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D. Horrocks and W. Johnson, “On Anticlastic Curvature with Special Reference to Plastic Bending,” International Journal of Mechanical Sciences, Vol. 9, No. 12, 1967, pp. 835-844.

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• TITLE: Quantum Entanglement: Where Dark Energy and Negative Gravity plus Accelerated Expansion of the Universe Comes from

  AUTHORS: Mohamed S. El Naschie

  KEYWORDS: Dark Kinetic Energy of the Quantum Wave; Ordinary Position Energy of the Quantum Particle; Anti Gravity; Negative Curvature; Collapse of the Hawking-Hartle Quantum Wave of the Universe; Revising Einstein’s Relativity; Quantum Gravity

  JOURNAL NAME: Journal of Quantum Information Science, Vol.3 No.2, June 10, 2013

  ABSTRACT: Dark energy is shown to be the absolute value of the negative kinetic energy of the halo-like quantum wave modeled mathematically by the empty set in a five dimensional Kaluza-Klein (K-K) spacetime. Ordinary or position energy of the particle on the other hand is the dual of dark energy and is contained in the dynamic of the quantum particle modeled by the zero set in the same five dimensional K-K spacetime. The sum of both dark energy of the wave and the ordinary energy of the particle is exactly equal to the energy given by the well known formula of Einstein E=mc2 which is set in a four dimensional spacetime. Various interpretations of the results are presented and discussed based on the three fundamental energy density equations developed. In particular where E is the energy, m is the mass and c is the speed of light, is Hardy’s quantum entanglement and gives results in complete agreement with the cosmological measurements of WMAP and Supernova. On the other hand gives an intuitive explanation of negative gravity and the observed increased rate of cosmic expansion. Adding E (ordinary) to E (dark) one finds which as we mentioned above is Einstein’s famous relativity formula. We conclude that similar to the fact that the quantum wave interpreted generally as probability wave which is devoid of ordinary energy decides upon the location of a quantum particle, it also exerts a negative gravity effect on the cosmic scale of our clopen, i.e. closed and open universe. Analysis and conclusions are framed in a reader friendly manner in Figures 1-14 with detailed commentary.