JAMP  Vol.2 No.8 , July 2014
From Modified Newtonian Gravity to Dark Energy via Quantum Entanglement
Abstract: Starting from the classical Newton inverse square law of gravitation we arrive at a modified Newtonian gravity in the spirit of the work of Milgrom-Bekenstein pioneering work. This is achieved by injecting the needed quantum mechanical dissection of special relativity into Newton’s law via the modified energy mass relationship which transforms Einstein’s famous formula from a smooth four dimensional space to a rugged fractal-like spacetime manifold. The confidence in the present result stems not only from the consistency of the mathematical scheme but also from agreement with the general direction of cosmological measurements and observations.
Cite this paper: Naschie, M. (2014) From Modified Newtonian Gravity to Dark Energy via Quantum Entanglement. Journal of Applied Mathematics and Physics, 2, 803-806. doi: 10.4236/jamp.2014.28088.

[1]   Penrose, R. (2004) The Road to Reality: A Complete Guide to the Laws of the Universe. Jonathan Cape, London.

[2]   Hawking, S. (2001) The Universe in a Nutshell. Bantam Press, London.

[3]   Kiacu, F. and Holmes, P. (1996) Celestial Encounters—The Origin of Chaos and Stability. Princeton University Press, Princeton.

[4]   El Naschie, M.S. (1990) Stress, Stability and Chaos in Structural Engineering—An Energy Approach. McGraw Hill, London.

[5]   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.

[6]   Arnold, V.I., Ed. (1988) Dynamical Systems III. Springer, New York.

[7]   Guckenheimer, J. and Holmes, P. (1983) Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. Springer, New York.

[8]   Hardy, G.H. and Wright, E.M. (2008) An Introduction to the Theory of Numbers. 6th Edition, Oxford University Press, Oxford.

[9]   Elwes, R. and Ultimate, L. (2011) Ultimate Logic. New Scientist, 211, 30-33.

[10]   Marek-Crnjac, L., El Naschie, M.S. and He, J.-H. (2013) Chaotic Fractals at the Root of Relativistic Quantum Physics and Cosmology. International Journal of Modern Nonlinear Theory and Application, 2, 78-88.

[11]   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.

[12]   He, J.-H., et al. (2011) The Importance of the Empty Set and Noncommutative Geometry in Underpinning the Foundations of Quantum Physics. Nonlinear Science Letters B, 1, 14-23.

[13]   Ho, M.-W. (2014) Golden Geometry of E-Infinity Fractal Spacetime. The Story of Phi, Part 5, Science of the Organism, Institute of Science in Society.

[14]   Milgrom, M. (1983) A Modification of the Newtonian Dynamics—Implications for Galaxies. Astrophysical Journal, 270, 371-389.

[15]   Bekenstein, J. (2006) The Modified Newtonian Dynamics—MOND—and Its Implication for New Physics. Contemporary Physics, 47, 387.

[16]   Zwicky, F. (1934) On the Principle of Flexibility of Scientific Truth. Philosophy of Science, 1, 353-359.

[17]   Zwicky, F. and Zwicky, M. (1971) Catalogue of Selected Compact Galaxies and Post-Eruptive Galaxies. Guemligen, Switzerland.

[18]   El Naschie, M.S. (2014) Cosmic Dark Energy from t Hooft’s Dimensional Regularization and Witten’s Topological Quantum Field Pure Gravity. Journal of Quantum Information Science, 4, 83-91.

[19]   El Naschie, M.S. (2014) Cosserat-Cartan Modification of Einstein-Riemann Relativity and Cosmic Dark Energy Density. American Journal of Modern Physics, 3, 82-87.

[20]   El Naschie, M.S. (2006) Is Einstein’s General Field Equation More Fundamental than Quantum Field Theory and Particle Physics? Chaos, Solitons & Fractals, 30, 525-531.

[21]   El Naschie, M.S. (2006) Is Gravity Less Fundamental than Elementary Particles Theory? Critical Remarks on Holography and E-Infinity Theory. Chaos, Solitons & Fractals, 29, 803-807.

[22]   El Naschie, M.S. (2008) Derivation of Newton’s Gravitational Fine Structure Constant from the Spectrum of Heterotic Superstring Theory. Chaos, Solitons & Fractals, 35, 303-307.

[23]   Czajko, J. (2005) On the Universe’s Missing Mass. Chaos, Solitons & Fractals, 23, 11-22.

[24]   El Naschie, M.S. (2008) Exact Non-Perturbative Derivation of Gravity Fine Structure Constant, the Mass of the Higgs and Elementary Black Holes. Chaos, Solitons & Fractals, 37, 346-359.

[25]   El Naschie, M.S. (2005) Gödel Universe, Dualities and High Energy Particles in E-Infinity. Chaos, Solitons & Fractals, 25, 759-764.

[26]   El Naschie, M.S. (2005) A Few Hints and Some Theorems about Witten’s M-Theory and T-Duality. Chaos, Solitons & Fractals, 25, 545-548.