Growing Classical and Quantum Entropies in the Early Universe

Article
  • 50 Downloads

Abstract

Following the idea that the global and local arrow of time has a cosmological origin, we define an entropy in the classical and in the quantum periods of the universe evolution. For the quantum period a semi-classical approach is adopted, modelling the universe with Wheeler-De Witt equation and using WKB. By applying the self-induced decoherence to the state of the universe it is proved that the quantum universe becomes a classical one. This allows us to define a conditional entropy which, in our simplified model, is proportional to e2γt where γ is the dumping factor associated with the interaction potential of the scalar fields. Finally we find both Gibbs and thermodynamical entropy of the universe based in the conditional entropy.

Entropy Quantum universe Decoherence 

References

  1. 1.
    Adler, S.: Quantum Theory as an Emergent Phenomenon. Cambridge University Press, Cambridge (2004) Google Scholar
  2. 2.
    Aiello, M., Castagnino, M., Lombardi, O.: Found. Phys. 38, 256–292 (2008) CrossRefMathSciNetADSGoogle Scholar
  3. 3.
    Antoniou, I., Suchanecki, Z., Laura, R., Tasaki, S.: Physica A 241, 737 (1997) CrossRefADSGoogle Scholar
  4. 4.
    Ballentine, L.: Quantum Mechanics. World Scientific, Singapore (1998) MATHGoogle Scholar
  5. 5.
    Barvinsky, A.O., et al.: Nucl. Phys. B 551, 374 (1999) CrossRefADSGoogle Scholar
  6. 6.
    Belanger, A., Thomas, G.F.: Can. J. Math. 42, 410 (1990) MATHMathSciNetGoogle Scholar
  7. 7.
    Birrell, N., Davies, P.: Quantum Field Theory in Curves Space. Cambridge University Press, Cambridge (1982) Google Scholar
  8. 8.
    Bohm, A.: Quantum Mechanics, Foundations and Applications. Springer, Berlin (1986) MATHGoogle Scholar
  9. 9.
    Bonifacio, R., et al.: Phys. Rev. A 61, 053802 (2000) CrossRefADSGoogle Scholar
  10. 10.
    Casati, G., Chirikov, B.: Phys. Rev. Lett. 75, 349 (1995) CrossRefADSGoogle Scholar
  11. 11.
    Casati, G., Chirikov, B.: Phys. Rev. D 86, 220 (1995) MATHMathSciNetGoogle Scholar
  12. 12.
    Casati, G., Prosen, T.: Phys. Rev. A 72, 032111 (2005) CrossRefMathSciNetADSGoogle Scholar
  13. 13.
    Castagnino, M.: Physica A 335, 511 (2004) CrossRefMathSciNetADSGoogle Scholar
  14. 14.
    Castagnino, M.: Phys. Lett. A 357, 97 (2006) MATHCrossRefMathSciNetADSGoogle Scholar
  15. 15.
    Castagnino, M., Gadella, M.: Found. Phys. 36, 920 (2006) MATHCrossRefMathSciNetADSGoogle Scholar
  16. 16.
    Castagnino, M., Gunzig, E.: Int. J. Theor. Phys. 36, 2545 (1997) MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Castagnino, M., Laura, R.: Phys. Rev. A 56, 108 (1997) CrossRefMathSciNetADSGoogle Scholar
  18. 18.
    Castagnino, M., Laura, R.: Int. J. Theor. Phys. 39, 1737 (2000) MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Castagnino, M., Laura, R.: Phys. Rev. A 62, 022107 (2000) CrossRefADSGoogle Scholar
  20. 20.
    Castagnino, M., Lombardi, O.: Stud. Hist. Phil. Mod. Phys. 35, 73 (2004) CrossRefMathSciNetGoogle Scholar
  21. 21.
    Castagnino, M., Lombardi, O.: J. Phys. A (Math. and Gen.) 37, 4445–4463 (2004) MATHCrossRefMathSciNetADSGoogle Scholar
  22. 22.
    Castagnino, M., Lombardi, O.: Decoherence time in self induced decoherence. arXiv:quant-ph/0502087 (2005)
  23. 23.
    Castagnino, M., Lombardi, O.X.: In: Reimer, A. (ed.) Spacetime Physics Research Trends. Horizons in World Physics. Nova Science, New York (2005) Google Scholar
  24. 24.
    Castagnino, M., Lombardi, O.: Phys. Rev. A 72, 012102 (2005) CrossRefMathSciNetADSGoogle Scholar
  25. 25.
    Castagnino, M., Lombardi, O.: Chaos, Solitons Fract. 28, 879 (2006) MATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    Castagnino, M., Lombardi, O.: Phil. Sci. 74, 968 (2007) CrossRefMathSciNetGoogle Scholar
  27. 27.
    Castagnino, M., Lombardi, O.: Physica A 388, 247 (2009) CrossRefADSGoogle Scholar
  28. 28.
    Castagnino, M., Ordoñez, A.: Int. J. Theor. Phys. 43, 695–719 (2004) MATHCrossRefGoogle Scholar
  29. 29.
    Castagnino, M., Fortin, S., Laura, R., Lombardi, O.: Class. Quantum Gravity 25, 154002 (2008) CrossRefMathSciNetADSGoogle Scholar
  30. 30.
    Castagnino, M., Lara, L., Lombardi, O.: Int. J. Theor. Phys. 42, 2487–2504 (2003) MATHCrossRefMathSciNetGoogle Scholar
  31. 31.
    Castagnino, M., Lara, L., Lombardi, O.: Class. Quantum Gravity 20, 369–391 (2003) MATHCrossRefMathSciNetADSGoogle Scholar
  32. 32.
    Castagnino, M., Laura, R., Liotta, R., Id Bettan, R.: J. Phys. A (Math. Gen.) 35, 6055 (2002) MATHCrossRefADSGoogle Scholar
  33. 33.
    Castagnino, M., Lombardi, O., Lara, L.: Found. Phys. 33, 877–912 (2003) CrossRefMathSciNetGoogle Scholar
  34. 34.
    Dioisi, L.: Phys. Rev. Lett. A 120, 377 (1987) ADSGoogle Scholar
  35. 35.
    Dioisi, L.: Phys. Rev. A 40, 1165 (1989) CrossRefADSGoogle Scholar
  36. 36.
    Ehrenfest, P., Ehrenfest, T.: The Conceptual Foundations of the Statistical Approach in Mechanics. Cornell University Press, Ithaca (1959). (original 1912) MATHGoogle Scholar
  37. 37.
    Ford, G., O’Connel, R.: Phys. Rev. Lett. A 286, 87 (2001) MATHADSGoogle Scholar
  38. 38.
    Frasca, M.: Phys. Lett. A 308, 135 (2003) MATHCrossRefMathSciNetADSGoogle Scholar
  39. 39.
    Gambini, R., Pullin, J.: Found. Phys. 37, 1074–1092 (2007) MATHCrossRefMathSciNetADSGoogle Scholar
  40. 40.
    Hartle, J.: In: Bowik, N.J., Gursey, F. (ed.) High Energy Physics, 1985, Proceedings of the Yale Summer School. World Scientific, Singapore (1985) Google Scholar
  41. 41.
    Hillery, M., O’Connell, R., Scully, M., Wigner, E.: Phys. Rep. 106, 121 (1984) CrossRefMathSciNetADSGoogle Scholar
  42. 42.
    Iguri, S., Castagnino, M.: Int. J. Theor. Phys. 38, 143 (1999) MATHCrossRefMathSciNetGoogle Scholar
  43. 43.
    Iguri, S., Castagnino, M.: J. Math. Phys. 49, 033510 (2008) CrossRefMathSciNetADSGoogle Scholar
  44. 44.
    Joos, E.: Phys. Lett. A 116, 6 (1986) CrossRefMathSciNetADSGoogle Scholar
  45. 45.
    Kiefer, C.: Class. Quantum Gravity 4, 1369 (1987) CrossRefMathSciNetADSGoogle Scholar
  46. 46.
    Kiefer, C., Lesgourgues, J., Polarski, D., Starobinsky, A.A.: Class. Quantum Gravity 15, L67 (1998) MATHCrossRefADSGoogle Scholar
  47. 47.
    Kiefer, C., Polarski, D.: Ann. Phys. (Leipzig) 7, 137 (1998) MATHADSGoogle Scholar
  48. 48.
    Kiefer, C., Polarski, D., Starobinsky, A.A.: Int. J. Mod. Phys. D 7, 455 (1998) MATHCrossRefADSGoogle Scholar
  49. 49.
    Kuyatt, C.E., Simpson, J.A., Mielczarek, S.R.: Phys. Rev. A 138, 385 (1965) CrossRefADSGoogle Scholar
  50. 50.
    Laura, R., Castagnino, M.: Phys. Rev. A 57, 4140 (1998) CrossRefMathSciNetADSGoogle Scholar
  51. 51.
    Laura, R., Castagnino, M.: Phys. Rev. E 57, 3948 (1998) CrossRefMathSciNetADSGoogle Scholar
  52. 52.
    Lombardo, F., Mazzitelli, D.: Phys. Rev. D 53, 2001-2011 (1996) CrossRefADSGoogle Scholar
  53. 53.
    Milbur, G.: Phys. Rev. A 44, 5401 (1991) CrossRefADSGoogle Scholar
  54. 54.
    Parker, L.: Phys. Rev. 183, 1057 (1969) MATHCrossRefADSGoogle Scholar
  55. 55.
    Paz, J.P., Zurek, W.H.: Environment-induced decoherence and transition from quantum to classical. arXiv:quant-ph/0010011v1 (2000)
  56. 56.
    Penrose, R.: Shadows of Mind. Oxford University Press, Oxford (1995) MATHGoogle Scholar
  57. 57.
    Price, H.: Time’s Arrow and Archimides’ Point. Oxford University Press, Oxford (1984) Google Scholar
  58. 58.
    Prigogine, I.: Non-Equilibrium Statistical Mechanics. Wiley, New York (1962) MATHGoogle Scholar
  59. 59.
    Sicardi Schifino, A., et al.: quant-ph/0308162 (2003)
  60. 60.
    Treves, A.: Topological Vector Spaces, Distributions and Kernels. Academic Press, New York (1967) MATHGoogle Scholar
  61. 61.
    van Hove, L.: Physica 21, 901 (1955) MATHCrossRefMathSciNetADSGoogle Scholar
  62. 62.
    Zee, H.D.: Phys. Lett. A 116, 9 (1986) CrossRefMathSciNetADSGoogle Scholar
  63. 63.
    Zeh, H.D.: Found. Phys. 1, 69 (1970) CrossRefADSGoogle Scholar
  64. 64.
    Zeh, H.D.: On the irreversibility of time and observation in quantum theory. In: d’Espagnat, B. (ed.) Foundations of Quantum Mechanics. Academic Press, New York (1971) Google Scholar
  65. 65.
    Zeh, H.D.: Found. Phys. 3, 109 (1973) CrossRefADSGoogle Scholar
  66. 66.
    Zurek, W.H.: Phys. Rev. D 24, 1516 (1981) CrossRefMathSciNetADSGoogle Scholar
  67. 67.
    Zurek, W.H.: Phys. Rev. D 26, 1962 (1982) CrossRefMathSciNetADSGoogle Scholar
  68. 68.
    Zurek, W.H.: Phys. Today 44, 36 (1991) CrossRefGoogle Scholar
  69. 69.
    Zurek, W.H.: Prog Theor. Phys. 89, 281 (1993) CrossRefMathSciNetADSGoogle Scholar
  70. 70.
    Zurek, W.H.: Philos. Trans. R. Soc. Lond. A 356, 1793 (1998) CrossRefMathSciNetADSGoogle Scholar
  71. 71.
    Zurek, W.H.: LANL quant-ph/9805065 (1998)

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Institute of Astronomy and Physics of SpaceBuenos AiresArgentina
  2. 2.Institutes of Physics of Rosario and Astronomy and Physics of SpaceBuenos AiresArgentina

Personalised recommendations