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), 2015. 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

[1]	L. Hardy, Nonlocality of two particles without inequalities for almost all entangled states. Phys. Rev. Lett. Vol. 71(11), 1993, pp. 1665-1668.
[2]	J.S. Bell, Speakable and Unspeakable in Quantum Mechanics. Cambridge University Press, Cambridge 1991)
[3]	Ji-Huan He et al, Quantum golden mean entanglement test as the signature of the fractality of micro spacetime. Nonlinear Sci. Lett B, Vol. 1(2), 2011, pp. 45-50.
[4]	Mohamed S. El Naschie, Quantum Entanglement as a Consequence of a Cantorian Micro Spacetime Geometry. Journal of Quantum Information Science, Vol. 1(2), 2011, pp. 50-53.
[5]	Mohamed S. El Naschie, Quantum Entanglement: Where Dark Energy and Negative, Accelerated Expansion of the Universe Comes from. Journal of Quantum Information Science, Vol. 3(2), 2013, pp 55-57.
[6]	R. Penrose, The Road to Reality. J. Cape, London, UK. 2004
[7]	M.S. El Naschie, M.A. Helal, L. Marek-Crnjac and Ji-Huan He, Transfinite corrections as a Hardy type quantum entanglement. Fractal Spacetime & Noncommutative Geometry in Quantum & High Energy Physics, Vol. 2(1), 2012, pp. 98-101.
[8]	M.S. El Naschie, Ji-Huan He, S. Nada, L. Marek-Crnjac and M. Helal, Golden mean computer for high energy physics. Fractal Spacetime and Noncommutative Geometry in Quantum and High Energy Physics. Vol. 2(2), 2012, pp. 80-92.
[9]	M.S. El Naschie and S.A. Olsen, When zero is equal one: A set theoretical resolution of quantum paradoxes. Fractal Spacetime & Noncommutative Geometry in Quantum High energy Physics, Vol. 1(1), 2011, pp. 11-24.
[10]	M.S. El Naschie, Electroweak connection and universality of Hardy’s quantum entanglement. Fractal Spacetime & Noncommutative Geometry in Quantum High energy Physics, Vol. 1(1), 2011, pp. 25-30.
[11]	L. Marek-Crnjac, Ji-Huan He and M.S. El Naschie, On the universal character of Hardy’s quantum entanglement and its geometrical-topological interpretation. Fractal Spacetime & Noncommutative Geometry in Quantum & High Energy Phys. Vol. 2(2), 2012, pp. 118-12.
[12]	M.S. El Naschie, L. Marek-Crnjac and Ji-Huan He, Using Hardy’s entanglement, Nash embedding and quantum groups to derive the four dimensionality of spacetime. Fractal Spacetime & Noncommutative Geometry in Quantum & High Energy Phys. Vol. 2(2), 2012, pp. 107-112.
[13]	Mohamed S. El Naschie, Experimentally Based Theoretical Arguments that Unruh's Temperature, Hawking's Vacuum Fluctuation and Rindler's Wedge Are Physically Real. American Journal of Modern Physics, Vol. 2(6), 2013, pp. 357-361.
[14]	Mohamed S. El Naschie, A Rindler-KAM Spacetime Geometry and Scaling the Planck Scale Solves Quantum Relativity and Explains Dark Energy. International Journal of Astronomy and Astrophysics, Vol. 3(4), 2013, pp. 483-493.
[15]	Mohamed S. El Naschie, Topological-Geometrical and Physical Interpretation of the Dark Energy of the Cosmos as a “Halo” Energy of the Schrödinger Quantum Wave Journal of Modern Physics, Vol. 4(5), 2013, pp. 591-596.
[16]	M.S. El Naschie, The quantum gravity Immirzi parameter – A general physical and topological interpretation. Gravity and Cosmology, Vol. 19(3), 2013, pp. 151-153.
[17]	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. American Journal of Astronomy & Astrophysics, Vol. 2(3), 2014, pp. 34-37.
[18]	Mohamed S. El Naschie, Electromagnetic—pure gravity connection via Hardy’s quantum entanglement.  Journal of Electromagnetic Analysis and Applications, Vol. 6(9), 2014, pp. 233-237.
[19]	L. Marek-Crnjac and Ji-Huan He, An Invitation to El Naschie’s theory of Cantorian space-time and dark energy. International Journal of Astronomy and Astrophysics, Vol. 3(4), 2013, pp. 464-471.
[20]	M.S. El Naschie, A review of E-infinity and the mass spectrum of high energy particle physics. Chaos, Solitons & Fractals, Vol. 19(1), 2004, pp. 209-236.
[21]	M.S. El Naschie, Superstrings, knots and noncommutative geometry in E-infinity space. International Journal of Theoretical Physics, Vol. 37(12), 1998, pp. 2935-2951.
[22]	Mohamed S. El Naschie, On a new elementary particle from the disintegration of the symplectic 't Hooft-Veltman-Wilson fractal spacetime. World Journal of Nuclear Science and ATechnology, Vol. 4(4), 2014, pp. 216-221.
[23]	W. Tan, Y. Li, H.Y. Kong and M.S. El Naschie, From nonlocal elasticity to nonlocal spacetime and nanoscience. Bubbfil Nano Technology, Vol. 1(1), 2014, pp. 3-12.
[24]	D. Heiss (Editor):, Fundamentals of Quantum Information. Springer, Berlin 2002.
[25]	I. Gengtsson and K. Zyczkowski, Geometry of Quantum States. Cambridge University Press, Cambridge 2006.
[26]	M.A. Nielsen and I.L. Chuang, Quantum Computation and Quantum Information. Cambridge University Press, Cambridge, 2010.
[27]	A. Furusawa and P. van Loock, Quantum Teleportation and Entanglement. Wiley-VCH, Weinheim, Germany, 2011.
[28]	J.K. Pachos, Introduction to Topological Quantum Computation. Cambridge University Press, Cambridge, 2012.
[29]	D.G. Marinescu and G.M. Marinescu, Classical and Quantum Information. Elsevier, Amsterdam, 2012.
[30]	Mohamed S. El Naschie, Casimir-like energy as a double Eigenvalues of quantumly entangled system leading to the missing dark energy density of the cosmos. International Journal of High Energy Physics, Vol. 1(5), 2014, pp. 55-63.
[31]	J. Matsumoto, The Casimir effect as a candidate of dark energy. arXiv: 1303.4067[hep-th]26December 2013.
[32]	K. Eric Drexler, Engines of Creation. Fourth Estate Ltd., London, 1990.
[33]	P. Day (Editor), Unveiling The Microcosmos. Oxford University Press, Oxford, 1996.
[34]	S.E. Lyshevski, Nano and Microelectromechanical Systems. CRC Press, Boca Ratan, 2001.
[35]	L.E. Foster, Nanotechnology, Science, Innovation and Opportunity. Prentice Hall, Boston, 2006.
[36]	M. Krummenacker and J. Lewis (Editors), Prospects in Nanotechnology. John Wiley, New York, 1995.
[37]	M.S. El Naschie, Nanotechnology for the developing world. Chaos, Solitons & Fractals, Vol. 30(4), 2006, pp. 769-773.
[38]	M.S. El Naschie, Chaos and fractals in nano and quantum technology. Chaos, Solitons & Fractals, Vol. 9(10), 1998, pp. 1793-1802.
[39]	M.S. El Naschie, Nanotechnology and the political economy of the developing world. International, May 2007, pp. 7-12. (Periodical International Economic Magazine by AS&S Publishing Ltd, Camden Town, London, UK, Registration No. 04761267).
[40]	M.S. El Naschie, Can nanotechnology slow the aging process by inteferring with the arrow of time. International, June 2007, pp. 10-15. (Periodical International Economic Magazine by AS&S Publishing Ltd, Camden Town, London, UK, Registration No. 04761267).
[41]	M. Aboulanan, The making of the future via nanotechnology (in Arabic). International, July 2007, pp. 32-35. (Periodical International Economic Magazine by AS&S Publishing Ltd, Camden Town, London, UK, Registration No. 04761267).
[42]	M.S. El Naschie, From relativity to deterministic chaos in science and society. International, August 2007, pp. 11-17. (Periodical International Economic Magazine by AS&S Publishing Ltd, Camden Town, London, UK, Registration No. 04761267).
[43]	M.S. El Naschie, The political economy of nanotechnology and the developing world. International Journal of Electrospun Nanofibers and Application. I(I), 2007, pp. 41-50. Published by Research Science Press, India.
[44]	D. Brito and J. Rosellon, Energy and Nanotechnology: Prospects for solar energy in the 21st century. The James A. Baker III Institute for Public Policy of Rice University, December 2005, pp. 1-16.
[45]	O.E. Rössler and M.S. El Naschie, Interference through causality vacillation. In Symposium on the Foundations of Modern Physics, Helsinki, Finland, June 1994, pp. 13-16.
[46]	O.E. Rössler and M.S. El Naschie: Interference is Exophysically Absent. In Endophysics – The World As An Interface. World Scientific, Singapore, 1998, pp. 159-160.
[47]	M.S. El Naschie, A note on quantum gravity and Cantorian spacetime. Chaos, Solitons & Fractals, 8(1), p. 131-133 (1997).
[48]	M.S. El Naschie, The symplictic vacuum exotic quasi particles and gravitational instantons. Chaos, Solitons & Fractals, 22(1), 2004, pp. 1-11.
[49]	M. Agop, E-infinity Cantorian spacetime, polarization gravitational field and van der Waals-type forces. Chaos, Solitons & Fractals, 18(1), 2003, pp. 1-16.
[50]	Mohamed S. El Naschie, A Rindler-KAM spacetime geometry and scaling the Planck scale solves quantum relativity and explains dark energy. International Journal of Astronomy and Astrophysics, Vol. 3(4), 2013, pp. 483-493.
[51]	J. Cugnon, The Casimir effect and the vacuum energy. Few-body System, 53(1-2), 2012, pp. 181-188.
[52]	K.A. Milton, Resource Letter VWCPF-1 van der Waals and Casimir-Polder forces. American Journal of Physics, 79, 2011, pp. 697.
[53]	M. Ito, Gravity, higher dimensions, nanotechnology and particles physics. Journal of Physics, Conference Series, 89(1), 2007, p. 1-8.
[54]	M.S. El Naschie, Casimir-like energy as a double Eigenvalue of quantumly entangled system leading to the missing dark energy density of the cosmos. International Journal of High Energy Physics, 1(5), 2014, pp. 55-63.

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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
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
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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