Advertisement

Foundations of Physics

, Volume 35, Issue 4, pp 577–603 | Cite as

The Bohm Interpretation of Quantum Cosmology

  • Nelson Pinto-NetoEmail author
Article

Abstract

I make a review on the aplications of the Bohm-de Broglie interpretation of quantum mechanics to quantum cosmology. In the framework of minisuperspaces models, I show how quantum cosmological effects in Bohm’s view can avoid the initial singularity, and isotropize the Universe. In the general case, I enumerate the possible structures of quantum space and time.

Keywords

Quantum Mechanic Quantum Cosmology Quantum Space Initial Singularity Cosmological Effect 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Hawking, S. W., Ellis, G. F. R. 1973The Large Scale Structure of Space-timeCambridge University PressCambridgeGoogle Scholar
  2. Gibbons, G. W.Hawking, S. W. eds. 1993Euclidean Quantum GravityWorld ScientificLondonGoogle Scholar
  3. Guth, A. H. 1981Phys. Rev. D28347Google Scholar
  4. Kolb, E. W., Turner, M. S. 1990The Early UniverseAddison-Wesley Publishing CompanyNew YorkGoogle Scholar
  5. Bohr, N. 1961Atomic Physics and Human KnowledgeScience EditionsNew YorkGoogle Scholar
  6. Heisenberg, W. 1949The Physical Principles of the Quantum TheoryDoverNew YorkGoogle Scholar
  7. Neumann, J. 1955Mathematical Foundations of Quantum MechanicsPrinceton University PressPrincetonGoogle Scholar
  8. Omnès, R. 1994The Interpretation of Quantum MechanicsPrinceton University PressPrincetonGoogle Scholar
  9. H. D. Zeh, Found. Phys. 1, 69 (1970); E. Joos and H. D. Zeh, Z. Phys. B 59, 223 (1985); W. H. Zurek, Phys. Rev. D 26, 1862 (1982); W. H. Zurek, Phys. Today 44, 36 (1991).Google Scholar
  10. C. Kiefer, Class. Quantum Grav. 18, 379 (1991); D. Giulini, E. Joos, C. Kiefer, J. Kupsch, I. O. Stamatescu and H. D. Zeh, Decoherence and the Appearance of a Classical World in Quantum Theory (Springer-Verlag, Berlin, 1996).Google Scholar
  11. V. F. Mukhanov, in Physical Origins of Time Asymmetry, J. J. Halliwell, J. Pérez-Mercader and W. H. Zurek eds. (Cambridge University Press, 1994).Google Scholar
  12. Zeh, H. D. 1996Decoherence and the Appearance of a Classical World in Quantum TheorySpringer-VerlagBerlinGoogle Scholar
  13. M. Gell-Mann and J. B. Hartle, in Complexity, Entropy and the Physics of Information, W. H. Zurek ed. (Addison Wesley, 1990).Google Scholar
  14. Paz, J. P., Zurek, W. H. 1993Phys. Rev.D 482728Google Scholar
  15. G. C. Ghirardi, A. Rimini and T. Weber, Phys. Rev. D 34, 470 (1986); G. C. Ghirardi, P. Pearle and A. Rimini, Phys. Rev. A 42, 78 (1990).Google Scholar
  16. Implications: Essays in Honour of David Bohm, B. J. Hiley and F. David Peat eds. (Routledge, London, 1987).Google Scholar
  17. DeWitt, B. S.Graham, N. eds. 1973The Many-Worlds Interpretation of Quantum MechanicsPrinceton University PressPrincetonGoogle Scholar
  18. D. Bohm, Phys. Rev. 85, 166 (1952); D. Bohm, B. J. Hiley and P. N. Kaloyerou, Phys. Rep. 144, 349 (1987).Google Scholar
  19. Holland, P. R. 1993The Quantum Theory of Motion: An Account of the de Broglie-Bohm Causal Interpretation of Quantum MechanichsCambridge University PressCambridgeGoogle Scholar
  20. Bohm, D., Vigier, J. P. 1954Phys. Rev96208Google Scholar
  21. Valentini, A. 1991Phys. Lett.A 1565Google Scholar
  22. Vink, J. C. 1992Nucl. Phys.B 369707Google Scholar
  23. Shtanov, Y.V. 1996Phys. RevDn 542564Google Scholar
  24. Valentini, A. 1991Phys.LettAb1581Google Scholar
  25. Barros, J. A. de, Pinto-Neto, N. 1998Int. J. of Mod. PhysD7201Google Scholar
  26. Kowalski-Glikman, J., Vink, J. C. 1990Class. Quantum Grav7901Google Scholar
  27. Squires, E. J. 1992Phys. Lett.A 16235Google Scholar
  28. Barros, J. A. de, Pinto-Neto, N., Sagioro-Leal, M. A. 1998Phys. LettA 241229Google Scholar
  29. Colistete, R., Fabris, J.C., Pinto-Neto , N. 1998Phys. RevD 574707Google Scholar
  30. Colistete, R., Fabris, J.C., Pinto-Neto , N. 2000Phys. RevD 6283507Google Scholar
  31. Pinto-Neto, N., Velasco, A. F., Colistete, R. 2000Phys. LettA 277194Google Scholar
  32. Halliwell, J. J., Hartle, J. B. 1990Phys. RevD 411815Google Scholar
  33. Pinto-Neto, N., Santini, E. S. 2003Phys. LettA 30536Google Scholar
  34. Perlmutter, S.,  et al. 1998Nature39151Google Scholar
  35. Riess, A.,  et al. 1998Astron. J1161009CrossRefGoogle Scholar
  36. Blyth, W. F., Isham, C. J. 1974Phys. RevD 11768Google Scholar
  37. M. J. Gotay and J. Demaret, Nucl. Phys. Proc. Suppl. 57, 227 (1997); N. A. Lemos, Class. Quantum Grav. 8, 1303 (1991); M. J. Gotay and J. Demaret, Phys. Rev. D 28, 2402 (1983).Google Scholar
  38. Pinto-Neto, N., Sergio Santini, E. 1999Phys. RevD 59123517Google Scholar
  39. E. Cartan, Annales Scientifiques de l’Ecole Normale Sup’erieure 40, 325 (1923); 41, 1 (1924).Google Scholar
  40. Tsamis, N. C., Woodward, R. P. 1987Phys. RevD 363641Google Scholar
  41. Maeda, K., Sakamoto, M. 1996Phys. RevD 541500Google Scholar
  42. Horiguchi, T., Maeda, K., Sakamoto, M. 1995Phys. Lett.B 344105Google Scholar
  43. Kowalski-Glikman, J., Meissner, K. A. 1996Phys. Lett.B 37648Google Scholar
  44. Lévy Leblond , J. M. 1965Ann. Inst. Henri Poincarè31Google Scholar
  45. Hojman, S. A., Kucha, K., Teitelboim, C. 1976Ann. Phys9688Google Scholar
  46. J. A. Wheeler, in Battelle Rencontres: 1967 Lectures in Mathematical Physics, B. De- Witt and J. A. Wheeler eds. (Benjamin, New York, 1968).Google Scholar
  47. DeWitt, B.S. 1967Phys. Rev.1601113Google Scholar
  48. Halliwell, J. J. 1987Phys. RevD 363626Google Scholar
  49. M. P. Ryan, Lecture Notes from the $6th$ Brazillian School on Cosmology and Gravitation (Rio de Janeiro, 1989).Google Scholar
  50. Kuchar, K. V., Ryan, M. P. 1989Phys. RevD 403982Google Scholar
  51. Ya. B. Zel’dovich, Zh. Eksp. Teoret. Fiz. 41, 1609 (1961) (Ya. B. Zel’dovich, Sov. Phys. JETP, 14, 1143).Google Scholar
  52. Wright, W. A., Moss, I. G. 1985Phys. Lett154B115Google Scholar
  53. Amsterdamski, P. 1985Phys. RevD 313073Google Scholar
  54. Berger, B. K., Vogeli, C. N. 1985Phys. RevD 322477Google Scholar
  55. Campo, S. Del, Vilenkin, A. 1989Phys. LettB 22445Google Scholar
  56. Moncrief, V., Ryan, M.P. 1991Phys. RevD 442375Google Scholar
  57. Gradshteyn, I. S., Ryzhik, I. M. 1980Table of Integrals Series and ProductsAcademic PressNew YorkGoogle Scholar
  58. Teitelboim, C. 1973Ann. Phys80542Google Scholar
  59. Teitelboim, C. 1982Phys. RevD 253159Google Scholar
  60. Henneaux, M., Pilati, M., Teitelboim, C. 1982Phys. Lett110B123Google Scholar
  61. Dautcourt, G. 1998Acta Phys. PolonB 291047Google Scholar
  62. J. A. Wheeler, Ann. Phys. 2, 604 (1957); J. A. Wheeler, Relativity, Groups and Topology, B. DeWitt and C. DeWitt eds. (Gordon and Breach, New York, 1964); G. M. Patton and J. A. Wheeler, in Quantum Gravity. An Oxford Symposium, C. J. Isham, R. Penrose and D. Sciama eds. (Clarendon Press, Oxford, 1975).Google Scholar
  63. N. Pinto-Neto and E.S. Santini, GRG, 34, 505 (2002).Google Scholar
  64. Banks, T. 1985Nucl. PhysB 249332Google Scholar
  65. Singh, T. P., Padmanabhan, T. 1989Ann. Phys196296Google Scholar
  66. Giulini, D., Kiefer, C. 1995Class. Quantum Grav12403Google Scholar
  67. J. J. Halliwell, in Quantum Cosmology and Baby Universes, S. Coleman, J. B. Hartle, T. Piran and S. Weinberg eds. (World Scientific, Singapore, 1991).Google Scholar
  68. Kenmoku, M., Kubotani, H., Takasugi, E., Yamazaki, Y. 2000Int. J. Mod. Phys.A 152059Google Scholar
  69. Kucha, K. 1994Phys. RevD 503961Google Scholar
  70. Louko, J., Winters-Hilt, S. N. 1996Phys. RevD 542647Google Scholar
  71. Brotz, T., Kiefer, C. 1997Phys. RevD 552186Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Centre Brasileiro de pesquisas FísicasRio de JaneiroBrazil

Personalised recommendations