Chaotic Fractals at the Root of Relativistic Quantum Physics and Cosmology


At its most basic level physics starts with space-time topology and geometry. On the other hand topology’s and geometry’s simplest and most basic elements are random Cantor sets. It follows then that nonlinear dynamics i.e. deterministic chaos and fractal geometry is the best mathematical theory to apply to the problems of high energy particle physics and cosmology. In the present work we give a short survey of some recent achievements of applying nonlinear dynamics to notoriously difficult subjects such as quantum entanglement as well as the origin and true nature of dark energy, negative absolute temperature and the fractal meaning of the constancy of the speed of light.

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L. Marek-Crnjac, M. Naschie and J. He, "Chaotic Fractals at the Root of Relativistic Quantum Physics and Cosmology," International Journal of Modern Nonlinear Theory and Application, Vol. 2 No. 1A, 2013, pp. 78-88. doi: 10.4236/ijmnta.2013.21A010.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] J. P. Gollub and P. C. Hohenberg, “Summary Session,” Physica Scripta, 1985, pp. 209-216. doi:10.1088/0031-8949/1985/T9/035
[2] M. S. El Naschie, “Elementary Prerequisites for E-Infinity,” Chaos, Solitons & Fractals, Vol. 30, No. 3, 2006, pp. 579-605. doi:10.1016/j.chaos.2006.03.030
[3] L. Amendola and S. Tsujikawa, “Dark Energy: Theory and Observations,” Cambridge University Press, Cambridge, 2010.
[4] J.-P. Hsu and L. Hsu, “A Broader View of Relativity,” 2nd Edition, World Scientific, Singapore City, 2006.
[5] 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, Vol. 1, No. 4, 2012, pp. 118-124. doi:10.4236/ijmnta.2012.14018
[6] E. J. Copeland, M. Sami and S. Tsujikawa, “Dynamics of Dark Energy,” 2006.
[7] G. Ord, M. S. El Naschie and J. H. He, “Fractal Space-Time and Non-Commutative Geometry in High Energy Physics,” A New Journal by Asian Academic Publishing Ltd., Vol. 2, No. 1, 2012, pp. 1-79.
[8] A. Connes, “Non-Commutative Geometry,” Academic Press, San Diego, 1994.
[9] L. Marek-Crnjac, “The Hausdorff Dimension of the Penrose Universe,” Physics Research International, Vol. 2011, 2011, Article ID: 874302.
[10] 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
[11] M. S. El Naschie, “The Theory of Cantorian Space-Time 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
[12] J. H. He, L. Marek-Crnjac, M. A. Helal, S. I. Nada and O. E. R?ssler, “Quantum Golden Mean Entanglement Test as the Signature of the Fractality of Micro Space-Time,” Nonlinear Scientific Letter B, Vol. 1, No. 2, 2011, pp. 45-50.
[13] M. S. El Naschie, “Quantum Entanglement as a Consequence of a Cantorian Micro Space-Time Geometry,” Journal of Quantum Information Science, Vol. 1, No. 2, 2011, pp. 50-53. doi:10.4236/jqis.2011.12007
[14] 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
[15] D. Mermin, “Quantum Mysteries Refined,” American Journal of Physics, Vol. 62, No. 10, 1994, pp. 880-887. doi:10.1119/1.17733
[16] J. Mageuijo and L. Smolin, “Lorentz Invariance with an Invariant Energy Scale,” 2001.
[17] J. Mageuijo, “Faster than the Speed of Light,” William Heinemann, London, 2003.
[18] 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.
[19] R. Elwes, “Ultimate L,” The New Scientist, Vol. 211, No. 2823, 2011, pp. 30-33. doi:10.1016/S0262-4079(11)61838-1
[20] S. Hendi and M. Zadeh, “Special Relativity and the Golden Mean,” Journal of Theoretic Physics, Vol. 1, No. 1, 2012, pp. 37-45.
[21] E. Wit and J. McClure, “Statistics for Microarrays: Design, Analysis, and Inference,” 5th Edition, John Wiley & Sons Ltd., Chichester, 2004. doi:10.1002/0470011084
[22] 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
[23] J. Aron, “Atoms beyond Absolute Zero,” New Scientist, Vol. 12, No. 2899, 2013, p. 12. doi:10.1016/S0262-4079(13)60081-0

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