ABSTRACT The 95.5 percent of discrepancy between theoretical prediction based on Einstein’s theory of relativity and the accurate cosmological measurement of WMAP and various supernova analyses is resolved classically using Newtonian mechanics in conjunction with a fractal Menger sponge space proposal. The new energy equation is thus based on the familiar kinetic energy of Newtonian mechanics scaled classically by a ratio relating our familiar three dimensional space homology to that of a Menger sponge. The remarkable final result is an energy equation identical to that of Einstein’s E=mc2but divided by 22 so that our new equation reads as . Consequently the energy Lorentz-like reduction factor of percent is in astonishing agreement with cosmological measurements which put the hypothetical dark energy including dark matter at percent of the total theoretical value. In other words our analysis confirms the cosmological data putting the total value of measured ordinary matter and ordinary energy of the entire universe at 4.5 percent. Thus ordinary positive energy which can be measured using conventional methods is the energy of the quantum particle modeled by the Zero set in five dimensions. Dark energy on the other hand is the absolute value of the negative energy of the quantum Schrodinger wave modeled by the empty set also in five dimensions.
Cite this paper
M. 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, Vol. 2 No. 2, 2013, pp. 107-121. doi: 10.4236/ijmnta.2013.22014.
 E. J. Copeland, M. Sami and S. Tsujikawa, “Dynamics of Dark Energy,” 2006.
 L. Amendola and S. Tsujikawa, “Dark Energy: Theory and Observations,” Cambridge University Press, Cambridge, 2010. doi:10.1017/CBO9780511750823
 S. Perlmutter, et al., “Supernova Cosmology Project Collaboration. Measurements of Omega and Lambda from 42 High-Redshift Supernova,” The Astrophysical Journal, Vol. 517, 1999, pp. 565-585.
 B. Mandelbrot, “The Fractal Geometry of Nature,” Freeman, San Francisco, 1982.
 M. S. El Naschie, “Elementary Prerequisites for E-Infinity,” Chaos, Solitons & Fractals, Vol. 30, No. 3, 2006, pp. 579-605. doi:10.1016/j.chaos.2006.03.030
 M. S. El Naschie and 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, Vol. 1, No. 4, 2012, pp. 118-124.
 M. S. El Naschie, “A Review of E-Infinity and the Mass spectrum of high energy particle physics,” Chaos, Solitons & Fractals, Vol. 19, No. 1, 2004, pp. 209-236.
 M. S. El Naschie, “Quantum entanglement as a Consequence of a Cantorian Micro Space-Time Geometry,” Journal of Quantum Information Science, Vol. 1, No. 2, 2011, pp. 50-53. doi:10.4236/jqis.2011.12007
 W. Rindler, “Relativity, Special, General and Cosmological,” Oxford Press, Oxford, 2004.
 J.-P. Hsu and L. Hsu, “A Broad View of Relativity,” World Scientific, Singapore, 2006.
 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.
 D. Joyce, “Compact Manifold with Special Holonomy,” Oxford Press, Oxford, 2003.
 M. S. El Naschie, “On Two New Fuzzy Kahler Manifolds, Klein Modular Space and ’t Hooft’s Holographic Principles,” Chaos, Solitons & Fractals, Vol. 29, No. 4, 2006, pp. 876-881. doi:10.1016/j.chaos.2005.12.027
 J. Polchinski, “String Theory,” Cambridge University Press, Cambridge, 1998.
 M. Duff, “The World in Eleven Dimensions,” IOP Publishing, Bristol, 1999.
 S. Hendi and M. Sharifzadeh, “Special Relativity and the Golden Mean,” International Journal of Theoretical Physics, Vol. 1, No.1, 2012, pp. 37-45.
 W. Koiter, “Elastic Stability and Post Buckling Behavior in Nonlinear Problems,” University of Wisconsin Press, Madison, 1963, pp. 257-275.
 M. S. El Naschie, “Stress, Stability and Chaos in Structural Engineering,” McGraw Hill, London, 1990.
 E. Cosserat and F. Cosserat, “Theorie des Corps Deformable,” Paris, 1909.
 D. Horrocks and W. Johnson, “On Anticlastic Curvature with Special Reference to Plastic Bending,” International Journal of Mechanical Sciences, Vol. 9, No 12, 1967, pp. 835-861. doi:10.1016/0020-7403(67)90011-2