Author(s)
Mohamed S. El Naschie
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.
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.
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