal Φ6 as well as a three partite much smaller value equal Φ3(1− Φ3)/ = 0.018033989. We conclude by outlining the relevant and extremely timely ideas and remarks on the possible connection, via a state of the art nanotechnology, to the Casimir effect as a conjectured origin of dark energy.

Published in	American Journal of Nano Research and Applications (Volume 3, Issue 1)
DOI	10.11648/j.nano.20150301.11
Page(s)	1-5
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

Three Quantum Particles Entanglement, Hardy’s Topological Entanglement, E-Infinity, Hilbert Space, Cantorian Spacetime, Golden Mean Number System, Casimir Effect Connection to Dark Energy, Nanotechnology

References

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APA Style

Mohamed S. El Naschie. (2015). 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, 3(1), 1-5. https://doi.org/10.11648/j.nano.20150301.11

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ACS Style

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. Am. J. Nano Res. Appl. 2015, 3(1), 1-5. doi: 10.11648/j.nano.20150301.11

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AMA Style

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. Am J Nano Res Appl. 2015;3(1):1-5. doi: 10.11648/j.nano.20150301.11

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@article{10.11648/j.nano.20150301.11,
  author = {Mohamed S. El Naschie},
  title = {Three Quantum Particles Hardy Entanglement from the Topology of Cantorian-Fractal Spacetime and the Casimir Effect as Dark Energy – A Great Opportunity for Nanotechnology},
  journal = {American Journal of Nano Research and Applications},
  volume = {3},
  number = {1},
  pages = {1-5},
  doi = {10.11648/j.nano.20150301.11},
  url = {https://doi.org/10.11648/j.nano.20150301.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.nano.20150301.11},
  abstract = {The present work brings together three different fields which depend crucially upon nano hardware under the umbrella of E-infinity theoretical framework. We start by following E-infinity topological methodology by dividing Hardy’s entanglement into two parts, a global ‘counterfactual’ part given by Φ3 where Φ = 2/(1+ √5) and a ‘local’ part Φn where n is the number of quantum particles. For Hardy’s celebrated gedankenexperiment with two quantum particles, which was moreover experimentally confirmed with high accuracy, the quantum probability is found for n = 2 to be P(2) (Hardy) = Φ3+2= Φ5 exactly as calculated by Hardy using orthodox quantum mechanics. Applying the same topological E-infinity entanglement theory to three quantum particles give a maximal Φ6 as well as a three partite much smaller value equal Φ3(1− Φ3)/ = 0.018033989. We conclude by outlining the relevant and extremely timely ideas and remarks on the possible connection, via a state of the art nanotechnology, to the Casimir effect as a conjectured origin of dark energy.},
 year = {2015}
}

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TY  - JOUR
T1  - Three Quantum Particles Hardy Entanglement from the Topology of Cantorian-Fractal Spacetime and the Casimir Effect as Dark Energy – A Great Opportunity for Nanotechnology
AU  - Mohamed S. El Naschie
Y1  - 2015/02/06
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N1  - https://doi.org/10.11648/j.nano.20150301.11
DO  - 10.11648/j.nano.20150301.11
T2  - American Journal of Nano Research and Applications
JF  - American Journal of Nano Research and Applications
JO  - American Journal of Nano Research and Applications
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AB  - The present work brings together three different fields which depend crucially upon nano hardware under the umbrella of E-infinity theoretical framework. We start by following E-infinity topological methodology by dividing Hardy’s entanglement into two parts, a global ‘counterfactual’ part given by Φ3 where Φ = 2/(1+ √5) and a ‘local’ part Φn where n is the number of quantum particles. For Hardy’s celebrated gedankenexperiment with two quantum particles, which was moreover experimentally confirmed with high accuracy, the quantum probability is found for n = 2 to be P(2) (Hardy) = Φ3+2= Φ5 exactly as calculated by Hardy using orthodox quantum mechanics. Applying the same topological E-infinity entanglement theory to three quantum particles give a maximal Φ6 as well as a three partite much smaller value equal Φ3(1− Φ3)/ = 0.018033989. We conclude by outlining the relevant and extremely timely ideas and remarks on the possible connection, via a state of the art nanotechnology, to the Casimir effect as a conjectured origin of dark energy.
VL  - 3
IS  - 1
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). 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, 3(1), 1-5. https://doi.org/10.11648/j.nano.20150301.11

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ACS Style

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. Am. J. Nano Res. Appl. 2015, 3(1), 1-5. doi: 10.11648/j.nano.20150301.11

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AMA Style

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. Am J Nano Res Appl. 2015;3(1):1-5. doi: 10.11648/j.nano.20150301.11

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@article{10.11648/j.nano.20150301.11,
  author = {Mohamed S. El Naschie},
  title = {Three Quantum Particles Hardy Entanglement from the Topology of Cantorian-Fractal Spacetime and the Casimir Effect as Dark Energy – A Great Opportunity for Nanotechnology},
  journal = {American Journal of Nano Research and Applications},
  volume = {3},
  number = {1},
  pages = {1-5},
  doi = {10.11648/j.nano.20150301.11},
  url = {https://doi.org/10.11648/j.nano.20150301.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.nano.20150301.11},
  abstract = {The present work brings together three different fields which depend crucially upon nano hardware under the umbrella of E-infinity theoretical framework. We start by following E-infinity topological methodology by dividing Hardy’s entanglement into two parts, a global ‘counterfactual’ part given by Φ3 where Φ = 2/(1+ √5) and a ‘local’ part Φn where n is the number of quantum particles. For Hardy’s celebrated gedankenexperiment with two quantum particles, which was moreover experimentally confirmed with high accuracy, the quantum probability is found for n = 2 to be P(2) (Hardy) = Φ3+2= Φ5 exactly as calculated by Hardy using orthodox quantum mechanics. Applying the same topological E-infinity entanglement theory to three quantum particles give a maximal Φ6 as well as a three partite much smaller value equal Φ3(1− Φ3)/ = 0.018033989. We conclude by outlining the relevant and extremely timely ideas and remarks on the possible connection, via a state of the art nanotechnology, to the Casimir effect as a conjectured origin of dark energy.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Three Quantum Particles Hardy Entanglement from the Topology of Cantorian-Fractal Spacetime and the Casimir Effect as Dark Energy – A Great Opportunity for Nanotechnology
AU  - Mohamed S. El Naschie
Y1  - 2015/02/06
PY  - 2015
N1  - https://doi.org/10.11648/j.nano.20150301.11
DO  - 10.11648/j.nano.20150301.11
T2  - American Journal of Nano Research and Applications
JF  - American Journal of Nano Research and Applications
JO  - American Journal of Nano Research and Applications
SP  - 1
EP  - 5
PB  - Science Publishing Group
SN  - 2575-3738
UR  - https://doi.org/10.11648/j.nano.20150301.11
AB  - The present work brings together three different fields which depend crucially upon nano hardware under the umbrella of E-infinity theoretical framework. We start by following E-infinity topological methodology by dividing Hardy’s entanglement into two parts, a global ‘counterfactual’ part given by Φ3 where Φ = 2/(1+ √5) and a ‘local’ part Φn where n is the number of quantum particles. For Hardy’s celebrated gedankenexperiment with two quantum particles, which was moreover experimentally confirmed with high accuracy, the quantum probability is found for n = 2 to be P(2) (Hardy) = Φ3+2= Φ5 exactly as calculated by Hardy using orthodox quantum mechanics. Applying the same topological E-infinity entanglement theory to three quantum particles give a maximal Φ6 as well as a three partite much smaller value equal Φ3(1− Φ3)/ = 0.018033989. We conclude by outlining the relevant and extremely timely ideas and remarks on the possible connection, via a state of the art nanotechnology, to the Casimir effect as a conjectured origin of dark energy.
VL  - 3
IS  - 1
ER  -

Copy | Download