A Unified Newtonian-Relativistic Quantum Resolution of the Supposedly Missing Dark Energy of the Cosmos and the Constancy of the Speed of Light

ABSTRACT

Time dilation, space contraction and relativistic mass are combined in a novel fashion using Newtonian dynamics. In this way we can surprisingly retrieve an effective quantum gravity energy-mass equation which gives the accurate experimental value of vacuum density. Furthermore Einstein’s equation of special relativity *E* = *mc*^{2}, where m_{ }is the mass and *c* is the velocity of light developed assuming smooth 4*D* space time is transferred to a rugged Calabi-Yau and *K*3 fuzzy Kahler manifolds and revised to become *E*=(*mc*^{2})/(22), where the division factor 22 maybe interpreted as the compactified bosonic dimensions of Veneziano-Nambu strings. The result is again an accurate effective quantum gravity energy-mass relation akin to the one found using Newtonian dynamics which correctly predicts that 95.4915028% of the energy in the cosmos is the hypothetical missing dark energy. The agreement with WMAP and supernova measurements is in that respect astounding. In addition different theories are used to check the calculations and all lead to the same quantitative result. Thus the theories of varying speed of light, scale relativity, E-infinity theory, M-theory, Heterotic super strings, quantum field in curved space time, Veneziano’s dual resonance model, Nash Euclidean embedding and super gravity all reinforce, without any reservation, the above mentioned theoretical result which in turn is in total agreement with the most sophisticated cosmological measurements which was deservingly awarded the 2011 Nobel Prize in Physics. Finally and more importantly from certain viewpoints, we reason that the speed of light is constant because it is a definite probabilistic expectation value of a variable velocity in a hierarchical fractal clopen,* i.e.* closed and open micro space time.

Cite this paper

M. 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.

M. Naschie, "A Unified Newtonian-Relativistic Quantum Resolution of the Supposedly Missing Dark Energy of the Cosmos and the Constancy of the Speed of Light,"

References

[1] R. Penrose, “The Road to Reality,” Jonathan Cape, London, 2004.

[2] Y. Baryshev and P. Teerikorpi, “Discovery of Cosmic Fractals,” World Scientific, Singapore, 2002.

[3] L. Nottale, “Scale Relativity,” Imperial College Press, London, 2011.

[4] L. Amendola and S. Tsujikawa, “Dark Energy: Theory and Observations,” Cambridge University Press, Cambridge, 2010.

[5] J. Mageuijo and L. Smolin, “Lorentz Invariance with an Invariant Energy Scale,” 18 December 2001, arXiv:hepth/0112090V2.

[6] J. Mageuijo, “Faster Than the Speed of Light,” William Heinemann, London, 2003.

[7] 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

[8] M. S. El Naschie, “The Discrete Charm of Certain Eleven Dimensional Spacetime Theory,” International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 7, No. 4, 2006, pp. 477-481.

[9] C. Nash and S. Sen, “Topology and Geometry for Physicists,” Academic Press, San Diego, 1983.

[10] D. Joyce, “Compact Manifolds with Special Holonomy,” Oxford Press, Oxford, 2003.

[11] S. Yau and S. Nadis, “The Shape of Inner Space,” Perseus Book Group, New York, 2010.

[12] J. Polchinski, “String Theory,” Cambridge University Press, Cambridge, 1999.

[13] M. S. El Naschie, “On a Class of Fuzzy K?hler-Like Manifolds,” Chaos, Solitons & Fractals, Vol. 26, No. 2, 2005, pp. 257-261. doi:10.1016/j.chaos.2004.12.024

[14] M. S. El Naschie, “E-Infinity—Some Recent Results and New Interpretations,” Chaos, Solitons & Fractals, Vol. 29, No. 4, 2006, pp. 845-853. doi:10.1016/j.chaos.2006.01.073

[15] C. Rovelli, “Quantum Gravity,” Cambridge Press, Cambridge, 2004. doi:10.1017/CBO9780511755804

[16] M. S. El Naschie, “Quantum Entanglement as a Consequence of a Cantorian Micro Spacetime Geometry,” Journal of Quantum Information Science, Vol. 1, 2011, pp. 50-53. doi:10.4236/jqis.2011.12007 http://www.SCRIP.org/journal/jqis

[17] J.-H. He, et al., “Quantum Golden Mean Entanglement Test as the Signature of the Fractality of Micro Space- time,” Nonlinear Science Letters B, Vol. 1, No. 2, 2011, pp. 45-50.

[18] M. Planck, “Spacecraft,” Wikipedia, 2012. http://en.wikipedia.org/wiki/Planck

[19] R. Panek, “Dark Energy: The Biggest Mystery in the Universe,” The Smithsonian Magazine, 2010. http://www.smithsonianmagazine.com/science-nature/Dark-Energy-April (2010)

[20] D. R. Finkelstein, “Quantum Relativity,” Springer, Berlin, 1996. doi:10.1007/978-3-642-60936-7

[21] H. Saller, “Operational Quantum Theory,” Springer, Berlin, 2006.

[22] L. Hardy, “Non-Locality of Two Particles without Inequalities for Almost All Entangled States,” Physical Review Letters, Vol. 71, No. 11, 1993, pp. 1665-1668. doi:10.1103/PhysRevLett.71.1665

[23] M. Duff, “The World in Eleven Dimensions,” IOP Publishing, Bristol, 1999.

[24] M. S. El Naschie, “Revising Einstein’s E = mc^{2}. A Theoretical resolution of the Mystery of Dark Energy,” Conference Program and Abstracts of the Fourth Arab International Conference in Physics and Material Sciences, Alexandria, 1-3 October 2012, p. 1.

[25] 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 Application, in Press, 2012.

[26] J.-H. He, “A Historical Scientific Finding on Dark Energy,” Fractal Spacetime and Non-Commutatitve Geometry in Quantum and High Energy Physics, Vol. 2, No. 2, 2012. p. 154.

[27] 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

[28] S. Hendi and M. Sharif Zadeh, “Special Relativity and the Golden Mean,” Journal of Theoretical Physics, Vol. 1, IAU Publishing, 2012, pp. 37-45.

[29] L. Smolin, “Three Roads to Quantum Gravity,” Weindenfald & Nicolson, London, 2000.

[30] M. S. El Naschie, “Stress, Stability and Chaos in Structural Engineering,” McGraw Hill, London, 1990.

[31] C. Lanczos, “The Variational Principles of Mechanics,” 4th Edition, University of Toronto Press, Toronto, 1949.

[32] G. Barenblatt, “Scaling,” Cambridge University Press, Cambridge, 2003. doi:10.1017/CBO9780511814921

[1] R. Penrose, “The Road to Reality,” Jonathan Cape, London, 2004.

[2] Y. Baryshev and P. Teerikorpi, “Discovery of Cosmic Fractals,” World Scientific, Singapore, 2002.

[3] L. Nottale, “Scale Relativity,” Imperial College Press, London, 2011.

[4] L. Amendola and S. Tsujikawa, “Dark Energy: Theory and Observations,” Cambridge University Press, Cambridge, 2010.

[5] J. Mageuijo and L. Smolin, “Lorentz Invariance with an Invariant Energy Scale,” 18 December 2001, arXiv:hepth/0112090V2.

[6] J. Mageuijo, “Faster Than the Speed of Light,” William Heinemann, London, 2003.

[7] 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

[8] M. S. El Naschie, “The Discrete Charm of Certain Eleven Dimensional Spacetime Theory,” International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 7, No. 4, 2006, pp. 477-481.

[9] C. Nash and S. Sen, “Topology and Geometry for Physicists,” Academic Press, San Diego, 1983.

[10] D. Joyce, “Compact Manifolds with Special Holonomy,” Oxford Press, Oxford, 2003.

[11] S. Yau and S. Nadis, “The Shape of Inner Space,” Perseus Book Group, New York, 2010.

[12] J. Polchinski, “String Theory,” Cambridge University Press, Cambridge, 1999.

[13] M. S. El Naschie, “On a Class of Fuzzy K?hler-Like Manifolds,” Chaos, Solitons & Fractals, Vol. 26, No. 2, 2005, pp. 257-261. doi:10.1016/j.chaos.2004.12.024

[14] M. S. El Naschie, “E-Infinity—Some Recent Results and New Interpretations,” Chaos, Solitons & Fractals, Vol. 29, No. 4, 2006, pp. 845-853. doi:10.1016/j.chaos.2006.01.073

[15] C. Rovelli, “Quantum Gravity,” Cambridge Press, Cambridge, 2004. doi:10.1017/CBO9780511755804

[16] M. S. El Naschie, “Quantum Entanglement as a Consequence of a Cantorian Micro Spacetime Geometry,” Journal of Quantum Information Science, Vol. 1, 2011, pp. 50-53. doi:10.4236/jqis.2011.12007 http://www.SCRIP.org/journal/jqis

[17] J.-H. He, et al., “Quantum Golden Mean Entanglement Test as the Signature of the Fractality of Micro Space- time,” Nonlinear Science Letters B, Vol. 1, No. 2, 2011, pp. 45-50.

[18] M. Planck, “Spacecraft,” Wikipedia, 2012. http://en.wikipedia.org/wiki/Planck

[19] R. Panek, “Dark Energy: The Biggest Mystery in the Universe,” The Smithsonian Magazine, 2010. http://www.smithsonianmagazine.com/science-nature/Dark-Energy-April (2010)

[20] D. R. Finkelstein, “Quantum Relativity,” Springer, Berlin, 1996. doi:10.1007/978-3-642-60936-7

[21] H. Saller, “Operational Quantum Theory,” Springer, Berlin, 2006.

[22] L. Hardy, “Non-Locality of Two Particles without Inequalities for Almost All Entangled States,” Physical Review Letters, Vol. 71, No. 11, 1993, pp. 1665-1668. doi:10.1103/PhysRevLett.71.1665

[23] M. Duff, “The World in Eleven Dimensions,” IOP Publishing, Bristol, 1999.

[24] M. S. El Naschie, “Revising Einstein’s E = mc

[25] 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 Application, in Press, 2012.

[26] J.-H. He, “A Historical Scientific Finding on Dark Energy,” Fractal Spacetime and Non-Commutatitve Geometry in Quantum and High Energy Physics, Vol. 2, No. 2, 2012. p. 154.

[27] 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

[28] S. Hendi and M. Sharif Zadeh, “Special Relativity and the Golden Mean,” Journal of Theoretical Physics, Vol. 1, IAU Publishing, 2012, pp. 37-45.

[29] L. Smolin, “Three Roads to Quantum Gravity,” Weindenfald & Nicolson, London, 2000.

[30] M. S. El Naschie, “Stress, Stability and Chaos in Structural Engineering,” McGraw Hill, London, 1990.

[31] C. Lanczos, “The Variational Principles of Mechanics,” 4th Edition, University of Toronto Press, Toronto, 1949.

[32] G. Barenblatt, “Scaling,” Cambridge University Press, Cambridge, 2003. doi:10.1017/CBO9780511814921