TITLE:
Dark Energy Explained via the Hawking-Hartle Quantum Wave and the Topology of Cosmic Crystallography
AUTHORS:
Mohamed S. El Naschie, Atef Helal
KEYWORDS:
Doubly Special Relativity; Week’s Manifold; Experimental Test of Einstein’s Relativity; Witten’s M-Theory; Ordinary Energy of the Quantum Particle; Hawking-Hartle Wave of Cosmos; Crystallographic Symmetry Groups; Revising Special Relativity
JOURNAL NAME:
International Journal of Astronomy and Astrophysics,
Vol.3 No.3,
September
3,
2013
ABSTRACT:
The aim of
the present paper is to explain and accurately calculate the missing dark
energy density of the cosmos by scaling the Planck scale and using the
methodology of the relatively novel discipline of cosmic crystallography and
Hawking-Hartle quantum wave solution of Wheeler-DeWitt equation. Following this
road we arrive at a modified version of Einstein’s energy mass relation E = mc2 which predicts a cosmological energy density in astonishing accord with the
WMAP and supernova measurements and analysis. We develop non-constructively
what may be termed super symmetric Penrose fractal tiling and find that the
isomorphic length of this tiling is equal to the self affinity radius of a
universe which resembles an 11 dimensional Hilbert cube or a fractal M-theory
with a Hausdorff dimension where.
It then turns out that the correct maximal quantum relativity energy-mass equation
for intergalactic scales is a simple relativistic scaling, in the sense of
Weyl-Nottale, of Einstein’s classical equation, namely EQR = (1/2)(1/)
moc2 = 0.0450849 mc2 and that this energy is the ordinary
measurable energy density of the quantum particle. This means that almost 95.5%
of the energy of the cosmos is dark energy which by quantum particle-wave
duality is the absolute value of the energy of the quantum wave and is
proportional to the square of the curvature of the curled dimension of
spacetime namely where and is Hardy’s probability of quantum entanglement. Because of the
quantum wave collapse on measurement this energy cannot be measured using our
current technologies. The same result is obtained by involving all the 17 Stein
spaces corresponding to 17 types of the wallpaper groups as well as the 230-11=219 three dimensional crystallographic group which
gives the number of the first level of massless particle-like states in
Heterotic string theory. All these diverse subjects find here a unified view
point leading to the same result regarding the missing dark energy of the
universe, which turned out to by synonymous with the absolute value of the
energy of the Hawking-Hartle quantum wave solution of Wheeler-DeWitt equation
while ordinary energy is the energy of the quantum particle into which the
Hawking-Hartle wave collapse at cosmic energy measurement. In other words it is
in the very act of measurement which causes our inability to measure the “Dark
energy of the quantum wave” in any direct way. The only hope if any to detect
dark energy and utilize it
in nuclear reactors is future development of sophisticated quantum wave non-demolition measurement instruments.