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 |
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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. |
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Copyright © The Author(s), 2015. Published by Science Publishing Group |
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
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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
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
@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} }
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 -