Recurrence of Space-Time Events

Affiliation(s)

^{1}
Astronomy Department, National Research Institute of Astronomy and Geophysics, Helwan, Cairo, Egypt.

^{2}
Mathematics Department, Faculty of Science, Taibah University, Madina, Saudi Arabia.

ABSTRACT

A causal-directed graphical space-time model has been suggested in which the recurrence phenomena that happen in history and science can be naturally explained. In this Ramsey theorem inspired model, the regular and repeated patterns are interpreted as identical or semi-identical space-time causal chains. The “same colored paths and subgraphs” in the classical Ramsey theorem are interpreted as identical or semi-identical causal chains. In the framework of the model, Poincare recurrence and the cosmological recurrence arise naturally. We use Ramsey theorem to prove that there’s always a possibility of predictability no matter how chaotic the system is.

A causal-directed graphical space-time model has been suggested in which the recurrence phenomena that happen in history and science can be naturally explained. In this Ramsey theorem inspired model, the regular and repeated patterns are interpreted as identical or semi-identical space-time causal chains. The “same colored paths and subgraphs” in the classical Ramsey theorem are interpreted as identical or semi-identical causal chains. In the framework of the model, Poincare recurrence and the cosmological recurrence arise naturally. We use Ramsey theorem to prove that there’s always a possibility of predictability no matter how chaotic the system is.

Cite this paper

Ahmed, N. (2015) Recurrence of Space-Time Events.*Journal of Modern Physics*, **6**, 1793-1797. doi: 10.4236/jmp.2015.613182.

Ahmed, N. (2015) Recurrence of Space-Time Events.

References

[1] Trompf, G.W. (1979) The Idea of Historical Recurrence in Western Thought, from Antiquity to the Reformation. University of California Press, Berkeley.

[2] Toynbee, A.J. (1948) Does History Repeat Itself? Civilization on Trial. Oxford University Press, New York.

[3] Kennedy, P. (1987) The Rise and Fall of the Great Powers: Economic Change and Military Conflict from 1500 to 2000. Random House, New York.

[4] Graham, G. (1997) The Shape of the Past: A Philosophical Approach to History. Oxford University Press, Oxford.

http://dx.doi.org/10.1093/acprof:oso/9780192892553.001.0001

[5] Sorokin, P.A. (1957) Social and Cultural Dynamics: A Study of Change in Major Systems of Art, Truth, Ethics, Law, and Social Relationships. Porter Sargent Publishing, Boston.

[6] Twain, M. (1903) The Jumping Frog. Harper and Brothers, New York.

[7] Barreira, L. (2006) Poincaré Recurrence: Old and New. Proceedings of the 14th International Congress on Mathematical Physics, Lisbon, 28 July-2 August 2003, 415-422.

http://dx.doi.org/10.1142/9789812704016_0039

[8] Brush, S.G. (1996) A History of Modern Planetary Physics: Nebulous Earth V1. Cambridge University Press, Cambridge.

[9] Bocchieri, P. and Loinger, A. (1957) Quantum Recurrence Theorem. Physical Review, 107, 337-338.

http://dx.doi.org/10.1103/PhysRev.107.337

[10] Livina, V., Tuzov, S., Havlin, S. and Bunde, A. (2005) Recurrence Intervals between Earthquakes Strongly Depend on History. Physica A: Statistical Mechanics and its Applications, 348, 591-595.

http://dx.doi.org/10.1016/j.physa.2004.08.032

[11] Lehners, J.-L. (2008) Ekpyrotic and Cyclic Cosmology. Physics Reports, 465, 223-263.

http://dx.doi.org/10.1016/j.physrep.2008.06.001

[12] Penrose, R. (2011) Cycles of Time: An Extraordinary New View of the Universe. Alfred Knopf, New York.

[13] Steinhardt, P.J. and Turok, N. (2001) A Cyclic Model of the Universe. Science, 296, 1436-1439.

http://dx.doi.org/10.1126/science.1070462

[14] Ramsey, F.P. (1930) On a Problem of Formal Logic. Proceedings of the London Mathematical Society, s2-30, 264-286.

http://dx.doi.org/10.1112/plms/s2-30.1.264

[15] Halasz, et al., Eds. (2002) Paul Erds and His Mathematics. Springer, Berlin.

[16] Pr?mel, H.J. (2005) Complete Disorder Is Impossible: The Mathematical Work of Walter Deuber. Combinatorics, Probability and Computing, 14, 3-16.

[17] Burr, S.A. (1974) Generalized Ramsey Theory for Graphs—A Survey. In: Bari, R. and Harary, F., Eds., Graphs and Combinatorics, Springer, Berlin, 52-75.

[18] Cartwright, D. and Harary, F. (1977) A Graph Theoretic Approach to the Investigation of System-Environment Relationships. Journal of Mathematical Sociology, 5, 87-111.

http://dx.doi.org/10.1080/0022250X.1977.9989866

[19] http://www.cs.umd.edu/~gasarch/BLOGPAPERS/ramseykings.pdf

[20] Graham, R.L., Rothschild, B.L. and Spencer, J.H. (1990) Ramsey Theory: Wiley-Interscience Series in Discrete Mathematics and Optimization. 2nd Edition, John Wiley and Sons, Inc., New York.

[21] Kittipassorn, T. and Narayanan, B.P. (2014) A Canonical Ramsey Theorem for Exactly m-Coloured Complete Subgraphs. Combinatorics, Probability and Computing, 23, 102-115.

http://dx.doi.org/10.1017/S0963548313000503

[22] Folkman, J. (1970) Graphs with Monochromatic Complete Subgraphs in Every Edge Coloring. SIAM Journal on Applied Mathematics, 18, 19-24.

http://dx.doi.org/10.1137/0118004

[23] Bollobás, B. and Gyárfás, A. (2008) Highly Connected Monochromatic Subgraphs. Discrete Mathematics, 308, 1722-1725.

http://dx.doi.org/10.1016/j.disc.2006.01.030

[24] Scott, A. and White, M. (2011) Monochromatic Cycles and the Monochromatic Circumference in 2-Coloured Graphs.

http://arxiv.org/abs/1107.5177

[25] Benevides, F., Luczak, T., Skokan, J., Scott, A. and White, M. (2012) Monochromatic Cycles in 2-Coloured Graphs. Combinatorics, Probability and Computing, 21, 57-87.

http://dx.doi.org/10.1017/S0963548312000090

[26] Gyárfás, A. (1983) Vertex Coverings by Monochromatic Paths and Cycles. Journal of Graph Theory, 7, 131-135.

http://dx.doi.org/10.1002/jgt.3190070116

[27] Hawking, S.W. and Ellis, G.F.R. (1973) The Large-Scale Structure of Space-Time. Cambridge University Press, Cambridge.

http://dx.doi.org/10.1017/CBO9780511524646

[28] Gopnik, A. and Schulz, L. (2007) Causal Learning: Psychology, Philosophy and Computation. Oxford University Press, New York.

http://dx.doi.org/10.1093/acprof:oso/9780195176803.001.0001

[29] Erds, P. and Moser, L. (1964) On the Representation of Directed Graphs as Unions of Orderings. Publications of the Mathematical Institute of the Hungarian Academy of Sciences, 9, 125-132.

[30] Bermond, J.C. (1974) Some Ramsey Numbers for Directed Graphs. Discrete Mathematics, 9, 313-321.

http://dx.doi.org/10.1016/0012-365X(74)90077-6

[1] Trompf, G.W. (1979) The Idea of Historical Recurrence in Western Thought, from Antiquity to the Reformation. University of California Press, Berkeley.

[2] Toynbee, A.J. (1948) Does History Repeat Itself? Civilization on Trial. Oxford University Press, New York.

[3] Kennedy, P. (1987) The Rise and Fall of the Great Powers: Economic Change and Military Conflict from 1500 to 2000. Random House, New York.

[4] Graham, G. (1997) The Shape of the Past: A Philosophical Approach to History. Oxford University Press, Oxford.

http://dx.doi.org/10.1093/acprof:oso/9780192892553.001.0001

[5] Sorokin, P.A. (1957) Social and Cultural Dynamics: A Study of Change in Major Systems of Art, Truth, Ethics, Law, and Social Relationships. Porter Sargent Publishing, Boston.

[6] Twain, M. (1903) The Jumping Frog. Harper and Brothers, New York.

[7] Barreira, L. (2006) Poincaré Recurrence: Old and New. Proceedings of the 14th International Congress on Mathematical Physics, Lisbon, 28 July-2 August 2003, 415-422.

http://dx.doi.org/10.1142/9789812704016_0039

[8] Brush, S.G. (1996) A History of Modern Planetary Physics: Nebulous Earth V1. Cambridge University Press, Cambridge.

[9] Bocchieri, P. and Loinger, A. (1957) Quantum Recurrence Theorem. Physical Review, 107, 337-338.

http://dx.doi.org/10.1103/PhysRev.107.337

[10] Livina, V., Tuzov, S., Havlin, S. and Bunde, A. (2005) Recurrence Intervals between Earthquakes Strongly Depend on History. Physica A: Statistical Mechanics and its Applications, 348, 591-595.

http://dx.doi.org/10.1016/j.physa.2004.08.032

[11] Lehners, J.-L. (2008) Ekpyrotic and Cyclic Cosmology. Physics Reports, 465, 223-263.

http://dx.doi.org/10.1016/j.physrep.2008.06.001

[12] Penrose, R. (2011) Cycles of Time: An Extraordinary New View of the Universe. Alfred Knopf, New York.

[13] Steinhardt, P.J. and Turok, N. (2001) A Cyclic Model of the Universe. Science, 296, 1436-1439.

http://dx.doi.org/10.1126/science.1070462

[14] Ramsey, F.P. (1930) On a Problem of Formal Logic. Proceedings of the London Mathematical Society, s2-30, 264-286.

http://dx.doi.org/10.1112/plms/s2-30.1.264

[15] Halasz, et al., Eds. (2002) Paul Erds and His Mathematics. Springer, Berlin.

[16] Pr?mel, H.J. (2005) Complete Disorder Is Impossible: The Mathematical Work of Walter Deuber. Combinatorics, Probability and Computing, 14, 3-16.

[17] Burr, S.A. (1974) Generalized Ramsey Theory for Graphs—A Survey. In: Bari, R. and Harary, F., Eds., Graphs and Combinatorics, Springer, Berlin, 52-75.

[18] Cartwright, D. and Harary, F. (1977) A Graph Theoretic Approach to the Investigation of System-Environment Relationships. Journal of Mathematical Sociology, 5, 87-111.

http://dx.doi.org/10.1080/0022250X.1977.9989866

[19] http://www.cs.umd.edu/~gasarch/BLOGPAPERS/ramseykings.pdf

[20] Graham, R.L., Rothschild, B.L. and Spencer, J.H. (1990) Ramsey Theory: Wiley-Interscience Series in Discrete Mathematics and Optimization. 2nd Edition, John Wiley and Sons, Inc., New York.

[21] Kittipassorn, T. and Narayanan, B.P. (2014) A Canonical Ramsey Theorem for Exactly m-Coloured Complete Subgraphs. Combinatorics, Probability and Computing, 23, 102-115.

http://dx.doi.org/10.1017/S0963548313000503

[22] Folkman, J. (1970) Graphs with Monochromatic Complete Subgraphs in Every Edge Coloring. SIAM Journal on Applied Mathematics, 18, 19-24.

http://dx.doi.org/10.1137/0118004

[23] Bollobás, B. and Gyárfás, A. (2008) Highly Connected Monochromatic Subgraphs. Discrete Mathematics, 308, 1722-1725.

http://dx.doi.org/10.1016/j.disc.2006.01.030

[24] Scott, A. and White, M. (2011) Monochromatic Cycles and the Monochromatic Circumference in 2-Coloured Graphs.

http://arxiv.org/abs/1107.5177

[25] Benevides, F., Luczak, T., Skokan, J., Scott, A. and White, M. (2012) Monochromatic Cycles in 2-Coloured Graphs. Combinatorics, Probability and Computing, 21, 57-87.

http://dx.doi.org/10.1017/S0963548312000090

[26] Gyárfás, A. (1983) Vertex Coverings by Monochromatic Paths and Cycles. Journal of Graph Theory, 7, 131-135.

http://dx.doi.org/10.1002/jgt.3190070116

[27] Hawking, S.W. and Ellis, G.F.R. (1973) The Large-Scale Structure of Space-Time. Cambridge University Press, Cambridge.

http://dx.doi.org/10.1017/CBO9780511524646

[28] Gopnik, A. and Schulz, L. (2007) Causal Learning: Psychology, Philosophy and Computation. Oxford University Press, New York.

http://dx.doi.org/10.1093/acprof:oso/9780195176803.001.0001

[29] Erds, P. and Moser, L. (1964) On the Representation of Directed Graphs as Unions of Orderings. Publications of the Mathematical Institute of the Hungarian Academy of Sciences, 9, 125-132.

[30] Bermond, J.C. (1974) Some Ramsey Numbers for Directed Graphs. Discrete Mathematics, 9, 313-321.

http://dx.doi.org/10.1016/0012-365X(74)90077-6