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
[01]	A.G. Riess et al, Observation evidence from supernova for an accelerating universe and a cosmological constant. The Astronomical Journal. Vol. 116, pp. 1009, 1998. Doi: 10.1086/300499.
[02]	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.
[03]	C.L. Bennett, WMAP Collaboration. Astrophys. J. Suppl,Vol. 148, No. 1, 2003, [astro-ph/0302207].
[04]	B.P. Schmidt et al, The distance to five type II supernova using the expanding photosphere method and the value of Ho. The Astrophys. J., Vol. 432, 1994, pp. 42-48.
[05]	T. Padmanabhan, Dark Energy: The cosmological challenge of the millennium. arXiv: astro-ph/0411044V1, 2 Nov 2004.
[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.

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

Download as PDF (Size:221KB) PP. 1-5  

Author(s)

Mohamed S. El Naschie     

ABSTRACT

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.

References

[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.

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

Download as PDF

Author(s)

Mohamed S. El Naschie     Leave a comment

ABSTRACT

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.

References

[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