What Is the Missing Dark Energy in a Nutshell and the Hawking-Hartle Quantum Wave Collapse
- 1 Department of Physics, University of Alexandria, Alexandria, Egypt
Abstract
We reason that in quantum cosmology there are two kinds of energy. The first is the ordinary energy of the quantum particle which we can measure. The second is the dark energy of the quantum wave by quantum duality. Because measurement collapses the Hawking-Hartle quantum wave of the cosmos, dark energy cannot be detected or measured in any conventional manner. The quantitative results are confirmed using some exact solutions for the hydrogen atom. In particular the ordinary energy of the quantum particle is given by E (0) = ( /2)( mc 2 ) where is Hardy’s probability of quantum entanglement, =( - 1)/2 is the Hausdorff dimension of the zero measure thin Cantor set modeling the quantum particle, while the dark energy of the quantum wave is given by E ( D ) = (5 /2)( mc 2 ) where is the Hausdorff dimension of the positive measure thick empty Cantor set modeling the quantum wave and the factor five (5) is the Kaluza-Klein spacetime dimension to which the measure zero thin Cantor set D (0) = (0, ) and the thick empty set D (-1) = (1, ) must be lifted to give the five dimensional analogue sets namely and 5 needed for calculating the energy density E (0) and E ( D ) which together add to Einstein’s maximal total energy density E (total) = E (0) + E ( D ) = mc 2 = E (Einstein). These results seem to be in complete agreement with the WMAP, supernova and recent Planck cosmic measurement as well as the 2005 quantum gravity experiments of V. V. Nesvizhersky and his associates. It also confirms the equivalence of wormhole solutions of Einstein’s equations and quantum entanglement by scaling the Planck scale.
- B. Mandelbrot, “The Fractal Geometry of Nature,” Freeman, New York, 1983.
- F. Morgan, “Geometric Measure Theory,” Elsevier, Amsterdam, 2009.
- A. Stakhov, “The Mathematics of Harmony,” World Scientific, New Jersey, 2009.
- M. S. El Naschie, O. E. Rossler and I. Prigogine, “Quantum Mechanics, Diffusion and Chaotic Fractals,” Pergamon Press, Elsevier, Oxford, 1995.
- J. Huan-He and M. S. El Naschie, “On the Monadic Nature of Quantum Gravity as Highly Structured Golden Ring Spaces and Spectra,” Fractal Spacetime & NonCommutative Geometry in Quantum & High Energy Physics, Vol. 2, No. 2, 2012, pp. 94-98.
- M. S. El Naschie, “A Review of E-Infinity and the Mass Spectrum of High Energy Particle Physics,” Chaos, Solitons & Fractals, Vol. 19, No. 1, 2004, pp. 209-236. doi:10.1016/S0960-0779(03)00278-9
- M. S. El Naschie, “The Theory of Cantorian Spacetime and High Energy Particle Physics. (An Informal Review),” Chaos, Solitons & Fractals, Vol. 41, No. 5, 2009, pp. 2635-2646. doi:10.1016/j.chaos. 2008.09.059
- R. Penrose, “The Road to Reality,” Jonathan Cape, London, 2004.
- H. Coxeter, “The Beauty of Geometry,” Dover Publications, New York, 1999.
- H. Coxeter, “Regular Polytops,” Dover Publication, New York, 1973.
- I. Bengtsson and K. Zyczkowski, “Geometry of Quantum States,” Cambridge University Press, Cambridge, 2006. doi:10.1017/CBO9780511535048
- P. Halpern, “The Great Beyond, Higher Dimensions, Parallel Universes and the Extraordinary Search for a Theory of Everything,” John Wiley, New Jersey, 2004.
- M. S. El Naschie, “Kaluza-Klein Unification—Some Possible Extensions,” Chaos, Solitons & Fractals, Vol. 37, No. 1, 2008, pp. 16-22. doi:10.1016/j.chaos.2007.09.079
- M. S. El Naschie and L. Marek-Crnjac, “Deriving the Exact Percentage of Dark Energy Using a Transfinite Version of Nottale’s Scale Relativity,” International Journal of Modern Nonlinear Theory and Application, Vol. 1, No. 4, 2012, pp. 118-124. doi:10.4236/ijmnta.2012.14018
- M. S. El Naschie, “Entanglement as a Consequence of a Cantorian Micro Spacetime Geometry,” Journal of Quantum Information Science, Vol. 1, No. 2, 2011, pp. 50-53. doi:10.4236/jqis.2011.12007
- L. Amendola and S. Tsujikawa, “Dark Energy Theory and Observations,” Cambridge University Press, Cambridge, 2010.