The Missing Dark Energy of the Cosmos from Light Cone Topological Velocity and Scaling of the Planck Scale

Mohamed S. El Naschie

Department of Physics, Faculty of Science, University of Alexandria, Alexandria, Egypt.

DOI: 10.4236/ojm.2013.33012                

Abstract

The paper presents an exact analysis leading to an accurate theoretical prediction of the amount of the mysteriously missing hypothetical dark energy density in the cosmos. The value found, namely 95.4915028% is in full agreement with earlier analysis, the WMAP and the supernova cosmic measurements. The work follows first the strategy of finding a critical point which separates a semi-classical regime from a fully relativistic domain given by topological unit interval velocity parameter then proceeds to wider aspects of a topological quantum field of fractal unit interval. This idea of a critical velocity parameter was first advanced by Sigalotti and Mejias in 2006 who proposed a critical value equal . A second interesting proposal made in 2012 by Hendi and Sharifzadeh set the critical point at 0.8256645. The present analysis is based upon a light cone velocity quantized coordinate. This leads to the same quantum relativity energy mass relation found in earlier publications by rescaling that of Einstein’s special relativity. Two effective quantum gravity formulae are obtained. The first is for the ordinary measurable energy of the quantum particle while the second is for dark energy density of the quantum wave which we cannot measure directly and we can only infer its existence from the measured accelerated expansion of the universe E(D) = where . The critical velocity parameter in this case arises naturally to be . The results so obtained are validated using a heuristic Lorentzian transformation. Finally the entire methodology is put into the wider perspective of a fundamental scaling theory for the Planck scale proposed by G. Gross.

Keywords

Scaling the Planck Scale; Weyl Scaling; Nottale Scaling; Dark Energy; Quantum Relativity

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	L. Sigalotti and A. Mejias, “The Golden Mean in Special Relativity,” Chaos, Solitons & Fractals, Vol. 30, No. 3, 2006, pp. 521-524. doi:10.1016/j.chaos.2006.03.005
[2]	S. Hendi and M. Sharif Zadeh, “Special Relativity and the Golden Ratio,” Journal of Theoretical Physics, Vol. 1, 2012, pp. 37-45.
[3]	L. Amendola and S. Tsujikawa, “Dark Energy: Theory and Observations,” Cambridge University Press, Cambridge, 2010.
[4]	Nobel Foundation, “The Nobel Prize in Physics,” 2011. http://nobelprize.org.nobelprizes/physics/Laureates/2011/index.html
[5]	B. Zwiebach, “A First Course in String Theory,” Cambridge University Press, Cambridge, 2004. doi:10.1017/CBO9780511841682
[6]	W. Rindler, “Relativity,” Oxford Science Publications, Oxford, 2004.
[7]	L. B. Okun, “Energy and Mass in Relativity Theory,” World Scientific, Singapore, 2009.
[8]	J. Mageuijo and L. Smolin, “Lorentz Invariance with an Invariant Energy Scale,” arXiv: hepth/0112090V2.
[9]	G. Veneziano, “An Introduction to Dual Models of Strong Interactions and Their Physical Motivations,” Physical Reports, Vol. C9, 1974, p. 199.
[10]	M. Green, J. Schwarz and E. Witten, “Superstring Theory,” Cambridge University Press, Cambridge, 1994.
[11]	B. Bavnbek, G. Esposito and M. Lesch, “New Paths towards Quantum Gravity,” Springer, Berlin 2010. doi:10.1007/978-3-642-11897-5
[12]	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
[13]	M. S. El Naschie, “A Review of E-Infinity and the Mass Spectrum of High Energy Particle Physics,” Chaos, Solitons & Fractals, Vol. 19, No. 1, 2004, pp. 209-236. doi:10.1016/S0960-0779(03)00278-9
[14]	L. Nottale, “Scale Relativity and Fractal Space-Time,” Imperial College Press, London, 2011.
[15]	M. S. El Naschie, “Topological-Geometrical and Physical Interpretation of the Dark Energy of the Cosmos as a ‘Halo’ Energy of the Schr?dinger Quantum Wave,” Journal of Modern Physics, Vol. 4, 2013, pp. 591-596. doi:10.4236/jmp.2013.45084
[16]	L. Marek-Crnjac, M. S. El Naschie and J.-H. He, “Chaotic Fractals at the Root of Relativistic Quantum Physics and Cosmology,” International Journal of Modern Nonlinear Theory and Application, Vol. 2, 2013, pp. 78-88. doi:10.4236/ijmnta.2013.21A010
[17]	M. S. El Naschie, “A Resolution of Cosmic Dark Energy via a Quantum Entanglement Relativity Theory,” Journal of Quantitative Information Science, Vol. 3, 2013, pp. 23-26. doi:10.4236/jqis.2013.31006
[18]	T. Hübsch, “Calabi-Yau Manifolds,” World Scientific, Singapore, 1992. doi:10.1142/1410
[19]	J. Guckenheimer and P. Holmes, “Nonlinear Dynamical Systems and Bifurcation of Vector Fields,” Springer Verlag, New York, 1994.
[20]	P. S. Wesson, “Five-Dimensional Physics,” World Scientific, Singapore, 2006.
[21]	M. S. El Naschie, “A Fractal Menger Sponge Spacetime Proposal to Reconcile Measurements and Theoretical Predictions of Cosmic Dark Energy,” International Journal of Modern Nonlinear Theory and Application, Vol. 2, 2013, pp. 107-121. doi:10.4236/ijmnta.2013.22014
[22]	M. S. El Naschie, “Dark Energy from Kaluza-Klein Spacetime and Noether’s Theorem via Lagrangian Multiplier Method,” Journal of Modern Physics, Vol. 4, 2013, pp. 757-760. doi:10.4236/jmp.2013.46103
[23]	M.S. El Naschie, “Quantum Entanglement: Where Dark Energy and Negative Gravity plus Accelerated Expansion of the Universe Comes from,” Journal of Quantitative Information Science, Vol. 3, No. 2, 2013, pp. 57-77. doi:10.4236/jqis.2013.32011
[24]	M. S. El Naschie, “A Unified Newtonian-Relativistic Quantum Resolution of the Supposedly Missing Dark Energy of the Cosmos and the Constancy of the Speed of Light,” International Journal of Modern Nonlinear Theory and Application, Vol. 2, No. 1, 2013, pp. 43-54. doi:10.4236/ijmnta.2013.21005
[25]	J. Magueijo, “Faster than the Speed of Light,” Arrow Books, London, 2003.
[26]	D. Gross, “Can We Scale the Planck Scale?” Physics Today, Vol. 42, No. 6, 1989, p. 9.
[27]	A. Albrecht and C. Skordis, “Phenomenology of a Realistic Accelerating Universe Using only Planck scale Physics,” arXiv: astro-ph/9908085V2
[28]	L. Biedenharn and L. Horwitz, “Quantum Theory and Exceptional Gauge Groups,” Proceedings of Second John Hopkins Workshop, California, 21 April 1978.
[29]	M. S. El Naschie, “Dimensional Symmetry Breaking, Information and Fractal Gravity in Cantorian Space,” Biosystems, Vol. 46, No. 1-2, 1998, pp. 41-46. doi:10.1016/S0303-2647(97)00079-8
[30]	M. Crasmareanu and C. Hretcanu, “Golden Differential Geometry,” Chaos, Solitons & Fractals, Vol. 38, No. 5, 2008, pp. 1229-1238. doi:10.1016/j.chaos.2008.04.007
[31]	M. S. El Naschie, “Fractal Gravity and Symmetry Breaking in Hierarchal Cantorian Space,” Chaos, Solitons & Fractals, Vol. 8, No. 11, 1997, pp. 1865-1872. doi:10.1016/S0960-0779(97)00039-8
[32]	E. Witten, “Topological Quantum Field,” Communications in Mathematical Physics, Vol. 117, No. 3, 1988, pp. 353-386. doi:10.1007/BF01223371
[33]	J. Mageuijo and J. Moffat, “Comments on “Note on Varying Speed of Light Theories,” arXiv:0705.4507V1[gr-9c]
[34]	J. Maldacena and L. Susskind, “Cool Horizons for Entangled Black Holes,” 11 July 2013. arXiv: 1306.0533V2[hep-th]