M.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, 2(3), 2014, pp. 34-37.
http://dx.doi.org/10.11648/j.ajaa.20140203.12

has been cited by the following article:

• TITLE: On a Fractal Version of Witten’s M-Theory

  AUTHORS: Mohamed S. El Naschie

  KEYWORDS: M-Theory, E-Infinity Theory, Hardy’s Quantum Entanglement, Transfinite Turing Computer, Dark Energy, Accelerated Cosmic Expansion, Noncommutative Geometry, Superstring Theory, Scale Relativity, Cantorian-Fractal Spacetime, Witten’s Theory, ‘tHooft Renormalon, Pure Gravity, Penrose Tiling

  JOURNAL NAME: International Journal of Astronomy and Astrophysics, Vol.6 No.2, April 8, 2016

  ABSTRACT: Starting from Witten’s eleven dimensional M-theory, the present work develops in an analogous way a corresponding dimensional fractal version where . Subsequently, the new fractal formalism is utilized to determine the measured ordinary energy density of the cosmos which turns out to be intimately linked to the new theory’s fractal dimension via non-integer irrational Lorentzian-like factor: where is Hardy’s probability of quantum entanglement. Consequently, the energy density is found from a limiting classical kinetic energy to be Here, is ‘tHooft’s renormalon of dimensional regularization. The immediate logical, mathematical and physical implication of this result is that the dark energy density of the cosmos must be in astounding agreement with cosmic measurements and observations.