Time Symmetry Breaking, Duality and Cantorian Space-time

Chaos, Solitons and Fractals

Volumn 7, Issue 4 SPEC. ISS., 1996, Pages 499-503

  El Naschie, M S ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000355573     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/0960-0779(96)00007-0     Document Type: Article

References (64)

1. I. Prigogine, From Being to Becoming. Freeman, New York (1980).
2. T. Petrosky and I. Prigogine, Complex spectral representation and time-symmetry breaking. In Quantum Mechanics, Diffusion and Chaotic Fractals, edited by M. S. El Naschie, O. Rössler and I. Prigogine, pp. 1-49. Elsevier, Oxford (1995).
3. I. Prigogine, T. Petrosky, H. Hasegawa and S. Tasaki, Integrability and chaos in classical and quantum mechanics. Chaos, Solitons & Fractals 1, 3-24 (1991).
4. T. Petrosky and I. Prigogine, Poincaré resonances and the extension of classical dynamics. Chaos, Solitons & Fractals 7, (1996).
5. I. Prigogine and Y. Elskens, Irreversibility, stochasticity and non-locality in classical dynamics. In Quantum Implications, edited by B. Hiley and D. Peat, pp. 205-226. Routledge, London (1988).
6. R. Penrose, The Emperor's New Mind. Oxford University Press, Oxford (1989).
7. M. Gell-Mann, The Quark and Jaguar. Little & Brown, London (1994).
8. K. Menger, Die Relativitaetstheorie und die Geometrie. In Einstein als Philosoph und Naturforscher, edited by Schlipp, pp. 328-342. Vieweg, Braunschweig (1993).
9. D. Bohm, Wholeness and the Implicate Order. Routledge, London (1980).
10. D. Finkelstein, All is flux. In Quantum Implications, edited by B. Hiley and D. Peat, pp. 289-294. Routledge, London (1987).
11. C. W. Misner, K. Thorne and J. A. Wheeler, Gravitation. Freeman, New York (1970).
12. R. Feymann and A. Hibbs, Quantum Mechanics and Path Integrals. McGraw-Hill, New York (1965).
13. E. Schrödinger, Sitzungsberichte der Preussischen. Akad. Wiss. Phys. Math. Klasse 24, 418-428 (1930).
14. M. S. El Naschie, Young's double-slit experiment, Heisenberg. Uncertainty principle and correlation in Cantorian space-time. In Quantum Mechanics, Diffusion and Chaotic Fractals, edited by M. S. El Naschie, O. Rössler and I. Prigogine, pp. 93-99. Elsevier, Oxford (1995).
15. J. W. Dauben, G. Cantor. Princeton University Press, Princeton, NJ (1979).
16. M. S. El Naschie, Banach-Tarski theorem and Cantorian micro space-time. Chaos, Solitons & Fractals 5, 1503-1508 (1995).
17. D. Finkelstein, Theory of vacuum. In The Philosophy of Vacuum, edited by S. Sanders and H. Brown, pp. 252-274. Clarendon Press, Oxford (1991).
18. M. S. El Naschie, A note on quantum mechanics, Diffusional interference and informions. Chaos, Solitons & Fractals 5, 881-884 (1995).
19. E. Schrödinger, Sur la theorie relativistice de l'electron et l'interpretation de la mecanique quantique. Annales de l'Institut H. Poincaré (1931). Reprinted in Erwin Schrodinger Gesammelte Abhandlungen. Austrian Academy of Science, Wien.
20. M. S. El Naschie and A. Hussein, Prolongation and inverse problems in non-conservative variational mechanics. In Proceedings of the 8th Canadian Congress of Applied Mechanics, CanCam Moncton, pp. 807-808 (1981).
21. M. S. El Nachie and A. Al Athel, Sur un principe variationel pour l'analyse de la stabilite des barres sous forces polygeniques. ZAMM T256-T257 (1980).
22. M. S. El Naschie and A. Al Athel, Solid Mech. Arch. 4, 173-182 (1979).
23. M. S. El Naschie, Stress, Stability and Chaos. McGraw-Hill, New York (1990) (see in particular pp. 138-142, 155 and 397-398).
24. E. Schrödinger, Sitzungsberichte der Preussischen. Akad. Wiss. Phys. Math. Klasse 24, 418-428 (1930).
25. L. Abbott and A. Wise, Dimension of quantum mechanical path. Am. J. Phys. 49, 37-39 (1981).
26. M. S. El Naschie, Average symmetry, stability and ergodicity off multidimensional Cantor sets. Nuovo Cimento 109 B, 149-157 (1994).
27. L. Nottale, Scale relativity, fractal space-time and quantum mechanics. In Quantum Mechanics, Diffusion and Chaotic Fractals, edited by M. S. El Naschie, O. Rössler and I. Prigogine, pp. 51-78. Elsevier, Oxford (1995).
28. M. S. El Naschie, O. Rössler and I. Prigogine, Quantum Mechanics, Diffusion and Chaotic Fractals. Elsevier, Oxford (1995).
29. M. S. El Naschie, On the nature of complex time, diffusion and the two-slit experiment. Chaos, Solitons & Fractals 5, 1031-1032 (1995).
30. M. S. El Naschie, On conjugate complex time and information in relativistic quantum theory. Chaos, Solitons & Fractals 5, 1551-1555 (1995).
31. J. L. Casti, Paradigms Lost. Avon Books, New York (1989) (see in particular pp. 465-467).
32. M. Nagasawa, Quantum theory, theory of Brownian motions and relativity theory. Chaos, Solitons & Fractals 7 (1996). In press.
33. M. S. El Naschie, Orbit stability and dimensional criticality of Cantor sets. Appl. Math. Lett. 7, 91-94 (1994).
34. M. S. El Naschie, Dimensions and Cantor-spectra. Chaos, Solitons & Fractals 4, 2121-2132 (1994).
35. M. J. Duff, Kaluza-Klein theory in perspective. In The Oskar Klein Centenary, pp, 22-33. World Scientific, Singapore (1995).
36. M. S. El Naschie, Iterate function systems, information and the two-slit experiment of quantum mechanics. In Quantum Mechanics, Diffusion and Chaotic Fractals, edited by M. S. El Naschie, O. Rössler and I. Prigogine, pp. 185-189. Elsevier, Oxford (1995).
37. M. S. El Naschie, Qauntum mechanics, information, diffusion and Cantorian geodesics. In Quantum Mechanics, Diffusion and Chaotric Fractals, edited by M. S. El Naschie, O. Rössler and I. Prigogine, pp. 191-205. Elsevier, Oxford (1995).
38. M. S. El Naschie, Renormalization approach to the dimension of diffusion in Cantorian space. Appl. Math. Lett. 8, 59-63 (1995).
39. M. S. El Naschie and O. Rössler, Foreword to Quantum Mechanics, Diffusion and Chaotic Fractals, pp. vii-x Elsevier, Oxford (1995).
40. M. S. El Naschie, On universal behaviour and statistical mechanics of multidimensional triadic Cantor sets. SAMS 11, 217-225 (1993).
41. M. S. El Naschie, Semiconductors, Fermi statistics and multidimensional Cantor sets. Chaos, Solitons & Fractals 3, 481-488 (1993).
42. K. Svozil, 'Linear' chaos via paradoxical set decomposition. Chaos. Solitons and Fractals 7 (1996). In press.
43. G. Ord, Fractal space-time. J. Phys. A Math. Gen. 16, 1869-1884 (1983).
44. G. Ord, Fractal space-time and statistical mechanics of random walks. Chaos, Solitons & Fractals 7 (1996). In press.
45. O. Rössler, Relative-state theory: four new aspects. Chaos, Solitons & Fractals 7 (1996). In press.
46. M. S. El Naschie, Quantum mechanics and the possibility of a Cantorian space-time. Chaos, Solitons & Fractals 1, 485-487 (1991).
47. P. Dirac, The Principles of Quantum Mechanics, p. 267. Oxford University Press, Oxford (1987).
48. M. S. El Naschie, Kolmogorov scaling in Appollonian fractals as a model of Cantorian space-time. Chaos, Solitons & Fractals 7, 147-149 (1996).
49. O. Klein, On the quantum mechanical derivation of the second law. Z. Phys. 72, 767 (1931).
50. B. Magee, The Great Philosophers (a remark about N. Chomsky on p. 21). Oxford University Press, Oxford (1987).
51. D. Bohm and B. J. Hiley, The Undivided Universe. Routledge, London (1993).
52. I. Prigogine and I. Stengers, Order Out of Chaos. Flamingo London (1985).
53. S. Al Athel, On dimension of space time. Chaos, Solitons & Fractals 7 (1996). In press.
54. A. Boyarsky and P. Gora, A model for the structure of space time. Chaos, Solitons & Fractals 7 (1996). In press.
55. A. Rae, Quantum Physics Illusion or Reality? Cambridge University Press, Cambridge (1991).
56. R. Penrose, Shadow of the Mind. Oxford University Press, Oxford (1994).
57. J. Pitman, Probability Springer, New York (1993).
58. S. W. Hawking, Arrow of time in cosmology. Phys. Rev. D 32, 2489-2496 (1985).
59. H. D. Zeh, The Direction of Time. Springer, Berlin (1992).
60. S. Weinberg, Dreams of a Final Theory. Pantheon Books, New York (1992); Ann. Phys., N.Y. 194, 336 (1989).
61. S. Weinberg, Dreams of a Final Theory. Pantheon Books, New York (1992); Ann. Phys., N.Y. 194, 336 (1989).
62. E. Cosserat and F. Cosserat, Theorie des Corps déforormables. Hermann, Paris (1909).
63. K. Nakamura and M. S. El Naschie, Quantum Chaos. Chaos, Solitons & Fractals 5 (1995).
64. A. Einstein and W. Ritz, Phys. Z. 10, 323 (1909).