A black hole is essentially a relativistic as well as a quantum object. Therefore the information paradox of black holes is a consequence of the clash between these two most fundamental theories of modern physics. It is logical to conclude that a resolution of the problem requires some form of a quantum gravity theory. The present work proposes such a resolution using set theory and pointless spacetime geometry.
Marek-Crnjac, L. (2013) Cantorian Space-Time Theory: The Physics of Empty Sets in Connection with Quantum Entanglement and Dark Energy. Lambert Academic Publishing, Saarbrucken.
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
El Naschie, M.S. (1998) Some Tentative Proposals for the Experimental Verification of Cantorian Micro Spacetime. Chaos, Solitons & Fractals, 9, 143-144. http://dx.doi.org/10.1016/S0960-0779(97)00175-6
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El Naschie, M.S. (1998) The Fractal Dimension of Spacetime—Remarks on Theoretical Derivation and Experimental Verification. Chaos, Solitons & Fractals, 9, 1211-1217. http://dx.doi.org/10.1016/S0960-0779(97)00194-X
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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
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. http://dx.doi.org/10.4236/ojm.2013.34020
Marek-Crnjac, L. and He, J.-H. (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
Auffray, J.-P. (2014) E-Infinity Dualities, Discontinuous Spacetimes, Xonic Quantum Physics and the Decisive Experiment. Journal of Modern Physics, 5, 1427-1436. http://dx.doi.org/10.4236/jmp.2014.515144
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. (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
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
El Naschie, M.S. (2013) Quantum Entanglement: Where Dark Energy and Negative Gravity plus Accelerated Expansion of the Universe Comes from. Journal of Quantum Information Science, 3, 57-77. http://dx.doi.org/10.4236/jqis.2013.32011
El Naschie, M.S. (2013) 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, 107-121. http://dx.doi.org/10.4236/ijmnta.2013.22014
El Naschie, M.S. (2013) 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, 167-169. http://dx.doi.org/10.4236/ijmnta.2013.23023
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, 3, 483-493. http://dx.doi.org/10.4236/ijaa.2013.34056
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
El Naschie, M.S. (2013) The Missing Dark Energy of the Cosmos from Light Cone Topological Velocity and Scaling of the Planck Scale. Open Journal of Microphysics, 3, 64-70. http://dx.doi.org/10.4236/ojm.2013.33012
El Naschie, M.S. (2013) From Yang-Mills Photon in Curved Spacetime to Dark Energy Density. Journal of Quantum Information Science, 3, 121-126. http://dx.doi.org/10.4236/jqis.2013.34016
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. (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. (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) 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. (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. (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. (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. (2014) The Meta Energy of Dark Energy. Open Journal of Philosophy, 4, 157-159. http://dx.doi.org/10.4236/ojpp.2014.42022
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) 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. (2013) Nash Embedding of Witten’s M-Theory and the Hawking-Hartle Quantum Wave of Dark Energy. Journal of Modern Physics, 4, 1417-1428. http://dx.doi.org/10.4236/jmp.2013.410170
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. (2013) 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, 354-356. http://dx.doi.org/10.4236/jmp.2013.43049
El Naschie, M.S. (2013) 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, 591-596. http://dx.doi.org/10.4236/jmp.2013.45084
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
He, J.-H. and Marek-Crnjac, L. (2013) 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, 55-59. http://dx.doi.org/10.4236/ijmnta.2013.21006
El Naschie, M.S. and Marek-Crnjac, L. (2012) 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, 118-124. http://dx.doi.org/10.4236/ijmnta.2012.14018
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
Marek-Crnjac, L. and El Naschie, M.S. (2013) Chaotic Fractal Tiling for the Missing Dark Energy and Veneziano Model. Applied Mathematics, 4, 22-29. http://dx.doi.org/10.4236/am.2013.411A2005
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. http://dx.doi.org/10.4236/jmp.2013.411A1005
Auffray, J.P. (2015) E-Infinity, the Zero Set, Absolute Space and Photon Spin. Journal of Modern Physics, 6, 536-545. http://dx.doi.org/10.4236/jmp.2015.65058
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., 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. (2014) Compactified Dimensions as Produced by Quantum Entanglement, the Four Dimensionality of Einstein’s Smooth Spacetime and ‘t Hooft’s 4-ε Fractal Spacetime. American Journal of Astronomy & Astrophysics, 2, 34-37. http://dx.doi.org/10.11648/j.ajaa.20140203.12
El Naschie, M.S. (2014) Hardy’s Entanglement as the Ultimate Explanation for the Observed Cosmic Dark Energy and Accelerated Expansion. International Journal of High Energy Physics, 1, 13-17. http://dx.doi.org/10.11648/j.ijhep.20140102.11
El Naschie, M.S. (2014) 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, 6-9. http://dx.doi.org/10.11648/j.ajma.20140202.11
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. http://dx.doi.org/10.11648/j.ajmp.20140302.17
El Naschie, M.S. (2014) Asymptotically Safe Pure Gravity as the Source of Dark Energy of the Vacuum. International Journal of Astrophysics and Space Science, 2, 12-15. http://dx.doi.org/10.11648/j.ijass.20140201.13
El Naschie, M.S. (2014) Logarithmic Running of ‘t Hooft-Polyakov Monopole to Dark Energy. International Journal of High Energy Physics, 1, 1-5. http://dx.doi.org/10.11648/j.ijhep.20140101.11
El Naschie, M.S. (2013) 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, 357-361. http://dx.doi.org/10.11648/j.ajmp.20130206.23
Marek-Crnjac, L. (2013) Modification of Einstein’s E = mc2 to E = (1/22)mc2. American Journal of Modern Physics, 2, 255-263. http://dx.doi.org/10.11648/j.ajmp.20130205.14
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
El Naschie, M.S. (2013) Determining the Missing Dark Energy Density of the Cosmos from a Light Cone Exact Relativistic Analysis. Journal of Physics, 2, 19-25.
El Naschie, M.S. (2013) The Quantum Entanglement behind the Missing Dark Energy. Journal of Modern Physics and Applications, 2, 88-96.
El Naschie, M.S. (2014) Dark Energy via Quantum Field Theory in Curved Spacetime. Journal of Modern Physics and Applications, 2, 1-7.
El Naschie, M.S. (2014) Rindler Space Derivation of Dark Energy. Journal of Modern Physics Applications, 6, 1-10.
Tang, W., Li, Y., Kong, H.Y. and El Naschie, M.S. (2014) From Nonlocal Elasticity to Nonlocal Spacetime and Nano Science. Bubbfil Nanotechnology, 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. (2012) Revising Einstein’s E = mc2; A Theoretical Resolution of the Mystery of Dark Energy. Proceedings of the Fourth Arab International Conference in Physics and Material Science, Alexandria, 1-3 October 2012, 1.
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He, J.-H. and El Naschie, M.S. (2012) On the Monadic Nature of Quantum Gravity as a Highly Structured Golden Ring, Spaces and Spectra. Journal of Fractal Spacetime & Noncommutative Geometry in Quantum and High Energy Physics, 2, 94-98.
El Naschie, M.S. (2012) Towards a General Transfinite Set Theory for Quantum Mechanics. Journal of Fractal Spacetime & Noncommutative Geometry in Quantum and High Energy Physics, 2, 135-142.
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El Naschie, M.S. (1997) Remarks on Super Strings, Fractal Gravity, Nagasawa’s Diffusion and Cantorian Spacetime. Chaos, Solitons & Fractals, 8, 1873-1886. http://dx.doi.org/10.1016/S0960-0779(97)00124-0
El Naschie, M.S. (1997) Introduction to Nonlinear Dynamics, General Relativity and the Quantum—The Uneven Flow of Fractal Time. Chaos, Solitons & Fractals, 8, vii-x. http://dx.doi.org/10.1016/S0960-0779(97)88695-X
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El Naschie, M.S. (2001) On Twistors in Cantorian E-Infinity Space. Chaos, Solitons & Fractals, 12, 741-746. http://dx.doi.org/10.1016/S0960-0779(00)00193-4
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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
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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) 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, 55-63. http://dx.doi.org/10.11648/j.ijhep.20140105.11
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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 Science, 5, 313-324. http://dx.doi.org/10.4236/ojapps.2015.57032
Kodiyalam, V. and Sunder, V.S. (2001) Topological Quantum Field Theories from Subfactors. Chapman & Hall/CRC, London.
El Naschie, M.S. (2005) A Few Hints and Some Theorem 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., 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
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El Naschie, M.S. (1995) Iterated Function System, Information and the Two-Slit Experiment of Quantum Mechanics. In: El Naschie, M.S., Rössler, O.E. and Prigogine, I., Eds., Quantum Mechanics, Diffusion and Chaotic Fractals, Pergamon Press/Elsevier, Oxford, 185-189.
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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) 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) 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. (2015) Casimir-Dark Energy Nano Reactor Design Proposal Based on Fractals. International Journal of Innovation is Science and Mathematics, 3, 187-194.
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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, 401-420. http://dx.doi.org/10.1016/S0960-0779(03)00098-5
El Naschie, M.S. (2003) VAK, Vacuum Fluctuation and the Mass Spectrum of High Energy Physics. Chaos, Solitons & Fractals, 30, 579-605. http://dx.doi.org/10.1016/s0960-0779(02)00684-7
El Naschie, M.S. (1991) Stress, Stability and Chaos in Structural Engineering: An Energy Approach. McGraw Hill, London.
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El Naschie, M.S. (2015) A Casimir Dark Energy Nano Reactor Design—Phase One. Natural Science, 7, 287-298. http://dx.doi.org/10.4236/ns.2015.76032
El Naschie, M.S. (2016) Cosserat-Cartan and de Sitter-Witten Spacetime Setting for Dark Energy. Quantum Matter, 5, 1-4. http://dx.doi.org/10.1166/qm.2016.1247
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) A Nonperturbative Quantum Relativity Theory Leading to a Casimir-Dark Energy Nanotech Reactor Proposal. Open Journal of Applied Science, 5, 313-324. http://dx.doi.org/10.4236/ojapps.2015.57032
Ho, M.-W., El Naschie, M.S. and Giuseppe Vitello, M.W. (2015) Is Spacetime Fractal and Quantum Coherent in the Golden Mean? Global Journal of Science Frontier Research, 15, 61-80.
El Naschie, M.S. (1998) Von Neumann Geometry and E-Infinity Quantum Spacetime. Chaos, Solitons & Fractals, 9, 2023-2030.
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