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

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

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Authors 

Mohamed S. El Naschie, Dept. of Physics, University of Alexandria, Alexandria, Egypt 

To cite this article 
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, American Journal of Nano Research and Application. Vol. 3, No. 1, 2015, pp. 1-5. doi: 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.

KeywordsThree 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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