Dark Energy Introduction

Monday, May 12, 2014

Entanglement of E8E8 Exceptional Lie Symmetry Group Dark Energy, Einstein’s Maximal Total Energy and the Hartle-Hawking No Boundary Proposal as the Explanation for Dark Energy

Author(s)    
The present note is concerned with two connected and highly important fundamental questions of physics and cosmology, namely if E8E8 Lie symmetry group describes the universe and where cosmic dark energy comes from. Furthermore, we reason following Wheeler, Hartle and Hawking that since the boundary of a boundary is an empty set which models the quantum wave of the cosmos, then it follows that dark energy is a fundamental physical phenomenon associated with the boundary of the holographic boundary. This leads directly to a clopen universe which is its own Penrose tiling-like multiverse with energy density in full agreement with COBE, WMAP and Type 1a supernova cosmic measurements.
KEYWORDS

Cite this paper
Naschie, M. (2014) Entanglement of E8E8 Exceptional Lie Symmetry Group Dark Energy, Einstein’s Maximal Total Energy and the Hartle-Hawking No Boundary Proposal as the Explanation for Dark Energy. World Journal of Condensed Matter Physics, 4, 74-77. doi: 10.4236/wjcmp.2014.42011.
[1]El Naschie, M.S. (2013) 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, 2, 43-54.
http://dx.doi.org/10.4236/ijmnta.2013.21005
[2]El Naschie, M.S. (2013) From Yang-Mills photon in Curved Spacetime to Dark Energy Density. Journal of Quantum Information Science, 3, 121-126.
http://dx.doi.org/10.4236/jqis.2013.34016
[3]El Naschie, M.S. (2014) Pinched Material Einstein Spacetime Produces Accelerated Cosmic Expansion. International Journal of Astronomy and Astrophysics, 4, 80-90.
http://dx.doi.org/10.4236/ijaa.2014.41009
[4]El Naschie, M.S. (2014) Capillary Surface Energy Elucidation of the Cosmic Dark Energy-Ordinary Energy Duality. Open Journal of Fluid Dynamics, 4, 15-17.
http://dx.doi.org/10.4236/ojfd.2014.41002
[5]El Naschie, M.S. (2014) Why E Is Not Equal to mc2. Journal of Modern Physics, in Press.
[6]Linder, E., (2008) Dark Energy. “Scholarpediablog”. The Peer-Reviewed Open Access Encyclopedia, Scholarpedia, 3, Article ID: 4900.
[7]Amendola, L. and Tsujikawa, S. (2010) Dark Energy. Cambridge University Press, Cambridge.
http://dx.doi.org/10.1017/CBO9780511750823
[8]Copeland, E.J., Sami, M. and Tsujikawa, S. (2006) Dynamics of Dark Energy. arXiv: hep-th/0603057V3
[9]Coldea, R. et al. (2010) Quantum Criticality in an Ising Chain: Experimental Evidence for Emergent E8 Symmetry. Science, 327, 177-180.
http://dx.doi.org/10.1126/science.1180085
[10]El Naschie, M.S. (2013) The Quantum Entanglement behind the Missing Dark Energy. Journal of Physics and Applications, 2, 88-96.
[11]Kheyfets, A. and Wheeler, J.A. (1986) Boundary of a Boundary Principle and Geometric Structure of Field Theories. International Journal of Theoretical Physics, 25, 573-580.
[12]Wheeler, J.A. (1989) Information, Physics, Quantum the Search for Links. The 3rd International Symposium Foundations of Quantum Mechanics, Tokyo, 310-336.
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http://dx.doi.org/10.1103/PhysRevD.28.2960
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http://dx.doi.org/10.1103/PhysRevLett.100.201301
[15]Henle, J.M.(1986) An Outline of Set Theory. Springer, New York.
http://dx.doi.org/10.1007/978-1-4613-8680-3
[16]Devlin, K. (1993) The Joy of Sets. Springer, New York (in Particular See p. 5).
[17]El Naschie, M.S. (2013) 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, 4, 591-596.
http://dx.doi.org/10.4236/jmp.2013.45084
[18]El Naschie, M.S. (2013) Nash embedding of Witten’s M-Theory and the Hawking-Hartle Quantum Wave of Dark Energy. Journal of Modern Physics, 4, 1417-1428.
http://dx.doi.org/10.4236/jmp.2013.410170
[19]El Naschie, M.S. and Helal, A. (2013) Dark energy Explained via the Hawking-Hartle Quantum Wave and the Topology of Cosmic Crystallography. International Journal of Astronomy and Astrophysics, 3, 318-343.
http://dx.doi.org/10.4236/ijaa.2013.33037
[20]Helal, M.A., Marek-Crnjac, L. and He, J.-H. (2013) The Three Page Guide to the Most Important Results of M. S. El Naschie’s Research in E-Infinity and Quantum Physics and Cosmology. Open Journal of Microphysics, 3, 141-145.
http://dx.doi.org/10.4236/ojm.2013.34020
[21]Marek-Crnjac, L. (2013) Cantorian Space-Time Theory—The Physics of Empty Sets in Connection with Quantum Entanglement and Dark Energy. Lambert Academic Publishing, Saarbrücken.
[22]El Naschie, M.S., Marek-Crnjac, L., He, J.-H. and Helal, M.A. (2013) Computing the Missing Dark Energy of a Clopen Universe Which Is Its Own Multiverse in Addition to Being Both Flat and Curved. Fractal Spacetime and Noncommutative Geometry in Quantum and High Energy Physics, 3, 3-10.
[23]Grossman, L. (2014) Ripples of the Multiverse. New Scientist, 221, 8-10.
http://dx.doi.org/10.1016/S0262-4079(14)60557-1
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Saturday, March 22, 2014

Logarithmic Running of ‘t Hooft-Polyakov Monopole to Dark Energy

  Full PDF Paper 

Authors 
M. S. El Naschie, Dept. of Physics, University of Alexandria, Alexandria, Egypt


To cite this article 
M. S. El Naschie, Logarithmic Running of ‘t Hooft-Polyakov Monopole to Dark Energy, International Journal of High Energy Physics. Vol. 1, No. 1, 2014, pp. 1-5. doi: 10.11648/j.ijhep.20140101.11

Abstract 
The paper presents a particle physicists’ interpretation of the mathematical abstract concept of a five dimensional empty set as the source of dark energy and dark matter. It turns out that the simplest alternative physical interpretation at least from the view point of the GUT unification of fundamental interaction is the theoretically well established but experimentally never found yet ‘t Hooft-Polyakov magnetic giant monopole with the predicted huge mass of ten to the power of 16 Gev. In fact it will be shown here using exact renormalization equations that running the preceding energy logarithmically leads to a prediction of the ordinary and the total dark energy density of the cosmos in complete agreement with our earlier result E(O) = mc2/22 and E(D) = mc2(21/22) based on the afore mentioned set theoretical concepts as well as with all the relatively recent cosmological measurements. The decisive steps in the present derivation consists of two realizations. First and to our deepest surprise and delight, E =γmc2 = mc2 is actually a unification formula uniting classical, relativistic and quantum mechanics where γ= 1 corresponds to a 100% energy density. Second and also not expectedly, the logarithmic running of ‘t Hooft-Polyakov’s monopole energy leads to a reduction factor γ= 1/λwhere λ=1/2 ln (M(monopole))/(m(electron))=22.18033989, in full agreement with our previous results using entirely different approaches. Finally the results are validated using ‘t Hooft’s dimensional regularization D = 4 ∈ by setting = 2∅^5 where ∅^5 is Hardy’s quantum entanglement and φ=2/ √5+1.

Keywords 
Dark energy, Grand Unification, Giant ‘T Hooft-Polyakov Monopole, Quantum Relativity Renormalization Equations, Fractal Spacetime, Quantum Field Theory, Super Symmetry, Dark Matter, Planckton, ‘T Hooft Renormalization
Reference 
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[06]M.S. El Naschie, A resolution of cosmic dark energy via a quantum entanglement relativity theory. J. Quantum Info. Sci., Vol. 3, No. 1, 2013, pp. 23-26.
  
[07]M.S. El Naschie, A Rindler-KAM spacetime geometry and scaling the Planck scale solves quantum relativity and explains dark energy. Int. J. of Astron. and Astrophys.Vol. 3, No. 4, 2013, pp. 483-493.
  
[08]M.S. El Naschie, From Yang-Mills photon in curved spacetime to dark energy density. J. Quantum Info. Sci., Vol. 3, No. 4, 2013, pp. 121-126.
  
[09]M.S. El Naschie and M.A. Helal, Dark energy explained via the Hawking-Hartle quantum wave and the topology of cosmic crystallography. Int. J. Astron. & Astrophys, Vol. 3, 3, 2013, pp. 318-343.
  
[10]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.” J. Mod. Phys., Vol. 4 , No. 5, 2013, pp. 591-596.
  
[11]L. Marek-Crnjac and Ji-Huan He, An invitation to El Naschie’s theory of Cantorian spacetime and dark energy. Int. J. of Astron. & Astrophys., Vol. 3, 2013, pp. 464-471.
  
[12]M.A. Helal, L. Marek-Crnjac and Ji-Huan He, The three page guide to the most important results of M.S. El Naschie’s research in E-infinity and quantum physics and cosmology. Open J. Microphys., Vol. 3, No. 4, 2013, pp. 141-145.
  
[13]M.S. El Naschie, Experimentally based theoretical arguments that Unruh’s temperature, Hawkings’s vacuum fluctuation and Rindler’s wedge are physically real. American J. of Modern Phys., Vol. 2, No. 6, 2013, pp. 57-361.
  
[14]L. Marek-Crnjac, Modification of Einstein’s E = mc2 to E = 1/22 mc2. American J. Modern Phys., Vol. 2, No. 5, 2013, pp. 255-263.
  
[15]L. Marek-Crnjac and M.S. El Naschie, Chaotic fractal tiling for the missing dark energy and Veneziano model. Appl. Math., Vol. 4, No. 11B, 2013, pp. 22-29.
  
[16]Ji-Huan 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. Int. J. Modern Nonlinear Sci. & Application., Vol. 2, No. 1, 2013, pp. 55-59.
  
[17]M.S. El Naschie, Dark energy via quantum field theory in curved spacetime. J. Mod. Phys. & Appli. Vol. 2, 2014, pp.
  
[18]Ji-Huan He and L. Marek-Crnjac, The quintessence of El Naschie’s theory of fractal relativity and dark energy. Fractal Spacetime & Noncommutative Geometry in Quantum & High Energy Phys., Vol. 3, No. 2, 2013, pp. 130-137.
  
[19]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. Int. J. Modern Nonlinear Sci. & Application., Vol. 2, No. 1, 2013, pp. 43-54.
  
[20]F. Hehl, Space-Time as Generalized Cosserat Coninuum. In “Mechanics of Generalized Continua”. Editor E. Kronev., Springer Verlag, Berlin, 1968. pp. 347-349.
  
[21]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.
  
[22]M.S. El Naschie, Extended renormalization group analysis for quantum gravity and Newton’s gravitation constant. Chaos, Solitons & Fractals, Vol. 35, No. 3, 2008, pp. 425-431.
  
[23]M.S. El Naschie, Asymptotic freedom and unification in a golden quantum field theory. Chaos, Solitons & Fractals, Vol. 36, No. 3, 2008, pp. 521-525.
  
[24]E. Goldfain, Renormalization group and the emergence of random fractal topology in quantum field theory. Chaos, Solitons & Fractals, Vol. 19, No. 5, 2004, pp. 1023-1030.
  
[25]M.S. El Naschie, Towards a quantum golden field theory. Int. J. of Nonlinear Sci. & Numerical simulation., Vol. 8, No. 4, 2007, pp. 477-482.
  
[26]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.
  
[27]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.
  
[28]M.S. El Naschie, SO (10) grand unification in a fuzzy setting. Chaos, Solitons & Fractals, Vol. 32, No. 3, 2007, pp. 958-961.
  
[29]M.S. El Naschie, SU(5) grand unification in a transfinite form. Chaos, Solitons & Fractals, Vol. 32, No. 2, 2007, pp. 370-374.
  
[30]P. Langacker, Grand unification. Scholarpedia 7(10):11419, 2012. (See in particular Fig. 3).
  
[31]D. Gross and M.J. Perry, Magnetic Monopoles in Kaluza-Klein Theories. Nuclear Phys. Vol. B226, 1983, pp. 29-48.
  
[32]M.S. El Naschie, Bounds on the number of possible Higgs particles using grand unification and exceptional Lie groups. Chaos, Solitons & Fractals, Vol. 37, No. 3, 2008, pp. 633-637.
  
[33]J.R. Ellis, Particle physicists’ candidates for dark matter. Phil. Trans. R. Soc. London A, Vol. 320(1556), 1986, pp. 475-485.
  
[34]Yong Tao, The validity of dimensional regularization method on fractal spacetime. Journal of Appl. Math. 2013. arXiv: http://dx.doi.org/10.1155/2013/308691.
  
[35]A. Elokaby: Knot wormholes and the dimensional invariant exceptional Lie groups and Stein sspace hierarchies. Chaos, Solitons & Fractals, Vol. 41, No. 4, 2009, pp. 1616 - 1618.
  
[36]M.J. Duff, The World in Eleven Dimensions. Inst. of Phys. Publications, Bristol 1999.
  
[37]G. ‘t Hooft, A Confrontation With Infinity. In “Frontiers of Fundamental Physics” 4. Editors B. Sidharth and M. Altaisky. Kluwer-Plenum, New York (2001), pp. 1-12.
  
[38]M.S. El Naschie, ‘t Hooft’s dimensional regularization implies transfinite Heterotic string theory and dimensional transmutation. In “Frontiers of Fundamental Physics” 4. Editors B. Sidharth and M. Altaisky. Kluwer-Plenum, New York (2001), pp. 81-86.
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Thursday, March 20, 2014

Calculating the Exact Experimental Density of the Dark Energy in the Cosmos Assuming a Fractal Speed of Light

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Author(s)
Mohamed S. El Naschie     
Fractal speed of light theory is a variation of Magueijo-Smolin varying speed of light (VSL) theoretical modification of Einstein’s energy mass relation. We use this theory to derive an exact value for the missing dark energy which is found to be in astonishing agreement with the latest result of the WMAP measurement and the independent supernova analysis. Thus while Einstein’s formula predicts 95.5% more energy than found in highly precise astrophysical measurement, our VSL- based calculation indicates an exact theoretical value of only 4.508497% real energy. Consequently, the exact conjectured missing dark energy must be 95.491502%. By any standards, this is an astounding confirmation for both the cosmological measurement and the VSL theory.
KEYWORDS
Nonlinear Dynamics; Fractals; Dark Energy; Quantum Gravity; Varying Speed of Light Theory

Cite this paper
M. Naschie, "Calculating the Exact Experimental Density of the Dark Energy in the Cosmos Assuming a Fractal Speed of Light," International Journal of Modern Nonlinear Theory and Application, Vol. 3 No. 1, 2014, pp. 1-5. doi: 10.4236/ijmnta.2014.31001.
[1]Amendola, L. and Tsujikawa, S. (2010) Dark Energy: Theory and Observations. Cambridge University Press, Cambridge. http://dx.doi.org/10.1017/CBO9780511750823
[2]Baryshev, Y. and Teerikorpi, P. (2002) Discovery of Cosmic Fractals. World Scientific, Singapore.
[3]Nottale, L. (2011) Scale Relativity. Imperial College Press, London.
[4]Ord, G. (1983) Fractal Space-Time: A Geometric Analogue of Relativistic Quantum Mechanics. Journal of Physics A: Mathematical and General, 16, 1869. http://dx.doi.org/10.1088/0305-4470/16/9/012
[5]El Naschie, M.S. (2011) Quantum Entanglement as a Consequence of a Cantorian Micro Spacetime Geometry. Journal of Quantum Information Science, 1, 50-53. http://www.SCRIP.org/journal/jqis
http://dx.doi.org/10.4236/jqis.2011.12007
[6]He, J.-H., et al. (2011) Quantum Golden Mean Entanglement Test as the Signature of the Fractality of Micro Spacetime. Nonlinear Science Letters B, 1, 45-50.
[7]El Naschie, M.S. (2009) The Theory of Cantorian Spacetime and High Energy Particle Physics (An Informal Review). Chaos, Solitons & Fractals, 41, 2635-2646. http://dx.doi.org/10.1016/j.chaos.2008.09.059
[8]El Naschie, M.S. (2004) A Review of E-Infinity Theory and the Mass Spectrum of High Energy Particle Physics. Chaos, Solitons & Fractals, 19, 209-236. http://dx.doi.org/10.1016/S0960-0779(03)00278-9
[9]Magueijo, J. and Smolin, L. (2002) Lorentz Invariance with an Invariant Energy Scale. Physical Review Letters, 88, Article ID:190403.
[10]Magueijo, J. (2003) Faster than the Speed of Light. William Heinemann, London.
[11]El Naschie, M.S. (2006) On an Eleven Dimensional E-Infinity Fractal Spacetime Theory. International Journal of Nonlinear Sciences and Numerical Simulation, 7, 407-409.
[12]El Naschie, M.S. (2006) The “Discrete” Charm of Certain Eleven Dimensional Spacetime Theory. International Journal of Nonlinear Sciences and Numerical Simulation, 7, 477-481.
[13]Duff, M. (1999) The World in Eleven Dimensions. IOP Publishing Ltd., Bristol.
[14]Yau, S.T. and Nadis, S. (2010) The Shape of Inner Space. Basic Book, Persens Group, New York.
[15]Randal, L. (2005) Warped Passages. Allen Lane-Penguin Books, London.
[16]Penrose, R. (2004) The Road to Reality. Jonathan Cape, London.
[17]Becker, K., Becker, M. and Schwarz, J. (2007) String Theory and M-Theory. Cambridge University Press, Cambridge.
[18]Schwarz, P.M. and Schwarz, J.H. (2004) Special Relativity from Einstein to Strings. Cambridge University Press, Cambridge.
[19]Hardy, L. (1993) Nonlocality of Two Particles without Inequalities for almost All Entangled States. Physical Review Letters, 71, 1665-1668.
[20]Bengtsson, I. and Zyczkowski, K. (2008) Geometry of Quantum States. Cambridge University Press, Cambridge.
[21]El Naschie, M.S. (2013) What Is the Missing Dark Energy in a Nutshell and the Hawking-Hartle Quantum Wave Collapse. International Journal of Astronomy and Astrophysics, 3, 205-211.
[22]Marek Crnjac, L. and El Naschie, M.S. (2013) Quantum Gravity and Dark Energy Using Fractal Planck Scaling. Journal of Modern Physics, 4, 31-38.
[23]Helal, M.A., Marek-Crnjac, L. and He. J.-H. (2013) 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, 3, 141-145.
[24]El Naschie, M.S. (2007) From Symmetry to Particles. Chaos, Solitons & Fractals, 427-430.
http://dx.doi.org/10.1016/j.chaos.2006.09.016
[25]El Naschie, M.S. (2013) 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, 43-54.
[26]El Naschie, M.S. (2013) Using Varying Speed of Light Theory to Elucidate and Calculate the Exact Experimental Percentage of the Dark Energy in the Cosmos. Fractal Spacetime and Noncommutative Geometry in Quantum and High Energy Physics, 3, 35-38.
[27]He, J.-H. and Marek-Crnjac, L. (2013) The Quintessence of El Naschie’s Theory of Fractal Relativity and Dark Energy. Fractal Spacetime and Noncommutative Geometry in Quantum and High Energy Physics, 3, 130-137.
[28]Marek-Crnjac, L. and He. J. (2013) The Three Page Guide to the Most Important Results of M. S. El Naschie’s Research in E-Infinity Quantum Physics and Cosmology. International Journal of Astronomy and Astrophysics, 464-471.
[29]El Naschie, M.S. (2013) A Rindler-KAM Spacetime Geometry and Scaling the Planck Scale Solves Quantum Relativity and Explains Dark Energy. International Journal of Astronomy and Astrophysics, 483-493.
[30]El Naschie, M.S. (2013) Electromagnetic and Gravitational Origin of Dark Energy in Kaluza-Klein D = 5 Spacetime. PIERS Proceeding, Stockholm, Sweden, 91-97.
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Wednesday, March 5, 2014

Capillary Surface Energy Elucidation of the Cosmic Dark Energy—Ordinary Energy Duality

Author(s)
Mohamed S. El Naschie     Leave a comment
This short letter reports on an unsuspected and quite surprising connection between capillary forces and dark energy. We start with a very brief introduction of the role played by relativistic hydrodynamics in cosmic dark energy research, and then proceed from there to outline the proposed analogy between dark energy and non-relativistic effects of capillary surface energy.
KEYWORDS
Dark Energy; Cantorian Space-Time; Relativistic Hydrodynamics; Capillary Surface Energy; Quantum Physics; Buckling of Elastic Shells; Imperfection Sensitivity

Cite this paper
M. S. El Naschie, "Capillary Surface Energy Elucidation of the Cosmic Dark Energy—Ordinary Energy Duality,"Open Journal of Fluid Dynamics, Vol. 4 No. 1, 2014, pp. 15-17. doi: 10.4236/ojfd.2014.41002.
[1]Linder, E. (2008) Dark Energy. Scholarpedia, 3, 4900.
[2]Sahni, V. (2003) Theoretical Models of Dark Energy. Chaos, Solitons & Fractals, 16, 527-537. http://dx.doi.org/10.1016/S0960-0779(02)00221-7
[3]Helal, M.A., Marek-Crnjac, L. and He, J.-H. (2013) The Three Page Guide to the Most Important Results of M.S. El Naschie’s Research in E-Infinity and Quantum Physics and Cosmology. Open Journal of Microphysics, 3, 141-145. http://dx.doi.org/10.4236/ojm.2013.34020
[4]Marek-Crnjac, L. (2013) An Invitation to El Naschie’s Theory of Cantorian Space-Time and Dark Energy. International Journal of Astronomy and Astrophysics, 3, 464-471. http://dx.doi.org/10.4236/ijaa.2013.34053
[5]Finn, R. (1999) Capillary Surface Interface. Notices of the American Mathematical Society, 46, 770-781.
[6]Dierkes, V., Hildebrandt, S., et al. (1992) Minimal Surfaces I. Springer Verlag, Berlin.
[7]El Naschie, M.S. (1990) Stress, Stability and Chaos in Structural Engineering: An Energy Approach. McGraw Hill, Int. Editions Civil Eng. Series, London, Tokyo.
[8]El Naschie, M.S. (2013) The Quantum Gravity Immirzi Parameter—A General Physical and Topological Interpretation. Gravitation and Cosmology, 19, 151-155. http://dx.doi.org/10.1134/S0202289313030031
[9]El Naschie, M.S. (2011) Quantum Entanglement as a Consequence of a Cantorian Micro Space-Time Geometry. Journal of Quantum Information Science, 1, 50-53. http://dx.doi.org/10.4236/jqis.2011.12007
[10]Rezzolla, L. and Zanotti, O. (2013) Relativistic Hydrodynamics. Oxford University Press, Oxford. http://dx.doi.org/10.1093/acprof:oso/9780198528906.001.0001
[11]El Naschie, M.S. (2014) Pinched Material Einstein Space-Time Produces Accelerated Cosmic Expansion. International Journal of Astronomy and Astrophysics, in Press.
[12]El Naschie, M.S. (2013) A Rindler-KAM Space-Time Geometry and Scaling the Planck Scale Solves Quantum Relativity and Explains Dark Energy. International Journal of Astronomy and Astrophysics, 3, 483-493. http://dx.doi.org/10.4236/ijaa.2013.34056
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Thursday, December 26, 2013

Experimentally Based Theoretical Arguments that Unruh’s Temperature, Hawking’s Vacuum Fluctuation and Rindler’s Wedge Are Physically Real

Experimentally Based Theoretical Arguments that Unruh’s Temperature, Hawking’s Vacuum Fluctuation and Rindler’s Wedge Are Physically Real


Authors 
Mohamed S. El Naschie, Dept. of Physics, University of Alexandria, Egypt


To cite this article 
Mohamed S. El Naschie, Experimentally Based Theoretical Arguments that Unruh’s Temperature, Hawking’s Vacuum Fluctuation and Rindler’s Wedge Are Physically Real, American Journal of Modern Physics. Vol. 2, No. 6, 2013, pp. 357-361. doi: 10.11648/j.ajmp.20130206.23

Abstract 
The objective of the present paper is to argue that based on the reality of the observed increased rate of cosmic expansion, Unruh’s temperature, Hawking’s negative vacuum energy and Rindler’s wedge must also be a physical reality. We present first a brief derivation of the missing dark energy density of the universe which is in absolute agreement with the most recent accurate cosmological measurements and observations. The derivation is based upon a Rindler space setting, the associated wedge horizon and Unruh temperature. That way the topological ordinary energy is found to be half of the topological Unruh fluctuation mass m(O) = φ3 multiplied with the square of the topological speed of light c2 = φ2 where φ = 2 /(√5+ 1). This is exactly equal to the area of the spear-like hyperbolic triangular part of the Rindler wedge. The corresponding physical ordinary energy density is thus E(O) = (1/2)( φ3)( φ2) mc2 = (φ5/2)( mc2), where φ5 is Hardy’s probability of quantum entanglement. The topological dark energy density on the other hand is equal half of the topological Kaluza-Klein five dimensional mass m(D) = 5 multiplied with c2 = φ2. This in turn is exactly equal to the circular segment part of the wedge which together with the hyperbolic triangular entangled area forms the complete Lorentzian invariant triangular area of the wedge. Consequently the physical dark energy density which is uncorrelated, i.e. disentangled is given by E(D) = (1/2)(5)( φ2)( mc2) = (5 φ2 /2)( mc2) in full agreement with observation. Adding E(O) and E(D) one finds E(Einstein) = mc2 in full agreement with all our previous derivations. From the above we argue that since measurements, observations and theory have shown the increased expansion to be real and because the present derivation of the same results is based on Rindler’s space and Unruh’s temperature, it follows as a logical necessity that Unruh’s temperature, Hawking’s fluctuation and Rindler’s wedge are all physically real and can be measured, at least in principle.

Keywords 
Hawking Vacuum Fluctuation, Unruh Temperature, Rindler Wedge, Dark Energy, Quantum Gravity, Cantorian Spacetime, Hyperbolic Fractal Geometry

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Reference 
[01]M.S. El Naschie: What is the missing dark energy in a nutshell and the Hawking-Hartle quantum wave collapse. Int. J. Astronomy & Astrophysics, Vol. 3, No. 3, 2013, pp. 205-211.
  
[02]L. Amendola and S. Tsujikawa: Dark Energy – Theory and Observations. Cambridge University Press, Cambridge (2010).
  
[03]S. Perlmutter et al: Supernova cosmology project collaboration. “Measurement of omega and lambda from 42 high-redshift supernova. The Astrophysical Journal, Vol. 517, No. 2, 1999, pp. 565-585.
  
[04]A.G. Riess et al: Observation evidence from supernova for an accelerating universe and cosmological constants. The Astronomical Journal. Vol. 116, P. 1009, 1998. Doi: 10.1086/300499.
  
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The Hydrogen Atom Fractal Spectra, the Missing Dark Energy of the Cosmos and Their Hardy Quantum Entanglement

The Hydrogen Atom Fractal Spectra, the Missing Dark Energy of the Cosmos and Their Hardy Quantum Entanglement

Author(s)
Mohamed S. El Naschie
In this letter, I outline the intimate connection between the fractal spectra of the exact solution of the hydrogen atom and the issue of the missing dark energy of the cosmos. A proposal for a dark energy reactor harnessing the dark energy of the Schrodinger wave via a quantum wave nondemolition measurement is also presented.
KEYWORDS
Fractal Spectra; Dark Energy; Golden Mean; KAM Theorem; Quantum Entanglement; Special Relativity


Cite this paper
M. 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. doi: 10.4236/ijmnta.2013.23023.
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Dark Energy Explained via the Hawking-Hartle Quantum Wave and the Topology of Cosmic Crystallography

Dark Energy Explained via the Hawking-Hartle Quantum Wave and the Topology of Cosmic Crystallography
Author(s)
Mohamed S. El Naschie, Atef Helal
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.
KEYWORDS
Doubly Special Relativity; Week’s Manifold; Experimental Test of Einstein’s Relativity; Witten’s M-Theory; Ordinary Energy of the Quantum Particle; Hawking-Hartle Wave of Cosmos; Crystallographic Symmetry Groups; Revising Special Relativity


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.
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