Trajectories for the wave function of the universe from a simple detector model

Physical Review D

Volumn 64, Issue 4, 2001, Pages

  Halliwell, J J ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; ASTRONOMY; COSMOS; MATHEMATICAL ANALYSIS; MEASUREMENT; MODEL; OSCILLATION; QUANTUM MECHANICS;

EID: 0035881324     PISSN: 05562821     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevD.64.044008     Document Type: Article

References (112)

1. J. B. Hartle, in Proceedings of the 1992 Les Hauches School, Gravity and its Quantizations, edited by B. Julia and J. Zinn-Justin (Elsevier Science B.V., New York, 1995).
2. C. J. Isham, gr-qc/9210011.
3. K. Kuchar, in Conceptual Problems of Quantum Gravity, edited by A. Ashtekar and J. Stachel (Birkhauser, Boston, 1991);
4. and in Proceedings of the 4th Canadian Conference on General Relativity and Relativistic Astrophysics, edited by G. Kunstatter, D. E. Vincent, and J. G. Williams (World Scientific, River Edge, NJ, 1992); see also gr-qc/9304012.
5. J. Barbour, The End of Time: The Next Revolution in our Understanding of the Universe (Oxford University Press, New York, 2000).
6. J. Butterfield and C. J. Isham, gr-qc/9901024.
7. For a review see, C. Rovelli, gr-qc/9710008.
8. J. J. Halliwell, in Proceedings of the 13th International Conference on General Relativity and Gravitation, edited by R. J. Gleiser, C. N. Kozameh, and O. M. Moreschi (IOP, Bristol, 1992); gr-qc/9208001.
9. A. Ashtekar, J. Lewandowski, D. Marolf, J. Mourao, and T. Thiemann, J. Math. Phys. 36, 6456 (1995);
10. A. Higuchi, Class. Quantum Grav. 8, 1983 (1991);
11. D. Giulini and D. Marolf, Class. Quantum Grav. ibid. 16, 2489 (1999);
12. D. Giulini and D. Marolf, Class. Quantum Grav. 16, 2479 (1999);
13. R Embacher, Hadronic J. 21, 337 (1998);
14. N. Landsmann, J. Geom. Phys. 15, 285 (1995).
15. D. Marolf, Class. Quantum Grav. 12, 1199 (1995).
16. B. DeWitt, in Gravitation: An Introduction to Current Research, edited by L. Witten (Wiley, New York, 1962).
17. C. Rovelli, Class. Quantum Grav. 8, 297 (1991);
18. C. Rovelli, Class. Quantum Grav. 8, 317 (1991).
19. C. Teitelboim, Phys. Rev. D 25, 3159 (1983);
20. C. Teitelboim, Phys. Rev. D 28, 297 (1983);
21. C. Teitelboim, Phys. Rev. D 28, 310 (1983).
22. J. J. Halliwell, Phys. Rev. D 38, 2468 (1988).
23. J. J. Halliwell and M. E. Ortiz, Phys. Rev. D 48, 748 (1993).
24. M. Gell-Mann and J. B. Hartle, in Complexity, Entropy and the Physics of Information, SFI Studies in the Sciences of Complexity, edited by W. Zurek (Addison Wesley, Reading, MA, 1990);
25. Proceedings of the Third International Symposium on the Foundations of Quantum Mechanics in the Light of New Technology, edited by S. Kobayashi, H. Ezawa, Y. Murayama, and S. Nomura (Physical Society of Japan, Tokyo, 1990);
26. Phys. Rev. D 47, 3345 (1993);
27. R. B. Griffiths, J. Stat. Phys. 36, 219 (1984);
28. Phys. Rev. Lett. 70, 2201 (1993);
29. Am. J. Phys. 55, 11 (1987);
30. R. Omnès, J. Stat. Phys. 53, 893 (1988);
31. R. Omnès, J. Stat. Phys. 53, 933 (1988);
32. R. Omnès, J. Stat. Phys. 53, 957 (1988);
33. R. Omnès, J. Stat. Phys. 57, 357 (1989);
34. R. Omnès, J. Stat. Phys. 62, 841 (1991);
35. Ann. Phys. (N.Y.) 201, 354 (1990);
36. Rev. Mod. Phys. 64, 339 (1992);
37. J. B. Hartle, in Quantum Cosmology and Baby Universes, edited by S. Coleman, J. Hartle, T. Piran, and S. Weinberg (World Scientific, Singapore, 1991);
38. J. J. Halliwell, Ann. N.Y. Acad. Sci. 775, 726 (1994);
39. For further developments in the decoherent histories approach, particularly adapted to the problem of spacetime coarse grainings, see C. Isham, J. Math. Phys. 35, 2157 (1994);
40. C. Isham and N. Linden, J. Math. Phys. ibid. 35, 5452 (1994);
41. C. Isham and N. Linden, J. Math. Phys. 36, 5392 (1995).
42. J. J. Halliwell and J. Thorwart (unpublished);
43. see also the related works, J. Whelan, Phys. Rev. D 50, 6344 (1994);
44. J. B. Hartle and D. Marolf, Phys. Rev. D ibid. 56, 6247 (1997).
45. C. Rovelli, Phys. Rev. D 42, 2638 (1990).
46. C. Rovelli, Phys. Rev. D 43, 442 (1991).
47. D. Marolf, Phys. Rev. D 53, 6979 (1996);
48. Class. Quantum Grav. 12, 2469 (1995);
49. Class. Quantum Grav. 12, 1441 (1995).
50. H. D. Zeh, The Physical Basis of the Direction of Time, 3rd ed. (Springer, New York, 1999); www.time-direction.de;
51. Phys. Lett. A 116, 9 (1986);
52. Phys. Lett. A 126, 311 (1988);
53. C. Kiefer and H. Zeh, Phys. Rev. D 51, 4145 (1995).
54. J. Barbour, Class. Quantum Grav. 11, 2853 (1994).
55. J. Barbour, Class. Quantum Grav. 11, 2875 (1994).
56. N. F. Mott, Proc. R. Soc. London, Ser. A 124, 375 (1929);
57. reprinted in Quantum Theory and Measurement, edited by J. Wheeler and W. Zurek (Princeton University Press, Princeton, NJ, 1983).
58. See also, A. A. Broyles, Phys. Rev. A 48, 1055 (1993); M. Castagnino and R. Laura, gr-qc/0006012, for further discussions of the Mott calculation.
59. J.B. Hartle and S. W. Hawking, Phys. Rev.D 28, 2960 (1983).
60. K. Hepp, Helv. Phys. Acta 45, 237 (1972).
61. This detector model was used in a simple nonrelativistic context by J. J. Halliwell, Phys. Rev. D 60, 105031 (1999)
62. ; Some subsequent developments of the Coleman-Hepp model are H. Nakazato and S. Pascazio, Phys. Rev. Lett. 70, 1 (1993);
63. Phys. Rev. A 48, 1066 (1993);
64. R. Blasi, S. Pascazio, and S. Takagi, Phys. Rev. A ibid. 250, 230 (1998).
65. Y. Aharonov and D. Bohm, Phys. Rev. 122, 1649 (1961);
66. Y. Aharonov, J. Oppenheim, S. Popescu, B. Reznik, and W. Unruh, Phys. Rev. A 57, 4130 (1998);
67. G. R. Allcock, Ann. Phys. (N.Y.) 53, 253 (1969);
68. G. R. Allcock, Ann. Phys. (N.Y.) 53, 286 (1969);
69. G. R. Allcock, Ann. Phys. (N.Y.) 53, 311 (1969);
70. Ph. Blanchard and A. Jadczyk, Helv. Phys. Acta 69, 613 (1996);
71. I. Bloch and D. A. Burba, Phys. Rev. D 10, 3206 (1974);
72. V. Delgado, Phys. Rev. A 57, 762 (1998); R. Giannitrapani, quant-ph/9611015;
73. N. Grot, C. Rovelli, and R. S. Tate, Phys. Rev. A 54, 46 (1996);
74. E. Gurjoy and D. Coon, Superlattices Microstruct. 5, 305 (1989);
75. A. S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory (North Holland, Amsterdam, 1982), pp. 130-197;
76. A. Jadcyk, Prog. Theor. Phys. 93, 631 (1995);
77. D. H. Kobe and V. C. Aguilera-Navarro, Phys. Rev. A 50, 933 (1994);
78. N. Kumar, Pramana J. Phys. 25, 363 (1985);
79. J. Léon, J. Phys. A 30, 4791 (1997);
80. D. Marolf, Phys. Rev. A 50, 939 (1994);
81. L. Mandelstamm and I. Tamm, J. Phys. A 9, 249 (1945);
82. J. G. Muga, S. Brouard, and D. Macías, Ann. Phys. (N.Y.) 240, 351 (1995);
83. J. G. Muga, J. P. Palao, and C. R. Leavens, Phys. Lett. A 253, 21 (1999);
84. J. G. Muga, R. Sala, and J. P. Palao, Superlattices Microstruct. 23, 833 (1998);
85. C. Piron, in Interpretation and Foundations of Quantum Theory, edited by H. Newmann (Bibliographisches Institute, Mannheim, 1979);
86. M. Toller, Phys. Rev. A 59, 960 (1999);
87. H. Salecker and E. P. Wigner, Phys. Rev. 109, 571 (1958);
88. F. T. Smith, Phys. Rev. ibid. 118, 349 (1960);
89. E. P. Wigner, Phys. Rev. ibid. 98, 145 (1955).
90. N. Yamada and S. Takagi, Prog. Theor. Phys. 85, 985 (1991);
91. N. Yamada and S. Takagi, Prog. Theor. Phys. 86, 599 (1991);
92. N. Yamada and S. Takagi, Prog. Theor. Phys. 87, 77 (1992);
93. N. Yamada, Sci. Rep. Res. Inst. Tôhoku Univ. A 12, 177 (1992);
94. Phys. Rev. A 54, 182 (1996);
95. J. J. Halliwell and E. Zafiris, Phys. Rev. D 57, 3331 (1998);
96. J. B. Hartle, Phys. Rev. D ibid. 44, 3173 (1991);
97. R. J. Micanek and J. B. Hartle, Phys. Rev. A 54, 3795 (1996).
98. J. B. Hartle, Phys. Rev. D 38, 2985 (1988).
99. J. J. Halliwell, Phys. Rev. D 48, 4785 (1993).
100. L. Schulman, Techniques and Applications of Path Integrals (Wiley, New York, 1981).
101. H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, MA, 1980).
102. J- S- Bell Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, England, 1987).
103. A. Auerbach and S. Kivelson, Nucl. Phys. B257, 799 (1985).
104. S. W. Hawking, Phys. Rev. D 32, 2489 (1985).
105. See, for example, the collection of articles in Physical Origins of Time Asymmetry, edited by J. J. Halliwell, J. Perez-Mercader, and W. Zurek (Cambridge University Press, Cambridge, 1994).
106. A recent discussion is K. Ridderbos, Stud. Hist. Philos. Mod. Phys. 30, 41 (1999).
107. C. W. Gardiner, Quantum Noise (Springer, Berlin, 1991).
108. J. Klauder, Ann. Phys. (N.Y.) 254, 419 (1997);
109. Nucl. Phys. B547, 397 (1999); hep-th/0003297.
110. C. Kiefer, Phys. Rev. D 38, 1761 (1988).
111. Y. Kazama and R. Nakayama, Phys. Rev. D 32, 2500 (1985).
112. J. J. Halliwell, Prog. Theor. Phys. 102, 707 (1999).