Skip to main content
Log in

The direction of time

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

The meaning of the phrase “the direction of time” and the physical problems involved are considered. These problems are discussed and plausibility arguments are given to show that all clocks run in the same direction (almost always), that the most probable development of the Universe during the early stages of the expansion would result in the introduction of some internal organization, and that the expansion of the Universe and the increase in entropy define time directions that have the same sense. The question of what properties of the laws governing the Universe lead to these results is studied.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. A. Grünbaum,Am. Sci. 43, 550 (1955).

    Google Scholar 

  2. H. Reichenbach,The Direction of Time (University of California Press, Berkeley California, 1956).

    Google Scholar 

  3. A. Grünbaum,Philosophical Problems of Space and Time (Alfred A. Knopf, New York, 1963).

    Google Scholar 

  4. S. Watanabe,Prog. Theor. Physics Supp., Extra Number (between Nos. 32 and 33), 135 (1965).

  5. J. Zeman, ed.,Time in Science and Philosophy (American Elsevier, New York, 1971).

    Google Scholar 

  6. J. T. Fraser, F. C. Haber, and G. H. Müller, eds.,The Study of Time, (Springer-Verlag, New York, 1972).

    Google Scholar 

  7. T. Gold, “The world map and the apparent flow of time,” inModern Developments in Thermodynamics, B. Gal-Or, ed. (Keter Publishing House, Jerusalem).

  8. Ya. P. Terletskii,Statistical Physics (North-Holland, Amsterdam, 1971), #52.

    Google Scholar 

  9. K. Kraus,Physikalische Blätter 29(1), 9 (1973).

    Google Scholar 

  10. B. Gal-Or,Ann. N.Y. Acad. Sci. 1972, 307.

  11. F. J. Belinfante,Causality and Physical Theories, Conference Proceedings #16 (American Institute of Physics, New York), pp. 49, 157.

  12. J. V. Narlikar,Pure Appl. Chem. 22, 449 (1970).

    Google Scholar 

  13. R. Mirman,Found. Phys. 3, 321 (1973).

    Google Scholar 

  14. D. ter Haar,Rev. Mod. Phys. 27, 289 (1955).

    Google Scholar 

  15. A. Hobson,Am. J. Phys. 34, 411 (1966);J. Chem. Phys. 46, 1365 (1967);Phys. Letters 28a, 183 (1968).

    Google Scholar 

  16. A. Hobson and D. N. Loomis,Phys. Rev. 173, 285 (1968).

    Google Scholar 

  17. W. Pompe and K. Voss,Ann. der Phys. 19, 253 (1967).

    Google Scholar 

  18. R. Davidson and J. Rae,J. Phys. A (General Phys.) 3(2), 128 (1970).

    Google Scholar 

  19. T. Y. Wu,Int. J. Theor. Phys. 2, 325 (1969).

    Google Scholar 

  20. R. Zwanzig,Pure Appl. Chem. 22, 371 (1970).

    Google Scholar 

  21. I. Prigogine,Bull. Acad. Roy. Belg. (Cl. Sci.) 1967 (April 15), 273;Theoretical Physics and Biology (1969), p. 23.

  22. I. Prigogine,Nature 246, 67 (1973).

    Google Scholar 

  23. J. Biel and J. Rae,Irreversibility in the Many-Body Problem (Plenum Press, New York, 1972).

    Google Scholar 

  24. J. Mehra and E. C. G. Sudarshan,Nuovo Cimento 11B, 215 (1972).

    Google Scholar 

  25. T. P. Eggarter,Am. J. Phys. 41, 874 (1973).

    Google Scholar 

  26. I. Prigogine, G. Nicolis, and A. Babloyantz,Physics Today 25 (November), 42 (1972);25 (December), 38 (1972).

    Google Scholar 

  27. L. Sklar,Space, Time and Spacetime (University of California Press, Berkeley, California, 1974).

    Google Scholar 

  28. T. Gold,Publications of the Eleventh Solvay Conference in Physics (Stoops, Brussels, 1958), Part I, pp. 81–95;Am. J. Phys. 30, 403 (1962).

    Google Scholar 

  29. O. Penrose and I. C. Percival,Proc. Phys. Soc. 79(3), 605 (1962).

    Google Scholar 

  30. F. C. Andrews,Proc. Nat. Acad. Sci. 54, 13 (1965).

    Google Scholar 

  31. F. R. Stannard,Nature 211, 693 (1966).

    Google Scholar 

  32. T. Gold, ed.,The Nature of Time (Cornell U. Press, Ithaca, New York, 1967).

    Google Scholar 

  33. P. L. Csonka,Phys. Rev. 180, 1266 (1969).

    Google Scholar 

  34. L. S. Schulman,Phys. Rev. D 7, 2686 (1973).

    Google Scholar 

  35. D. L. Schumacher,Proc. Camb. Phil. Soc. 60, 575 (1964).

    Google Scholar 

  36. W. J. Cocke,Phys. Rev. 160, 1165 (1967).

    Google Scholar 

  37. W. Pompe and H. G. Schopf,Ann. der Phys. 21, 26 (1968).

    Google Scholar 

  38. F. Jegerlehner,Fortschritte der Physik (Progress of Physics) 16, 137 (1968).

    Google Scholar 

  39. P. R. Chaudhuri,J. Phys. A (General Phys.) 3(2), L5 (1970).

  40. J. V. Narlikar,Pure Appl. Chem. 22, 449 (1970).

    Google Scholar 

  41. D. Layzer,Pure Appl. Chem. 22, 457 (1970).

    Google Scholar 

  42. Y. Ne'eman,Int. J. Theor. Phys. 3, 1 (1970).

    Google Scholar 

  43. A. Aharony and Y. Ne'eman,Lett. Nuovo Cimento IV, 862 (1970).

    Google Scholar 

  44. A. Aharony,Lett. Nuovo Cimento 4, 988 (1972);Ann. Phys. (N.Y.) 67, 1 (1971);68, 163 (1971).

    Google Scholar 

  45. B. Gal-Or,Science 176, 11 (1972).

    Google Scholar 

  46. A. Kovetz,Astrophys. Lett. 9, 17 (1971).

    Google Scholar 

  47. P. C. W. Davies,Nature Phys. Sci. 240, 3 (1972).

    Google Scholar 

  48. L. D. Landau and E. M. Lifshitz,Statistical Physics (Addison-Wesley, Reading, Massachusetts, 1958), p. 28.

    Google Scholar 

  49. Y. Aharonov, P. G. Bergmann, and J. L. Lebowitz,Phys. Rev. 134, B1410 (1964).

    Google Scholar 

  50. R. H. Penfield,Am. J. Phys. 34, 422 (1966).

    Google Scholar 

  51. G. Lindblad,Comm. Math. Phys. 28, 245 (1972).

    Google Scholar 

  52. H. D. Zeh, inFoundations of Quantum Mechanics, B. d'Espagnat, ed. (Academic Press, New York, 1971), p. 263.

    Google Scholar 

  53. Kerson Huang,Statistical Mechanics (Wiley, New York, 1965).

    Google Scholar 

  54. Richard C. Tolman,The Principles of Statistical Mechanics (Oxford University Press, New York, 1938).

    Google Scholar 

  55. W. Thirring,Z. Phys. 235(4), 339 (1970).

    Google Scholar 

  56. E. D. Fackerell, J. R. Ipser, and K. S. Thorne,Comm. Astrophys. Space Phys. 1, 134 (1969).

    Google Scholar 

  57. D. Lynden-Bell,Monthly Notices Roy. Astron. Soc. 136, 101 (1967).

    Google Scholar 

  58. D. Lynden-Bell and R. Wood,Monthly Notices Roy. Astron. Soc. 138, 495 (1968).

    Google Scholar 

  59. D. ter Haar, “Proceedings of the International Conference on Statistical Mechanics,” inJ. Phys. Soc. Japan 26, Suppl. 25 (1969).

  60. W. C. Saslaw,Monthly Notices Roy. Astron. Soc. 141, 1 (1968);143, 437 (1969).

    Google Scholar 

  61. D. Lynden-Bell, inBrandeis University Summer Institute in Theoretical Physics, Vol. 1, 1968, M. Chretianet al., eds. (Gordon and Breach Science Publishers, New York).

    Google Scholar 

  62. M. J. Rees and D. W. Sciama,Comm. Astrophys. Space Phys. 1, 140, 153 (1969).

    Google Scholar 

  63. P. J. E. Peebles,Ap. J. 142, 1317 (1965);Phys. Rev. D 1, 397 (1970).

    Google Scholar 

  64. S. W. Hawking,Ap. J. 145, 544 (1966).

    Google Scholar 

  65. C. W. Misner,Nature 214, 40 (1967).

    Google Scholar 

  66. W. C. Saslaw,Monthly Notices Roy. Astron. Soc. 136, 39 (1967).

    Google Scholar 

  67. E. R. Harrison, “Quatorzième Collique International d'Astrophysique,” inMem. Soc. Roy. Sci. Liege 15, 15 (1967), and other papers in this volume which have relevance to the subject.

    Google Scholar 

  68. E. R. Harrison,Rev. Mod. Phys. 39, 862 (1967);Monthly Notices Roy. Astron. Soc. 141, 397 (1968).

    Google Scholar 

  69. G. B. Field, “The formation and early dynamical history of the galaxies,” inStars and Stellar Systems, Vol. IX:Galaxies and the Universe, A. and M. Sandage, eds. (to be published).

  70. T. Hirasawa,Prog. Theor. Phys. 42, 523 (1969).

    Google Scholar 

  71. H. Nariai,Prog. Theor. Phys. 42, 544 (1969).

    Google Scholar 

  72. J. N. Bahcall and P. C. Joss,Comm. Astrophys. Space Sci. 4, 95 (1972).

    Google Scholar 

  73. B. T. J. Jones and P. J. E. Peebles,Comm. Astrophys. Space Sci. 4, 121 (1972).

    Google Scholar 

  74. Ya. B. Zel'dovich and I. D. Novikov,JETP Letters 4, 80 (1966).

    Google Scholar 

  75. A. G. Doroshkevich, Ya. B. Zel'dovich, and I. D. Novikov,Soviet Physics—JETP 26, 408 (1968).

    Google Scholar 

  76. M. J. Rees and J. Silk,Sci. Am. 222 (6), 26 (1970).

    Google Scholar 

  77. E. L. Schucking and E. A. Spiegel,Comm. Astrophys. Space Phys. 2, 121 (1970).

    Google Scholar 

  78. I. Prigogine,Nature 209, 602 (1966).

    Google Scholar 

  79. I. Prigogine and G. Severne,Physica 32, 1376 (1966).

    Google Scholar 

  80. Y. Freundlich,Phil. Sci. 40, 496 (1973).

    Google Scholar 

  81. P. C. W. Davies,The Physics of Time Asymmetry (Surrey U. P., London, 1974).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mirman, R. The direction of time. Found Phys 5, 491–511 (1975). https://doi.org/10.1007/BF00708892

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00708892

Keywords

Navigation