TITLE:
Chaotic Fractal Tiling for the Missing Dark Energy and Veneziano Model
AUTHORS:
L. Marek-Crnjac, M. S. El Naschie
KEYWORDS:
Hausdorff Dimension; Cantor Set; Dark Energy; Kähler Manifold; Quantum Entanglement; Veneziano Model
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.11B,
November
7,
2013
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.