IJAA  Vol.4 No.1 , March 2014
Pinched Material Einstein Space-Time Produces Accelerated Cosmic Expansion
Author(s) M. S. El Naschie
ABSTRACT
An instructive analogy between the deformation of a pinched elastic cylindrical shell and the anti-gravity behind accelerated cosmic expansion is established. Subsequently the entire model is interpreted in terms of a hyperbolic fractal Rindler space-time leading to the same robust results regarding real energy and dark energy being 4.5% and 95.5% respectively in full agreement with all recent cosmological measurements.

Cite this paper
El Naschie, M. (2014) Pinched Material Einstein Space-Time Produces Accelerated Cosmic Expansion. International Journal of Astronomy and Astrophysics, 4, 80-90. doi: 10.4236/ijaa.2014.41009.
References
[1]   Heisenberg, W. (1969) Der Teil und das Ganze,” Piper, Munich,

[2]   Weyl, H. (1923) Raum-Zeit–Materie.Sprin ger, Berlin. http://dx.doi.org/10.1007/978-3-642-98950-6

[3]   Hawking, S. and Penrose, R. () The Nature of Space and time. Princeton University Press, New Jersey, 1996.

[4]   Weibel, P., Ord, G. and Rossler, O. (2005) Space-Time Physics and Fractality: Festschrift in Honour of Mohamed El Naschie on the Occasion of His 60th Birthday. Springer, Vienna-New York.

[5]   Halpern, P. (2004) The Great Beyond. John Wiley, Hoboken.

[6]   Ye, F.Y. (2009) From Chaos to Unification: U Theory vs M Theory. Chaos, Solitons & Fractals, 42, 89-93. http://dx.doi.org/10.1016/j.chaos.2008.10.030

[7]   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

[8]   He, J.-H. and Marek-Crnjac, L. (2013) The Quintessence of El Naschie’s Theory of Fractal Relativity and Dark Energy. Fractal Space-Time and Non-Commutative Geometry in High Energy Physics, 3, 130-137.

[9]   El Naschie, M.S. (2013) Experimentally Based Theoretical Arguments that Unruh’s Temperature, Hawkings’s Vacuum Fluctuation and Rindler’s Wedge Are Physically Real. American Journal of Modern Physics, 2, 357-361.

[10]   Persinger, M. and Koren, S. (2013) Dimensional Analysis of Geometric Products and the Boundary Conditions of the Universe: Implications for Quantitative Value for the Latency to Display Entanglement. The Open Astronomy Journal, 6, 10-13. http://dx.doi.org/10.2174/18743811013060 10010

[11]   Yang, X.-J., Baleanu, D. and Zhong, W.-P. (2013) Approximate Solutions for Diffusion Equations on Cantor Space-Time,” Proceedings of the Romanian Academy, Series A, 14, 127-133.

[12]   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.

[13]   El Naschie, M.S. (2007) Transfinite Neoimpressionistic Reality of Quantum Space-Time,” New Advances in Physics, 1, 11-122.

[14]   Malinowski, J.J. (2011) Fractal Physics Theory—Foundation. Fundamental Journal of Modern Physics, 1, 133-168.

[15]   El Naschie, M.S. (2013) Nash Embedding of Witten’s M-Theory and Hawking-Hartle Quantum Wave of Dark Energy. Journal of Modern Physics, 4, 1417-1428. http://dx.doi.org/10.4236/jmp.2013.410170

[16]   El Naschie, M.S. (2013) From Yang-Mills Photon in Curved Space-Time to Dark Energy Density. Journal of Quantum Information Science, 3, 121-126. http://dx.doi.org/10.4236/jqis.2013.34016

[17]   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

[18]   El Naschie, M.S. (2012) On the Need for Fractal Logic in High Energy Quantum Physics,” International Journal of Modern Nonlinear Theory and Application, 1, 84-92. http://dx.doi.org/10.4236/ijmnta.2012. 13012

[19]   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

[20]   El Naschie, M.S. (2013) A Resolution of Cosmic Dark Energy via a Quantum Entanglement Relativity Theory. Journal of Quantum Information Science, 3, 23-26. http://dx.doi.org/10.4236/jqis.2013. 31006

[21]   El Naschie, M.S. (2004) A Review of E-Infinity 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

[22]   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

[23]   El Naschie, M.S. (2013) Quantum Gravity and Dark Energy Using Fractal Planck Scaling. Journal of Modern Physics, 4, 31-38.

[24]   Penrose, R. (2004) The Road to Reality. Jonathan Cape, London.

[25]   El Naschie, M.S. (1990) Stress, Stability and Chaos in Structural Engineering: An Energy Approach. McGraw-Hill international Editions: Civil Engineering Series, London, Tokyo.

[26]   He, J.-H. and Marek-Crnjac, L. (2013) 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, 2, 55-59. http://dx.doi.org/10.4236/ijmnta.2013.21006

[27]   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

[28]   Marek-Crnjac, L., et al. (2013) Chaotic Fractal Tiling for the Missing Dark Energy and Veneziano Model. Applicationes Mathematicae, 4, 22-29. http://dx.doi.org/10.4236/am.2013.411A2005

[29]   Susskind, L. and Lidesay, J. (2005) The Holographic Universe—An Introduction to Black Holes, Information and the String Theory Revolution. World Scientific, Singapore.

[30]   Ellis, G.F.R. and Williams, R.M. (2000) Flat and Curved Space-Time. Oxford University Press, Oxford.

[31]   Bronshtein, I.N. and Semendyayev, K.A. (1985) Handbook of Mathematics. Van Nostrand Reinhold Company, New York.

[32]   Padmanabhan, T. (2004) Dark Energy: The Cosmological Challenge of the Millennium. arXiv: astro-ph/0411044V1

[33]   Padmanabhan, T. (2003) Gravity from Space-Time Thermodynamics,” Astrophysics and Space Science, 285, 407-417. http://dx.doi.org/10.1023/A:1025448712533

[34]   El Naschie, M.S. (2013) 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, 4, 591-596. http://dx.doi.org/10.4236/jmp.2013.45084

[35]   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.
http://dx.doi.org/10.4236/ijaa.2013.33024

[36]   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

[37]   El Naschie, M.S. (2008) Adic Unification of the Fundamental Forces and the Standard Model. Chaos, Solitons & Fractals, 38, 1011-1012. http://dx.doi.org/10.1016/j.chaos.2008.04.047

[38]   El Naschie, M.S. (2006) Advanced Prerequisites for E-Infinity. Chaos, Solitons & Fractals, 30, 636-641. http://dx.doi.org/10.1016/j.chaos.2006.04.044

[39]   El Naschie, M.S. (2004) Quantum Gravity from Descriptive Set Theory. Chaos, Solitons & Fractals, 19, 1339-1344. http://dx.doi.org/10.1016/j.chaos.2003.08.009

[40]   El Naschie, M.S. (2004) Quantum Gravity from Descriptive Set Theory. Chaos, Solitons & Fractals, 19, 1339-1344. http://dx.doi.org/10.1016/j.chaos.2003.08.009

[41]   El Naschie, M.S. (2007) A Review of Application and Results of E-Infinity Theory. International Journal of Nonlinear Sciences and Numerical Simulation, 8, 11-20. http://dx.doi.org/10.1515/IJNSNS.2007.8. 1.11

[42]   Vladimirov, V., Valovich, I. and Zelenov, E. (1994) P-Adic Analysis and Mathematical Physics. World Scientific, Singapore. http://dx.doi.org/10.1142/1581

[43]   Khrennikov, A. (1997) Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Methods. Kluwer Academic Publishers, Dordrecht. http://dx.doi.org/10.1007/978-94-009-1483-4

[44]   El Naschie, M.S. (2009) The Theory of Cantorian Space-Time 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

[45]   El Naschie, M.S. (2006) Elementary Prerequisites for E-Infinity (Recommended Background Readings in Nonlinear Dynamics, Geometry and Topology). Chaos, Solitons & Fractals, 30, 579-605.
http://dx.doi.org/10.1016/j.chaos.2006.03.030

[46]   El Naschie, M.S. (2004) The Concepts of E-Infinity: An Elementary Introduction to the Cantorian-Fractal Theory of Quantum Physics. Chaos, Solitons & Fractals, 22, 495-511.
http://dx.doi.org/10.1016/j.chaos.2004.02.028

[47]   Ruiz-Lapuente, P. (2010) Dark Energy. Cambridge University Press, Cambridge.

[48]   Perkins, D. (2009) Particle Astrophysics. 2nd Edition, Oxford University Press, Oxford.

[49]   Amendola, L. and Tsujikawa, S. (2010) Dark Energy-Theory and Observations. Cambridge University Press, Cambridge. http://dx.doi.org/10.1017/CBO9780511750823

[50]   Bahcall, J., Pivan, T. and Weinberg, S. (2004) Dark Matter in the Universe. 2nd Edition, World Scientific, Singapore.

[51]   Weinberg, S. (2008) Cosmology. Oxford University Press, Oxford.

[52]   Vilenkin, A. and Shellard, E.S. (1994) Cosmic Strings and Other Topological Defects. Cambridge University Press, Cambridge.

[53]   El Naschie, M.S. (2002) Wild Topology, Hyperbolic Geometry and Fusion Algebra of High Energy Particle Physics. Chaos, Solitons & Fractals, 13, 1935-1945. http://dx.doi.org/10.1016/S0960-0779 (01)00242-9

[54]   El Naschie, M.S. (2002) Quantum Loops, Wild Topology and Fat Cantor Sets in Transfinite High Energy Physics. Chaos, Solitons & Fractals, 13, 1167-1174. http://dx.doi.org/10.1016/S0960-0779 (01)00210-7

[55]   Tao, Y. (2013) The Validity of Dimensional Regularization Method on Fractal Space-Time. Journal of Applied Mathematics, 2013, Article ID: 308691. http://dx.doi.org/10.1155/2013/308691

[56]   Marek-Crnjac, L. (2009) A Feynman Path Integral-Like Method for Deriving the Four Dimensionality of Space-Time from First Principles. Chaos, Solitons & Fractals, 41, 2471-2473.
http://dx.doi.org/10.1016/j.chaos.2008.09.014

[57]   El Naschie, M.S. (2002) Determining the Temperature of the Microwave Background Radiation from the Topology and Geometry of Space-Time. Chaos, Solitons & Fractals, 14, 1121-1126.
http://dx.doi.org/10.1016/S0960-0779(02)00172-8

[58]   El Naschie, M.S. (1997) A Note on Quantum Gravity and Cantorian Space-Time. Chaos, Solitons & Fractals, 8, 131-133. http://dx.doi.org/10.1016/S0960-0779(96)00128-2

[59]   El Naschie, M.S. (1998) Superstrings, Knots and Non-Commutative Geometry in E-Infinity Space. International Journal of Theoretical Physics, 37, 2935-2951. http://dx.doi.org/10.1023/A:102667962 8582

[60]   Lehmann, T. (1966) Form?nderung Eines Klassischen Kontinuums in Vierdimensionaler Darstellung. In: G?rtler, H., Ed., Applied Mechanics, Springer-Verlag, Heidelberg, 376-382.

[61]   Mukhamedov, A.M. (2007) E-Infinity as a Fiber Bundle and Its Theormodynamics. Chaos, Solitons & Fractals, 33, 717-724. http://dx.doi.org/10.1016/j.chaos.2006.11.016

[62]   El Naschie, M.S. (1979) Die Ableitung Einer Konsistenten Schalentheorie in Dem Dreidimensionalen Kontinuum. ?sterreichische Ingenieur-Zeitschrift (Austrian Engineering Journal), 22, 339-344.

[63]   El Naschie, M.S. (2009) Curvature, Lagrangian and Holonomy of Cantorian-Fractal Space-Time. Chaos, Solitons & Fractals, 41, 2163-2167. http://dx.doi.org/10.1016/j.chaos.2008.08.015

[64]   El Naschie, M.S. (2009) An Irreducibly Simple Derivation of the Hausdorff Dimension of Space-Time. Chaos, Solitons & Fractals, 41, 1902-1904. http://dx.doi.org/10.1016/j.chaos.2008.07.043

[65]   El Naschie, M.S. (1999) Quantum Groups and Hamiltonian Sets on a Nuclear Space-Time Cantorian Manifold. Chaos, Solitons & Fractals, 10, 1251-1256. http://dx.doi.org/10.1016/S0960-0779(99) 00009-0

[66]   El Naschie, M.S. (2004) The Symplectic Vacuum, Exotic Quasi Particles and Gravitational Instantons. Chaos, Solitons & Fractals, 22, 1-11. http://dx.doi.org/10.1016/j.chaos.2004.01.015

[67]   El Naschie, M.S. (2008) Transfinite Harmonization by Taking the Dissonance out of the Quantum Field Symphony. Chaos, Solitons & Fractals, 36, 781-786. http://dx.doi.org/10.1016/j.chaos.2007.09.018

[68]   Vrobel, S. (2011) Fractal Time. World Scientific, Singapore.

[69]   El Naschie, M.S. (2012) The Minus One Connection of Relativity, Quantum Mechanics and Set Theory. Fractal Space-Time and Non-Commutative Geometry in High Energy Physics, 2, 131-134.

[70]   El Naschie, M.S. and Olsen, S. (2011) When Zero Is Equal to One—A Set Theoretical Resolution of Quantum Paradoxes. Fractal Space-Time and Non-Commutative Geometry in High Energy Physics, 1, 11-24.

[71]   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/S0202289313 030031

[72]   El Naschie, M.S. (2013) Determining the Missing Dark Energy of the Cosmos from a Light Cone Exact Relativistic Analysis. Journal of Physics, 2, 18-23.

[73]   Adams, C.C. (1994) The Knot Book. H. Freeman, New York, 244-246.

[74]   Pathvia, R.K. (1972) The Universe as a Black Hole. Nature, 240, 298-299.
http://dx.doi.org/10.1038/240298a0

[75]   Nesteruk, A. (2013) Physics in Christianity. In: Runehov, A. and Oviedo, L., Eds., Encyclopedia of Sciences and Religion, 3, 1718-1729.

[76]   Watson, A., Reid, S., Johnson, W. and Thomas, S. (1976) Large Deformations of Thin-Walled Circular Tubes under Transverse Loading—II. International Journal of Mechanical Sciences, 18, 389-397. http://dx.doi.org/10.1016/0020-7403(76)90015-1

[77]   Marek-Crnjac, L. (2012) Quantum Gravity in Cantorian Space-Time. In: Soberio, R., Ed., Quantum Gravity, INTECH Publishing, 87-100. www.intechopen.com.

[78]   Cosserat, E. and Cosserat, F. (1909) Théorie des Corps déformables. Hermann, Paris.

[79]   El Naschie, M.S. (2013) The Hyperbolic Extension of Sigalotti-Heni-Sharifzadeh’s Golden Triangle of Special Theory of Relativity and the Nature of Dark Energy. Journal of Modern Physics, 4, 354-356. http://dx.doi.org/10.4236/jmp.2013.43049

 
 
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