Author(s) M. S. El Naschie^*

Affiliation(s)
Department of Physics, University of Alexandria, Alexandria, Egypt.

ABSTRACT

Previous work by Sigalotti in 2006 and recently by Hendi and Sharifzadeh in 2012 showed that all the fundamental equations of special relativity may be derived from a golden mean proportioned classical-Euclidean triangle and confirmed Einstein’s famous equation E=mc². In the present work it is shown that exchanging the Euclidean triangle with a hyperbolic one an extended quantum relativity energy equation, namely , is obtained. The relevance of this result in understanding the true nature of the “missing” so-called dark energy of the cosmos is discussed in the light of the fact that the ratio of to E=mc² is which agrees almost completely with the latest supernova and WMAP cosmological measurements. To put it succinctly what is really missing is a quantum mechanical factor equal 1/22 in Einstein’s purely relativistic equation. This factor on the other hand is derivable from the intrinsic hyperbolic Cantor set nature of quantum entanglement.

KEYWORDS
Dark Energy; Quantum Relativity; Dark Dimensions; Hyperbolic Geometry; WMAP Measurement; Supernova Analysis; Ordinary Energy of Quantum Particles; Dark Energy of Quantum Wave

Cite this paper
M. Naschie, "The hyperbolic Extension of Sigalotti-Hendi-Sharifzadeh’s Golden Triangle of Special Theory of Relativity and the Nature of Dark Energy," Journal of Modern Physics, Vol. 4 No. 3, 2013, pp. 354-356. doi: 10.4236/jmp.2013.43049.

References
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[3]   A. Einstein, “The Meaning of Relativity,” Routledge, London, 2003.

[4]   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 Applications, Vol. 1, No. 4, 2012, pp. 118-124.

[5]   M. S. El Naschie, “Elementary Prerequisites for E-Infinity (Recommended Background Readings in Nonlinear Dynamics, Geometry and Topology,” Chaos, Solitons & Fractals, Vol. 30, No. 4, 2006, pp. 579-605. doi:10.1016/j.chaos.2006.03.030

[6]   M. S. El Naschie, “The Theory of Cantorian Spacetime and High Energy Particle Physics (An Informal Review),” Chaos, Solitons & Fractals, Vol. 41, No. 5, 2009, pp. 2635-2646. doi:10.1016/j.chaos.2008.09.059

[7]   E. J. Copeland, M. Sami and S. Tsujikawa, “Dynamics of Dark Energy,” 2006. arXiv:hep-th/0603057V3

[8]   M. S. El Naschie, “Quantum Entanglement as a Consequence of a Cantorian Micro-Spacetime Geometry,” Journal of Quantum Information Science, 2012. http://www.scirp.org/journal/jqis

[9]   N. D. Mermin, “Quantum Mysteries Refined,” American Journal of Physics, Vol. 62, No. 10, 1994, pp. 880-887. doi:10.1119/1.17733