Dark Energy Explained via the Hawking-Hartle Quantum Wave and the Topology of Cosmic Crystallography
Affiliation(s)
Department of Physics, University of Alexandria, Alexandria, Egypt. Department of Mathematics, University of Cairo, Cairo, Egypt.
Department of Physics, University of Alexandria, Alexandria, Egypt. Department of Mathematics, University of Cairo, Cairo, Egypt.
ABSTRACT
The aim of
the present paper is to explain and accurately calculate the missing dark
energy density of the cosmos by scaling the Planck scale and using the
methodology of the relatively novel discipline of cosmic crystallography and
Hawking-Hartle quantum wave solution of Wheeler-DeWitt equation. Following this
road we arrive at a modified version of Einstein’s energy mass relation E = mc2 which predicts a cosmological energy density in astonishing accord with the
WMAP and supernova measurements and analysis. We develop non-constructively
what may be termed super symmetric Penrose fractal tiling and find that the
isomorphic length of this tiling is equal to the self affinity radius of a
universe which resembles an 11 dimensional Hilbert cube or a fractal M-theory
with a Hausdorff dimension 
where
.
It then turns out that the correct maximal quantum relativity energy-mass equation
for intergalactic scales is a simple relativistic scaling, in the sense of
Weyl-Nottale, of Einstein’s classical equation, namely EQR = (1/2)(1/
)
moc2 = 0.0450849 mc2 and that this energy is the ordinary
measurable energy density of the quantum particle. This means that almost 95.5%
of the energy of the cosmos is dark energy which by quantum particle-wave
duality is the absolute value of the energy of the quantum wave and is
proportional to the square of the curvature of the curled dimension of
spacetime namely 
where 
and 
is Hardy’s probability of quantum entanglement. Because of the
quantum wave collapse on measurement this energy cannot be measured using our
current technologies. The same result is obtained by involving all the 17 Stein
spaces corresponding to 17 types of the wallpaper groups as well as the 230-11=219 three dimensional crystallographic group which
gives the number of the first level of massless particle-like states in
Heterotic string theory. All these diverse subjects find here a unified view
point leading to the same result regarding the missing dark energy of the
universe, which turned out to by synonymous with the absolute value of the
energy of the Hawking-Hartle quantum wave solution of Wheeler-DeWitt equation
while ordinary energy is the energy of the quantum particle into which the
Hawking-Hartle wave collapse at cosmic energy measurement. In other words it is
in the very act of measurement which causes our inability to measure the “Dark
energy of the quantum wave” in any direct way. The only hope if any to detect
dark energy and utilize it
in nuclear reactors is future development of sophisticated quantum wave non-demolition measurement instruments.
Cite this paper
M. Naschie and A. Helal, "Dark Energy Explained via the Hawking-Hartle Quantum Wave and the Topology of Cosmic Crystallography," International Journal of Astronomy and Astrophysics, Vol. 3 No. 3, 2013, pp. 318-343. doi: 10.4236/ijaa.2013.33037.
M. Naschie and A. Helal, "Dark Energy Explained via the Hawking-Hartle Quantum Wave and the Topology of Cosmic Crystallography," International Journal of Astronomy and Astrophysics, Vol. 3 No. 3, 2013, pp. 318-343. doi: 10.4236/ijaa.2013.33037.
References
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El Naschie, “Hilbert Space, Poincaré Dodecahedron and Golden Mean Transfiniteness,” Chaos, Solitons & Fractals, Vol. 31, No. 4, 2007, pp. 787-793. doi:10.1016/j.chaos.2006.06.003 [33] M. S. El Naschie, “Transfinite Harmonization by Taking the Dissonance Out of the Quantum Field Symphony,” Chaos, Solitons & Fractals, Vol. 36, No. 4, 2008, pp. 781-786. doi:10.1016/ j.chaos.2007.09.018 [34] S. Nakajima, et al., “Foundations of Quantum Mechanics in the Light of New Technologies,” World Scientific, Singapore, 1996. [35] W. Rindler, “Relativity (Special, General and Cosmological),” Oxford University Press, Oxford, 2004. [36] G. W. Gibbons, et al., “The Future of Theoretical Physics and Cosmology,” Cambridge University Press, Cambridge, 2003. [37] S. Hawking, et al., “Brane New World,” Physical Review D, Vol. 62, No. 4, 2000, Article ID: 043501. doi:10.1103/PhysRevD.62.043501 [38] M. S. El Naschie, “A Unified Newtonian-Relativistic Quantum Resolution of the Supposedly Missing Dark Energy of the Cosmos and the Constancy of the Speed of Light,” International Journal of Modern Nonlinear Theory and Application, Vol. 2, No. 1, 2013, pp. 43-54. doi:10.4236/ ijmnta.2013.21005 [39] L. Marek-Crnjac, et al., “Chaotic Fractals at the Root of Relativistic Quantum Physics and Cosmology,” International Journal of Modern Nonlinear Theory and Application, Vol. 2, No. 1A, 2013, pp. 78-88. [40] M. S. El Naschie, “The Hyperbolic Extension of Sigalotti-Hendi-Sharifzadeh’s Golden Triangle of Special Theory of Relativity and the Nature of Dark Energy,” Journal of Modern Physics, Vol. 4, No. 3, 2013, pp. 354-356. doi:10.4236/jmp.2013.43049 [41] M. S. El Naschie, S. Olsen, J. H. He, S. Nada, L. Marek-Crnjac, A. Helal, et al., “On the Need for Fractal Logic in High Energy Quantum Physics,” International Journal of Modern Nonlinear Theory and Application, Vol. 1, No. 3, 2012, pp. 84-92. doi:10.4236/ijmnta.2012.13012 [42] J. Guckenheimer and P. Holmes, “Nonlinear Dynamical Systems and Bifurcation of Vector Fields,” Springer Verlag, New York, 1994. [43] P. S. Wesson, “Five-Dimensional Physics,” World Scientific, Singapore, 2006. [44] F. Morgan, “Geometric Measure Theory,” Academic Press, Amsterdam, 2009. [45] M. S. El Nasche, “A Fractal Menger Sponge Spacetime Proposal to Reconcile Measurements and Theoretical Predictions of Cosmic Dark Energy,” International Journal of Modern Nonlinear Theory and Application, Vol. 2, No. 2, 2013, pp. 107-121. [46] M. S. El Naschie, “Quantum Entanglement: Where Dark Energy and Negative Gravity plus Accelerated Expansion of the Universe Comes from,” Journal of Quantum Information Science, Vol. 3, No. 2, 2013, pp. 57-77. doi:10.4236/jqis.2013.32011 [47] M. S. El Naschie, “Dark Energy from Kaluza-Klein Spacetime and Noether’s Theorem via Lagrangian Multiplier Method,” Journal of Modern Physics, Vol. 4, No. 6, 2013, pp. 757-760. doi:10.4236/ jmp.2013.46103 [48] M. S. El Naschie, “Elementary Prerequisites for E-Infinity,” Chaos, Solitons & Fractals, Vol. 30, No. 3, 2006, pp. 579-605. doi:10.1016/j.chaos.2006.03.030 [49] B. Kosko, “Fuzzy Thinking,” Flamingo-Harper Collins Publishers, London, 1993. [50] M. S. El Naschie, “Is Einstein’s General Field Equation More Fundamental than Quantum Mechanics and Particle Physics,” Chaos, Solitons & Fractals, Vol. 30, No. 3, 2006, pp. 525-531. doi:10.1016/ j.chaos.2005.04.123 [51] P. Halpern, “The Great Beyond,” John Wiley & Sons, New York, 2004. [52] E. J. Copeland, M. Sami and S. Tsujikawa, “Dynamics of Dark Energy,” International Journal of Modern Physics D, Vol. 15, No. 11, 2006, pp. 1753-1936. [53] J. Magueijo and J. W. Moffat, “Comments on ‘Note on Varying Speed of Light Theories’,” General Relativity and Gravitation, Vol. 40, 2007, pp. 1797-1803. [54] J. Magueijo and L. Smolin, “Gravity’s Rainbow,” Classical and Quantum Gravity, Vol. 21, No. 7, 2004, p. 1725. [55] R. Calella, A. Woverhauser and S. A. Werner, “Observation of Gravitationally Induced Quantum Interference,” Physical Review Letters, Vol. 34, No. 23, 1975, pp. 1472-1474. doi:10.1103/ PhysRevLett.34.1472 [56] M. S. El Naschie, “A Resolution of the Cosmic Dark Energy via Quantum Entanglement Relativity Theory,” Journal of Quantum Information Science, Vol. 3, No. 1, 2013, pp. 23-26. doi:10.4236/ jqis.2013.31006 [57] V. V. Nesvizhevky and A. K. Petukhov, “Study of Neutron Quantum States in the Gravity Field,” European Physical Journal C, Vol. 40, No. 4, 2005, p. 479. doi:10.1140/epjc/s2005-02135-y [58] D. Gross, “Can We Scale the Planck Scale?” Physics Today, Vol. 42, No. 6, 1989, p. 9.
[1] L. Amendola and S. Tsujikawa, “Dark Energy: Theory and Observations,” Cambridge University Press, Cambridge, 2010. doi:10.1017/CBO9780511750823 [2] Y. Baryshev and P. Teerikorpi, “Discovery of Cosmic Fractals,” World Scientific, Singapore, 2002. [3] L. Nottale, “Scale Relativity,” Imperial College Press, London, 2011. [4] R. Penrose, “The Road to Reality,” Jonathan Cape, London, 2004. [5] J. Mageuijo and L. Smolin, “Lorentz Invariance with an Invariant Energy Scale,” Physical Review Letters, Vol. 88, No. 19, 2002, Article ID: 190403. [6] J.-P. Luminet, “The Wraparound Universe,” A.K. Peters Ltd., Wellesley, 2008. [7] M. S. El Naschie, “The Crystallographic Space Groups and Heterotic String Theory,” Chaos, Solitons & Fractals, Vol. 41, No. 5, 2009, pp. 2282-2284. doi:10.1016/j.chaos.2008.09.001 [8] J. R. Weeks, “The Shape of Space,” Marcel Dekker, New York, 2002. [9] L. Marek-Crnjac, “The Hausdorff Dimension of the Penrose Universe,” Physics Research International, Vol. 2011, 2011, Article ID: 874302. [10] I. Aitchison, “Super Symmetry in Particle Physics,” Cambridge University Press, Cambridge, 2007. [11] A. Elokaby, “The Deep Connection between Instantons and String States Encoded in Klein’s Modular Space,” Chaos, Solitons & Fractals, Vol. 42, No. 1, 2009, pp. 303-305. doi:10.1016/ j.chaos.2008.12.001 [12] M. S. El Naschie, “Anomalies Free E-Infinity from von Neumann’s Continuous Geometry,” Chaos, Solitons & Fractals, Vol. 38, No. 5, 2008, pp. 1318-1322. doi:10.1016/j.chaos.2008.06.025 [13] M. S. El Naschie, “Quasi Exceptional E12 Lie Symmetry Group with 685 Dimensions, KAC-Moody Algebra and E-Infinity Cantorian Spacetime,” Chaos, Solitons & Fractals, Vol. 38, No. 4, 2008, pp. 990-992. doi:10.1016/j.chaos.2008.06.015 [14] M. S. El Naschie, “Average Exceptional Lie and Coxeter Group Hierarchies with Special Reference to the Standard Model of High Energy Particle Physics,” Chaos, Solitons & Fractals, Vol. 37, No. 3, 2008, pp. 662-668. doi:10.1016/j.chaos.2008.01.018 [15] M. S. El Naschie, “KAC-Moody Exceptional E12 from Simplictic Tiling,” Chaos, Solitons & Fractals, Vol. 41, No. 4, 2009, pp. 1569-1571. doi:10.1016/j.chaos.2008.06.020 [16] M. S. El Naschie, “The Internal Dynamics of the Exceptional Lie Symmetry Groups Hierarchy and the Coupling Content of Unification,” Chaos, Solitons & Fractals, Vol. 38, No. 4, 2008, pp. 1031-1038. [17] M. S. El Naschie, “High Energy Physics and the Standard Model from the Exceptional Lie Groups,” Chaos, Solitons & Fractals, Vol. 36, No. 1, 2008, pp. 1-17. doi:10.1016/j.chaos.2007.08.058 [18] M. S. El Naschie, “Symmetry Group Prerequisites for E-Infinity in High Energy Physics,” Chaos, Solitons & Fractals, Vol. 35, No. 1, 2008, pp. 202-211. doi:10.1016/j.chaos.2007.05.006 [19] M. S. El Naschie, “Fuzzy Knot Theory Interpretation of Yang-Mills Instantons and Witten’s 5-Brane Model,” Chaos, Solitons & Fractals, Vol. 38, No. 5, 2008, pp. 1349-1354. doi:10.1016/ j.chaos.2008.07.002 [20] J.-H. He, “Hilbert Cube Model for Fractal Spacetime,” Chaos, Solitons & Fractals, Vol. 42, No. 5, 2009, pp. 2754-2759. doi:10.1016/j.chaos.2009.03.182 [21] M. S. El Naschie, “An Irreducibly Simple Derivation of the Hausdorff Dimension of Spacetime,” Chaos, Solitons & Fractals, Vol. 41, No. 5, 2009, pp. 1902-1904. doi:10.1016/j.chaos.2008.07.043 [22] 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 [23] M. S. El Naschie, “On an Eleven Dimensional E-Infinity Fractal Spacetime Theory,” International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 7, No. 4, 2006, pp. 407-409. [24] M. S. El Naschie, “The Discrete Charm of Certain Eleven Dimensional Spacetime Theory,” International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 7, No. 4, 2006, pp. 477-481. [25] 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 [26] J.-H. He, et al., “Quantum Golden Mean Entanglement Test as the Signature of the Fractality of Micro Spacetime,” Nonlinear Science Letters B, Vol. 1, No. 2, 2011, pp. 45-50. [27] M. S. El Naschie, “Quantum 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 [28] M. S. El Naschie, “Derivation of the Euler Characteristic and Curvature of Cantorian Fractal Spacetime Using Nash Euclidean Embedding and the Universal Menger Sponge,” Chaos, Solitons & Fractals, Vol. 41, No. 5, 2009, pp. 2394-2398. doi:10.1016/j.chaos.2008.09.021 [29] M. S. El Naschie, “Arguments for Compactness and Multiple Connectivity of Our Cosmic Spacetime,” Chaos, Solitons & Fractals, Vol. 41, No. 5, 2009, pp. 2787-2789. doi:10.1016/j.chaos.2008.10.011 [30] M. S. El Naschie, “Light Cone Quantization, Heterotic Strings and E-Infinity Derivation of the Number of Higgs Bosons,” Chaos, Solitons & Fractals, Vol. 23, No. 5, 2005, pp. 1931-1933. doi:10.1016/ j.chaos.2004.08.004 [31] M. S. El Naschie, “Fuzzy Platonic Spaces as a Model for Quantum Physics,” Mathematical Models, Physical Methods and Simulation in Science & Technology, Vol. 1, No. 1, 2008, pp. 69-90. [32] M. S. El Naschie, “Hilbert Space, Poincaré Dodecahedron and Golden Mean Transfiniteness,” Chaos, Solitons & Fractals, Vol. 31, No. 4, 2007, pp. 787-793. doi:10.1016/j.chaos.2006.06.003 [33] M. S. El Naschie, “Transfinite Harmonization by Taking the Dissonance Out of the Quantum Field Symphony,” Chaos, Solitons & Fractals, Vol. 36, No. 4, 2008, pp. 781-786. doi:10.1016/ j.chaos.2007.09.018 [34] S. Nakajima, et al., “Foundations of Quantum Mechanics in the Light of New Technologies,” World Scientific, Singapore, 1996. [35] W. Rindler, “Relativity (Special, General and Cosmological),” Oxford University Press, Oxford, 2004. [36] G. W. Gibbons, et al., “The Future of Theoretical Physics and Cosmology,” Cambridge University Press, Cambridge, 2003. [37] S. Hawking, et al., “Brane New World,” Physical Review D, Vol. 62, No. 4, 2000, Article ID: 043501. doi:10.1103/PhysRevD.62.043501 [38] M. S. El Naschie, “A Unified Newtonian-Relativistic Quantum Resolution of the Supposedly Missing Dark Energy of the Cosmos and the Constancy of the Speed of Light,” International Journal of Modern Nonlinear Theory and Application, Vol. 2, No. 1, 2013, pp. 43-54. doi:10.4236/ ijmnta.2013.21005 [39] L. Marek-Crnjac, et al., “Chaotic Fractals at the Root of Relativistic Quantum Physics and Cosmology,” International Journal of Modern Nonlinear Theory and Application, Vol. 2, No. 1A, 2013, pp. 78-88. [40] M. S. El Naschie, “The Hyperbolic Extension of Sigalotti-Hendi-Sharifzadeh’s Golden Triangle of Special Theory of Relativity and the Nature of Dark Energy,” Journal of Modern Physics, Vol. 4, No. 3, 2013, pp. 354-356. doi:10.4236/jmp.2013.43049 [41] M. S. El Naschie, S. Olsen, J. H. He, S. Nada, L. Marek-Crnjac, A. Helal, et al., “On the Need for Fractal Logic in High Energy Quantum Physics,” International Journal of Modern Nonlinear Theory and Application, Vol. 1, No. 3, 2012, pp. 84-92. doi:10.4236/ijmnta.2012.13012 [42] J. Guckenheimer and P. Holmes, “Nonlinear Dynamical Systems and Bifurcation of Vector Fields,” Springer Verlag, New York, 1994. [43] P. S. Wesson, “Five-Dimensional Physics,” World Scientific, Singapore, 2006. [44] F. Morgan, “Geometric Measure Theory,” Academic Press, Amsterdam, 2009. [45] M. S. El Nasche, “A Fractal Menger Sponge Spacetime Proposal to Reconcile Measurements and Theoretical Predictions of Cosmic Dark Energy,” International Journal of Modern Nonlinear Theory and Application, Vol. 2, No. 2, 2013, pp. 107-121. [46] M. S. El Naschie, “Quantum Entanglement: Where Dark Energy and Negative Gravity plus Accelerated Expansion of the Universe Comes from,” Journal of Quantum Information Science, Vol. 3, No. 2, 2013, pp. 57-77. doi:10.4236/jqis.2013.32011 [47] M. S. El Naschie, “Dark Energy from Kaluza-Klein Spacetime and Noether’s Theorem via Lagrangian Multiplier Method,” Journal of Modern Physics, Vol. 4, No. 6, 2013, pp. 757-760. doi:10.4236/ jmp.2013.46103 [48] M. S. El Naschie, “Elementary Prerequisites for E-Infinity,” Chaos, Solitons & Fractals, Vol. 30, No. 3, 2006, pp. 579-605. doi:10.1016/j.chaos.2006.03.030 [49] B. Kosko, “Fuzzy Thinking,” Flamingo-Harper Collins Publishers, London, 1993. [50] M. S. El Naschie, “Is Einstein’s General Field Equation More Fundamental than Quantum Mechanics and Particle Physics,” Chaos, Solitons & Fractals, Vol. 30, No. 3, 2006, pp. 525-531. doi:10.1016/ j.chaos.2005.04.123 [51] P. Halpern, “The Great Beyond,” John Wiley & Sons, New York, 2004. [52] E. J. Copeland, M. Sami and S. Tsujikawa, “Dynamics of Dark Energy,” International Journal of Modern Physics D, Vol. 15, No. 11, 2006, pp. 1753-1936. [53] J. Magueijo and J. W. Moffat, “Comments on ‘Note on Varying Speed of Light Theories’,” General Relativity and Gravitation, Vol. 40, 2007, pp. 1797-1803. [54] J. Magueijo and L. Smolin, “Gravity’s Rainbow,” Classical and Quantum Gravity, Vol. 21, No. 7, 2004, p. 1725. [55] R. Calella, A. Woverhauser and S. A. Werner, “Observation of Gravitationally Induced Quantum Interference,” Physical Review Letters, Vol. 34, No. 23, 1975, pp. 1472-1474. doi:10.1103/ PhysRevLett.34.1472 [56] M. S. El Naschie, “A Resolution of the Cosmic Dark Energy via Quantum Entanglement Relativity Theory,” Journal of Quantum Information Science, Vol. 3, No. 1, 2013, pp. 23-26. doi:10.4236/ jqis.2013.31006 [57] V. V. Nesvizhevky and A. K. Petukhov, “Study of Neutron Quantum States in the Gravity Field,” European Physical Journal C, Vol. 40, No. 4, 2005, p. 479. doi:10.1140/epjc/s2005-02135-y [58] D. Gross, “Can We Scale the Planck Scale?” Physics Today, Vol. 42, No. 6, 1989, p. 9.