Foundations of Physics

, Volume 33, Issue 6, pp 877–912 | Cite as

The Global Arrow of Time as a Geometrical Property of the Universe

  • Mario Castagnino
  • Olimpia Lombardi
  • Luis Lara


Traditional discussions about the arrow of time in general involve the concept of entropy. In the cosmological context, the direction past-to-future is usually related to the direction of the gradient of the entropy function of the universe. But the definition of the entropy of the universe is a very controversial matter. Moreover, thermodynamics is a phenomenological theory. Geometrical properties of space-time provide a more fundamental and less controversial way of defining an arrow of time for the universe as a whole. We will call the arrow defined only on the basis of the geometrical properties of space-time, independently of any entropic considerations, “the global arrow of time.” In this paper we will argue that: (i) if certain conditions are satisfied, it is possible to define a global arrow of time for the universe as a whole, and (ii) the standard models of contemporary cosmology satisfy these conditions.


Entropy Geometrical Property Entropy Function Phenomenological Theory Cosmological Context 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. Castagnino, L. Lara, and O. Lombardi, “The cosmological origin of time-asymmetry, ” Classical and Quantum Gravity 20, 369–391 (2003).Google Scholar
  2. 2.
    J. Barrow, The Origin of the Universe (Basic Books, New York, 1994).Google Scholar
  3. 3.
    L. Bergstrom and A. Goobar, Cosmology and Particle Astrophysics (Wiley, New York, 1999).Google Scholar
  4. 4.
    J. P. Ostriker and P. J. Steinhardt, “The observational case for a low-density universe with a non-zero cosmological constant, ” Nature 377, 600–602 (1995).Google Scholar
  5. 5.
    R. Smith, The Expanding Universe: Astronomy's Great Debate (Cambridge University Press, Cambridge, 1982).Google Scholar
  6. 6.
    G. Burbidge, “Modern cosmology. The harmonious and discordant facts, ” Internat. J. Theoret. Phys. 28, 983–1004 (1989).Google Scholar
  7. 7.
    R. Penrose, “Singularities and time asymmetry, ” in General Relativity, an Einstein Centenary Survey, S. W. Hawking and W. Israel, eds. (Cambridge University Press, Cambridge, 1979).Google Scholar
  8. 8.
    R. G. Sachs, The Physics of Time Reversal (University of Chicago Press, Chicago, 1987).Google Scholar
  9. 9.
    L. Sklar, Space, Time, and Spacetime (University of California Press, Berkeley, 1974).Google Scholar
  10. 10.
    J. Earman, “An attempt to add a little direction to 'the problem of the direction of time', ” Philosophy of Science 41, 15–47 (1974).Google Scholar
  11. 11.
    H. Price, Time's Arrow and Archimedes' Point: New Directions for the Physics of Time (Oxford University Press, New York/Oxford, 1996).Google Scholar
  12. 12.
    S. Brush, The Kind of Motion We Call Heat (North-Holland, Amsterdam, 1976).Google Scholar
  13. 13.
    J. Earman, op. cit., p. 15.Google Scholar
  14. 14.
    H. Reichenbach, The Direction of Time (University of California Press, Berkeley, 1956), pp. 127–128.Google Scholar
  15. 15.
    P. C. W. Davies, “Stirring up trouble, ” in Physical Origins of Time Asymmetry, in J. J. Halliwell, J. Perez-Mercader, and W. H. Zurek, eds. (Cambridge University Press, Cambridge, 1994), p. 124.Google Scholar
  16. 16.
    L. Sklar, Physics and Chance (Cambridge University Press, Cambridge, 1993).Google Scholar
  17. 17.
    P. C. W. Davies, The Physics of Time Asymmetry (University of California Press, Berkeley-Los Angeles, 1974).Google Scholar
  18. 18.
    R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics (Addison–Wesley, New York, 1964).Google Scholar
  19. 19.
    D. Layzer, “The arrow of time, ” Sci. Am. 234, 56–69 (1975).Google Scholar
  20. 20.
    M. C. Mackey, “The dynamic origin of increasing entropy, ” Reviews of Modern Physics 61, 981–1015 (1989).Google Scholar
  21. 21.
    J. Earman, op. cit., p. 20.Google Scholar
  22. 22.
    J. Earman, op. cit., p. 22.Google Scholar
  23. 23.
    G. Matthews, “Time's arrow and the structure of spacetime, ” Philosophy of Science 46, 82–97 (1979), p. 90.Google Scholar
  24. 24.
    G. Matthews, op. cit., p. 92.Google Scholar
  25. 25.
    H. Reichenbach, op. cit., p. 127.Google Scholar
  26. 26.
    S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-Time (Cambridge University Press, Cambridge, 1973).Google Scholar
  27. 27.
    B. F. Schutz, Geometrical Methods of Mathematical Physics (Cambridge University Press, Cambridge, 1980).Google Scholar
  28. 28.
    C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (Freeman, San Francisco, 1973).Google Scholar
  29. 29.
    A. Grunbaum, Philosophical Problems of Space and Time (Reidel, Dordrecht, 1973), p. 790.Google Scholar
  30. 30.
    S. F. Savitt, “Introduction, ” in Time's Arrows Today, S. F. Savitt, ed. (Cambridge University Press, Cambridge, 1995).Google Scholar
  31. 31.
    M. Castagnino and E. Gunzig, “A landscape of time asymmetry, ” Internat. J. Theoret. Phys. 36, 2545–2581 (1997), p. 2545.Google Scholar
  32. 32.
    H. Price, op. cit., p. 88.Google Scholar
  33. 33.
    J. J. Halliwell, “Quantum cosmology and time asymmetry, ” in Physical Origins of Time Asymmetry, J. J. Halliwell, J. Perez-Mercader, and W. H. Zurek, eds. (Cambridge University Press, Cambridge, 1994).Google Scholar
  34. 34.
    M. Castagnino, H. Giacomini, and L. Lara, “Dynamical properties of the conformally coupled FRW model, ” Physical Review D 61, 107302(2000).Google Scholar
  35. 35.
    M. Castagnino, H. Giacomini, and L. Lara, “Qualitative dynamical properties of a spatially closed FRW universe conformally coupled to a scalar field, ” Physical Review D 63, 044003(2001).Google Scholar
  36. 36.
    S. F. Savitt, “The direction of time, ” British J. Phil. Sci. 47, 347–370 (1996).Google Scholar
  37. 37.
    T. Gold, “Cosmic processes and the nature of time, ” in Mind and Cosmos, R. Colodny, ed. (University of Pittsburgh Press, Pittsburgh, 1966).Google Scholar
  38. 38.
    J. Earman, op. cit., p. 24.Google Scholar
  39. 39.
    J. Earman, op. cit., pp. 26–27.Google Scholar
  40. 40.
    J. Earman and J. Norton, “What price spacetime substantivalism? The hole story, ” British J. Phil. Sci. 38, 515–525, 522 (1987).Google Scholar
  41. 41.
    J. Earman, op. cit., p. 25.Google Scholar
  42. 42.
    J. Earman, World Enough and Space-Time (The MIT Press, Cambridge MA, 1989).Google Scholar
  43. 43.
    O. Lombardi, “Determinism, internalism and objectivity, ” in Between Chance and Choice, H. Atmanspacher and R. Bishop, eds. (Imprint-Academic, Thorverton, 2002).Google Scholar
  44. 44.
    M. Castagnino and E. Gunzig, “Minimal irreversible quantum mechanics: An axiomatic formalism, ” Internat. J. Theoret. Phys. 38, 47–92 (1999).Google Scholar

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • Mario Castagnino
    • 1
  • Olimpia Lombardi
    • 2
  • Luis Lara
    • 3
  1. 1.CONICETInstituto de Astronomía y Física del EspacioBuenos AiresArgentina
  2. 2.CONICET, Departamento de Filosofía de la CienciaUniversidad Autónoma de MadridMadridEspaña
  3. 3.Departamento de FísicaUniversidad Nacional de RosarioRosarioArgentina

Personalised recommendations