, Volume 169, Issue 1, pp 1–25 | Cite as

The global non-entropic arrow of time: from global geometrical asymmetry to local energy flow

  • Mario Castagnino
  • Olimpia Lombardi


Since the nineteenth century, the problem of the arrow of time has been traditionally analyzed in terms of entropy by relating the direction past-to-future to the gradient of the entropy function of the universe. In this paper, we reject this traditional perspective and argue for a global and non-entropic approach to the problem, according to which the arrow of time can be defined in terms of the geometrical properties of spacetime. In particular, we show how the global non-entropic arrow can be transferred to the local level, where it takes the form of a non-spacelike local energy flow that provides the criterion for breaking the symmetry resulting from time-reversal invariant local laws.


Global arrow of time Non-entropic arrow of time Local energy flow Time-symmetric twins 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bohm A. (1979) Quantum mechanics: Foundations and applications. Springer-Verlag, BerlinGoogle Scholar
  2. Bohm A., Gadella M. (1989) Dirac Kets, Gamow vectors, and Gel’fand triplets. Springer-Verlag, BerlinCrossRefGoogle Scholar
  3. Bohm A., Antoniou I., Kielanowski P. (1994) The Preparation-registration arrow of time in quantum mechanics. Physics Letters A 189: 442–448CrossRefGoogle Scholar
  4. Brush S. (1976) The kind of motion we call heat. North Holland, AmsterdamGoogle Scholar
  5. Castagnino M., Laura R. (1997) Minimal irreversible quantum mechanics: Pure-state formalism. Physical Review A 56: 108–119CrossRefGoogle Scholar
  6. Castagnino M., Gueron J., Ordoñez A. (2002) Global time-asymmetry as a consequence of a wave packets theorem. Journal of Mathematical Physics 43: 705–713CrossRefGoogle Scholar
  7. Castagnino M., Lara L., Lombardi O. (2003a) The cosmological origin of time-asymmetry. Classical and Quantum Gravity 20: 369–391CrossRefGoogle Scholar
  8. Castagnino M., Lombardi O., Lara L. (2003b) The global arrow of time as a geometrical property of the universe. Foundations of Physics 33: 877–912CrossRefGoogle Scholar
  9. Davies P.C.W. (1974) The physics of time asymmetry. University of California Press, Berkeley-Los AngelesGoogle Scholar
  10. Davies P.C.W. (1994) Stirring up trouble. In: Halliwell J.J., Pérez-Mercader J., Zurek W.H.(eds) Physical origins of time asymmetry. Cambridge University Press, CambridgeGoogle Scholar
  11. Earman J. (1974) An attempt to add a little direction to “the problem of the direction of time”. Philosophy of Science 41: 15–47CrossRefGoogle Scholar
  12. Earman J. (2002) What time reversal invariance is and why it matters. International Studies in the Philosophy of Science 16: 245–264CrossRefGoogle Scholar
  13. Ehrenfest P., Ehrenfest T. (1959) The conceptual foundations of the statistical approach in mechanics. Cornell University Press, IthacaGoogle Scholar
  14. Feynman R.P., Leighton R.B., Sands M. (1964) The Feynman lectures on physics. Addison-Wesley, New YorkGoogle Scholar
  15. Gold T. (1966) Cosmic processes and the nature of time. In: Colodny R.(eds) Mind and cosmos. University of Pittsburgh Press, PittsburghGoogle Scholar
  16. Grünbaum A. (1963) Philosophical problems of space and time. Alfred A. Knopf, New YorkGoogle Scholar
  17. Haag R. (1996) Local quantum physics: fields, particles, algebras. Springer, BerlinGoogle Scholar
  18. Hawking S.W., Ellis G.F.R. (1973) The large scale structure of space-time. Cambridge University Press, CambridgeGoogle Scholar
  19. Lax P.D., Phillips R.S. (1979) Scattering theory. Academic Press, New YorkGoogle Scholar
  20. Layzer D. (1975) The arrow of time. Scientific American 234: 56–69CrossRefGoogle Scholar
  21. Mackey M.C. (1989) The dynamic origin of increasing entropy. Reviews of Modern Physics 61: 981–1015CrossRefGoogle Scholar
  22. Matthews G. (1979) Time’s arrow and the structure of spacetime. Philosophy of Science 46: 82–97CrossRefGoogle Scholar
  23. Misner C.W., Thorne K.S., Wheeler J.A. (1973) Gravitation. Freeman and Co., San FranciscoGoogle Scholar
  24. Penrose R. (1979) Singularities and time asymmetry. In: Hawking S., Israel W.(eds) General relativity, an Einstein centenary survey. Cambridge University Press, CambridgeGoogle Scholar
  25. Popper K. (1956) The arrow of time. Nature 177: 538CrossRefGoogle Scholar
  26. Price H. (1996) Time’s arrow and Archimedes’ point: new directions for the physics of time. Oxford University Press, New York, OxfordGoogle Scholar
  27. Reichenbach H. (1956) The direction of time. University of California Press, BerkeleyGoogle Scholar
  28. Sachs R.G. (1987) The physics of time reversal. University of Chicago Press, ChicagoGoogle Scholar
  29. Schutz B.F. (1980) Geometrical methods of mathematical physics. Cambridge University Press, CambridgeGoogle Scholar
  30. Sklar L. (1974) Space, time and spacetime. University of California Press, BerkeleyGoogle Scholar
  31. Sklar L. (1993) Physics and chance. Cambridge University Press, CambridgeGoogle Scholar
  32. Smart J.J.C. (1967) Time, Encyclopedia of philosophy, Vol. 8. Macmillan, New YorkGoogle Scholar
  33. Torretti R. (1983) Relativity and geometry. Dover, New YorkGoogle Scholar
  34. Visser M. (1995) Lorentzian Wormholes: From Einstein to Hawking. Springer-Verlag, New YorkGoogle Scholar
  35. Weinberg S. (1995) The quantum theory of fields. Cambridge University Press, CambridgeGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.CONICET-IAFE-IFIR-Universidad de Buenos AiresBuenos AiresArgentina
  2. 2.CONICET-Universidad de Buenos AiresBuenos AiresArgentina

Personalised recommendations