Dark Energy Introduction

Thursday, December 26, 2013

An Invitation to El Naschie’s Theory of Cantorian Space-Time and Dark Energy

An Invitation to El Naschie’s Theory of Cantorian Space-Time and Dark Energy
Author(s)
Leila Marek-Crnjac, Jihuan He
The paper is a condensed but accurate account of El Naschie’s theory of Cantorian space-time which was used by him to clarify some major problems in theoretical physics and cosmology. In particular El Naschie’s revision and completion of relativity theory and demystification of dark energy are destined to be two milestones in the history of theoretical physics.
KEYWORDS
Cantorian Philosophy; Nonlinear Dynamics and Relativity; Fractal Einstein Gravity; Dark Energy; Ordinary Energy of the Quantum Particle; Dark Energy of the Quantum Wave

Cite this paper
L. Marek-Crnjac and J. He, "An Invitation to El Naschie’s Theory of Cantorian Space-Time and Dark Energy,"International Journal of Astronomy and Astrophysics, Vol. 3 No. 4, 2013, pp. 464-471. doi: 10.4236/ijaa.2013.34053.
[1]M. S. El Naschie and I. Prigogine, “Time Symmetry Breaking in Classical and Quantum Mechanics,” Chaos, Solitons & Fractals (Special Issue), Vol. 7, No. 4, 1996, pp. 499-503.
[2]M. S. El Naschie, O. E. R?ssler and I. Prigogine, “Quantum Mechanics, Diffusion and Chaotic Fractals,” Pergamon Press/Elsevier, Oxford, 1995.
[3]J.-H. He, “A Historical Scientific Finding on Dark Energy,” Fractal Space-Time & Non-Commutative Geometry in Quantum & High Energy Phys., Vol. 2, No. 2, 2012, p. 14.
[4]J.-H. He and L. Marek-Crnjac, “Mohamed El Naschie’s revision of Albert Einstein’s E = mc2: A Definite Resolution of the Mystery of the Missing Dark Energy of the Cosmos,” International Journal of Modern Nonlinear Theory and Application, Vol. 2, No. 1, 2013, pp. 55-59. http://dx.doi.org/10.4236/ ijmnta.2013.21006
[5]L. Marek-Crnjac, “Modification of Einstein’s E = mc2 to E = 1/22 mc2,” American Journal of Modern Physics, Vol. 2, No. 5, 2013, pp. 255-263.
[6]M. S. El 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.
[7]M. S. El Naschie, “The Quantum Gravity Immirzi Parameter—A General Physical and Topological Interpretation,” Gravitation and Cosmology, Vol. 19, No. 3, 2013, pp. 151-155. http://dx.doi.org/ 10.1134/S0202289313030031
[8]M. S. El Naschie, “What Is the Missing Dark Energy in a Nutshell and the Hawking-Hartle Quantum Wave Collapse,” International Journal of Astronomy and Astrophysics, Vol. 3, No. 3, 2013, pp. 205-211. http://dx.doi.org/10.4236/ijaa.2013.33024
[9]M. S. El Naschie, “A Resolution of Cosmic Dark Energy via a Quantum Entanglement Relativity Theory,” Journal of Quantum Information Science, Vol. 3, No. 1, 2013, pp. 23-26. http://dx.doi.org/ 10.4236/jqis.2013.31006
[10]M. S. El Naschie, “Topological-Geometrical and Physical Interpretation of the Dark Energy of the Cosmos as a “Halo” Energy of the Schr?dinger Quantum Wave,” Journal of Modern Physics, Vol. 4, No. 5, 2013, pp. 591-596. http://dx.doi.org/10.4236/jmp.2013.45084
[11]M. S. El Naschie, “Superstrings, Knots and Non-Commutative Geometry in E-Infinity Space,” International Journal of Theoretical Physics, Vol. 37, No. 12, 1998, pp. 2935-2951. http://dx.doi.org/ 10.1023/A:1026679628582
[12]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. http://dx.doi.org/10.1016/S0960-0779(03)00278-9
[13]M. S. El Naschie, “Topological Defects in the Symplictic Vacuum, Anomalous Positron Production and the Gravitational Instanton,” International Journal of Modern Physics E, Vol. 13, No. 4, 2004, pp. 835-849. http://dx.doi.org/10.1142/S0218301304002429
[14]M. S. El Naschie, “Average Exceptional Lie Group Hierarchy and High Energy Physics,” In: American Institute of Physics (AIP) Conference Proceedings, Vol. 1018, American Institute of Physics (AIP), New York, 2008, pp. 15-20.
[15]P. S. Wesson, “Five-Dimensional Physics,” World Scientific, Singapore, 2006.
[16]P. Weibel, G. Ord and O. Rossler, “Space-Time Physics and Fractality, Festschrift in Honour of Mohamed El Naschie on the Occasion of His 60th Birthday,” Springer, Vienna, New York, 2005.
[17]M. S. El Naschie, “The Theory of Cantorian Space-Time and High Energy Particle Physics (an Informal Review),” Chaos, Solitons & Fractals, Vol. 41, No. 5, 2009, pp. 2635-2646. http://dx.doi.org/10. 1016/j.chaos.2008.09.059
[18]J.-H. He, “Hilbert Cube Model for Fractal Space-Time,” Chaos, Solitons & Fractals, Vol. 42, No. 5, 2009, pp. 2754-2759. http://dx.doi.org/10.1016/j.chaos.2009.03.182
[19]J.-H. He, et al., “Twenty-Six Dimensional Polytope and High Energy Space-Time Physics,” Chaos, Solitons & Fractals, Vol. 33, No. 1, 2007, pp. 5-13. http://dx.doi.org/10.1016/j.chaos.2006.10.048
[20]M. S. El Naschie, “From Classical Gauge Theory Back to Weyl Scaling via E-Infinity Space-Time,” Chaos, Solitons & Fractals, Vol. 38, No. 4, 2008, pp. 980-985. http://dx.doi.org/10.1016/j.chaos. 2008.05.017
[21]L. Marek-Crnjac, “The Hausdorff Dimension of the Penrose Universe,” Physics Research International, Vol. 2011, 2011, Article ID: 874302. http://dx.doi.org/10.1155/2011/874302
[22]J.-H. He, et al., “Transfinite Physics—A Collection of Publications on E-Infinity Cantorian Space-Time Theory,” China Culture & Scientific Publishing, Hongkong, 2005.
[23]J.-H. He, E. Goldfain, et al., “Beyond the 2006 Physics Nobel Prize for COBE,” China Culture & Scientific Publishing, Beijing, 2006.
[24]M. S. El Naschie, “Nonlinear Dynamics of the Two-Slit Experiment with Quantum Particles,” Problems of Nonlinear Analysis in Engineering Systems, Vol. 26, No. 2, 2006.
[25]L. Marek-Crnjac, “A Feynman Path Integral-Like Method for Deriving the Four Dimensionality of Space-Time from First Principles,” Chaos, Solitons & Fractals, Vol. 41, No. 5, 2009, pp. 2471-2473. http://dx.doi.org/10.1016/j.chaos.2008.09.014
[26]M. S. El Naschie, “On ‘tHooft’s Dimensional Regularization in E-Infinity Space,” Chaos, Solitons & Fractals, Vol. 12, No. 5, 2001, pp. 851-858. http://dx.doi.org/10.1016/S0960-0779(00)00138-7
[27]A. Connes, “Non-Commutative Geometry,” Academic Press, San Diego, 1994.
[28]M. S. El Naschie, “The Missing Dark Energy of the Cosmos from Light Cone Topological Velocity and Scaling the Planck Scale,” Open Journal of Microphysics, Vol. 3, No. 3, 2013, pp. 64-70.
http://dx.doi.org/10.4236/ojm.2013.33012
[29]M. S. El Naschie, “A Note on Quantum Gravity and Cantorian Space-Time,” Chaos, Solitons & Fractals, Vol. 8, No. 1, 1997, pp. 131-133. http://dx.doi.org/10.1016/S0960-0779(96)00128-2
[30]M. S. El Naschie, “Remarks on Superstrings, Fractal Gravity, Nagasawa’s Diffusion and Cantorian Space-Time,” Chaos, Solitons & Fractals, Vol. 8, No. 11, 1997, pp. 1873-1886.
http://dx.doi.org/10.1016/S0960-0779(97)00124-0
[31]M. S. El Naschie, “Fractal Gravity and Symmetry Breaking in a Hierarchical Cantorian Space,” Chaos, Solitons & Fractals, Vol. 8, No. 11, 1997, pp. 1865-1872. http://dx.doi.org/10.1016/S0960-0779(97) 00039-8
[32]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. http://dx.doi.org/10.4236/ijmnta.2013.21A010
[33]M. S. El Naschie, “Electroweak Connection and Universality of Hardy’s Quantum Entanglement,” Fractal Space-Time & Non-Commutative Geometry in Quantum & High Energy Physics, Vol. 1, No. 1, 2011, pp. 25-30.
[34]M. S. El Naschie, “Fuzzy Multi-Instanton Knots in the Fabric of Space-Time and Dirac’s Vacuum Fluctuation,” Chaos, Solitons & Fractals, Vol. 38, No. 5, 2008, pp. 1260-1268. http://dx.doi.org/10. 1016/j.chaos.2008.07.010
[35]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. http://dx.doi.org/10.1016/j. chaos.2008.07.002
[36]M. S. El Naschie, “Knots and Exceptional Lie Groups as Building Blocks of High Energy Particle Physics,” Chaos, Solitons & Fractals, Vol. 41, No. 4, 2009, pp. 1799-1803. http://dx.doi.org/10.1016/ j.chaos.2008.07.025
[37]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. 91-101.
[38]M. S. El Naschie, S. Olsen, J. H. He, S. Nada, L. Marek-Crnjac and A. Helal, “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.
[39]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.
http://dx.doi.org/10.4236/jqis.2011.12007
[40]R. Coldea, D. A. Tennant, E. M. Wheeler, et al., “Quantum Ratio Discovered in a Quantum World,” Science, Vol. 8, No. 32, 2010, pp. 177-180.
[41]M. S. El Naschie, “The Hydrogen Atom Fractal Spectra, the Missing Dark Energy of the Cosmos and Their Hardy Quantum Entanglement,” International Journal of Modern Nonlinear Theory and Application, Vol. 2, No. 3, 2013, pp. 167-169. http://dx.doi.org/10.4236/ijmnta.2013.23023
[42]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. http://dx.doi.org/10.4236/jmp.2013.43049
[43]M. S. El Naschie, “Dark Energy from Kaluza-Klein Space-Time and Noether’s Theorem via Lagrangian Multiplier Method,” Journal of Modern Physics, Vol. 4, No. 6, 2013, pp. 757-760. http://dx.doi.org/ 10.4236/jmp.2013.46103
[44]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. http://dx.doi.org/10.4236/ijmnta.2012.14018
[45]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. http://dx.doi.org/10.4236/jqis.2013.32011
[46]M. S. El Naschie, “The Quantum Entanglement behind the Missing Dark Energy,” Journal of Modern Physics and Applications, Vol. 2, No. 1, 2013, pp. 88-96.
[47]M. S. El Naschie, “Determining the Missing Dark Energy of the Cosmos from a Light Cone Exact Relativistic Analysis,” Journal of Physics, Vol. 2, No. 2, 2013, pp. 18-23.
[48]G. Iovane, “Mohamed El Naschie’s E(Infinity) Cantorian Space-Time and Its Consequences in Cosmology,” Chaos, Solitons & Fractals, Vol. 25, No. 3, 2005, pp. 775-779. http://dx.doi.org/10.1016/ j.chaos.2005.02.024
[49]M. Persinger and C. Lavellee, “Theoretical and Experimental Evidence of Macroscopic Entanglement between Human Brain Activity and Photon Emission,” Journal of Consciousness Exploration & Research, Vol. 1, No. 7, 2010, pp. 785-807.
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The Three Page Guide to the Most Important Results of M. S. El Naschie’s Research in E-Infinity Quantum Physics and Cosmology

The Three Page Guide to the Most Important Results of M. S. El Naschie’s Research in E-Infinity Quantum Physics and Cosmology

In this short survey, we give a complete list of the most important results obtained by El Naschie’s E-infinity Cantorian space-time theory in the realm of quantum physics and cosmology. Special attention is paid to his recent result on dark energy and revising Einstein’s famous formula .

KEYWORDS
Review of E-infinity; Summary of Cantorian Space-Time; El Naschie Nottale and Ord Fractal Space-Time; Rindler Space-Time; Revising Einstein Theory; Dark Energy Revealed


Cite this paper
M. A. Helal, L. Marek-Crnjac and J. He, "The Three Page Guide to the Most Important Results of M. S. El Naschie’s Research in E-Infinity Quantum Physics and Cosmology," Open Journal of Microphysics, Vol. 3 No. 4, 2013, pp. 141-145. doi: 10.4236/ojm.2013.34020.
[1]M. S. El Naschie, O. E. Rossler and I. Prigogine, “Quantum Mechanics, Diffusion and Chaotic Fractals,” Elsevier Science Ltd., Oxford, 1995.
[2]M. Jammer, “Concepts of Space,” Dover Publications, New York, 1969.
[3]B. G. Sidharth, “The Universe of Fluctuations (The Architecture of Space-Time and the Universe),” Springer, Dordrecht, 2005.
[4]M. S. El Naschie, “Deterministic Quantum Mechanics versus Classical Mechanical Indeterminism,” International Journal of Nonlinear Science & Numerical Simulation, Vol. 8, No. 1, 2007, pp. 5-10.
[5]M. S. El Naschie, “Average Exceptional Lie Group Hierarchy and High Energy Physics,” American Inst. of Physics, 9th Int. Symposium Proceedings, 7-9 June 2008, AIP Conferences, 101018, pp. 15-20.
[6]J.-H. He, “Transfinite Physics: A Collection of Publication on E-Infinity Cantorian Space-Time Theory,” China Education and Culture Publishing Co., Beijing, 2005.
[7]J.-H. He, E. Goldfain, L. D. Sigalotti and A. Mejias, “Beyond the 2006 Physics Nobel Price for COBE: An Introduction to E-infinity Theory,” China Education and Culture Publishing Co., Beijing, 2006.
[8]J. Brindly, T. Kapitaniak and M. S. El Naschie, “Analytical Conditions for Strange Chaotic and Non-Chaotic Attractors of the Quasi Periodically Forced van der Pol Equation,” Physica D: Nonlinear Phenomena, Vol. 51, No. 1-3, 1991, pp. 28-38.
http://dx.doi.org/10.1016/0167-2789(91)90219-Y
[9]M. S. El Naschie and S. Al Athel, “On the Connection between Statical and Dynamical Chaos,” Zeitschrift fur Naturforshung, Vol. 44a, 1989, pp. 645-650.
[10]D. K. Campbell, “Chaos,” AIP, New York, 1990.
[11]G. Cherbit, “Fractals,” J. Wiley, Chichester, 1991.
[12]S. Weinberg, “The Quantum Theory of Fields,” Parts I, II, III, Cambridge Press, 1998,2000.
[13]M. S. El Naschie, “Quantum Golden Field Theory—Ten theorems and Various Conjectures,” Chaos, Solitons & Fractals, Vol. 36, No. 5, 2008, pp. 1121-1125.
http://dx.doi.org/10.1016/j.chaos.2007.09.023
[14]M. S. El Naschie, “Towards a Quantum Golden Field Theory,” International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 8, No. 4, 2007, pp. 477-482.
[15]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.
http://dx.doi.org/10.1016/j.chaos.2007.08.058
[16]M. S. El Naschie, “P-Adic Unification of the Fundamental Forces and the Standard Model,” Chaos, Solitons & Fractals, Vol. 38, No. 4, 2008, pp. 1011-1012.
http://dx.doi.org/10.1016/j.chaos.2008.04.047
[17]M. S. El Naschie, “On a Canonical Equation for All Fun- damental Interactions,” Chaos, Solitons & Fractals, Vol. 36, No. 5, 2008, pp. 1200-1204.
http://dx.doi.org/10.1016/j.chaos.2007.09.039
[18]M. S. El Naschie, “Statistical Mechanics of Multi-Dimensional Cantor Sets Godel Theorem and Quantum Space-Time,” Journal of Franklin Institute, Vol. 33, No. 1, 1993, pp. 199-211.
http://dx.doi.org/10.1016/0016-0032(93)90030-X
[19]M. S. El Naschie, “Complex Dynamics in 4D Peano-Hilbert Space,” Il Nuovo Cimento, Vol. 1, No. 5, 1992, pp. 583-594.
[20]M. S. El Naschie, “Peano Dynamics as a Model for Turbulence and Strange Non-Chaotic Behavior,” Acta Physica Polonica A, Vol. 80, No. 1, 1991.
[21]M. S. El Naschie, “Quantum Mechanics and the Possibility of a Cantorian Space-Time,” Chaos, Solitons & Fractals, Vol. 1, No. 5, 1991, pp. 485-487.
http://dx.doi.org/10.1016/0960-0779(91)90019-6
[22]M. S. El Naschie, “Renormalization Semi-Groups and the Dimension of Cantorian Space-Time,” Chaos, Solitons & Fractals, Vol. 4, No. 7, 1994, pp. 1141-1145.
http://dx.doi.org/10.1016/0960-0779(94)90027-2
[23]M. S. El Naschie, “On a Class of General Theories for High Energy Particle Physics,” Chaos, Solitons & Fractals, Vol. 14, No. 4, 2002, pp. 649-668.
http://dx.doi.org/10.1016/S0960-0779(02)00033-4
[24]M. S. El Naschie, “A Review of E-Infinity Theory and the Mass Spectrum of High Energy Particle Physics,” Chaos, Solitons & Fractals, Vol. 19, No. 1, 2004, pp. 209-236. http://dx.doi.org/10.1016/S0960-0779(03)00278-9
[25]M. S. El Naschie, “The Theory of Cantorian Space-Time and High Energy Particle Physics (An Informal Review),” Chaos, Solitons & Fractals, Vol. 41, No. 5, 2009, pp. 2635-2646. http://dx.doi.org/10.1016/j.chaos.2008.09.059
[26]M. S. El Naschie, “Application of Chaos and Fractals in Fundamental Physics and Set Theoretical Resolution of the Two-Slit Experiment and Wave Collapse,” The 3rd International Symposium on Nonlinear Dynamics, Donghua University, China, 2010, pp. 7-8.
[27]M. S. El Naschie, “Kaluza-Klein Unification—Some Possible Extensions,” Chaos, Solitons & Fractals, Vol. 37, No. 1, 2008, pp. 16-22.
http://dx.doi.org/10.1016/j.chaos.2007.09.079
[28]M. S. El Naschie, “On Dualities between Nordstrom-Ka- luza-Klein Newtonian and Quantum Gravity,” Chaos, Solitons & Fractals, Vol. 36, No. 4, 2008, pp. 808-810.
http://dx.doi.org/10.1016/j.chaos.2007.09.019
[29]M. S. El Naschie, “Superstring Theory: What It Cannot Do but E-Infinity Could,” Chaos, Solitons & Fractals, Vol. 29, No. 1, 2006, pp. 65-68.
http://dx.doi.org/10.1016/j.chaos.2005.11.021
[30]G. N. Ord, “Fractal Space-Time,” Journal of Physics A: Mathematical and General, Vol. 16, No. 9, 1983, p. 1869.
http://dx.doi.org/10.1088/0305-4470/16/9/012
[31]L. Nottale, “Fractal Space-Time and Microphysics,” World Scientific, Singapore, 1993.
[32]M. S. El Naschie, “Quantum Mechanics, Cantorian Space-Time and the Heisenberg Uncertainty Principle,” Vistas in Astronomy, Vol. 37, 1993, pp. 249-252.
http://dx.doi.org/10.1016/0083-6656(93)90040-Q
[33]A. Connes, “Non-commutative Geometry,” Academic Press, San Diego, 1994.
[34]M. S. El Naschie, “Penrose Universe and Cantorian Space-Time as a Model for Non-Commutative Quantum Geometry,” Chaos, Solitons & Fractals, Vol. 9, No. 6, 1998, pp. 931-933.
http://dx.doi.org/10.1016/S0960-0779(98)00077-0
[35]M. S. El Naschie, “Quantum Gravity Unification via Transfinite Arithmetic and Geometrical Averaging,” Chaos, Solitons & Fractals, Vol. 35, No. 2, 2008, pp. 252-256. http://dx.doi.org/10.1016/j.chaos.2007.07.019
[36]M. S. El Naschie, “On a Transfinite Symmetry Group with 10 to the Power of 19 Dimensions,” Chaos, Solitons & Fractals, Vol. 36, No. 3, 2008, pp. 539-541.
http://dx.doi.org/10.1016/j.chaos.2007.09.006
[37]Y. Tanaka, “The Mass Spectrum of Hadrons and E-Infi- nity Theory,” Chaos, Solitons & Fractals, Vol. 27, No. 4, 2006, pp. 851-863.
http://dx.doi.org/10.1016/j.chaos.2005.04.080
[38]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. http://dx.doi.org/10.1016/j.chaos.2007.09.018
[39]M. S. El Naschie, “Quantum E-Infinity Field Theoretical Derivation of Newton’s Gravitational Constant,” International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 8, No. 4, 2007, pp. 469-474.
[40]M. S. El Naschie, “From E-Eight to E-Infinity,” Chaos, Solitons & Fractals, Vol. 35, No. 2, 2008, pp. 285-290.
http://dx.doi.org/10.1016/j.chaos.2007.06.111
[41]M. S. El Naschie, “Higgs Mechanism, Quarks Confinement and Black Holes as a Cantorian Space-Time Phase Transition Scenario,” Chaos, Solitons & Fractals, Vol. 41, No. 2, 2009, pp. 869-874.
http://dx.doi.org/10.1016/j.chaos.2008.04.013
[42]M. S. El Naschie, “On Phase Transition to Quarks Confinement,” Chaos, Solitons & Fractals, Vol. 38, No. 2, 2008, pp. 332-333.
http://dx.doi.org/10.1016/j.chaos.2008.03.003
[43]M. S. El Naschie, “On Quarks Confinement and Asymptotic Freedom,” Chaos, Solitons & Fractals, Vol. 37, No. 5, 2008, pp. 1289-1291.
http://dx.doi.org/10.1016/j.chaos.2008.02.002
[44]M. S. El Naschie, “The Internal Dynamics of the Exceptional Lie Symmetry Groups Hierarchy and the Coupling Constants of Unification,” Chaos, Solitons & Fractals, Vol. 38, No. 4, 2008, pp. 1031-1038.
http://dx.doi.org/10.1016/j.chaos.2008.04.028
[45]M. S. El Naschie, “The Exceptional Lie Symmetry Groups Hierarchy and the Expected Number of Higgs Bosons,” Chaos, Solitons & Fractals, Vol. 35, No. 2, 2008, pp. 268-273. http://dx.doi.org/10.1016/j.chaos.2007.07.036
[46]M. S. El Naschie, “On D. Gross’ Criticism of S. Eddington and an Exact Calculation of ,” Chaos, Solitons & Fractals, Vol. 32, No. 4, 2007, pp. 1245-1249. http://dx.doi.org/10.1016/j.chaos.2006.10.035
[47]M. S. El Naschie, “Rigorous Derivation of the Inverse Electromagnetic Fine Structure Constant ā = 1/137.036 Using Super String Theory and the Holographic Boundary of E-Infinity,” Chaos, Solitons & Fractals, Vol. 32, No. 3, 2007, pp. 893-895.
http://dx.doi.org/10.1016/j.chaos.2006.09.055
[48]I. Affleck, “Golden Ratio Seen in a Magnet,” Nature, Vol. 464, No. 18, 2010, pp. 362-363.
http://dx.doi.org/10.1038/464362a
[49]M. S. El Naschie, “Von Neumann Geometry and E-Infinity Quantum Spacetime,” Chaos, Solitons & Fractals, Vol. 9, No. 12, 1998, pp. 2023-2030.
[50]M. S. El Naschie, “Arguments for the Compactness and Multiple Connectivity of Our Cosmic Spacetime,” Chaos, Solitons & Fractals, Vol. 41, No. 5, 2009, pp. 2787-2789. http://dx.doi.org/10.1016/j.chaos.2008.10.011
[51]M. S. El Naschie, “Banach-Tarski Theorem and Cantorian Micro Spacetime,” Chaos, Solitons & Fractals, Vol. 5, No. 8, 1995, pp. 1503-1508.
http://dx.doi.org/10.1016/0960-0779(95)00052-6
[52]M. S. El Naschie, “A Review of Applications and Results of E-Infinity Theory,” International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 8, No. 1, 2007, pp. 11-20.
[53]M. S. El Naschie, “The Quantum Gravity Immirzi Pa- rameter—A General Physical and Topological Interpretation,” Gravitation and Cosmology, Vol. 19, No. 3, 2013, pp. 151-155.
http://dx.doi.org/10.1134/S0202289313030031
[54]M. S. El Naschie, “A Resolution of the Cosmic Dark Energy via a Quantum Entanglement Relativity Theory,” Journal of Quantum Information Science, Vol. 3, No. 1, 2013, pp. 23-26.
http://dx.doi.org/10.4236/jqis.2013.31006
[55]M. S. El Naschie, “Topological-Geometrical and Physical Interpretation of the Dark Energy of the Cosmos as a ‘Halo’ Energy of the Schrodinger Quantum Wave,” Journal of Modern Physics, Vol. 4, No. 5, 2013, pp. 591-596.
http://dx.doi.org/10.4236/jmp.2013.45084
[56]M. S. El Naschie, “The Missing Dark Energy of the Cosmos from Light Cone Topological Velocity and Scaling the Planck Scale,” Open Journal of Microphysics, Vol. 3, No. 3, 2013, pp. 64-70.
http://dx.doi.org/10.4236/ojm.2013.33012
[57]M. S. El Naschie, “What Is the Missing Dark Energy in a Nutshell and the Hawking-Hartle Quantum Wave Collapse,” International Journal of Astronomy and Astrophysics, Vol. 3, No. 3, 2013, pp. 205-211.
http://dx.doi.org/10.4236/ijaa.2013.33024
[58]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. 55-59.
[59]L. Marek-Crnjac, “Modification of Einstein’s E = mc2 to E = mc2/22,” American Journal of Modern Physics, Vol. 2, No. 5, 2013, pp. 255-263.
[60]M. S. El Naschie, “The Quantum Entanglement behind the Missing Dark Energy,” Journal of Modern Physics and Applications, Vol. 2, No. 1, 2013, pp. 88-96.
[61]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.
http://dx.doi.org/10.4236/jmp.2013.46103
[62]J.-H. He, “Special Issue on Recent Developments on Dark Energy and Dark Matter,” Fractal Space-Time and Non-commutative Geometry in Quantum and High Energy Physics, Vol. 3, No. 1, 2013.
[63]M. S. El Naschie and A. Helal, “Dark Energy Explained via the Hawking-Hartle Quantum Wave and the Topology of Cosmic Crystallography,” International Journal of As- tronomy and Astrophysics, Vol. 3, No. 3, 2013, pp. 318- 343. http://dx.doi.org/10.4236/ijaa.2013.33037
[64]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.
http://dx.doi.org/10.4236/jqis.2011.12007
[65]M. S. El Naschie, “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.
[66]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.
http://dx.doi.org/10.4236/jqis.2013.32011
[67]M. S. El Naschie, “The Hydrogen Atom Fractal Spectra, the Missing Dark Energy of the Cosmos and Their Hardy Quantum Entanglement,” International Journal of Modern Nonlinear Theory and Application, Vol. 2, No. 3, 2013, pp. 167-169.
http://dx.doi.org/10.4236/ijmnta.2013.23023
[68]M. S. El Naschie, “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.
http://dx.doi.org/10.4236/ijmnta.2013.22014
[69]M. Krizek and L. Somer, “Antigravity—Its Manifestation and Origin,” International Journal of Astronomy and Astrophysics, Vol. 3, No. 3, 2013, pp. 227-235.
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[73]M. Pusey, J. Barrett and T. Randolph, “On the Reality of Quantum State,” Nature Physics, Vol. 8, 2012, pp. 475- 478.
[74]M. S. El Naschie, “On Twisters in Cantorian E-Infinity Space,” Chaos, Solitons & Fractals, Vol. 12, No. 4, 2011, pp. 741-746.
http://dx.doi.org/10.1016/S0960-0779(00)00193-4
[75]M. S. El Naschie, “On the Uncertainty of Cantorian Geometry and the Two-Slit Experiment,” Chaos, Solitons & Fractals, Vol. 9, No. 3, 1998. pp. 517-529.
http://dx.doi.org/10.1016/S0960-0779(97)00150-1
[76]M. S. El Naschie, “Fractal Black Holes and Information,” Chaos, Solitons & Fractals, Vol. 29, No. 1, 2006, pp. 23-35. http://dx.doi.org/10.1016/j.chaos.2005.11.079
[77]M. S. El Naschie, “Wild Topology, Hyperbolic Geometry and Fusion Algebra of High Energy Particle Physics,” Chaos, Solitons & Fractals, Vol. 13, No. 9, 2002, pp. 1935-1945. http://dx.doi.org/10.1016/S0960-0779(01)00242-9
[78]M. S. El Naschie, “Quantum Loops, Wild Topology and Fat Cantor Sets in Transfinite High Energy Physics,” Chaos, Solitons & Fractals, Vol. 13, No. 5, 2002, pp. 1167-1174.
http://dx.doi.org/10.1016/S0960-0779(01)00210-7
[79]M. S. El Naschie, “Average Symmetry, Stability and Ergodicity of Multidimensional Cantor Sets,” II Nuovo Cimento B Series 11, Vol. 109, No. 2, 1994, pp. 149-157.
http://dx.doi.org/10.1007/BF02727425
[80]M. S. El Naschie, “The VAK of Vacuum Fluctuation, Spontaneous Self-Organization and Complexity Theory Interpretation of High Energy Particle Physics and the Mass Spectrum,” Chaos, Solitons & Fractals, Vol. 18, No. 2, 2003, pp. 401-420.
http://dx.doi.org/10.1016/S0960-0779(03)00098-5
[81]L. Marek-Crnjac, G. Iovane, S. I. Nada and T. Zhong, “The Mathematical Theory of Finite and Infinite Dimensional Topological Spaces and Its Relevance to quantum gravity,” Chaos, Solitons & Fractals, Vol. 42, No. 4, 2009, pp. 1974-1979.
http://dx.doi.org/10.1016/j.chaos.2009.03.142
[82]M. S. El Naschie, “The Feynman Path Integral and E-Infinity from Two-Slit Gedanken Experiment,” International Journal of Nonlinear Science & Numerical Simulation, Vol. 6, No. 4, 2005, pp. 335-342.
[83]M. S. El Naschie, “Mohamed El Naschie Answers a Few Questions about this Month’s Emerging Research Front in the Field of Physics,” Thomason Essential Science Indicators. http://esi-topics.com/erf/2004/october04-MohamedElNaschie.html
[84]M. S. El Naschie, “Revising Einstein’s E = mc2: A Theoretical Resolution of the Mystery of Dark Energy,” Conference Program and Abstracts of The Fourth Arab Int. Conference in Physics & Material Science, Bibliotheca Alexandrina, Alexandria, October 2012, pp. 1-3.
[85]M. S. El Naschie, “Nash Embedding of Witten’s M-Theory and the Hawking-Hartle Quantum Wave of Dark Energy,” Journal of Modern Physics, Vol. 4, No. 10, 2013, pp. 1417-1428.
http://dx.doi.org/10.4236/jmp.2013.410170
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From Yang-Mills Photon in Curved Spacetime to Dark Energy Density

From Yang-Mills Photon in Curved Spacetime to Dark Energy Density
We start from quantum field theory in curved spacetime to derive a new Einstein-like energy mass relation of the type E=γmc2 where γ=1/22 is a Yang-Mills Lorentzian factor, m is the mass and c is the velocity of light. Although quantum field in curved spacetime is not a complete quantum gravity theory, our prediction here of 95.4545% dark energy missing in the cosmos is almost in complete agreement with the WMAP and supernova measurements. Finally, it is concluded that the WMAP and type 1a supernova 4.5% measured energy is the ordinary energy density of the quantum particle while the 95.5% missing dark energy is the energy density of the quantum wave. Recalling that measurement leads to quantum wave collapse, it follows that dark energy as given by E(D) = mc2(21/22) cannot be detected using conventional direct measurement although its antigravity effect is manifested through the increasing rather than decreasing speed of cosmic expansion.
KEYWORDS
Yang-Mills Theory; Dark Energy; Quantum Field in Curved Space; String Theory

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Cite this paper
M. Naschie, "From Yang-Mills Photon in Curved Spacetime to Dark Energy Density," Journal of Quantum Information Science, Vol. 3 No. 4, 2013, pp. 121-126. doi: 10.4236/jqis.2013.34016.
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[10]J. H. He and L. Marek-Crnjac, “Mohamed El Naschie’s Revision of Albert Einstein’s E = mc2: A Definite Resolution of the Mystery of the Missing Dark Energy of the Cosmos,” IJMNTA, No. 1, 2013, pp. 55-59.
[11]L. Marek-Crnjac, “Modification of Einstein’s E = mc2 to E = mc2/22,” American Journal of Modern Physics, Vol. 2, No. 5, 2013, pp. 255-263.
[12]M. S. El Naschie, “The Quantum Gravity Immirzi Parameter— A General Physical and Topological Interpretation,” Gravitation and Cosmology, Vol. 19, No. 3, 2013, pp. 151-155.
http://dx.doi.org/10.1134/S0202289313030031
[13]M. S. El Naschie, “What Is the Missing Dark Energy in a Nutshell and the Hawking-Hartle Quantum Wave Collapse,” International Journal of Astronomy & Astrophysics, Vol. 3, No. 3, 2013, pp. 205-211.
http://dx.doi.org/10.4236/ijaa.2013.33024
[14]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. http://dx.doi.org/10.4236/jmp.2013.46103
[15]M. S. El 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.
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[17]M. S. El Naschie, “On the Unification of the Fundamental Forces and Complex Time in E-Infinity Space,” Chaos, Solitons & Fractals, Vol. 11, No. 7, 2000, pp. 1149-1162.
http://dx.doi.org/10.1016/S0960-0779(99)00185-X
[18]M. S. El Naschie, “Transfinite Neoimpressionistic Reality of Quantum Spacetime,” New Advances in Physics, Vol. 1, No. 2, 2007, pp. 111-122.
[19]M. S. El Naschie, “On the Uncertainty of Cantorian Geometry and the Two-Slit Experiment,” Chaos, Solitons & Fractals, Vol. 9, No. 3, 1998, pp. 517-529.
http://dx.doi.org/10.1016/S0960-0779(97)00150-1
[20]M. S. El Naschie, “Gravitational Instanton in Hilbert Space and the Mass of High Energy Elementary Particles,” Chaos, Solitons & Fractals, Vol. 20, No. 5, 2004, pp. 917-923.
http://dx.doi.org/10.1016/j.chaos.2003.11.001
[21]M. S. El Naschie, “How Gravitational Instanton Could Solve the Mass Problem of the Standard Model of High Energy Particle Physics,” Chaos, Solitons & Fractals, Vol. 21, No. 1, 2004, p. 249-260.
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[22]M. S. El Naschie, “Topological Defects in the Symplictic Vacuum, Anomalous Positron Production and the Gravitational Instanton,” International Journal of Modern Physics E, Vol. 13, No. 4, 2004, pp. 835-849.
http://dx.doi.org/10.1142/S0218301304002429
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[24]L. Marek-Crnjac, “On the Unification of All Fundamental Forces in a Fundamentally Fuzzy Cantorian E-Infinity Manifold and High Energy Particle Physics,” Chaos, Solitons & Fractals, Vol. 20, No. 4, 2004, pp. 669-682.
http://dx.doi.org/10.1016/j.chaos.2003.10.013
[25]M. Pusey, J. Barrett and T. Randolph, “On the Reality of Quantum State,” Nature Physics, Vol. 8, 2012, pp. 475-478.
[26]M. S. 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.
http://dx.doi.org/10.4236/jmp.2013.45084
[27]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, 2013, pp. 57-77.
http://dx.doi.org/10.4236/jqis.2013.32011
[28]M. S. El Naschie, “A Resolution of the Cosmic Dark Energy via a Quantum Entanglement Relativity Theory,” Journal of Quantum Information Science, Vol. 3, No. 1, 2013, pp. 23-26.
http://dx.doi.org/10.4236/jqis.2013.31006
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A Rindler-KAM Spacetime Geometry and Scaling the Planck Scale Solves Quantum Relativity and Explains Dark Energy

A Rindler-KAM Spacetime Geometry and Scaling the Planck Scale Solves Quantum Relativity and Explains Dark Energy
We introduce an ultra high energy combined KAM-Rindler fractal spacetime quantum manifold, which increasingly resembles Einstein’s smooth relativity spacetime, with decreasing energy. That way we derive an effective quantum gravity energy-mass relation and compute a dark energy density in complete agreement with all cosmological measurements, specifically WMAP and type 1a supernova. In particular we find that ordinary measurable energy density is given by E1= mc2 /22 while the dark energy density of the vacuum is given by E2 = mc2 (21/22). The sum of both energies is equal to Einstein’s energy E = mc2. We conclude that E= mc2 makes no distinction between ordinary energy and dark energy. More generally we conclude that the geometry and topology of quantum entanglement create our classical spacetime and glue it together and conversely quantum entanglement is the logical consequence of KAM theorem and zero measure topology of quantum spacetime. Furthermore we show via our version of a Rindler hyperbolic spacetime that Hawking negative vacuum energy, Unruh temperature and dark energy are different sides of the same medal.
KEYWORDS
Quantum Relativity; KAM Theorem; Dark Energy; Hawking Negative Energy Vacuum Fluctuation; Unruh Temperature; Rindler Spacetime; Einstein-Rosen Bridges; Action at Distance; Susslin Operation

Cite this paper
M. Naschie, "A Rindler-KAM Spacetime Geometry and Scaling the Planck Scale Solves Quantum Relativity and Explains Dark Energy," International Journal of Astronomy and Astrophysics, Vol. 3 No. 4, 2013, pp. 483-493. doi: 10.4236/ijaa.2013.34056.
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[16]M. S. El Naschie, “Towards a General Transfinite Set Theory for Quantum Mechanics,” Fractal Space-Time and Non-Commutative Geometry in High Energy Physics, Vol. 2, No. 2, 2012, pp. 135-142.
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[21]M. S. El Naschie and O. E. Rossler, “The Zero Measure Fractal Ghost inside Quantum Mechanics,” Fractal Space-Time and Non-Commutative Geometry in High Energy Physics, Vol. 2, No. 1, 2012, p. 56.
[22]J.-H. He, T. Zhong, L. Xu, L. Marek-Crnjac, S. Nada and M. Atef Helal, “The Importance of the Empty Set and Noncommutative Geometry in Underpinning the Foundations of Quantum Physics,” Nonlinear Science Letters B, Vol. 1, No. 1, 2011, p. 15.
[23]M. S. El Naschie, “Quantum Collapse of Wave Interference Pattern in the Two-slit Experiment: A Set Theoretical Resolution,” Nonlinear Science Letters B, Vol. 2, No. 1, 2011, p. 1.
[24]M. S. El Naschie, L. Marek-Crnjac, J.-H. He and M. Atef Helal, “Computing the Missing Dark Energy of a Clopen Universe which Is Its Own Multiverse in Addition to Being Both Flat and Curved,” Fractal Space-Time and Non-Commutative Geometry in High Energy Physics, Vol. 3, No. 1, 2013, p. 3.
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[26]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. http://dx.doi.org/ 10.4236/jmp.2013.46103
[27]M. S. El Naschie, “Topological-Geometrical and Physical Interpretation of the Dark Energy of the Cosmos as a “Halo” Energy of the Schrodinger Quantum Wave,” Journal of Modern Physics, Vol. 4, No. 5, 2013, pp. 591-596. http://dx.doi.org/10.4236/jmp.2013.45084
[28]M. S. El Naschie, “The Quantum Gravity Immirzi Parameter—A General Physical and Topological Interpretation,” Gravitation and Cosmology, Vol. 19, No. 3, 2013, pp. 151-155. http://dx.doi.org/ 10.1134/S0202289313030031
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[40]M. S. El Naschie, “Fractal Black Holes and Information,” Chaos, Solitons & Fractals, Vol. 29, No. 1, 2006, pp. 23-35. http://dx.doi.org/10.1016/j.chaos.2005.11.079
[41]M. S. El Naschie, “Knots and Exceptional Lie Groups as Building Blocks of High Energy Particle Physics,” Chaos, Solitons & Fractals, Vol. 41, No. 4, 2009, pp. 1799-1803. http://dx.doi.org/10.1016/ j.chaos.2008.07.025
[42]M. S. El Naschie, “Arguments for the Compactness and Multiple Connectivity of Our Cosmic Spacetime,” Chaos, Solitons & Fractals, Vol. 41, No. 5, 2009, pp. 2787-2789. http://dx.doi.org/10. 1016/j.chaos.2008.10.011
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[46]M. S. El Naschie, “Determining the Temperature of the Microwave Background Radiation from the Topology and Geometry of Spacetime,” Chaos, Solitons & Fractals, Vol. 14, No. 7, 2002, pp. 1121-1126. http://dx.doi.org/10.1016/S0960-0779(02)00172-8
[47]M. S. El Naschie, “On the Vital Role Played by the Electron-Volt Units System in High Energy Physics and Mach’s Principle of ‘Denkokonomie’,” Chaos, Solitons & Fractals, Vol. 28, No. 5, 2006, pp. 1366-1371. http://dx.doi.org/10.1016/j.chaos.2005.11.001
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[49]M. S. El Naschie, “Modular Groups in Cantorian E(∞) High-Energy Physics,” Chaos, Solitons & Fractals, Vol. 16, No. 2, 2003, pp. 353-366. http://dx.doi.org/10.1016/ S0960-0779(02)00440-X
[50]M. S. El Naschie, “Quantum Loops, Wild Topology and Fat Cantor Sets in Transfinite High-Energy Physics,” Chaos, Solitons & Fractals, Vol. 13, No. 5, 2002, pp. 1167-1174. http://dx.doi.org/10. 1016/S0960-0779(01)00210-7
[51]M. S. El Naschie, “Wild Topology, Hyperbolic Geometry and Fusion Algebra of High Energy Particle Physics,” Chaos, Solitons & Fractals, Vol. 13 No. 9, 2002, pp. 1935-1945. http://dx.doi.org/10.1016/ S0960-0779(01)00242-9
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Monday, August 26, 2013

Dark Energy from Kaluza-Klein Spacetime and Noether’s Theorem via Lagrangian Multiplier Method

The supposedly missing dark energy of the cosmos is found quantitatively in a direct analysis without involving ordinary energy. The analysis relies on five dimensional Kaluza-Klein spacetime and a Lagrangian constrained by an auxiliary condition. Employing the Lagrangian multiplier method, it is found that this multiplier is equal to the dark energy of the cosmos and is given by  where E is energy, m is mass, c is the speed of light,  and λ is the Lagrangian multiplier. The result is in full agreement with cosmic measurements which were awarded the 2011 Nobel Prize in Physics as well as with the interpretation that dark energy is the energy of the quantum wave while ordinary energy is the energy of the quantum particle. Consequently dark energy could not be found directly using our current measurement methods because measurement leads to wave collapse leaving only the quantum particle and its ordinary energy intact.
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What Is the Missing Dark Energy in a Nutshell and the Hawking-Hartle Quantum Wave Collapse

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)(mc2) 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)(mc2) 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 setD(-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 densityE(total) = E(0) + E(D) = mc2 = 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.
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The Missing Dark Energy of the Cosmos from Light Cone Topological Velocity and Scaling of the Planck Scale

The paper presents an exact analysis leading to an accurate theoretical prediction of the amount of the mysteriously missing hypothetical dark energy density in the cosmos. The value found, namely 95.4915028% is in full agreement with earlier analysis, the WMAP and the supernova cosmic measurements. The work follows first the strategy of finding a critical point which separates a semi-classical regime from a fully relativistic domain given by topological unit interval velocity parameter then proceeds to wider aspects of a topological quantum field of fractal unit interval. This idea of a critical velocity parameter was first advanced by Sigalotti and Mejias in 2006 who proposed a critical value equal . A second interesting proposal made in 2012 by Hendi and Sharifzadeh set the critical point at 0.8256645. The present analysis is based upon a light cone velocity quantized coordinate. This leads to the same quantum relativity energy mass relation found in earlier publications by rescaling that of Einstein’s special relativity. Two effective quantum gravity formulae are obtained. The first is for the ordinary measurable energy of the quantum particle  while the second is for dark energy density of the quantum wave which we cannot measure directly and we can only infer its existence from the measured accelerated expansion of the universe E(D) = where . The critical velocity parameter in this case arises naturally to be . The results so obtained are validated using a heuristic Lorentzian transformation. Finally the entire methodology is put into the wider perspective of a fundamental scaling theory for the Planck scale proposed by G. Gross.
To continue reading the paper please downloads it from here
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