Three Quantum Particles Hardy Entanglement from the Topology of Cantorian-Fractal Spacetime and the Casimir Effect as Dark Energy – A Great Opportunity for Nanotechnology

Three Quantum Particles Hardy Entanglement from the Topology of Cantorian-Fractal Spacetime and the Casimir Effect as Dark Energy – A Great Opportunity for Nanotechnology

Full PDF Paper

Authors 

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

To cite this article 
Mohamed S. El Naschie, Three Quantum Particles Hardy Entanglement from the Topology of Cantorian-Fractal Spacetime and the Casimir Effect as Dark Energy – A Great Opportunity for Nanotechnology, American Journal of Nano Research and Application. Vol. 3, No. 1, 2015, pp. 1-5. doi: 10.11648/j.nano.20150301.11

Abstract 
The present work brings together three different fields which depend crucially upon nano hardware under the umbrella of E-infinity theoretical framework. We start by following E-infinity topological methodology by dividing Hardy’s entanglement into two parts, a global ‘counterfactual’ part given by Φ3 where Φ = 2/(1+ √5) and a ‘local’ part Φn where n is the number of quantum particles. For Hardy’s celebrated gedankenexperiment with two quantum particles, which was moreover experimentally confirmed with high accuracy, the quantum probability is found for n = 2 to be P(2) (Hardy) = Φ3+2= Φ5 exactly as calculated by Hardy using orthodox quantum mechanics. Applying the same topological E-infinity entanglement theory to three quantum particles give a maximal Φ6 as well as a three partite much smaller value equal Φ3(1− Φ3)/ = 0.018033989. We conclude by outlining the relevant and extremely timely ideas and remarks on the possible connection, via a state of the art nanotechnology, to the Casimir effect as a conjectured origin of dark energy.

KeywordsThree Quantum Particles Entanglement, Hardy’s Topological Entanglement, E-Infinity, Hilbert Space, Cantorian Spacetime, Golden Mean Number System, Casimir Effect Connection to Dark Energy, Nanotechnology

Reference

[01]
L. Hardy, Nonlocality of two particles without inequalities for almost all entangled states. Phys. Rev. Lett. Vol. 71(11), 1993, pp. 1665-1668.
[02]
J.S. Bell, Speakable and Unspeakable in Quantum Mechanics. Cambridge University Press, Cambridge 1991)
[03]
Ji-Huan He et al, Quantum golden mean entanglement test as the signature of the fractality of micro spacetime. Nonlinear Sci. Lett B, Vol. 1(2), 2011, pp. 45-50.
[04]
Mohamed S. El Naschie, Quantum Entanglement as a Consequence of a Cantorian Micro Spacetime Geometry. Journal of Quantum Information Science, Vol. 1(2), 2011, pp. 50-53.
[05]
Mohamed S. El Naschie, Quantum Entanglement: Where Dark Energy and Negative, Accelerated Expansion of the Universe Comes from. Journal of Quantum Information Science, Vol. 3(2), 2013, pp 55-57.
[06]
R. Penrose, The Road to Reality. J. Cape, London, UK. 2004
[07]
M.S. El Naschie, M.A. Helal, L. Marek-Crnjac and Ji-Huan He, Transfinite corrections as a Hardy type quantum entanglement. Fractal Spacetime & Noncommutative Geometry in Quantum & High Energy Physics, Vol. 2(1), 2012, pp. 98-101.
[08]
M.S. El Naschie, Ji-Huan He, S. Nada, L. Marek-Crnjac and M. Helal, Golden mean computer for high energy physics. Fractal Spacetime and Noncommutative Geometry in Quantum and High Energy Physics. Vol. 2(2), 2012, pp. 80-92.
[09]
M.S. El Naschie and S.A. Olsen, When zero is equal one: A set theoretical resolution of quantum paradoxes. Fractal Spacetime & Noncommutative Geometry in Quantum High energy Physics, Vol. 1(1), 2011, pp. 11-24.
[10]
M.S. El Naschie, Electroweak connection and universality of Hardy’s quantum entanglement. Fractal Spacetime & Noncommutative Geometry in Quantum High energy Physics, Vol. 1(1), 2011, pp. 25-30.
[11]
L. Marek-Crnjac, Ji-Huan He and M.S. El Naschie, On the universal character of Hardy’s quantum entanglement and its geometrical-topological interpretation. Fractal Spacetime & Noncommutative Geometry in Quantum & High Energy Phys. Vol. 2(2), 2012, pp. 118-12.
[12]
M.S. El Naschie, L. Marek-Crnjac and Ji-Huan He, Using Hardy’s entanglement, Nash embedding and quantum groups to derive the four dimensionality of spacetime. Fractal Spacetime & Noncommutative Geometry in Quantum & High Energy Phys. Vol. 2(2), 2012, pp. 107-112.
[13]
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(6), 2013, pp. 357-361.
[14]
Mohamed S. El Naschie, A Rindler-KAM Spacetime Geometry and Scaling the Planck Scale Solves Quantum Relativity and Explains Dark Energy. International Journal of Astronomy and Astrophysics, Vol. 3(4), 2013, pp. 483-493.
[15]
Mohamed S. El Naschie, Topological-Geometrical and Physical Interpretation of the Dark Energy of the Cosmos as a “Halo” Energy of the Schrödinger Quantum Wave
Journal of Modern Physics, Vol. 4(5), 2013, pp. 591-596.
[16]
M.S. El Naschie, The quantum gravity Immirzi parameter – A general physical and topological interpretation. Gravity and Cosmology, Vol. 19(3), 2013, pp. 151-153.
[17]
Mohamed S. El Naschie, Compactified dimensions as produced by quantum entanglement, the four dimensionality of Einstein’s smooth spacetime and ‘tHooft’s 4-ε fractal spacetime. American Journal of Astronomy & Astrophysics, Vol. 2(3), 2014, pp. 34-37.
[18]
Mohamed S. El Naschie, Electromagnetic—pure gravity connection via Hardy’s quantum entanglement. 
Journal of Electromagnetic Analysis and Applications, Vol. 6(9), 2014, pp. 233-237.
[19]
L. Marek-Crnjac and Ji-Huan He, An Invitation to El Naschie’s theory of Cantorian space-time and dark energy. International Journal of Astronomy and Astrophysics, Vol. 3(4), 2013, pp. 464-471.
[20]
M.S. El Naschie, A review of E-infinity and the mass spectrum of high energy particle physics. Chaos, Solitons & Fractals, Vol. 19(1), 2004, pp. 209-236.
[21]
M.S. El Naschie, Superstrings, knots and noncommutative geometry in E-infinity space. International Journal of Theoretical Physics, Vol. 37(12), 1998, pp. 2935-2951.
[22]
Mohamed S. El Naschie, On a new elementary particle from the disintegration of the symplectic 't Hooft-Veltman-Wilson fractal spacetime. World Journal of Nuclear Science and ATechnology, Vol. 4(4), 2014, pp. 216-221.
[23]
W. Tan, Y. Li, H.Y. Kong and M.S. El Naschie, From nonlocal elasticity to nonlocal spacetime and nanoscience. Bubbfil Nano Technology, Vol. 1(1), 2014, pp. 3-12.
[24]
D. Heiss (Editor):, Fundamentals of Quantum Information. Springer, Berlin 2002.
[25]
I. Gengtsson and K. Zyczkowski, Geometry of Quantum States. Cambridge University Press, Cambridge 2006.
[26]
M.A. Nielsen and I.L. Chuang, Quantum Computation and Quantum Information. Cambridge University Press, Cambridge, 2010.
[27]
A. Furusawa and P. van Loock, Quantum Teleportation and Entanglement. Wiley-VCH, Weinheim, Germany, 2011.
[28]
J.K. Pachos, Introduction to Topological Quantum Computation. Cambridge University Press, Cambridge, 2012.
[29]
D.G. Marinescu and G.M. Marinescu, Classical and Quantum Information. Elsevier, Amsterdam, 2012.
[30]
Mohamed S. El Naschie, Casimir-like energy as a double Eigenvalues of quantumly entangled system leading to the missing dark energy density of the cosmos. International Journal of High Energy Physics, Vol. 1(5), 2014, pp. 55-63.
[31]
J. Matsumoto, The Casimir effect as a candidate of dark energy. arXiv: 1303.4067[hep-th]26December 2013.
[32]
K. Eric Drexler, Engines of Creation. Fourth Estate Ltd., London, 1990.
[33]
P. Day (Editor), Unveiling The Microcosmos. Oxford University Press, Oxford, 1996.
[34]
S.E. Lyshevski, Nano and Microelectromechanical Systems. CRC Press, Boca Ratan, 2001.
[35]
L.E. Foster, Nanotechnology, Science, Innovation and Opportunity. Prentice Hall, Boston, 2006.
[36]
M. Krummenacker and J. Lewis (Editors), Prospects in Nanotechnology. John Wiley, New York, 1995.
[37]
M.S. El Naschie, Nanotechnology for the developing world. Chaos, Solitons & Fractals, Vol. 30(4), 2006, pp. 769-773.
[38]
M.S. El Naschie, Chaos and fractals in nano and quantum technology. Chaos, Solitons & Fractals, Vol. 9(10), 1998, pp. 1793-1802.
[39]
M.S. El Naschie, Nanotechnology and the political economy of the developing world. International, May 2007, pp. 7-12. (Periodical International Economic Magazine by AS&S Publishing Ltd, Camden Town, London, UK, Registration No. 04761267).
[40]
M.S. El Naschie, Can nanotechnology slow the aging process by inteferring with the arrow of time. International, June 2007, pp. 10-15. (Periodical International Economic Magazine by AS&S Publishing Ltd, Camden Town, London, UK, Registration No. 04761267).
[41]
M. Aboulanan, The making of the future via nanotechnology (in Arabic). International, July 2007, pp. 32-35. (Periodical International Economic Magazine by AS&S Publishing Ltd, Camden Town, London, UK, Registration No. 04761267).
[42]
M.S. El Naschie, From relativity to deterministic chaos in science and society. International, August 2007, pp. 11-17. (Periodical International Economic Magazine by AS&S Publishing Ltd, Camden Town, London, UK, Registration No. 04761267).
[43]
M.S. El Naschie, The political economy of nanotechnology and the developing world. International Journal of Electrospun Nanofibers and Application. I(I), 2007, pp. 41-50. Published by Research Science Press, India.
[44]
D. Brito and J. Rosellon, Energy and Nanotechnology: Prospects for solar energy in the 21st century. The James A. Baker III Institute for Public Policy of Rice University, December 2005, pp. 1-16.
[45]
O.E. Rössler and M.S. El Naschie, Interference through causality vacillation. In Symposium on the Foundations of Modern Physics, Helsinki, Finland, June 1994, pp. 13-16.
[46]
O.E. Rössler and M.S. El Naschie: Interference is Exophysically Absent. In Endophysics – The World As An Interface. World Scientific, Singapore, 1998, pp. 159-160.
[47]
M.S. El Naschie, A note on quantum gravity and Cantorian spacetime. Chaos, Solitons & Fractals, 8(1), p. 131-133 (1997).
[48]
M.S. El Naschie, The symplictic vacuum exotic quasi particles and gravitational instantons. Chaos, Solitons & Fractals, 22(1), 2004, pp. 1-11.
[49]
M. Agop, E-infinity Cantorian spacetime, polarization gravitational field and van der Waals-type forces. Chaos, Solitons & Fractals, 18(1), 2003, pp. 1-16.
[50]
Mohamed S. El Naschie, A Rindler-KAM spacetime geometry and scaling the Planck scale solves quantum relativity and explains dark energy. International Journal of Astronomy and Astrophysics, Vol. 3(4), 2013, pp. 483-493.
[51]
J. Cugnon, The Casimir effect and the vacuum energy. Few-body System, 53(1-2), 2012, pp. 181-188.
[52]
K.A. Milton, Resource Letter VWCPF-1 van der Waals and Casimir-Polder forces. American Journal of Physics, 79, 2011, pp. 697.
[53]
M. Ito, Gravity, higher dimensions, nanotechnology and particles physics. Journal of Physics, Conference Series, 89(1), 2007, p. 1-8.
[54]
M.S. El Naschie, Casimir-like energy as a double Eigenvalue of quantumly entangled system leading to the missing dark energy density of the cosmos. International Journal of High Energy Physics, 1(5), 2014, pp. 55-63.

Banach spacetime-like Dvoretzky volume concentration as cosmic holographic dark energy

Banach spacetime-like Dvoretzky volume concentration as cosmic holographic dark energy 

By 

Dr. Mohamed S. El Naschie

Full PDF Paper
Abstract 
We start from Banach spaces motivated theory of convex geometry in high dimensionality and give a new additional confirmation of previous derivations of the 96 per cent dark energy density of the cosmos. The result derives directly from the purely geometric-topological phenomenon of measure-mass concentration and gives an unqualified complete confirmation of our previous analysis including the hidden quantum nature of Einstein’s celebrated equation E = mc2. The straight forward relation to holographic dark energy and its endophysical nature is also outlined

KeywordsDvoretzky’s Theorem, Banach Spaces, K-Theory, Relativity, Cantorian Spacetime, Endophysics, Holographic Dark Energy

Reference

[01]
W. Rindler, Relativity (Special, General and Cosmological). Oxford University Press, Oxford. 2004.
[02]
L.B. Okun, Energy and mass in relativity theory. World Scientific, Singapore 2009.
[03]
W. Rindler, Introduction to Special Relativity. Oxford Science Publications, Oxford 1991.
[04]
Mohamed S. El Naschie, On a New Elementary Particle from the Disintegration of the Symplectic ‘tHooft-Veltman-Wilson Fractal Spacetime. World Journal of Nuclear Science and Technology, 4(4), 2014, pp. 216-221.
[05]
M. A. Helal, L. Marek-Crnjac, Ji-Huan He, 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(4), 2013, pp. 141-145.
[06]
L. Marek-Crnjac, Ji-Huan He, An Invitation to El Naschie’s Theory of Cantorian Space-Time and Dark Energy. International Journal of Astronomy and Astrophysics, 3(4), 2013, pp. 464-471.
[07]
Jean-Paul Auffray, E-Infinity Dualities, Discontinuous Spacetimes, Xonic Quantum Physics and the Decisive Experiment. Journal of Modern Physics, 5(15), 2014, pp. 1427-1436.
[08]
Mohamed S. El Naschie, Quantum Entanglement as a Consequence of a Cantorian Micro Spacetime Geometry. Journal of Quantum Information Science, 1(2), 2011, pp. 50-53.
[09]
Mohamed S. El Naschie, A Resolution of Cosmic Dark Energy via a Quantum Entanglement Relativity Theory. Journal of Quantum Information Science, 3(1), 2013, pp. 23-26.
[10]
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. International Journal of Modern Nonlinear Theory and Application, 2(1), 2013, pp. 43-54.
[11]
Mohamed S. El Naschie, Quantum Entanglement: Where Dark Energy and Negative Gravity plus Accelerated Expansion of the Universe Comes From. Journal of Quantum Information Science, 3(2), 2013, pp. 57-77.
[12]
Mohamed S. El Naschie, A Fractal Menger Sponge Space-Time Proposal to Reconcile Measurements and Theoretical Predictions of Cosmic Dark Energy. International Journal of Modern Nonlinear Theory and Application, 2(2), 2013, pp. 107-121.
[13]
Mohamed S. El 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, 2(3), 2013, pp. 167-169.
[14]
Mohamed S. El Naschie, A Rindler-KAM Spacetime Geometry and Scaling the Planck Scale Solves Quantum Relativity and Explains Dark Energy. International Journal of Astronomy and Astrophysics, 3(4), 2013, pp. 483-493.
[15]
M. S. El Naschie, What Is the Missing Dark Energy in a Nutshell and the Hawking-Hartle Quantum Wave Collapse. International Journal of Astronomy and Astrophysics, 3(3), 2013, pp. 205-211.
[16]
Mohamed S. El Naschie, The Missing Dark Energy of the Cosmos from Light Cone Topological Velocity and Scaling of the Planck Scale. Open Journal of Microphysics, 3(3), 2013, pp. 64-70.
[17]
Mohamed S. El Naschie, From Yang-Mills Photon in Curved Spacetime to Dark Energy Density. Journal of Quantum Information Science, 3(4), 2013, pp. 121-126.
[18]
Mohamed S. El 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, 3(1), 2014, pp. 1-5.
[19]
Mohamed S. El Naschie, 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(6), 2014, pp. 153-156.
[20]
Mohamed S. El Naschie, Capillary Surface Energy Elucidation of the Cosmic Dark Energy—Ordinary Energy Duality. Open Journal of Fluid Dynamics, 4(1), 2014, pp. 15-17.
[21]
Mohamed S. El Naschie, 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(2), 2014, pp. 332-339.
[22]
Mohamed S. El Naschie, Electromagnetic—Pure Gravity Connection via Hardy’s Quantum Entanglement. Journal of Electromagnetic Analysis and Applications, 6(9), 2014, pp. 233-237.
[23]
Mohamed S. El Naschie, Cosmic Dark Energy from ‘t Hooft’s Dimensional Regularization and Witten’s Topological Quantum Field Pure Gravity. Journal of Quantum Information Science, 4(2), 2014, pp. 83-91.
[24]
Mohamed S. El Naschie, 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(2), 2014, pp. 74-77.
[25]
Mohamed S. El Naschie, The Meta Energy of Dark Energy. Open Journal of Philosophy. 4(2), 2014, pp. 157-159.
[26]
Mohamed S. El Naschie, Pinched Material Einstein Space-Time Produces Accelerated Cosmic Expansion. International Journal of Astronomy and Astrophysics. 4(1), 2014, pp. 80-90.
[27]
Mohamed S. El Naschie, From Chern-Simon, Holography and Scale Relativity to Dark Energy. Journal of Applied Mathematics and Physics, 2(7), 2014, pp. 634-638.
[28]
Mohamed S. El Naschie, Why E Is Not Equal to mc2. Journal of Modern Physics, 5(9), 2014, pp. 743-750.
[29]
Mohamed S. El Naschie, Nash Embedding of Witten’s M-Theory and the Hawking-Hartle Quantum Wave of Dark Energy. Journal of Modern Physics, 4(10), 2013, pp. 1417-1428.
[30]
Mohamed S. El Naschie, Dark Energy from Kaluza-Klein Spacetime and Noether’s Theorem via Lagrangian Multiplier Method. Journal of Modern Physics, 4(6), 2013, pp. 757-760.
[31]
Mohamed S. El Naschie, The hyperbolic Extension of Sigalotti-Hendi-Sharifzadeh’s Golden Triangle of Special Theory of Relativity and the Nature of Dark Energy. Journal of Modern Physics, 4(3), 2013, pp. 354-356.
[32]
Mohamed S. El Naschie, 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(5), 2013, pp. 591-596.
[33]
M. S. El Naschie, From Modified Newtonian Gravity to Dark Energy via Quantum Entanglement. Journal of Applied Mathematics and Physics, 2(8), 2014, pp. 803-806.
[34]
Ji-Huan He, L. Marek-Crnjac, Mohamed El Naschie’s Revision of Albert Einstein’s E = m0c2: A Definite Resolution of the Mystery of the Missing Dark Energy of the Cosmos International. Journal of Modern Nonlinear Theory and Application, 2(1), 2013, pp. 55-59.
[35]
M. S. El Naschie, L. Marek-Crnjac, Deriving the Exact Percentage of Dark Energy Using a Transfinite Version of Nottale’s Scale Relativity. International Journal of Modern Nonlinear Theory and Application, 1(4), 2012, pp. 118-124.
[36]
Mohamed S. El Naschie, Atef Helal, Dark Energy Explained via the Hawking-Hartle Quantum Wave and the Topology of Cosmic Crystallography. International Journal of Astronomy and Astrophysics, 3(3), 2013, pp. 318-343.
[37]
L. Marek-Crnjac, Mohamed S. El Naschie: Chaotic Fractal Tiling for the Missing Dark Energy and Veneziano Model. Applied Mathematics, 4(11B), 2013, pp. 22-29.
[38]
L. Marek-Crnjac, M. S. El Naschie, Quantum Gravity and Dark Energy Using Fractal Planck Scaling. Journal of Modern Physics, 4(11A), 2013, pp. 31-38.
[39]
L. Marek-Crnjac, Mohamed S. El Naschie, Ji-Huan He, Chaotic Fractals at the Root of Relativistic Quantum Physics and Cosmology. International Journal of Modern Nonlinear Theory and Application, 2(1A), 2013, pp. 78-88.
[40]
M. S. El Naschie, S. Olsen, J. H. He, S. Nada, L. Marek-Crnjac, A. Helal, On the Need for Fractal Logic in High Energy Quantum Physics. International Journal of Modern Nonlinear Theory and Application, 1(3), 2012, pp. 84-92.
[41]
Mohamed Salah El Naschie, Leila Marek-Crnjac, Mohamed Atef Helal, Ji-Huan He, A Topological Magueijo-Smolin Varying Speed of Light Theory, the Accelerated Cosmic Expansion and the Dark Energy of Pure Gravity. Applied Mathematics, 5(12), 2014, pp. 1780-1790.
[42]
Mohamed S. El Naschie, Compactified dimensions as produced by quantum entanglement, the four dimensionality of Einstein’s smooth spacetime and ‘tHooft’s 4- fractal spacetime. American Journal of Astronomy & Astrophysics, 2(3), 2014, pp. 34-37.
[43]
Mohamed S. El Naschie, Hardy's Entanglement as the Ultimate Explanation for the Observed Cosmic Dark Energy and Accelerated Expansion. International Journal High Energy Physics, 1(2), 2014, pp. 13-17.
[44]
Mohamed S. El Naschie, Deriving E = mc2 /22 of Einstein’s ordinary quantum relativity energy density from the Lie symmetry group SO(10) of grand unification of all fundamental forces and without quantum mechanics. American Journal of Mechanics & Applications, 2(2), 2014, pp. 6-9.
[45]
Mohamed S. El Naschie, Cosserat-Cartan Modification of Einstein-Riemann Relativity and Cosmic Dark Energy Density. American Journal of Modern Physics. 3(2), 2014, pp. 82-87.
[46]
Mohamed S. El Naschie, Asymptotically safe pure gravity as the source of dark energy of the vacuum. Int. Journal Astrophysics & Space Science, 2(1), 2014, pp. 12-15.
[47]
Mohamed S. El Naschie, Logarithmic Running of’t Hooft-Polyakov Monopole to Dark Energy. International Journal of High Energy Physics, 1(1), 2014, pp. 1-5.
[48]
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, 2(6), 2013, pp. 357-361.
[49]
L. Marek-Crnjac, Modification of Einstein’s E = mc2 to E = (1/22)mc2. American Journal of Modern Physics, 2(5), 2013, pp. 255-263.
[50]
M.S. El Naschie, The quantum gravity Immirzi parameter – A general physical and topological interpretation. Gravitation and Cosmology, 19(3), 2013, pp. 151-155.
[51]
M.S. El Naschie, Determining the missing dark energy density of the cosmos from a light cone exact relativistic analysis. Journal of Physics, 2(2), 2013, pp. 19-25.
[52]
M.S. El Naschie, The quantum entanglement behind the missing dark energy. Journal of Modern Physics and Applications, 2(1), 2013, pp. 88-96.
[53]
M.S. El Naschie, Dark energy via quantum field theory in curved spacetime. Journal Modern Physics and Applications, 2, 2014, pp. 1-7.
[54]
M.S. El Naschie, Rindler space derivation of dark energy. Journal of Modern Physics Applications. 6, 2014, pp. 1-10.
[55]
Wei Tang et al, From nonlocal elasticity to nonlocal spacetime and nano science. Bubbfil Nanotechnology. 1(1), 2014, pp. 3-12.
[56]
M.S. El Naschie, To dark energy theory from a Cosserat-like model of spacetime. Problems of Nonlinear Analysis in Engineering Systems. 1(41), Vol. 20, 2014, pp. 79-98.
[57]
M.S. El Naschie, Revising Einstein’s E = mc2; A theoretical resolution of the mystery of dark energy. Proceedings of the Fourth Arab Int. Conference in Physics and Material Science, Egypt. 1-30 October, 2012, pp. 1.
[58]
K.M. Ball: Volume ratios and a reverse isoperimetric inequality. Journal of London Mathematical Society. 44, 1991, pp. 351-359.
[59]
G. Pisier, The volume of convex bodies and Banach space geometry. Tracts in Math 94, Cambridge University Press, Cambridge, 1989.
[60]
B.S. Kasin, The width of certain finite-dimensional sets and classes of smooth functions. IZV. Akad. Nauk. SSSR. Ser. Mat. 41(2), 1977, pp. 334-351 (in Russian).
[61]
O. Guedon, Concentration phenomena in high dimensional geometry. arXiv:1310.1204V1[math]4 Oct 2013.
[62]
Ji-Huan He (Guest Editor), Fractal Spacetime and Noncommutative Geometry in Quantum and High Energy Physics. 3(1). Special issue on recent developments on dark energy and dark matter, 2013, pp. 1-62.
[63]
Ji-Huan He, M.S. El Naschie, On the monadic nature of quantum gravity as a highly structured golden ring, spaces and spectra. Fractal Spacetime and Noncommutative Geometry in Quantum and High Energy Physics. 2(2), 2012, pp. 94-98.
[64]
M.S. El Naschie, Towards a general transfinite set theory for quantum mechanics. Fractal Spacetime and Noncommutative Geometry in Quantum and High Energy Physics. 2(2), 2012, pp. 135-142.
[65]
M.S. El Naschie, Ji-Huan He, S. Nada, L. Marek-Crnjac, M. Helal, Golden mean computer for high energy physics. Fractal Spacetime and Noncommutative Geometry in Quantum and High Energy Physics. 2(2), 2012, pp. 80-92.
[66]
M.S. El Naschie, The minus one connection of relativity, quantum mechanics and set theory. Fractal Spacetime and Noncommutative Geometry in Quantum and High Energy Physics. 2(2), 2012, pp. 131-134.
[67]
M.S. El Naschie, 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 Journal of Astronomy. In press.
[68]
M.S. El Naschie, A review of E-infinity and the mass spectrum of high energy particle physics. Chaos, Solitons & Fractals, 19(1), 2004, pp. 209-236.
[69]
M.S. El Naschie, The theory of Cantorian spacetime and high energy particle physics (An informal review). Chaos, Solitons & Fractals, 41, 2009, pp. 2635-2646.
[70]
A. Connes, Noncommutative Geometry. Academic Press, San Diego, USA, 1994.
[71]
S.G. Krantz and H.R. Parks, Geometric Integration Theory. Birkhauser, Boston, USA, 2008.
[72]
M.S. El Naschie, Remarks on super strings, fractal gravity, Nagasawa’s diffusion and Cantorian spacetime. Chaos, Solitons & Fractals, 8(11), 1997, pp. 1873-1886.
[73]
M.S. El Naschie, Introduction to nonlinear dynamics, general relativity and the quantum – The uneven flow of fractal time. Chaos, Solitons & Fractals, 8(5), 1997, pp. vii-x.
[74]
M.S. El Naschie, Hyper-dimensional geometry and the nature of physical spacetime. Chaos, Solitons & Fractals, 10(1), 1999, pp. 155-158.
[75]
M.S. El Naschie, E-infinity – High Energy Communications Nos. 1-90. April 2010 to December 2012.
[76]
Chen Nanxian, Möbius inversion in physics. World Scientific, Singapore 2010.
[77]
Ji-Huan He, A tutorial review on fractal spacetime and fractional calculus. Int. Journal of Theoretical Physics, 53(11), 2014, pp. 3698-3718.
[78]
M.S. El Naschie, On twistors in Cantorian E-infinity space. Chaos, Solitons & Fractals, 12(4), 2001, pp. 741-746.
[79]
O.E. Rössler, Endophysics, World Scientific, Singapore (1998).
[80]
M.S. El Naschie, On a general theory for quantum gravity. In ‘Science of the Interface. Editor H. Diebner, T. Druckrey and P. Weibel. Genista Verlag, Tübingen, Germany, 2001.
[81]
Miao Li, A model of holographic dark energy. Physics Letters B, 603(1-2), 2004, pp. 1-5.
[82]
M.S. El Naschie, Holographic dimensional reduction. Center manifold theorem and E-infinity. Chaos, Solitons & Fractals, 29(4), 2006, pp. 816-822.
[83]
A.P. Balachandran, S. Kürkcüoglu, S. Vaidya, Lectures on fuzzy and fuzzy Susy physics. World Scientific, Singapore 2007.
[84]
J. Bahcall, T. Pivan and S. Weinberg, Dark Matter in The Universe. Second Edition. World Scientific, Singapore, 2004.
[85]
L. Amendola and S. Tsujikawa, Dark Energy – Theory and Observation. Cambridge University Press, Cambridge, 2010.
[86]
P. Ruiz-Lapuente, Dark Energy, Observational and Theoretical Approaches. Cambridge University Press, Cambridge, 2010.
[87]
M.S. El Naschie, 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, 2014, pp. 284-291.
[88]
M.S. El Naschie, Casimir-like energy as a double Eigenvalue of quantumly entangled system leading to the missing dark energy density of the cosmos. Intnational Journal of High Energy Physics, 1(5), 2014, pp. 55-63.
[89]
S. Perlmutter et al, Supernova cosmology project collaboration “Measurements of omega and lambda from 42 high redshift supernova. Astrophysics Journal, 517, 1999, pp. 565-585.