Advertisement

Models of Time

  • Luigi AccardiEmail author

Abstract

The first part of the chapter describes, in a qualitative way, a scheme of axiomatic approach to the notion of time. It is shown that, even restricting the physical requirements to a minimum, a multiplicity of inequivalent models are possible. In particular the idea of topological relativity suggests the impossibility to distinguish, on experimental bases, between linear and circular time. The second part of the chapter is framed within the usual quantum mechanical context and is focused on the notion of statistical reversibility and its possible extensions to non-equilibrium situations.

Keywords

Stochastic limit Statistical reversibility Topological relativity Quantum Markov processes Detailed balance 

References

  1. 1.
    Accardi, L.: On the quantum Feynman–Kac formula. Rend. Semin. Mat. Fis. Milano 48, 135–179 (1978) CrossRefGoogle Scholar
  2. 2.
    Accardi, L.: Stato Fisico. Enciclopedia Einaudi, vol. 13, pp. 514–548 (1981) Google Scholar
  3. 3.
    Accardi, L., Imafuku, K.: Dynamical detailed balance condition and local KMS condition for non-equilibrium state. Preprint Volterra N. 532, October 2002 Google Scholar
  4. 4.
    Accardi, L., Kozyrev, S.V.: Quantum interacting particle systems. Lectures given at the Volterra–CIRM International School, Levico Terme, 23–29 September 2000. In: Accardi, L., Fagnola, F. (eds.) Quantum Interacting Particle Systems. World Scientific, Singapore (2002). Preprint Volterra, N. 431, September 2000 Google Scholar
  5. 5.
    Accardi, L., Mohari, A.: Time reflected Markov processes. Infin. Dimens. Anal. Quantum Probab. Relat. Top. (IDA–QP) 2(3), 397–425 (1999). Preprint Volterra N. 366, 1999 CrossRefGoogle Scholar
  6. 6.
    Accardi, L., Reviglio, E.: The concept of physical state and the foundations of physics. Preprint Volterra N. 198, 1996 Google Scholar
  7. 7.
    Accardi, L., Frigerio, A., Lewis, J.: Quantum stochastic processes. Publ. Res. Inst. Math. Sci., Kyoto Univ. 18, 97–133 (1982) CrossRefGoogle Scholar
  8. 8.
    Accardi, L., Laio, A., Lu, Y.G., Rizzi, G.: A third hypothesis on the origins of the red shift: applications to the Pioneer 6 data. Phys. Lett. A 209, 277–284 (1995). Preprint Volterra N. 208, 1995 CrossRefGoogle Scholar
  9. 9.
    Accardi, L., Imafuku, K., Kozyrev, S.V.: Stimulated emission with non-equilibrium state of radiation. In: Proceedings of XXII Solvay Conference in Physics, 24–29 November 2001. Springer, Berlin (2002). Preprint Volterra N. 521, July 2002 Google Scholar
  10. 10.
    Accardi, L., Imafuku, K., Lu, Y.G.: Onsager relation with the “slow” degrees of the field in the white noise equation based on stochastic limit. In: Proceedings of the Japan–Italy Joint Waseda Workshop on “Fundamental Problems in Quantum Mechanics”, Tokyo, Japan, 27–29 September 2001. World Scientific, Singapore (2002). Preprint Volterra N. 522, July 2002 Google Scholar
  11. 11.
    Accardi, L., Lu, Y.G., Volovich, I.: Quantum Theory and Its Stochastic Limit. Springer, Berlin (2002) CrossRefGoogle Scholar
  12. 12.
    Accardi, L., Fagnola, F., Quezada, R.: Weighted detailed balance and local KMS condition for non-equilibrium stationary states. Bussei Kenkyu 97(3), 318–356 (2011/2012). Perspectives of Nonequilibrium Statistical Physics, Dedicated to the memory of Shuichi Tasaki Google Scholar
  13. 13.
    Aveni, A.: Gli imperi del tempo: Calendari, orologi e culture (1999) Google Scholar
  14. 14.
    Bardis, P.D.: Cronus in the eternal city. Sociol. Int. 16(1–2), 5–54 (1978) Google Scholar
  15. 15.
    Caldirola, P., Recami, E.: The concept of time in physics (considerations on physical time). Epistemologia I, 263–304 (1978) Google Scholar
  16. 16.
    Cassinelli, G., De Vito, E., Levrero, A.: Symmetry groups in quantum mechanics and the theorem of Wigner on the symmetry transformations Rev. Math. Phys. 9(8), 921–941 (1997) CrossRefGoogle Scholar
  17. 17.
    Castagnino, M., Sanguineti, J.J: Tempo e Universo, Un approccio filosofico e scientifico. Armando Editore, Roma (2000) Google Scholar
  18. 18.
    Davies, P.: I misteri del tempo. L’Universo dopo Einstein. Arnoldo Mondadori Editore, Milan (1996) Google Scholar
  19. 19.
    Di Meo, A.: Circulus Aeterni Motus: Tempo ciclico e tempo lineare nella filosofia chimica della natura. Piccola Biblioteca Einaudi (1996) Google Scholar
  20. 20.
    Dominici, P.: Evoluzione delle misure orarie in Italia. Istituto dell’Enciclopedia Italiana, Dizionario della Fisica (1993) Google Scholar
  21. 21.
    Frigerio, A., Kossakowski, A., Gorini, V., Verri, M.: Quantum detailed balance and KMS condition. Commun. Math. Phys. 57, 97–110 (1977). Erratum: Commun. Math. Phys. 60, 96 (1978) CrossRefGoogle Scholar
  22. 22.
    Majewski, W.A.: On the relationship between the reversibility of dynamics and detailed balance conditions. Ann. Inst. Henri Poincaré XXXIX(1), 45–54 (1983) Google Scholar
  23. 23.
    Majewski, W.A.: The detailed balance condition in quantum statistical mechanics. J. Math. Phys. 25(3), 614–616 (1984) CrossRefGoogle Scholar
  24. 24.
    Majewski, W.A.: Dynamical semigroups in the algebraic formulation of statistical mechanics. Fortsch. Phys. 32(1), 89–133 (1984) CrossRefGoogle Scholar
  25. 25.
    Priestley, J.B.: L’Uomo e il Tempo. Sansoni, Firenze (1974) Google Scholar
  26. 26.
    Prigogine, I.: From Being to Becoming. Freeman, New York (1980) Google Scholar
  27. 27.
    Ricoeur, P.: Tempo e racconto. Jaca Book, Milano (1999), Italian translation. Temps et récit. Cerf, Paris Google Scholar
  28. 28.
    Wickramasekara, S.: A note on the topology of space-time in special relativity. Class. Quantum Gravity 18, 5353–5358 (2001) CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Centro Vito VolterraUniversità di Roma “Tor Vergata”RomeItaly

Personalised recommendations