The present paper is basically written as a non-apologetic strong defence of the thesis that computation is part and parcel of a physical theory and by no means a mere numerical evaluation of the prediction of a theory which comes towards the end. Various general considerations as well as specific examples are given to illustrate and support our arguments. These examples range from the practical aspect to almost esoteric considerations but at the end, everything converges towards a unity of theory and computation presented in the form of modern fractal logic and transfinite quantum field theory in a Cantorian spacetime. It is true that all our examples are taken from physics but our discussion is applicable in equal measure to a much wider aspect of life.
Waldschmidt, M., Moussa, P., Luck, J. and Itzykson, C. (1992) From Number Theory to Physics. Springer-Verlag, Berlin. http://dx.doi.org/10.1007/978-3-662-02838-4
Hardy, G.H. and Wright, E.M. (1979) An Introduction to the Theory of Numbers. Clarendon Press, Oxford, UK.
Zenil, H. (Editor) (2013) A Computable Universe. World Scientific, Singapore.
Tegmark, M. (2014) Our Mathematical Universe. Allen Lane-Penguin Books, London.
Lloyd, S. (2005) Programming the Universe. Jonathan Cape, London.
Pickover, C.A. (1990) Computers, Patterns Chaos and Beauty. St. Martin’s Press, New York.
Beiler, A.H. (1966) Recreations in the Theory of Numbers. Dover Publications, New York.
Dedekind, R. (1963) Essays on the Theory of Numbers. Dover Publications, New York.
Artman, B. (1988) The Concept of Numbers. Ellis Horwood Ltd.-John Wiley, New York.
Deutsch, D. (2011) The Beginning of Infinity. Allen Lane-Penguin Books, London.
Posamentier, A.S. and Lehmann, I. (2007) The Fabulous Fibonacci Numbers. Prometheus Books, New York.
Stakhov, A. (2009) The Mathematics of Harmony. World Scientific, Singapore.
Changeux, J.-P. and Connes, A. (1989) Conversations on Mind, Matter and Mathematics. Princeton University Press, Princeton.
Rendell, P. (2016) Turing Machine in Conway Game of Life. In: Designing Beauty: The Art of Cellular Automata, Springer, Heidelberg, 149-154. http://dx.doi.org/10.1007/978-3-319-27270-2_25
Deutsch, D. (1985) Quantum Theory, the Church-Turing Principle and the Universal Computer. Proceedings of the Royal Society A, Mathematical, Physical and Engineering Sciences, 400, 97-117.
Babai, L., Pomerance, C. and Vertesi, P. (1998) The Mathematics of Paul Erdos. Notices of the American Mathematical Society, 45, 19-31.
Hoffman, P. (1998) The Man Who Loved Only Numbers. Hyperion, New York.
Kanigel, R. (1991) The Man Who Knew Infinity. Scribners, New York.
Ramanujan, S. (2015) Collected Papers of Ramanujan. Cambridge University Press, Cambridge.
El Naschie, M.S. (1991) Physics-Like Mathematical Model for Chaos and Ergodic Criticality in Four Dimensions. 13th Canadian Congress of Applied Mechanics (CANCAM 91), Paper No. A90.19, 756-757.
El Naschie, M.S. (1991) Mathematical Model for Chaos and Ergodic Criticality in Four Dimensions. Mathematical and Computer Modelling, 15, 77-80. http://dx.doi.org/10.1016/0895-7177(91)90042-6
El Naschie, M.S. (1992) Complex Dynamics in a 4D Peano-Hilbert Space. Il Nuovo Cimento, 107B, 583-594. http://dx.doi.org/10.1007/BF02723635
El Naschie, M.S. (1992) Multi-Dimensional Cantor-Like Sets and Ergodic Behaviour. Speculations in Science & Technology, 15, 138-142.
El Naschie, M.S. (1993) On Universal Behaviour and Statistical Mechanics of Multi-Dimensional Triadic Cantor Sets. Systems Analysis Modelling Simulation, 11, 217-225.
El Naschie, M.S. (1993) On Turbulence and Complex Dynamics in a Four Dimensional Peano-Hilbert Space. Journal of the Franklin Institute, 330, 183-198. http://dx.doi.org/10.1016/0016-0032(93)90029-T
El Naschie, M.S. (1995) Statistical Geometry of a Cantor Discretum and Semi Conductors. Computers & Mathematics with Applications, 29, 103-110. http://dx.doi.org/10.1016/0898-1221(95)00062-4
Connes, A. (1994) Noncommutative Geometry. Academic Press, San Diego.
Von Neumann, J. (1960) Continuous Geometry. Vol. 25, Princeton University Press, Princeton.
Kappraff, J. (1991) Connections. McGraw-Hill Inc., New York.
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
El Naschie, M.S. (2005) A Guide to the Mathematics of E-Infinity Cantorian Spacetime Theory. Chaos, Solitons & Fractals, 25, 955-964. http://dx.doi.org/10.1016/j.chaos.2004.12.033
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
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
El Naschie, M.S. (2007) A Review of Application and Results of E-Infinity. International Journal of Nonlinear Science & Numerical Simulation, 8, 11-20. http://dx.doi.org/10.1515/IJNSNS.2007.8.1.11
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
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.
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://dx.doi.org/10.4236/jqis.2011.12007
El Naschie, M.S. (2007) Feigenbaum Scenario for Turbulence and Cantorian E-Infinity Theory of High Energy Particle Physics. Chaos, Solitons & Fractals, 32, 911-915. http://dx.doi.org/10.1016/j.chaos.2006.08.014
El Naschie, M.S. (2005) On a Fuzzy Kähler-Like Manifold Which Is Consistent with the Two Slit Experiment. International Journal of Nonlinear Sciences and Numerical Simulation, 6, 95-98. http://dx.doi.org/10.1515/IJNSNS.2005.6.2.95
El Naschie, M.S. (2007) On the Topological Ground State of E-Infinity Spacetime and the Super String Connection. Chaos, Solitons & Fractals, 32, 468-470. http://dx.doi.org/10.1016/j.chaos.2006.08.011
El Naschie, M.S. (2005) On the Cohomology and Instantons Number in E-Infinity Cantorian Spacetime. Chaos, Solitons & Fractals, 26, 13-17. http://dx.doi.org/10.1016/j.chaos.2004.12.019
El Naschie, M.S. (2006) Advanced Prerequisites for E-Infinity Theory. Chaos, Solitons & Fractals, 30, 636-641. http://dx.doi.org/10.1016/j.chaos.2006.04.044
El Naschie, M.S. (2006) Topics in the Mathematical Physics of E-Infinity Theory. Chaos, Solitons & Fractals, 30, 656-663. http://dx.doi.org/10.1016/j.chaos.2006.04.043
El Naschie, M.S. (2005) The Two-Slit Experiment as the Foundation of E-Infinity of High Energy Physics. Chaos, Solitons & Fractals, 25, 509-514. http://dx.doi.org/10.1016/j.chaos.2005.02.016
El Naschie, M.S. (2006) Holographic Dimensional Reduction: Center Manifold Theorem and E-Infinity. Chaos, Solitons & Fractals, 29, 816-822. http://dx.doi.org/10.1016/j.chaos.2006.01.013
El Naschie, M.S. (2006) Fuzzy Dodecahedron Topology and E-Infinity Spacetime as a Model for Quantum Physics. Chaos, Solitons & Fractals, 30, 1025-1033. http://dx.doi.org/10.1016/j.chaos.2006.05.088
El Naschie, M.S. (2006) Elementary Number Theory in Superstring Loop Quantum Mechanics, Twistors and E-Infinity High Energy Physics. Chaos, Solitons & Fractals, 27, 297-330. http://dx.doi.org/10.1016/j.chaos.2005.04.116
El Naschie, M.S. (2006) Hilbert, Fock and Cantorian Spaces in the Quantum Two-Slit Gedanken Experiment. Chaos, Solitons & Fractals, 27, 39-42. http://dx.doi.org/10.1016/j.chaos.2005.04.094
El Naschie, M.S. (2005) From Experimental Quantum Optics to Quantum Gravity via a Fuzzy Kähler Manifold. Chaos, Solitons & Fractals, 25, 969-977. http://dx.doi.org/10.1016/j.chaos.2005.02.028
El Naschie, M.S. (2008) Symmetry Group Prerequisite for E-Infinity in High Energy Physics. Chaos, Solitons & Fractals, 35, 202-211. http://dx.doi.org/10.1016/j.chaos.2007.05.006
El Naschie, M.S. (2006) Intermediate Prerequisites for E-Infinity Theory. Chaos, Solitons & Fractals, 30, 622-628. http://dx.doi.org/10.1016/j.chaos.2006.04.042
El Naschie, M.S. (2006) Superstrings, Entropy and the Elementary Particles Content of the Standard Model. Chaos, Solitons & Fractals, 29, 48-54. http://dx.doi.org/10.1016/j.chaos.2005.11.032
El Naschie, M.S. (2006) Hilbert Space, the Number of Higgs Particles and the Quantum Two-Slip Experiment. Chaos, Solitons & Fractals, 28, 9-13. http://dx.doi.org/10.1016/j.chaos.2005.05.010
El Naschie, M.S. (2006) On Two New Fuzzy Kähler Manifolds, Klein Modular Space and ‘tHooft’s Holographic Principles. Chaos, Solitons & Fractals, 29, 876-881. http://dx.doi.org/10.1016/j.chaos.2005.12.027
El Naschie, M.S. (2006) The Idealized Quantum Two-Slit Gedanken Experiment Revisited—Criticism and Reinterpretation. Chaos, Solitons & Fractals, 27, 843-849. http://dx.doi.org/10.1016/j.chaos.2005.06.002
El Naschie, M.S. (2003) Modular Groups in Cantorian E-Infinity High Energy Physics. Chaos, Solitons & Fractals, 16, 353-366. http://dx.doi.org/10.1016/S0960-0779(02)00440-X
El Naschie, M.S. (2003) E (Infinity) Cantorian Space-Time and Its Consequences in Cosmology. Chaos, Solitons & Fractals, 25, 775-779.
Helal, M., 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. Open Journal of Microphysics, 3, 141-145. http://dx.doi.org/10.4236/ojm.2013.34020
El Naschie, M.S. (2006) The Brain and E-Infinity. International Journal of Nonlinear Science & Numerical Simulation, 7, 129-132. http://dx.doi.org/10.1515/IJNSNS.2006.7.2.129
El Naschie, M.S. (2006) E-Infinity—Some Recent Results and New Interpretations. Chaos, Solitons & Fractals, 29, 845-853. http://dx.doi.org/10.1016/j.chaos.2006.01.073
El Naschie, M.S. (2004) The Symplictic Vacuum, Exotic Quasi Particles and Gravitational Instanton. Chaos, Solitons & Fractals, 22, 1-11. http://dx.doi.org/10.1016/j.chaos.2004.01.015
El Naschie, M.S. (2003) The VAK of Vacuum Fluctuation, Spontaneous Self Organization and Complexity Theory Interpretation of High Energy Particle Physics and the Mass Spectrum. Chaos, Solitons & Fractals, 18, 579-605.
El Naschie, M.S. (2008) Quasi Exceptional E12 Lie Symmetry Group with 685 Dimensions, KAC-Moody Algebra and E-Infinity Cantorian Spacetime. Chaos, Solitons & Fractals, 38, 990-992. http://dx.doi.org/10.1016/j.chaos.2008.06.015
Iovane, G. and Benedetto, E. (2006) El Naschie E-Infinity Cantorian Spacetime and Length Scales in Cosmology. International Journal of Nonlinear Sciences and Numerical Simulation, 7, 155-162. http://dx.doi.org/10.1515/ijnsns.2006.7.2.155
He, J.-H. (2006) Application of E-Infinity Theory to Biology. Chaos, Solitons & Fractals, 28, 285-289. http://dx.doi.org/10.1016/j.chaos.2005.08.001
El Naschie, M.S. (2003) Non-Linear Dynamics and Infinite Dimensional Topology in High Energy Particle Physics. Chaos, Solitons & Fractals, 17, 2635-2646. http://dx.doi.org/10.1016/S0960-0779(02)00402-2
El Naschie, M.S. (2007) Deterministic Quantum Mechanics versus Classical Mechanical Indeterminism. International Journal of Nonlinear Science & Numerical Simulation, 8, 5-10. http://dx.doi.org/10.1515/IJNSNS.2007.8.1.5
El Naschie, M.S. (2004) Quantum Gravity, Clifford Algebras, Fuzzy Set Theory and the Fundamental Constants of Nature. Chaos, Solitons & Fractals, 20, 437-450. http://dx.doi.org/10.1016/j.chaos.2003.09.029
El Naschie, M.S. (2005) On Penrose View of Transfinite Sets and Computability and the Fractal Character of E-Infinity Spacetime. Chaos, Solitons & Fractals, 25, 531-533. http://dx.doi.org/10.1016/j.chaos.2005.01.001
Iovane, G. and Giordano, P. (2007) Wavelets and Multiresolution Analysis: Nature of E-Infinity Cantorian Spacetime. Chaos, Solitons & Fractals, 32, 896-910. http://dx.doi.org/10.1016/j.chaos.2005.11.097
Sigalotti, L.D.G. and Mejias, A. (2006) On El Naschie’s Conjugate Complex, Time, Fractal E-Infinity Spacetime and Faster than Light. International Journal of Nonlinear Science & Numerical Simulation, 7, 467-472. http://dx.doi.org/10.1515/IJNSNS.2006.7.4.467
El Naschie, M.S. (2003) Kleinian Groups in E-Infinity and Their Connection to Particle Physics and Cosmology. Chaos, Solitons & Fractals, 16, 637-649. http://dx.doi.org/10.1016/S0960-0779(02)00489-7
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. http://dx.doi.org/10.1016/j.chaos.2006.01.012
El Naschie, M.S. (2013) A Unified Newtonian-Relativistic Quantum Resolution of Supposedly Missing Dark Energy of the Cosmos and the Constancy of the Speed of Light. International Journal of Modern Nonlinear Theory & Application, 2, 43-54. http://dx.doi.org/10.4236/ijmnta.2013.21005
El Naschie, M.S. (2005) On a Class of Fuzzy Kähler-Like Manifolds. Chaos, Solitons & Fractals, 26, 477-481. http://dx.doi.org/10.1016/j.chaos.2004.12.024
El Naschie, M.S. (2006) A Cold Fusion-Casimir Energy Nano Reactor Proposal. World Journal of Nano Science and Engineering, 5, 49-56. http://dx.doi.org/10.4236/wjnse.2015.52007
El Naschie, M.S. (2006) Fractal Black Holes and Information. Chaos, Solitons & Fractals, 29, 23-35. http://dx.doi.org/10.1016/j.chaos.2005.11.079
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. http://dx.doi.org/10.1016/j.chaos.2005.01.009
Marek-Crnjac, L. and He, J.-H. (2013) An Invitation to El Naschie’s Theory of Cantorian Spacetime and Dark Energy. International Journal of Astronomy and Astrophysics, 3, 464-471. http://dx.doi.org/10.4236/ijaa.2013.34053
Iovane, G. (2006) El Naschie E-Infinity Cantorian Spacetime and Length Scales in Cosmology. International Journal of Nonlinear Sciences and Numerical Simulation, 7, 155-162. http://dx.doi.org/10.1515/ijnsns.2006.7.2.155
El Naschie, M.S. (2007) The Fibonacci Code behind Superstrings and P-Branes. An Answer to M. Kaku’s Fundamental Question. Chaos, Solitons & Fractals, 31, 537-547. http://dx.doi.org/10.1016/j.chaos.2006.07.001
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. http://dx.doi.org/10.4236/ijmnta.2013.21a010
El Naschie, M.S. (2007) Towards a Quantum Golden Field Theory. International Journal of Nonlinear Sciences and Numerical Simulation, 8, 477-482. http://dx.doi.org/10.1515/IJNSNS.2007.8.4.477
El Naschie, M.S. (2007) The Cosmic Da Vinci Code for the Big Bang—A Mathematical Toy Model. International Journal of Nonlinear Sciences and Numerical Simulation, 8, 191-194. http://dx.doi.org/10.1515/IJNSNS.2007.8.2.191
El Naschie, M.S. (1998) Superstrings, Knots and Noncommutative Geometry in E-Infinity Space. International Journal of Theoretical Physics, 37, 2935-2951. http://dx.doi.org/10.1023/A:1026679628582
El Naschie, M.S. (2004) Transfinite Electrical Networks, Spinoral Varieties and Gravity Q Bits. International Journal of Nonlinear Sciences and Numerical Simulation, 5, 191-198.
Iovane, G., Laserra, E., El Naschie, M.S. and Tortoriello, F.S. (2004) Stochastic Self Similar and Fractal Universe. Chaos, Solitons & Fractals, 3, 415-426. http://dx.doi.org/10.1016/j.chaos.2003.08.004
El Naschie, M.S. (2007) On the Universality Class of All Universality Classes and E-Infinity Spacetime Physics. Chaos, Solitons & Fractals, 32, 927-936. http://dx.doi.org/10.1016/j.chaos.2006.08.017
He, J.-H., Liu, Y., Xu, L. and Yu, J.Y. (2007) Micro Sphere with Nanoporosity by Electrospinning. Chaos, Solitons & Fractals, 32, 1096-1100. http://dx.doi.org/10.1016/j.chaos.2006.07.045
El Naschie, M.S. (2006) Superstring Theory: What It Cannot Do but E-Infinity Could. Chaos, Solitons & Fractals, 29, 65-68. http://dx.doi.org/10.1016/j.chaos.2005.11.021
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. http://dx.doi.org/10.4236/jqis.2014.42008
El Naschie, M.S. (2015) Kerr Black Hole Geometry Leading to Dark Matter and Dark Energy via E-Infinity Theory and the Possibility of Nano Spacetime Singularity Reactor. Natural Science, 7, 210-225. http://dx.doi.org/10.4236/ns.2015.74024
El Naschie, M.S. (2014) From E = mc2 to E = mc2/22—A Short Account of the Most Famous Equation in Physics and Its Hidden Quantum Entangled Origin. Journal of Quantum Information Science, 4, 284-291. http://dx.doi.org/10.4236/jqis.2014.44023
El Naschie, M.S. (2014) Pinched Material Einstein Space-Time Produces Accelerated Cosmic Expansion. International Journal of Astronomy and Astrophysics, 4, 80-90. http://dx.doi.org/10.4236/ijaa.2014.41009
El Naschie, M.S. (2014) On a New Elementary Particle from the Disintegration of the Symplectic ‘t Hooft-Veltman-Wilson Fractal Spacetime. World Journal of Nuclear Science and Technology, 4, 216-221. http://dx.doi.org/10.4236/wjnst.2014.44027
El Naschie, M.S. (2014) The Measure Concentration of Convex Geometry in a Quasi Banach Spacetime behind the Supposedly Missing Dark Energy of the Cosmos. American Journal of Astronomy & Astrophysics, 2, 72-77. http://dx.doi.org/10.11648/j.ajaa.20140206.13
He, J.-H. (2014) A Tutorial Review on Fractal Spacetime and Fractional Calculus. International Journal of Theoretical Physics, 53, 3698-3718. http://dx.doi.org/10.1007/s10773-014-2123-8
El Naschie, M.S. (2014) Electromagnetic—Pure Gravity Connection via Hardy’s Quantum Entanglement. Journal of Electromagnetic Analysis and Applications, 6, 233-237. http://dx.doi.org/10.4236/jemaa.2014.69023
El Naschie, M.S. (2015) An Exact Mathematical Picture of Quantum Spacetime. Advances in Pure Mathematics, 5, 560-570. http://dx.doi.org/10.4236/apm.2015.59052
El Naschie, M.S. (2015) A Resolution of the Black Hole Information Paradox via Transfinite Set Theory. World Journal of Condensed Matter Physics, 5, 249-260. http://dx.doi.org/10.4236/wjcmp.2015.54026
Tang, W., Li, Y., Kong, H.Y. and El Naschie, M.S. (2014) From Nonlocal Elasticity to Nonlocal Spacetime and Nanoscience. Bubbfil Nano Technology, 1, 3-12.
El Naschie, M.S. (2014) To Dark Energy Theory from a Cosserat-Like Model of Spacetime. Problems of Nonlinear Analysis in Engineering Systems, 20, 79-98.
El Naschie, M.S. (2015) The Cantorian Monadic Plasma behind the Zero Point Vacuum Spacetime Energy. American Journal of Nano Research & Application, 3, 66-70.
El Naschie, M.S. (2015) The Casimir Topological Effect and a Proposal for a Casimir-Dark Energy Nano Reactor. World Journal of Nano Science & Engineering, 5, 26-33. http://dx.doi.org/10.4236/wjnse.2015.51004
El Naschie, M.S. (2014) 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, 3, 1-5. http://dx.doi.org/10.4236/ijmnta.2014.31001
El Naschie, M.S., Marek-Crnjac, L., Helal, M.A. and He, J.-H. (2014) A Topological Magueijo-Smolin Varying Speed of Light Theory, the Accelerated Cosmic Expansion and the Dark Energy of Pure Gravity. Applied Mathematics, 5, 1780-1790. http://dx.doi.org/10.4236/am.2014.512171
El Naschie, M.S. (2015) On a Non-Perturbative Quantum Relativity Theory Leading to a Casimir-Dark Energy Nanotech Reactor Proposal. Open Journal of Applied Sciences, 5, 313-324. http://dx.doi.org/10.4236/ojapps.2015.57032
El Naschie, M.S. (2014) From Chern-Simon, Holography and Scale Relativity to Dark Energy. Journal of Applied Mathematics and Physics, 2, 634-638. http://dx.doi.org/10.4236/jamp.2014.27069
El Naschie, M.S. (2014) Why E Is Not Equal to mc2. Journal of Modern Physics, 5, 743-750. http://dx.doi.org/10.4236/jmp.2014.59084
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
El Naschie, M.S. (2014) Cosmic Dark Energy Density from Classical Mechanics and Seemingly Redundant Riemannian Finitely Many Tensor Components of Einstein’s General Relativity. World Journal of Mechanics, 4, 153-156. http://dx.doi.org/10.4236/wjm.2014.46017
El Naschie, M.S. (2015) Dark Energy and Its Cosmic Density from Einstein’s Relativity and Gauge Fields Renormalization Leading to the Possibility of a New ‘tHooft Quasi Particle. The Open Astronomy Journal, 8, 1-17. http://dx.doi.org/10.2174/1874381101508010001
El Naschie, M.S. (2015) If Quantum “Wave” of the Universe Then Quantum “Particle” of the Universe: A Resolution of the Dark Energy Question and the Black Hole Information Paradox. International Journal of Astronomy & Astrophysics, 5, 243-247. http://dx.doi.org/10.4236/ijaa.2015.54027
El Naschie, M.S. (2014) From Modified Newtonian Gravity to Dark Energy via Quantum Entanglement. Journal of Applied Mathematics and Physics, 2, 803-806. http://dx.doi.org/10.4236/jamp.2014.28088
El Naschie, M.S. (2014) From Highly Structured E-Infinity Rings and Transfinite Maximally Symmetric Manifolds to the Dark Energy Density of the Cosmos. Advances in Pure Mathematics, 4, 641-648. http://dx.doi.org/10.4236/apm.2014.412073
El Naschie, M.S. (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. http://dx.doi.org/10.4236/wjcmp.2014.42011
El Naschie, M.S. (2015) From Fusion Algebra to Cold Fusion or from Pure Reason to Pragmatism. Open Journal of Philosophy, 5, 319-326. http://dx.doi.org/10.4236/ojpp.2015.56040
El Naschie, M.S. (2016) Einstein-Rosen Bridge (ER), Einstein-Podolsky-Rosen Experiment (EPR) and Zero Measure Rindler-KAM Cantorian Spacetime Geometry (ZMG) Are Conceptually Equivalent. Journal of Quantum Information Science, 6, 1-9. http://dx.doi.org/10.4236/jqis.2016.61001
El Naschie, M.S. (2015) A Casimir-Dark Energy Nano Reactor Design—Phase I. Natural Science, 7, 287-298. http://dx.doi.org/10.4236/ns.2015.76032
El Naschie, M.S. (2014) Einstein’s General Relativity and Pure Gravity in a Cosserat and De Sitter-Witten Spacetime Setting as the Explanation of Dark Energy and Cosmic Accelerated Expansion. International Journal of Astronomy and Astrophysics, 4, 332-339. http://dx.doi.org/10.4236/ijaa.2014.42027
El Naschie, M.S. (2015) Application of Dvoretzky’s Theorem of Measure Concentration in Physics and Cosmology. Open Journal of Microphysics, 5, 11-15. http://dx.doi.org/10.4236/ojm.2015.52002
El Naschie, M.S. (2015) Quantum Fractals and the Casimir-Dark Energy Duality—The Road to a Clean Quantum Energy Nano Reactor. Journal of Modern Physics, 6, 1321-1333. http://dx.doi.org/10.4236/jmp.2015.69137
Ho, M.-W., El Naschie, M.S. and Vitello, G. (2015) Is Spacetime Fractal and Quantum Coherent in the Golden Mean? Global Journal of Science Frontier Research, 15, 61-80.
Marek-Crnjac, L. (2015) On El Naschie’s Fractal-Cantorian Space-Time and Dark Energy—A Tutorial Review. Natural Science, 7, 581-598. http://dx.doi.org/10.4236/ns.2015.713058
El Naschie, M.S. (2015) Hubble Scale Dark Energy Meets Nano Scale Casimir Energy and the Rational of Their T-Duality and Mirror Symmetry Equivalence. World Journal of Nano Science and Engineering, 5, 57-67. http://dx.doi.org/10.4236/wjnse.2015.53008
El Naschie, M.S. (2015) The Casimir Effect as a Pure Topological Phenomenon and the Possibility of a Casimir Nano Reactor—A Preliminary Design. American Journal of Nano Research and Application, 3, 33-40.
El Naschie, M.S. (2016) On a Fractal Version of Witten’s M-Theory. International Journal of Astronomy & Astrophysics, 6, 135-144. http://dx.doi.org/10.4236/ijaa.2016.62011
El Naschie, M.S. (2014) Rindler Space Derivation of Dark Energy. Journal of Modern Physics Applications, 6, 1-10.
El Naschie, M.S. (2015) From Kantian-Reinen Vernunft to the Real Dark Energy Density of the Cosmos via the Measure Concentration of Convex Geometry in Quasi Banach Spacetime. Open Journal of Philosophy, 5, 123-130. http://dx.doi.org/10.4236/ojpp.2015.51014
El Naschie, M.S. (2016) From Witten’s 462 Supercharges of 5-D Branes in Eleven Dimensions to the 95.5 Percent Cosmic Dark Energy Density behind the Accelerated Expansion of the Universe. Journal of Quantum Information Science, 6, 57-61. http://dx.doi.org/10.4236/jqis.2016.62007
El Naschie, M.S. (2016) Quantum Dark Energy from the Hyperbolic Transfinite Cantorian Geometry of the Cosmos. Natural Science, 8, 152-159. http://dx.doi.org/10.4236/ns.2016.83018
El Naschie, M.S. (2016) On a Quantum Gravity Fractal Spacetime Equation: QRG HD + FG and Its Application to Dark Energy—Accelerated Cosmic Expansion. Journal of Modern Physics, 7, 729-736. http://dx.doi.org/10.4236/jmp.2016.78069
El Naschie, M.S. (2016) The Emergence of Spacetime from the Quantum in Three Steps. Advances in Pure Mathematics, 6, 446-454. http://dx.doi.org/10.4236/apm.2016.66032
El Naschie, M.S. (2016) Negative Norms in Quantized Strings as Dark Energy Density of the Cosmos. World Journal of Condensed Matter Physics, 6, 63-67. http://dx.doi.org/10.4236/wjcmp.2016.62009
El Naschie, M.S. (2016) On the Stringy Ghosts Which We Call the Missing Dark Energy of the Cosmos. Journal of Applied Mathematics and Physics, 4, 979-987. http://dx.doi.org/10.4236/jamp.2016.46105
El Naschie, M.S. (2016) Einstein’s Dark Energy via Similarity Equivalence, ‘tHooft Dimensional Regularization and Lie Symmetry Groups. International Journal of Astronomy & Astrophysics, 6, 56-81. http://dx.doi.org/10.4236/ijaa.2016.61005
Ott, E. (1993) Chaos in Dynamical Systems. Cambridge University Press, Cambridge.
Addison, P.S. (1997) Fractals and Chaos: An Illustrated Course. Institute of Physics Publishing, Bristol. http://dx.doi.org/10.1887/0750304006
Ruelle, D. (1991) Chance and Chaos. Princeton University Press, Princeton.
Diacu, F. and Holmes, P. (1996) Celestial Encounters. Princeton University Press, Princeton.
Kapitaniak, T. (1992) Chaotic Oscillators—Theory and Applications. World Scientific, Singapore. http://dx.doi.org/10.1142/9789814360258
El Naschie, M.S. (1998) The Average (n) Sphere Spans a Four Dimensional Manifold. Chaos, Solitons & Fractals, 9, 1789-1792. http://dx.doi.org/10.1016/S0960-0779(98)00126-X
El Naschie, M.S. (1998) COBE Satellite Measurement, Hyper Spheres, Superstrings and the Dimension of Spacetime. Chaos, Solitons & Fractals, 9, 1445-1471. http://dx.doi.org/10.1016/S0960-0779(98)00120-9
El Naschie, M.S. (1998) The Mean Sphere as a Three Manifold in R4. Chaos, Solitons & Fractals, 9, 1631-1635. http://dx.doi.org/10.1016/S0960-0779(98)00129-5
Conway, J.H. and Sloane, N.J. (1999) Sphere Packings, Lattices and Groups. Springer, New York. http://dx.doi.org/10.1007/978-1-4757-6568-7
El Naschie, M.S. (2013) Dark Energy from Kaluza-Klein Spacetime and Noether’s Theorem via Lagrangian Multiplier Method. Journal of Modern Physics, 4, 757-760. http://dx.doi.org/10.4236/jmp.2013.46103
El Naschie, M.S. (2008) Kaluza-Klein Unification—Some Possible Extensions. Chaos, Solitons & Fractals, 37, 16-22. http://dx.doi.org/10.1016/j.chaos.2007.09.079
El Naschie, M.S. (2013) Electromagnetic and Gravitational Origin of Dark Energy in Kaluza-Klein D = 5 Spacetime. Piers Proceedings, Stockholm, 12-15 August 2013, 94-97.
Polchinski, J. (1998) String Theory Vol. 1. Cambridge University Press, Cambridge. (See in Particular p. 22, Equation (1.3.33))
El Naschie, M.S., Olsen, S., He, J.H., Nada, S., Marek-Crnjac, L. and Helal, A. (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
El Naschie, M.S. (1991) Physics-Like Mathematics of Chaos and Ergodicity in Four Dimensions. Proceedings of the 13th World Congress on Computation and Applied Mathematics, 2, 851-852.
El Naschie, M.S. (1998) Von Neumann Geometry and E-Infinity Quantum Spacetime. Chaos, Solitons & Fractals, 9, 2023-2030.
El Naschie, M.S. (2004) Small World Network, E-Infinity Topology and the Mass Spectrum of High Energy Particle Physics. Chaos, Solitons & Fractals, 19, 689-697. http://dx.doi.org/10.1016/S0960-0779(03)00337-0