Chaotic Fractal Tiling for the Missing Dark Energy and Veneziano Model

L. Marek-Crnjac, M. S. El Naschie

epartment of Physics, Faculty of Science, University of Alexandria, Alexandria, Egypt.
Technical School Center, Maribor, Slovenia.

DOI: 10.4236/am.2013.411A2005                

Abstract

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 formula E = mc². Consequently Einstein’s formula makes no distinction between ordinary and dark energy.

Keywords

Hausdorff Dimension; Cantor Set; Dark Energy; Kähler Manifold; Quantum Entanglement; Veneziano Model

Conflicts of Interest

The authors declare no conflicts of interest.

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