Using von Neumann’s continuous geometry in conjunction with A. Connes’ noncommutative geometry an exact mathematical-topological picture of quantum spacetime is developed ab initio. The final result coincides with the general conclusion of E-infinity theory and previous results obtained in the realm of high energy physics. In particular it is concluded that the quantum particle and the quantum wave spans quantum spacetime and conversely quantum particles and waves mutates from quantum spacetime.
KeywordsE-InfinityQuantum SpacetimeNoncommutative GeometryFractalsTransfinite Set TheoryVon Neumann Continuous GeometryCantor SetsFusion AlgebraZero Point EnergyVacuum FluctuationQuantum Field TheoryCasimir EffectDark Energy
Wittgenstein, L. (1922) Tractatus Logico-Philosophicus. With Introduction by B. Russel. London-Kegan Paul, Trench, Trubner & Co. Ltd., New York Harcourt, Brace & Co. Inc.
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
Auffray, J.-P. (2014) Quantum Meteorites: An Extemporaneous Description of the System of the World. Journal of Modern Physics, 6, 878-889. http://dx.doi.org/10.4236/jmp.2015.67092
Nottale, L. (1996) Scale Relativity and Fractal Spacetime: Application to Quantum Physics, Cosmology and Chaotic Systems. Chaos, Solitons & Fractals, 7, 877-938. http://dx.doi.org/10.1016/0960-0779(96)00002-1
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
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
Peter May, J. (1977) E-Infinity Ring Spaces and E-Infinity Spectra. Lecture Notes in Mathematics, Springer, Berlin.
Witten, E. (1998) D-Branes and K-Theory. Journal of High Energy Physics, 12, 1-35.
Connes, A. (2000) Noncommutative Geometry Year 2000. Geometric and Functional Analysis. Special Volume, Birkhauser-Verlag, 481-599. http://dx.doi.org/10.1007/978-3-0346-0425-3_3
Penrose, R. (2004) The Road to Reality. Jonathan Cape, London.
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 Singularities Reactor. Natural Science, 7, 210-225. http://dx.doi.org/10.4236/ns.2015.74024
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
Schwinger, J. (1994) Cold Fusion Theory: A Brief History of Mine. A Talk Read in an Evening Session B Eugene Mallove at the Fourth International Conference on Cold Fusion ICCF4, Maui, 6-9 December 1994. Printed Online by Infinity Energy—The Magazine of New Energy Science & Technology (2014-2015). www.infinite-energy.com/iemagazine1/colfusthe-html
Jiang, X.L., Zhou, X.P. and Peng, W.M. (2014) Extraction of Clean and Cheap Energy from Vacuum. Materials for Renewable Energy & Environment, 2, 467-471.
El Naschie, M.S. (1999) From Implosion to Fractal Spheres. A Brief Account of the Historical Development of Scientific Ideas Leading to the Trinity Test and Beyond. Chaos, Solitons & Fractals, 10, 1955-1965. http://dx.doi.org/10.1016/s0960-0779(99)00030-2
El Naschie, M.S. (2015) Banach Spacetime-Like Dvoretzky Volume Concentration as Cosmic Holographic Dark Energy. International Journal of High Energy Physics, 2, 13-21. http://dx.doi.org/10.11648/j.ijhep.20150201.12
El Naschie, M.S. (2005) On 336 Kissing Spheres in 10 Dimensions, 528 P-Brane States in 11 Dimensions and the 60 Elementary Particles of the Standard Model. Chaos, Solitons & Fractals, 24, 337-457. http://dx.doi.org/10.1016/j.chaos.2004.09.071
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 Entanglement Origin. Journal of Quantum Information Science, 4, 284-291. http://dx.doi.org/10.4236/jqis.2014.44023
Schwinger, J. (1975) Casimir Effect in Source Theory. Letters in Mathematical Physics, 1, 43-47. http://dx.doi.org/10.1007/BF00405585
Finkelstein, D. (1996) Quantum Relativity. Springer, Berlin. http://dx.doi.org/10.1007/978-3-642-60936-7
‘tHooft, G. (2014) The Cellular Automata Interpretation of Quantum Mechanics: A View on the Quantum Nature of Our Universe, Compulsory or Impossible? http://arxiv.org/abs/1405.1548
El Naschie, M.S. (1995) Banach-Tarski Theorem and Cantorian Micro Spacetime. Chaos, Solitons & Fractals, 5, 1503-1508. http://dx.doi.org/10.1016/0960-0779(95)00052-6
El Naschie, M.S. (2009) Wild Topology, Hyperbolic Geometry and Fusion Algebra of High Energy Particle Physics. Chaos, Solitons & Fractals, 13, 1935-1945.
Gillet, H. (1981) Riemann-Roch Theorem for Higher Algebraic K-Theory. Advances in Mathematics, 40, 203-289. http://dx.doi.org/10.1016/s0001-8708(81)80006-0
Kodiyalam, V. and Saunder, V. (2001) Topological Quantum Field Theories from Subfactors. Chapman & Hall/CRC, Bacaraton and London.
Witten, E. (1988) Topological Quantum Field Theory. Communications in Mathematical Physics, 117, 353-386. http://dx.doi.org/10.1007/bf01223371
Baez, J.C. and Dolan, J. (1988) Higher-Dimensional Algebra III: n-Categories and the Algebra of Opetopes. Advances in Mathematics, 135, 145-206.
May, J.P. (2009) What Precisely Are E-Infinity Rings and E-Infinity Spectra. http://arxiv.org/abs/0903.2813
Ketov, S.V. (1995) Conformal Field Theory. World Scientific, Singapore.
Duplantier, B. and Rivasseau, V., Eds. (2003) Poincaré Seminar 2002: Vacuum Energy—Renormalization. Birkhauser, Basel. http://dx.doi.org/10.1007/978-3-0348-8075-6
Saller, H. (2006) Operational Quantum Theory I and II. Springer, Heidelberg.
Milonni, P.W. (1994) The Quantum Vacuum: An Introduction to Quantum Electrodynamics. Academic Press, Boston. http://dx.doi.org/10.1119/1.17618
Connes, A. and Marcolli, M. (2008) Noncommutative Geometry, Quantum Fields and Motives. American Mathematical Society, Providence and Hindustan Book Agency, New Delhi.
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
Fried, H.M. (2014) Modern Functional Quantum Field Theory. World Scientific, Singapore. http://dx.doi.org/10.1142/8544
Zadeh, L. (1996) Fuzzy Sets, Fuzzy Logic and Fuzzy Systems. World Scientific, Singapore. http://dx.doi.org/10.1142/2895
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. (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. (2000) On Nishina’s Estimate of the Critical Mass for Fussion and Early Nuclear Research in Japan. Chaos, Solitons & Fractals, 11, 1809-1818. http://dx.doi.org/10.1016/S0960-0779(99)00172-1
El Naschie, M.S. (2000) Remarks on Heisenberg’s Farm-Hall Lecture on the Critical Mass of Fast Neutron Fission. Chaos, Solitons & Fractals, 11, 1327-1333. http://dx.doi.org/10.1016/S0960-0779(99)00136-8
El Naschie, M.S. and Hussein, A. (2000) On the Eigenvalue of Nuclear Reaction and Self-Weight Buckling. Chaos, Solitons & Fractals, 11, 815-818. http://dx.doi.org/10.1016/S0960-0779(99)00106-X
El Naschie, M.S. (2000) Elastic Buckling Loads and Fission Critical Mass as an Eigenvalue of a Symmetry Breaking Bifurcation. Chaos, Solitons & Fractals, 11, 631-629. http://dx.doi.org/10.1016/S0960-0779(99)00063-6
El Naschie, M.S. (2000) On the Zel’dovich-Khuriton Critical Mass for Fast Fission. Chaos, Solitons & Fractals, 11, 819-824. http://dx.doi.org/10.1016/S0960-0779(99)00113-7
El Naschie, M.S. (2000) On the Eigenvalue of Transport Reaction Involving Fast Neutrons. Chaos, Solitons & Fractals, 11, 929-934. http://dx.doi.org/10.1016/S0960-0779(99)00066-1
El Naschie, M.S. (2000) Heisenberg’s Critical Mass Calculations for an Explosive Nuclear Reaction. Chaos, Solitons & Fractals, 11, 987-997. http://dx.doi.org/10.1016/S0960-0779(99)00110-1
El Naschie, M.S. (1998) Chaos and Fractals in Nano and Quantum Technology. Chaos, Solitons & Fractals, 9, 1793-1802.
El Naschie, M.S. (2006) Nanotechnology for the Developing World. Chaos, Solitons & Fractals, 30, 769-773. http://dx.doi.org/10.1016/j.chaos.2006.04.037
El Naschie, M.S. (2007) The Political Economy of Nanotechnology and the Developing World. International Journal of Electrospun Nanofibrers and Applications, 1, 41-50.
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
Johnston, H. (2012) Physicists Solve Casimir Conundrum. Physicsworld.com., July 18, 2012.
Rencroft, S. and Swain, J. (1998) What Is the Casimir Effect? Scientific American, June 22, 1998.
Wongjun, P. (2015) Casimir Dark Energy, Stabilization and the Extra Dimensions and Gauss-Bonnet Term. The European Physical Journal C, 75, 6.
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
Smolin, L. (2001) The Strong and the Weak Holographic Principles. Nuclear Physics B, 601, 209-247. http://dx.doi.org/10.1016/s0550-3213(01)00049-9
El Naschie, M.S. (2006) Holographic Dimensional Reduction Centre Manifold Theorem and E-Infinity. Chaos, Solitons & Fractals, 29, 816-822. http://dx.doi.org/10.1016/j.chaos.2006.01.013
Misner, C., Thorne, K. and Wheeler, J.A. (1973) Gravitation. Freeman, New York.
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. (2005) A Guide to the Mathematics of E-Infinity Cantorian Spacetime Theory. Chaos, Solitons & Fractals, 25, 935-964. http://dx.doi.org/10.1016/j.chaos.2005.02.029
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. (2003) Complex Vacuum Fluctuation as a Chaotic “Limit” Set of any Kleinian Group Transformation and the Mass Spectrum of High Energy Particle Physics via Spontaneous Self Organization. Chaos, Solitons & Fractals, 17, 631-638. http://dx.doi.org/10.1016/s0960-0779(02)00630-6
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. (1994) On Certain “Empty” Cantor Sets and Their Dimensions. Chaos, Solitons & Fractals, 4, 293-296. http://dx.doi.org/10.1016/0960-0779(94)90152-X
He, J.-H., Xu, L., Zhang, L.-N. and Wu, X.-H. (2007) Twenty Six Dimensional Polytope and High Energy Spacetime Physics. Chaos, Solitons & Fractals, 33, 5-13. http://dx.doi.org/10.1016/j.chaos.2006.10.048
El Naschie, M.S. (1994) Is Quantum Space a Random Cantor Set with a Golden Mean Dimension at the Core? Chaos, Solitons & Fractals, 4, 177-179. http://dx.doi.org/10.1016/0960-0779(94)90141-4
El Naschie, M.S. (2008) Mathematical Foundation of E-Infinity via Coxeter and Reflection Groups. Chaos, Solitons & Fractals, 37, 1267-1268. http://dx.doi.org/10.1016/j.chaos.2008.02.001
El Naschie, M.S. (1995) Banach-Tarski Theorem and Cantorian Micro Spacetime. Chaos, Solitons & Fractals, 5, 1503-1508. http://dx.doi.org/10.1016/0960-0779(95)00052-6
El Naschie, M.S. (1995) On the Initial Singularity and the Banach-Tarski Theorem. Chaos, Solitons & Fractals, 5, 1391-1392. http://dx.doi.org/10.1016/0960-0779(95)99645-2
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. (2001) Infinite Dimensional Branes and the E-Infinity Toplogy of Heterotic Superstrings. Chaos, Solitons & Fractals, 12, 1047-1055. http://dx.doi.org/10.1016/S0960-0779(00)00130-2
El Naschie, M.S. (2007) Ji-Huan He’s Ten Dimensional Polytope and High Energy Particle Physics. International Journal of Nonlinear Science & Numerical Simulation, 8, 475-476. http://dx.doi.org/10.1515/ijnsns.2007.8.4.475
El Naschie, M.S. (1999) Hyper-Dimensional Geometry and the Nature of Physical Spacetime. Chaos, Solitons & Fractals, 10, 155-158. http://dx.doi.org/10.1016/S0960-0779(98)00235-5
Finkelstein, D. (1982) Quantum Sets and Clifford Algebras. International Journal of Theoretical Physics, 21, 489-503.
El Naschie, M.S. (2002) Derivation of the Threshold and Absolute Temperature Tc = 273.16 K from the Topology of Quantum Spacetime. Chaos, Solitons & Fractals, 14, 1117-1120. http://dx.doi.org/10.1016/S0960-0779(02)00053-X
El Naschie, M.S. (2008) Quarks Confinement via Kaluza-Klein Theory as a Topological Property of Quantum-Classical Spacetime Phase Transition. Chaos, Solitons & Fractals, 35, 825-829. http://dx.doi.org/10.1016/j.chaos.2007.08.057
El Naschie, M.S. (2002) On a Class of General Theories for Higher Energy Particle Physics. Chaos, Solitons & Fractals, 14, 649-668. http://dx.doi.org/10.1016/S0960-0779(02)00033-4
He, J.-H. (2009) Hilbert Cube Model for Fractal Spacetime. Chaos, Solitons & Fractals, 42, 2754-2759. http://dx.doi.org/10.1016/j.chaos.2009.03.182
Lomas, R. (1999) The Man Who Invented The Twentieth Century, Nicola Tesla, Forgotten Genius of Electricity. Headline Books, London.
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
Ho, M.-W., El Naschie, M.S. and Vitiello, G. (2015) Is Spacetime Fractal and Quantum Coherent in the Golden Mean. Global Journal of Science Frontier Research—A: Physics and Space Science, 15, 61-80.
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
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
El Naschie, M.S. (2013) A Resolution of Cosmic Dark Energy via 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) What Is the Missing Dark Energy in a Nutshell and the Hawking-Hartle Quantum Wave Collapse. International Journal of Astronomy & Astrophysics, 3, 205-211. http://dx.doi.org/10.4236/ijaa.2013.33024
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
Peat, F.D. (1983) In Search of Nikola Tesla. Ashgrove Publications, London & Bath.
Susskind, L. and Lindesay, J. (2005) The Holographic Universe. World Scientific, Singapore.
Stiglitz, J. and Bilmes, L. (2008) The Three Trillion Dollar War: The True Cost of The Iraq Conflict. Allen-Lane, Penguin Books, London.
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
Malek, C. (2015) Abu Dhabi Crown Prince Details UAE Leaders’ Vision of Future without Oil. The National Newspaper, UAE, February 10, 2015. http://www.thenational.ae/uae/government/abu-dhabi-crown-prince-details-uae-leaders-vision-of-future-without-oil?utm_content='%20vision%20of%20future%20without%20oil
Zee, A. (2003) Quantum Field Theory in a Nutshell. Princeton University Press, Princeton.
Duplantier, B. and Rivasseau, V., Eds. (2003) Vacuum Energy-Renormalization. Birkhauser, Basel.
Milonni, P.W. (1994) The Quantum Vacuum. Academic Press, Boston.
Parsegian, V.A. (2006) van der Waals Forces. Cambridge University Press, Cambridge.
Huang, K. (2007) Fundamental Forces of Nature. World Scientific, Singapore. http://dx.doi.org/10.1142/6447
Wapner, L.M. (2005) The Pea and the Sun. A.K. Peters Ltd., Wellesley.
Auffray, J.-P. (2014) E-Infinity Dualities, Discontinuous Spacetime, Xonic Quantum Physics and the Decisive Experiment. Journal of Modern Physics, 1427-1436. http://dx.doi.org/10.4236/jmp.2014.515144
El Naschie, M.S. (2015) The Cantorian Monadic Plasma behind the Zero Point Vacuum Spacetime Energy. American Journal of Nano Research and Application, 3, 66-70.
Auffray, J.-P. (2015) E-Infinity, the Zero Set, Absolute Space and the Photon Spin. Journal of Modern Physics, 6, 536-545.
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) Dark Energy via Quantum Field Theory in Curved Spacetime. Journal of Modern Physics and Applications, 2, 1-7.
El Naschie, M.S. (2015) 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. (2015) A Casimir-Dark Energy Nano Reactor Design—Phase I. Natural Science, 7, 287-298. http://dx.doi.org/10.4236/ns.2015.76032