Somewhere in the universe: Where is the information stored when histories decohere?

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 60, Issue 10, 1999, Pages

  Halliwell, J J ^a  

^a Blackett Laboratory   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 18144412417     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.60.105031     Document Type: Article

References (65)

1. J. B. Hartle, in Proceedings of the Cornelius Lanczos International Centenary Conference, edited by J. D. Brown, M. T. Chu, D. C. Ellison, and R. J. Plemmons (SIAM, Philadelphia, 1994).
2. M. Gell-Mann and J. B. Hartle, Phys. Rev. D 47, 3345 (1993).
3. E. Joos and H. D. Zeh, Z. Phys. B: Condens. Matter 59, 223 (1985).
4. W. Zurek, Philos. Trans. R. Soc. London A356, 1793 (1998).
5. M. Gell-Mann and J. B. Hartle, in Quantum Classical Correspondence: Proceedings of the 4th Drexel Symposium on Quantum Nonintegrability, edited by D. H. Feng and B. L. Hu (International Press, New York, 1997).
6. 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, 1990), Vol. VIII;and in 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).
7. R. B. Griffiths, J. Stat. Phys. 36, 219 (1984)
8. R. B. GriffithsPhys. Rev. Lett. 70, 2201 (1993).
9. R. Omnès, J. Stat. Phys. 53, 893 (1988)
10. J. Stat. Phys.R. Omnès53, 933 (1988)
11. J. Stat. Phys.R. Omnès53, 957 (1988)
12. J. Stat. Phys.R. Omnès57, 357 (1989)
13. R. OmnèsAnn. Phys. (N.Y.) 201, 354 (1990)
14. R. OmnèsRev. Mod. Phys. 64, 339 (1992).
15. J. B. Hartle, in Gravitation et Quantifications, Proceedings of the 1992 Les Houches Summer School, edited by B. Julia and J. Zinn-Justin (Elsevier Science, Amsterdam, 1995).
16. J. J. Halliwell, Ann. (N.Y.) Acad. Sci. 775, 726 (1994).
17. See, for example, J. P. Paz and W. H. Zurek, Phys. Rev. D 48, 2728 (1993)
18. W. Zurek, in Physical Origins of Time Asymmetry, edited by J. J. Halliwell, J. Perez-Mercader, and W. Zurek (Cambridge University Press, Cambridge, England, 1994). Zurek’s contributions to the subject are extensive and the above is only a suggestive selection.
19. N. Gisin and I. C. Percival, J. Phys. A 25, 5677 (1992)
20. J. Phys. AN. GisinI. C. Percival26, 2233 (1993)
21. J. Phys. AN. GisinI. C. Percival26, 2245 (1993)
22. N. GisinI. C. PercivalPhys. Lett. A 167, 315 (1992).
23. J. J. Halliwell and A. Zoupas, Phys. Rev. D 52, 7294 (1995)
24. Phys. Rev. DJ. J. HalliwellA. Zoupas55, 4697 (1997).
25. J. B. Hartle, “Quantum Pasts and the Utility of Histories,” Report No. gr-qc/9712001.
26. H. F. Dowker and J. J. Halliwell, Phys. Rev. D 46, 1580 (1992).
27. J. N. McElwaine, Phys. Rev. A 53, 2021 (1996).
28. C. Isham and N. Linden, Phys. Rev. A 55, 4030 (1997).
29. J. B. Hartle, Phys. Rev. D 51, 1800 (1995).
30. T. A. Brun and J. B. Hartle, Phys. Rev. E 59, 6370 (1999).
31. G. S. Agarwal, Phys. Rev. A 3, 828 (1971)
32. Phys. Rev. AG. S. Agarwal4, 739 (1971)
33. Phys. Rev. AH. Dekker, 16, 2126 (1977)
34. H. DekkerPhys. Rep. 80, 1 (1991)
35. G. W. Ford, M. Kac, and P. Mazur, J. Math. Phys. 6, 504 (1965)
36. H. Grabert, P. Schramm, and G-L. Ingold, Phys. Rep. 168, 115 (1988)
37. V. Hakim and V. Ambegaokar, Phys. Rev. A 32, 423 (1985)
38. J. Schwinger, J. Math. Phys. 2, 407 (1961)
39. I. R. Senitzky, Phys. Rev. 119, 670 (1960).
40. See, for example, H. F. Dowker and A. Kent, J. Stat. Phys. 82, 1575 (1996). These authors actually made the weaker conjecture that an approximately consistent set of histories [i.e., (Formula presented) for (Formula presented)] are close to an exactly consistent set.R. Omnès (private communication) has pointed out that this is easily proved in some models: the real part of the decoherence functional is typically highly oscillatory as a function of the times of the projections, hence if it is close to zero, it can be made exactly zero by a small change in the times. The stronger conjecture involving decoherence (rather than just consistency)is very plausible but yet unproven in general.
41. J. A. Wheeler, in Complexity, Entropy and the Physics of Information, edited by W. Zurek (Addison-Wesley, Redwood City, CA, 1990).
42. C. Caves and C. A. Fuchs, in Sixty years of EPR, edited by A. Mann and M. Revzen (Ann. Phys. Soc., Israel, 1996)
43. C. Caves, in Physical Origins of Time Asymmetry, edited by J. J. Halliwell, J. Perez-Mercader, and W. Zurek (Cambridge University Press, Cambridge, 1994).
44. W. Wootters, Ph.D. thesis, University of Texas, 1980.
45. W. Zurek, Phys. Rev. D 24, 1516 (1981).
46. W. Zurek, Phys. Rev. D 26, 1862 (1982).
47. An interesting collection of article on many aspects of the physics of information may be found in Complexity, Entropy and the Physics of Information 22.
48. W. Zurek, in Quantum Optics, Experimental Gravitation and Measurement Theory, edited by P. Meystre and M. O. Scully, NATO ASI Series (Plenum, New York, 1983), p. 87.
49. J. B. Hartle, R. Laflamme, and D. Marolf, Phys. Rev. D 51, 7007 (1995).
50. C. Anastopoulos, “Hydrodynamic equations from quantum field theory,” Report No. gr-qc/9805074, 1998.
51. T. Brun and J. J. Halliwell, Phys. Rev. D 54, 2899 (1996).
52. T. Brun and J. B. Hartle, “Hydrodynamic Equations from Decoherent Histories, ” Santa Barbara report (in preparation).
53. J. J. Halliwell, Phys. Rev. D 58, 105015 (1998)
54. J. J. HalliwellPhys. Rev. Lett (to be published), quant-ph/9905094.
55. J. J. Halliwell, “Arrival Times in Quantum Theory from an Irreversible Detector Model,” quant-ph/9805057, Imperial College Report No. TP/97-98/49 [Prog. Theor. Phys. (to be published)].
56. A. Caldeira and A. Leggett, Physica A 121, 587 (1983).
57. R. P. Feynman and F. L. Vernon, Ann. Phys. (N.Y.) 24, 118 (1963).
58. M. Mensky, Zh. Eksp. Teor. Fiz. 77, 1326 (1979) [Sov. Phys. JETP 50, 667 (1979)]
59. M. MenskyTheor. Math. Phys. 75, 357 (1988);Continuous Quantum Measurements and Path Integrals (IOP Publishing, Bristol, 1993).
60. See, for example, H. Bacry, A. Grossman, and J. Zak, Phys. Rev. B 12, 1118 (1975).
61. J. J. Halliwell, Phys. Rev. D 39, 2912 (1989)
62. Phys. Rev. DT. Padmanabhan, 39, 2924 (1989)
63. C. Kiefer, Class. Quantum Grav. 6, 561 (1989).
64. C. Anastopoulos, Phys. Rev. D 54, 1600 (1996)
65. B. Kay, Class. Quantum Grav. 15, L89 (1998).