Topological-Geometrical and Physical Interpretation of the Dark Energy of the Cosmos as a “Halo” Energy of the Schrödinger Quantum Wave


The paper concludes that the energy given by Einstein’s famous formula E = mc2 consists of two parts. The first part is the positive energy of the quantum particle modeled by the topology of the zero set. The second part is the absolute value of the negative energy of the quantum Schr?dinger wave modeled by the topology of the empty set. We reason that the latter is nothing else but the so called missing dark energy of the universe which accounts for 94.45% of the total energy, in full agreement with the WMAP and Supernova cosmic measurement which was awarded the 2011 Nobel Prize in Physics. The dark energy of the quantum wave cannot be detected in the normal way because measurement collapses the quantum wave.

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M. 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 No. 5, 2013, pp. 591-596. doi: 10.4236/jmp.2013.45084.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] B. Mandelbrot, “The Fractal Geometry of Nature,” Freeman, New York, 1983.
[2] F. Morgan, “Geometric Measure Theory,” Elsevier, Amsterdam, 2009.
[3] A. Stakhov, “The Mathematics of Harmony,” World Scientific, New Jersey, 2009.
[4] M. S. El Naschie, O. E. Rossler and I. Prigogine, “Quantum Mechanics, Diffusion and Chaotic Fractals,” Pergamon Press, Elsevier, Oxford, 1995.
[5] J. Huan-He and M. S. El Naschie, Fractal Spacetime and Non-Commutative Geometry in Quantum and High Energy Physics, Vol. 2, 2012, pp. 94-98.
[6] M. S. El Naschie, Chaos, Solitons & Fractals, Vol. 19, 2004, pp. 209-236. doi:10.1016/S0960-0779(03)00278-9
[7] M. S. El Naschie, Chaos, Solitons & Fractals, Vol. 41, 2009, pp. 2635-2646. doi:10.1016/j.chaos.2008.09.059
[8] R. Penrose, “The Road to Reality,” Jonathan Cape, London, 2004.
[9] H. Coxeter, “The Beauty of Geometry,” Dover Publications, New York, 1999.
[10] H. Coxeter, “Regular Polytops,” Dover Publication, New York, 1973.
[11] I. Bengtsson and K. Zyczkowski, “Geometry of Quantum States,” Cambridge, 2006. doi:10.1017/CBO9780511535048
[12] P. Halpern, “The Great Beyond, Higher Dimensions, Parallel Universes and the Extraordinary Search for a Theory of Everything,” John Wiley, Hoboken, 2004.
[13] M. S. El Naschie, Chaos, Solitons & Fractals, Vol. 37, 2008, pp. 16-22. doi:10.1016/j.chaos.2007.09.079
[14] M. S. El Naschie and L. Marek-Crnjac, International Journal of Modern Nonlinear Theory and Applications, Vol. 1, 2012 pp. 118-124.
[15] M. S. El Naschie, Journal of Quantum Information Science, Vol. 1, 2011, pp. 50-53.
[16] E. J. Copeland, M. Sami and S. Tsujikawa, “Dynamics of Dark Energy,” 2006. arxiv:hep-th/0603057V3
[17] L. Amendola and S. Tsujikawa, “Dark Energy Theory and Observations,” Cambridge University Press, Cambridge, 2010. doi:10.1017/CBO9780511750823
[18] J. Magueijo and I. Smolin, “Lorenz Invariance with Invariant Energy Scale,” 2001. arxiv:hep-th/0112090vz
[19] J. Magueijio, “Faster than Speed of Light,” William Heinemann, London, 2008.

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