Advertisement

The Quantum Potential in Gravity and Cosmology

  • Ignazio LicataEmail author
  • Davide Fiscaletti
Chapter
Part of the SpringerBriefs in Physics book series (SpringerBriefs in Physics)

Abstract

The fundamental role of Bohm’s quantum potential in the treatment of gravity and thus in the general-relativistic domain has been explored by various authors (see, for example, the book of R. Carroll Fluctuations, information, gravity and the quantum potential [1]). Here we focus our attention on a very interesting recent research of A. Shojai and F. Shojai. These two authors examined the behaviour of particles at spin 0 in a curved space-time, demonstrating that quantum potential contributes to the curvature that is added to the classic one and reveals deep and unexpected connections between gravity and the quantum phenomena (Ref. [2, 3] in  Chap. 2). To develop the discussion about this topic we refer to the articles [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14].

Keywords

Quantum Gravity Quantum Effect Spacelike Hypersurface Quantum Cosmology Quantum Potential 
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.

References

  1. 1.
    Carroll, R.W.: Fluctuations, Information, Gravity and the Quantum Potential. Springer, Dordrecht (2006)zbMATHGoogle Scholar
  2. 2.
    Shojai, A.: Quantum, gravity and geometry. Int. J. Mod. Phys. A 15, 1757 (2000)MathSciNetADSzbMATHGoogle Scholar
  3. 3.
    Shojai, F., Shojai, A.: Pure quantum solutions of Bohmian quantum gravity. Jour. High Energy Physics 05, 037 (2001)MathSciNetADSCrossRefGoogle Scholar
  4. 4.
    Shojai, F., Shojai, A.: Quantum Einstein’s equations and constraints algebra. Pramana 58(1), 13–19 (2002)ADSCrossRefGoogle Scholar
  5. 5.
    Shojai, F., Shojai, A.: On the relation of Weyl geometry and and Bohmian quantum gravity. Gravitation Cosmol. 9(3), 163–168 (2003)MathSciNetADSzbMATHGoogle Scholar
  6. 6.
    Shojai, F., Shojai, A.: Constraints Algebra and equations of motion in Bohmian interpretation of quantum gravity. Classical Quant. Grav. 21, 1–9 (2004)MathSciNetADSCrossRefzbMATHGoogle Scholar
  7. 7.
    Shojai, F., Shojai, A.: Non-minimal scalar-tensor theories and quantum gravity. Inter. Jour. Mod. Phys. A15(13), 1859–1868 (2000)MathSciNetADSGoogle Scholar
  8. 8.
    Shojai, A., Golshani, M.: Direct particle interaction as the origin of the quantal behaviours. arXiv:quant-ph/9812019 (1996)Google Scholar
  9. 9.
    Shojai, A., Golshani, M.: On the relativistic quantum force. arXiv:quant-ph/9612023 (1996)Google Scholar
  10. 10.
    Shojai, A., Golshani, M.: Some observable results of the retarded’s Bohm’s theory. arXiv:quant-ph/9612020 (1996)Google Scholar
  11. 11.
    Shojai, A., Golshani, M.: Is superluminal motion in relativistic Bohm’s theory observable? arXiv:quant-ph/9612021 (1996)Google Scholar
  12. 12.
    Shojai, F., Shojai, A.: Constraint algebra and the equations of motion in the Bohmian interpretation of quantum gravity. Class. Quant. Grav. 21, 1–9 (2004)MathSciNetADSCrossRefzbMATHGoogle Scholar
  13. 13.
    Shojai, F., Shojai, A.: Causal loop quantum gravity and cosmological solutions. Europhys. Lett. 71(6), 886–892 (2005)ADSCrossRefGoogle Scholar
  14. 14.
    Shojai. F., Shojai, A. (2005). Constraint algebra in causal loop quantum gravity. In : Rahvar, S., Sadooghi, N., Shojai F (ed.) Proceedings of the XI Regional Conference, pp. 114–116. Tehran, Iran. World Scientific, 3–6 May 2004Google Scholar
  15. 15.
    de-Broglie, L.: Non-linear Wave Mechanics (translated by A.J. Knodel). Elsevier Publishing Company, Amsterdam (1960) Google Scholar
  16. 16.
    Horiguchi, T.: Quantum potential interpretation of the Wheeler-deWitt equation. Mod. Phys. Lett. A 9(16), 1429–1443 (1994)MathSciNetADSCrossRefzbMATHGoogle Scholar
  17. 17.
    Blaut, A., Glikman, J.K.: Quantum potential approach to class of quantum cosmological models. Class. Quant. Grav. 13, 39–50 (1996)MathSciNetADSCrossRefzbMATHGoogle Scholar
  18. 18.
    Kim, S.P.: Quantum potential and cosmological singularities. Phys. Lett. A 236(1/2), 11–15 (1997)ADSCrossRefGoogle Scholar
  19. 19.
    Kim, S.P.: Problem of unitarity and quantum corrections in semi-classical quantum gravity. Phys. Rev. D 55(12), 7511–7517 (1997)MathSciNetADSCrossRefGoogle Scholar
  20. 20.
    Cushing, J.T.: The causal quantum theory program. In: Cushing, J.T., Fine, A., Goldstein, S. (eds.) Bohmiam Mechanics and Quantum Theory: An Appraisal. Kluwer Academic Publishers, Boston (1996)CrossRefGoogle Scholar
  21. 21.
    Shojai, F., Shojai, A., Golshani, M.: Conformal transformations and quantum gravity. Mod. Phys. Lett. A 13(34), 2725–2729 (1998)MathSciNetADSCrossRefGoogle Scholar
  22. 22.
    Shojai, F., Shojai, A., Golshani, M.: Scalar-tensor theories and quantum gravity. Mod. Phys. Lett. A 13(36), 2915–2922 (1998)MathSciNetADSCrossRefGoogle Scholar
  23. 23.
    Shojai, A., Shojai, F., Golshani, M.: Nonlocal effects in quantum gravity. Mod. Phys. Lett. A 13(37), 2965–2969 (1998)MathSciNetADSCrossRefGoogle Scholar
  24. 24.
    Shojai, F., Shojai, A.: On the relation of Weyl geometry and Bohmian quantum mechanics. Gravitation Cosmol. 9, 163–168 (2003)MathSciNetADSzbMATHGoogle Scholar
  25. 25.
    Cho, Y.M., Park, D.H.: Higher-dimensional unification and fifth force. Il Nuovo Cimento B 105(8/9), 817–829 (1990)MathSciNetADSCrossRefGoogle Scholar
  26. 26.
    de Barros, J.A., Pinto-Neto, N., Sagioro-Leal, M.A.: The causal interpretation of dust and radiation fluid non-singular quantum cosmologies. Phys. Lett. A 241(4), 229–239 (1998)ADSCrossRefGoogle Scholar
  27. 27.
    Shojai, F., Golshani, M.: On the geometrization of Bohmian mechanics: a new suggested approach to quantum gravity. Int. J. Mod. Phys. A 13(4), 677–693 (1998)MathSciNetADSCrossRefzbMATHGoogle Scholar
  28. 28.
    Colistete, J.R., Fabris, J.C., Pinto–Neto, N.: Singularities and classical limit in quantum cosmology with scalar fields. Phys. Rev. D 57(8), 4707–4717 (1998)Google Scholar
  29. 29.
    Pinto-Neto, N., Colistete, R.: Graceful exit from inflation using quantum cosmology. Phys. Lett. A 290(5/6), 219–226 (2001)ADSCrossRefzbMATHGoogle Scholar
  30. 30.
    Kenmoku, M., Sato, R., Uchida, S.: Classical and quantum solutions of (2 + 1)-dimensional gravity under the de Broglie-Bohm interpretation. Class. Quantum Grav. 19(4), 799 (2002)MathSciNetADSCrossRefzbMATHGoogle Scholar
  31. 31.
    Pinto-Neto, N.: Quantum cosmology: how to interpret and obtain results. Braz. J. Phys. 30(2), 330–345 (2000)ADSCrossRefGoogle Scholar
  32. 32.
    Ashtekar, A., Lewandowski, J.: Quantum field theory of geometry. arXiv:hep-th/9603083 (1996)Google Scholar
  33. 33.
    Ashtekar, A., Corichi, A., Zapata, J.: Quantum theory of geometry III: non-commutativity of Riemannian structures. Class. Quant. Grav. 15, 2955–2972 (1998)MathSciNetADSCrossRefzbMATHGoogle Scholar
  34. 34.
    Ashtekar, A., Lewandowski, J.: Background independent quantum gravity: a status report. Class. Quant. Grav. 21, 53–152 (2004)MathSciNetADSCrossRefGoogle Scholar
  35. 35.
    Ashtekar, A., Isham, C.: Representations of holonomy algebras of gravity and non-abelian gauge theories. Class. Quantum Grav. 9, 1433–1467 (1992)MathSciNetADSCrossRefzbMATHGoogle Scholar
  36. 36.
    Ashtekar, A.: Gravity and the quantum. New J. Phys. 7, 198 (2005)MathSciNetADSCrossRefGoogle Scholar
  37. 37.
    Baez, J. (ed.): Knots and Quantum Gravity. Oxford University Press, Oxford (1994)zbMATHGoogle Scholar
  38. 38.
    Biswas, S., Shaw, A., Biswas, D.: Schrödinger Wheeler-DeWitt equation in multidimensional cosmology. Int. J. Mod. Phys. D 10, 585–594 (2001)MathSciNetADSCrossRefzbMATHGoogle Scholar
  39. 39.
    Dittrich, B., Thiemann, T.: Testing the master constraint programme for loop quantum gravity I. General framework. Class. Quant. Grav. 23, 1025–1046 (2006)MathSciNetADSCrossRefzbMATHGoogle Scholar
  40. 40.
    Dittrich, B., Thiemann, T.: Testing the master constraint programme for loop quantum gravity II. Finite dimensional systems. Class. Quant. Grav. 23, 1067–1088 (2006)MathSciNetADSCrossRefzbMATHGoogle Scholar
  41. 41.
    Dittrich, B., Thiemann, T.: Testing the master constraint programme for loop quantum gravity III. SL(2R) models. Class. Quant. Grav. 23, 1089–1120 (2006)MathSciNetADSCrossRefzbMATHGoogle Scholar
  42. 42.
    Dittrich, B., Thiemann, T.: Testing the master constraint programme for loop quantum gravity IV. Free field theories. Class. Quant. Grav. 23, 1121–1142 (2006)MathSciNetADSCrossRefzbMATHGoogle Scholar
  43. 43.
    Dittrich, B., Thiemann, T.: Testing the master constraint programme for loop quantum gravity V. Interaction field theories. Class. Quant. Grav. 23, 1143–1162 (2006)MathSciNetADSCrossRefzbMATHGoogle Scholar
  44. 44.
    Gambini, R., Pullin, J.: Loops, Knots, Gauge Theories and Quantum Gravity. Cambridge University Press, Cambridge (2000)Google Scholar
  45. 45.
    Horiguchi, T., Maeda, K., Sakamoto, M.: Analysis of the Wheeler-DeWitt equation beyond Planck scale and dimensional reduction. Phys. Lett. B344, 105–109 (1995)ADSCrossRefGoogle Scholar
  46. 46.
    Kenmoku, M., Kubortani, H., Takasugi, E., Yamazaki, Y.: De Broglie-Bohm interpretation for analytic solutions of the Wheeler-DeWitt equation in spherically symmetric space-time. Progress Theoret. Phys. 105(6), 897–914 (2001)ADSCrossRefzbMATHGoogle Scholar
  47. 47.
    Kiefer, C.: Quantum Gravity. Oxford University Press, Oxford (2004)zbMATHGoogle Scholar
  48. 48.
    Gambini, R., Pullin, J.: A First Course in Loop Quantum Gravity. Oxford University Press, Oxford (2011)Google Scholar
  49. 49.
    Markopoulou, F., Smolin, L.: Quantum theory from quantum gravity. Phys. Rev. D70, 124029 (2004)MathSciNetADSGoogle Scholar
  50. 50.
    Moss, I.: Quantum Theory, Black Holes, and Inflation. Wiley, New York (1996)zbMATHGoogle Scholar
  51. 51.
    Rovelli, C.: Quantum Gravity. Cambridge University Press, Cambridge (2004)CrossRefzbMATHGoogle Scholar
  52. 52.
    Rovelli, C.: Covariant hamiltonian formalism for field theory: Hamilton-Jacobi equation on the space G. arXiv:gr-qc/0207043 (2002)Google Scholar
  53. 53.
    Smolin, L.: Three Roads to Quantum Gravity. Oxford University Press, Oxford (2002)Google Scholar
  54. 54.
    Smolin, L.: An invitation to loop quantum gravity. arXiv:hep-th/0408048 (2004)Google Scholar
  55. 55.
    Smolin, L.: Matrix models as non-local hidden variables theories. arXiv:hep-th/0201031 (2002)Google Scholar
  56. 56.
    Thiemann, T.: Modern Canonical Quantum General Relativity. Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge (2008)Google Scholar
  57. 57.
    Thiemann, T.: Lectures on loop quantum gravity. Lect. Notes Phys. 631, 41–135 (2003)MathSciNetADSCrossRefGoogle Scholar
  58. 58.
    Thiemann, T.: Anomaly-free formulation of non-perturbative, four-dimensional. Lorentzian quantum gravity. Phys. Lett. B 380, 257–264 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  59. 59.
    Thiemann, T.: Quantum spin dynamics. Class. Quant. Grav. 15, 839–873 (1998)MathSciNetADSCrossRefzbMATHGoogle Scholar
  60. 60.
    Thiemann, T.: Quantum spin dynamics (qsd). 2. Class. Quant. Grav. 15, 875–905 (1998)MathSciNetADSCrossRefGoogle Scholar
  61. 61.
    Thiemann, T.: QSD IV: 2 + 1 Euclidean quantum gravity as a model to test. 3 + 1 Lorentzian quantum gravity. Class. Quant. Grav. 15, 1249–1280 (1998)MathSciNetADSCrossRefzbMATHGoogle Scholar
  62. 62.
    Thiemann, T.: QSD 5: Quantum gravity as the natural regulator of matter quantum field teories. Class. Quant. Grav. 15, 1281–1314 (1998)MathSciNetADSCrossRefzbMATHGoogle Scholar
  63. 63.
    Shojai, A., Shojai, F.: About some problems raised by the relativistic form of de Broglie-Bohm theory of pilot wave. Phys. Scr. 64, 413 (2001)ADSCrossRefzbMATHGoogle Scholar
  64. 64.
    Shojai, A., Shojai, F., Naresh, D.: Static Einstein’s universe as a quantum solution of causal quantum gravity. Int. Jour. of Mod. Phys. A 20(13), 2773–2780 (2005)ADSCrossRefzbMATHGoogle Scholar
  65. 65.
    Vink, J.: Quantum mechanics in terms of discrete beables. Phys. Rev. A 48(3), 1808–1818 (1993)ADSCrossRefGoogle Scholar
  66. 66.
    Vink, J.: Quantum potential interpretation of the wave function of the universe. Nucl. Phys. B 369(3), 707–728 (1992)MathSciNetADSCrossRefGoogle Scholar
  67. 67.
    de Barros, J.A., Pinto-Neto, N.: The causal interpretation of quantum mechanics and the singularity problem and time issue in quantum cosmology. Int. J. of Mod. Phys. D 7, 201 (1998)ADSCrossRefzbMATHGoogle Scholar
  68. 68.
    Kowalski-Glikman, J., Vink, J.C.: Gravity-matter mini-superspace: quantum regime, classical regime and in between. Class. Quantum Grav. 7, 901–918 (1990)MathSciNetADSCrossRefGoogle Scholar
  69. 69.
    Squires, E.J.: A quantum solution to a cosmological Mystery. Phys. Lett. A 162, 35 (1992)Google Scholar
  70. 70.
    Pinto-Neto, N.: The Bohm interpretation of quantum cosmology. Found. Phys. 35(4), 577–603 (2005)MathSciNetADSCrossRefzbMATHGoogle Scholar
  71. 71.
    Pinto-Neto, N.: Evolution of perturbations in bouncing cosmological models. AIP Conf. Proc. 782, 277–288 (2004)MathSciNetADSCrossRefGoogle Scholar
  72. 72.
    Pinto-Neto, N., Santini, S.E.: The consistency of causal quantum geometrodynamics and quantum field theory. Gen. Rel. Grav. 34(4), 505–532 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  73. 73.
    Pinto-Neto, N., Santini, S.E.: The accelerated expansion of the universe as a quantum cosmological effect. Phys. Lett. A 315(1/2), 36–50 (2003)ADSCrossRefzbMATHGoogle Scholar
  74. 74.
    Pinto-Neto, N., Fabris, J.C.: Quantum cosmology from the de Broglie-Bohm perspective. arXiv:1306.0820v1 [gr-qc] (2013)Google Scholar
  75. 75.
    Pinto-Neto, N., Santini, S.E.: Must quantum spacetimes be Euclidean? Phys. Rev. D 59(12), 123517 (1999)MathSciNetADSCrossRefGoogle Scholar
  76. 76.
    Dautcourt, G.: On the ultrarelativistic limit of general relativity. Acta Phys. Pol., B 29(4), 1047–1055 (1998)MathSciNetADSzbMATHGoogle Scholar
  77. 77.
    Barbosa, G., Pinto-Neto, N.: Noncommutative quantum mechanics and Bohm’s ontological interpretation. Physical Review D 69(6), 065014 (2004)MathSciNetADSCrossRefGoogle Scholar
  78. 78.
    Barbosa, G., Pinto-Neto, N.: Noncommutative geometry and cosmology. Phys. Rev. D 70, 103512 (2004)MathSciNetADSCrossRefGoogle Scholar
  79. 79.
    Barbosa, G.: Noncommutative conformally coupled scalar field cosmology and its commutative counterpart. Phys. Rev. D 71(6), 063511 (2005)MathSciNetADSCrossRefGoogle Scholar
  80. 80.
    Barbosa, G.: On the meaning of the string-inspired noncommutativity and its implications. Jour. High Energy Phys. 5, 24 (2003)MathSciNetADSCrossRefGoogle Scholar
  81. 81.
    Chapline, G.: Geometrization of gauge fields. Quantum Theory and Gravitation, pp. 177–186. Academic Press, A.R. Marlow (1980)Google Scholar
  82. 82.
    Licata, I., Chiatti, L.: The archaic universe: big-bang, cosmological term and the quantum origin of time in projective relativity. Int. Jour. Theor. Phys. 48, 1003–1018 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  83. 83.
    Licata, I., Chiatti, L.: Archaic universe and cosmological model: “big-bang” as nucleation by vacuum. Int. J. Theor. Phys. 49, 2379–2402 (2010)CrossRefzbMATHGoogle Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.Institute for Scientific MethodologyPalermoItaly

Personalised recommendations