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Dark Energy from Kaluza-Klein Spacetime and Noether’s Theorem via Lagrangian Multiplier Method

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DOI: 10.4236/jmp.2013.46103    4,284 Downloads   6,992 Views   Citations

ABSTRACT

The supposedly missing dark energy of the cosmos is found quantitatively in a direct analysis without involving ordinary energy. The analysis relies on five dimensional Kaluza-Klein spacetime and a Lagrangian constrained by an auxiliary condition. Employing the Lagrangian multiplier method, it is found that this multiplier is equal to the dark energy of the cosmos and is given by where E is energy, m is mass, c is the speed of light, and λ is the Lagrangian multiplier. The result is in full agreement with cosmic measurements which were awarded the 2011 Nobel Prize in Physics as well as with the interpretation that dark energy is the energy of the quantum wave while ordinary energy is the energy of the quantum particle. Consequently dark energy could not be found directly using our current measurement methods because measurement leads to wave collapse leaving only the quantum particle and its ordinary energy intact.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

M. El Naschie, "Dark Energy from Kaluza-Klein Spacetime and Noether’s Theorem via Lagrangian Multiplier Method," Journal of Modern Physics, Vol. 4 No. 6, 2013, pp. 757-760. doi: 10.4236/jmp.2013.46103.

References

[1] S. Perlmutter, et al., The Astrophysical Journal, Vol. 517, 1999, pp. 565-585. doi:10.1086/307221
[2] E. J. Copleand, M. Sami and S. Tsujikawa, “Dynamics of Dark Energy,” 2006. arxiv:hep-th/06030573.
[3] L. Amendola and S. Tsujikawa, Dark Energy: Theory and observations, Cambridge University Press, Cambridge. 2010. doi:10.1017/CBO9780511750823
[4] M. Planck, “Spacecraft,” Wikipedia, 2012.
[5] R. Penrose, “The Road to Reality,” Jonathan Cape, London, 2004.
[6] Y. Baryshev and P. Terrikorpi, “Discovery of Cosmic Fractals,” World Scientific, Singapore, 2002.
[7] L. Nottale, “Scale Relativity,” Imperial College Press, London, 2011.
[8] J. Mageuijo, “Faster than the Speed of Light,” William Heinemann, London, 2003.
[9] M. S. El Naschie, International Journal Modern Nonlinear Theory and Application, Vol. 2, 2013, pp. 43-54. doi:10.4236/ijmnta.2013.21005
[10] R. Panek, “Dark Energy: The Biggest Mystery in the Universe,” The Smithsonian Magazine, 2010. http://www.smithsonianmagazine.com/science-nature/Dark-Energy.
[11] E. Komatsu, et al., The Astrophysical Journal Supplement, 192, Vol. 18, 2011. arxiv: 1001.4538[astro-ph.co]
[12] A. G. Reiss, et al., The Astronomical Journal, Vol. 116, 1998, pp. 1009-1032.
[13] C. Rovelli, “Quantum Gravity,” Cambridge Press, Cambridge, 2004.
[14] D. R. Finkelstein, “Quantum Relativity,” Springer, Berlin, 1996. doi:10.1007/978-3-642-60936-7
[15] H. Saller, “Operational Quantum Theory,” Springer, Berlin, 2006.
[16] M. S. El Naschie, Journal of Quantum Information Science, Vol. 3, 2013, pp. 23-26. doi:10.4236/jqis.2013.31006
[17] J. Polchinski, “String Theory. Vol. I & II,” Cambridge University Press, Cambridge, 1998.
[18] M. Duff, “The World in Eleven Dimensions,” IOP Publication, Bristol, 1999.
[19] M. S. El Naschie, Chaos, Solitons & Fractals, Vol. 19, 2004, pp. 209-236. doi:10.1016/S0960-0779(03)00278-9
[20] L. Hardy, Physical Review Letters, Vol. 7, 1993, pp. 1665-1668. doi:10.1103/PhysRevLett.71.1665
[21] D. F. Styer, “The Strange World of Quantum Mechanics,” Cambridge University Press, Cambridge, 2000, pp. 54-55.
[22] J. Mageuijo and L. Smolin, “Lorenz Invariance with an Invariant Energy Scale,” 18 December 2001. Arxiv: hep.th/0112090v2
[23] D. Mermin, American Journal of Physics, Vol. 62, 1999, pp. 880-887. doi:10.1119/1.17733
[24] P. Davis, “The New Physics,” Cambridge University Press, Cambridge, 1989.
[25] M. S. El Naschie Journal of Quantum Information Science, Vol. 1, 2011, pp. 50-53. doi:10.4236/jqis.2011.12007
[26] P. Halpern, “The Great beyond, Higher Dimensions, Parallel Universes and the Extraordinary Search for a Theory of Everything,” John Wiley, New Jersey, 2004.
[27] M. S. El Naschie, Chaos, Solitons & Fractals, Vol. 37, 2008, pp. 16-22. doi:10.1016/j.chaos.2007.09.079
[28] A. Connes, “Non-Commutative Geometry,” Academic Press, New York, 1994, pp. 88-93.
[29] M. S. El Naschie, Chaos, Solitons & Fractals, Vol. 26, 2005, pp. 247-254. doi:10.1016/j.chaos.2005.01.016
[30] M. S. El Naschie, Chaos, Solitons & Fractals, Vol. 36, 2009, pp. 808-810. doi:10.1016/j.chaos.2007.09.019
[31] J. H. He, International Journal of Modern Nonlinear Theory and Application, Vol. 2, 2013, pp. 55-59. doi:10.4236/ijmnta.2013.21006
[32] L. Marek-Crnjac, et al., International Journal of Modern Nonlinear Theory and Application, Vol. 2, 2013, pp. 78-88. doi:10.4236/ijmnta.2013.21A010
[33] C. Lanzos, “The Variational Principles of Mechanics,” 4th Edition, University of Toronto Press, Toronto, 1949.
[34] M. S. El Naschie, International Journal of Modern Nonlinear Theory and Application, Vol. 1, 2012, pp. 84-92. doi:10.4236/ijmnta.2012.13012
[35] W. Rindler, “Relativity,” Oxford University Press, Oxford, 2001.
[36] J. Hsu and L. Hsu, “A Broader View of Relativity,” World Scientific, Singapore, 2006.
[37] J. Hartle, “Gravity,” Addison Wesley, New York, 2003.

  
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