Dark Energy Introduction

Thursday, December 26, 2013

Chaotic Fractal Tiling for the Missing Dark Energy and Veneziano Model

Chaotic Fractal Tiling for the Missing Dark Energy and Veneziano Model
Author(s)
L. Marek-Crnjac, M. S. El Naschie
The formula for the quantum amplitude of the Veneziano dual resonance model is shown to be formally analogous to the dimensionality of a K-theoretical fractal quotient manifold of the non-commutative geometrical type. Subsequently this analogy is used to deduce the ordinary energy of the quantum particle and the dark energy of the quantum wave. The results agree completely with cosmological measurements. Even more surprisingly the sum of both energy expressions turned out to be exactly equal to Einstein’s iconic formula E = mc2. Consequently Einstein’s formula makes no distinction between ordinary and dark energy.
KEYWORDS
Hausdorff Dimension; Cantor Set; Dark Energy; Kähler Manifold; Quantum Entanglement; Veneziano Model


Cite this paper
L. Marek-Crnjac and M. Naschie, "Chaotic Fractal Tiling for the Missing Dark Energy and Veneziano Model,"Applied Mathematics, Vol. 4 No. 11B, 2013, pp. 22-29. doi: 10.4236/am.2013.411A2005.
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Nash Embedding of Witten’s M-Theory and the Hawking-Hartle Quantum Wave of Dark Energy

Nash Embedding of Witten’s M-Theory and the Hawking-Hartle Quantum Wave of Dark Energy
Author(s)
Mohamed S. El Naschie
Euclidean embedding of the 11-dimensional M-theory turned out to require a very large space leaving lavish amounts of 242 dimensional pseudo truly empty “regions” devoid of space and time and consequently of anything resembling ordinary physical energy density. It is shown here using Nash embedding that the ratio of “solid” M-theory spacetime to its required embedding “non-spacetime” is 1/22 for a classical theory and1/22.18033989 for an analogous fractal theory. This then leads to a maximal ordinary energy density equation equal to that of Einstein’s famous formula E=mc2 but multiplied with  in full agreement with previous results obtained using relatively more conventional methods including running the electromagnetic fine structure constant in the exact solution of the hydrogen atom. Consequently, the new equation corresponds to a quantum relativity theory which unlike Einstein’s original equation gives quantitative predictions which agree perfectly with the cosmological measurements of WMAP and the analysis of certain supernova events. Never the less in our view dark energy also exists being the energy of the quantum wave amounting to 95.5 present of the total Einstein theoretical energy which is blind to any distinction between ordinary energy of the quantum particle and the dark energy of the quantum wave. However, since measurement leads to the collapse of the Hawking-Hartle quantum wave, dark energy being a quantum wave non-ordinary energy could not possibly be measured in the usual way unless highly refined quantum wave non-demolition technology is developed if possible. It is a further reason that dark energy having a different sign to ordinary energy is the cause behind the anti gravity force which is pushing the universe apart and accelerating cosmic expansion. Consequently it can be seen as the result of anticlastic Cartan-like curvature caused by extra compactified dimensions of spacetime. A simple toy model demonstration of the effect of curvature in a “material” space is briefly discussed.
KEYWORDS
Nash Euclidean Embedding; Quantum Entanglement; Dark Energy of the Quantum Wave; Quantum Gravity; Ordinary Energy of the Quantum Particle; Hawking-Hartle Wave of the Cosmos; Quantum Wave Non-Demolition; Witten’s M-Theory



Cite this paper
M. 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. doi: 10.4236/jmp.2013.410170.
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Quantum Gravity and Dark Energy Using Fractal Planck Scaling

Quantum Gravity and Dark Energy Using Fractal Planck Scaling
Author(s)
L. Marek Crnjac, M. S. El Naschie
Following an inspiring idea due to D. Gross, we arrive at a topological Planck energy Ep and a corresponding topological Planck length  effectively scaling the Planck scale from esoterically large  and equally esoterically small  numbers to a manageably  where P(H) is the famous Hardy’s probability for quantum entanglement which amounts to almost 9 percent and  Based on these results, we conclude the equivalence of Einstein-Rosen “wormhole” bridges and Einstein’s Podolsky-Rosen’s spooky action at a distance. In turn these results are shown to be consistent with distinguishing two energy components which results in , namely the quantum zero set particle component  which we can measure and the quantum empty set wave component which we cannot measure , i.e. the missing dark energy. Together the two components add to  where E is the total energy, m is the mass and c is the speed of light. In other words, the present new derivation of the world’s most celebrated formula explains in one stroke the two most puzzling problems of quantum physics and relativistic cosmology, namely the physicomathematical meaning of the wave function and the nature of dark energy. In essence they are one and the same when looked upon from the view point of quantum-fractal geometry.
KEYWORDS
Scaling the Planck Scale; Quantum Entanglement; Dark Energy; Kaluza-Klein Space-Time; Worm Hole; Action at a Distance; Unruh Temperature; Hawking’s Negative Energy; Black Hole Physics; Cantorian Geometry; Fractals in Physics

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Cite this paper
L. Crnjac and M. Naschie, "Quantum Gravity and Dark Energy Using Fractal Planck Scaling," Journal of Modern Physics, Vol. 4 No. 11A, 2013, pp. 31-38. doi: 10.4236/jmp.2013.411A1005.
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[53]J.-H. He and M. S. El Naschie, Fractal Space-Time and Non-Commutative Geometry in High Energy Physics, Vol. 3, 2013, pp. 59-62.
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http://dx.doi.org/10.4236/ojm.2013.33012
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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.
http://dx.doi.org/10.4236/ijaa.2013.33027
[70]C. Calcagni, J. Magueijo and D. Fernandez, “Varying Electric Charges in Multi-Scale Spacetimes,” 2013.
[71]D. Finkelstein, “Quantum Sets and Clifford Algebras,” International Journal of Theoretical Physics, Vol. 21, No. 6-7, 1982, pp. 489-503.
http://dx.doi.org/10.1007/BF02650180
[72]L. H. Kauffman, “Virtual Logic,” Systems Research, Vol. 13, No. 3, 1996, pp. 293-310.
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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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