The formula for the quantum amplitude of the Veneziano
dual resonance model is shown to be formally analogous to the dimensionality of
a K-theoretical fractal quotient manifold of the non-commutative geometrical
type. Subsequently this analogy is used to deduce the ordinary energy of the
quantum particle and the dark energy of the quantum wave. The results agree
completely with cosmological measurements. Even more surprisingly the sum of
both energy expressions turned out to be exactly equal to Einstein’s iconic formulaE = mc2. Consequently Einstein’s formula makes no distinction
between ordinary and dark energy.
L. Hardy, “Non-Locality of Two Particles without Inequalities for Almost All Entangled States,” Physical Review Letters, Vol. 71, No. 11, 1993, pp. 1665-1668. http://dx.doi.org/10.1103/PhysRevLett.71.1665
M. S. El Naschie, “Quantum Entanglement: Where Dark Energy and Negative Gravity plus Accelerated Expansion of the Universe Comes From,” Journal of Quantum Information Science, Vol. 3, No. 2, 2013, pp. 57-77. http://dx.doi.org/10.4236/jqis.2013.32011
M. S. El Naschie, “The Missing Dark Energy of the Cosmos From Light Cone Topological Velocity and Scaling the Planck Scale,” Open Journal of Microphysics, Vol. 3, No. 3, 2013, pp. 64-70. http://dx.doi.org/10.4236/ojm.2013.33012
M. S. El Naschie and A. Helal, “Dark Energy Explained via the Hawking-Hartle Quantum Wave and the Topology of Cosmic Crystallography,” International Journal of Astronomy and Astrophysics, Vol. 3, No. 3, 2013, pp. 318343.
M. S. El Naschie, “The Quantum Gravity Immirzi Parameter—A General Physical and Topological Interpretation,” Gravitation and Cosmology, Vol. 19, No. 3, 2013, pp. 151-155. http://dx.doi.org/10.1134/S0202289313030031
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, Vol. 3, No. 3, 2013, pp. 205-211. http://dx.doi.org/10.4236/ijaa.2013.33024
M. S. El Naschie, “A Resolution of the Cosmic Dark Energy via a Quantum Entanglement Relativity Theory,” Journal of Quantum Information Science, Vol. 3, No. 1, 2013, pp. 23-26. http://dx.doi.org/10.4236/jqis.2013.31006
M. S. El Naschie, “Dark Energy from Kaluza-Klein Spacetime and Noether’s Theorem via Lagrangian Multiplier Method,” Journal of Modern Physics, Vol. 4, No. 6, 2013, pp. 757-760. http://dx.doi.org/10.4236/jmp.2013.46103
V. Jacques, et al., “Delayed-Choice Test of Quantum Complementarity with Interfering Single Photons,” Physical Review Letters, Vol. 100, No. 22, 2008, Article ID: 220402. http://dx.doi.org/10.1103/PhysRevLett.100.220402
L. Li, N. L. Liu and Z. X. Yu, “Duality Relations in a Two Path Interferometer with an Asymmetric Beam Splitter,” Physical Review A, Vol. 85, No. 5, 2012, Article ID: 054101. http://dx.doi.org/10.1103/PhysRevA.85.054101
M. S. El Naschie, “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, Vol. 17, No. 4, 2003, pp. 631-638. http://dx.doi.org/10.1016/S0960-0779(02)00630-6
M. S. El Naschie, “VAK, Vacuum Fluctuation and the Mass Spectrum of High Energy Particle Physics,” Chaos, Solitons & Fractals, Vol. 17, No. 4, 2003, pp. 797-807. http://dx.doi.org/10.1016/S0960-0779(02)00684-7
M. S. El Naschie, “The VAK of Vacuum Fluctuation, Spontaneous Self-Organization and Complexity Theory Interpretation of High Energy Particle Physics and the Mass Spectrum,” Chaos, Solitons & Fractals, Vol. 18, No. 2, 2003, pp. 401-420. http://dx.doi.org/10.1016/S0960-0779(03)00098-5
M. S. El Naschie, “Mathematical Foundations of E-Infinity via Coxeter and Reflection Groups,” Chaos, Solitons & Fractals, Vol. 37, No. 5, 2008, pp. 1267-1268. http://dx.doi.org/10.1016/j.chaos.2008.02.001
M. S. El Naschie, “Removing Spurious Non-Linearity in the Structure of Micro-Space-Time and Quantum Field Renormalization,” Chaos, Solitons & Fractals, Vol. 37, No. 1, 2008, pp. 60-64. http://dx.doi.org/10.1016/j.chaos.2007.10.005
M. S. El Naschie, “This Month’s New Hot Paper in the Field of Engineering: On a Fuzzy Kahler-Like Manifold Which Is Consistent with the Two Slit Experiment,” International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 6, No. 2, 2005, pp. 95-98. http://esi-topics.com/nhp/2006/september-06-MohamedElNaschie.html
M. Persinger and C. Lavellee, “Theoretical and Experimental Evidence of Macroscopic Entanglement between Human Brain Activity and Photon Emission,” Journal of Consciousness Exploration & Research, Vol. 1, No. 7, 2010, pp. 785-807.
M. S. El Naschie, “Penrose Universe and Cantorian Spacetime as a Model for Noncommutative Quantum Geometry,” Chaos, Solitons & Fractals, Vol. 9, No. 6, 1998, pp. 931-933. http://dx.doi.org/10.1016/S0960-0779(98)00077-0
D. Horrockos and W. Johnson, “On Anticlastic Curvature with Special Reference to Plastic Bending,” The International Journal of Mechanical Sciences, Vol. 9, No. 12, 1967, pp. 835-861. http://dx.doi.org/10.1016/0020-7403(67)90011-2
M. S. El Naschie, “A Fractal Menger Sponge Spacetime Proposal to Reconcile Measurements and Theoretical Predictions of Cosmic Dark Energy,” International Journal of Modern Nonlinear Theory and Application, Vol. 2, No. 2, 2013, pp. 107-121. http://dx.doi.org/10.4236/ijmnta.2013.22014
M. S. El Naschie, “On the Mathematical Philosophy of Being and Nothingness in Quantum Physics,” Fractal Space-Time & Non-Commutative Geometry in Quantum and High Energy Physics, Vol. 2, No. 2, 2012, pp. 103106.