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Foundations of Physics

, Volume 41, Issue 7, pp 1163–1192 | Cite as

Consistent Histories of Systems and Measurements in Spacetime

  • Ed Seidewitz
Article

Abstract

Traditional interpretations of quantum theory in terms of wave function collapse are particularly unappealing when considering the universe as a whole, where there is no clean separation between classical observer and quantum system and where the description is inherently relativistic. As an alternative, the consistent histories approach provides an attractive “no collapse” interpretation of quantum physics. Consistent histories can also be linked to path-integral formulations that may be readily generalized to the relativistic case. A previous paper described how, in such a relativistic spacetime path formalism, the quantum history of the universe could be considered to be an eigenstate of the measurements made within it. However, two important topics were not addressed in detail there: a model of measurement processes in the context of quantum histories in spacetime and a justification for why the probabilities for each possible cosmological eigenstate should follow Born’s rule. The present paper addresses these topics by showing how Zurek’s concepts of einselection and envariance can be applied in the context of relativistic spacetime and quantum histories. The result is a model of systems and subsystems within the universe and their interaction with each other and their environment.

Keywords

Path integrals Spacetime paths Relativistic quantum mechanics Relativistic dynamics Measurements Subsystems Born’s rule Einselection Envariance 

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References

  1. 1.
    Griffiths, R.B.: J. Stat. Phys. 36, 219 (1984) ADSMATHCrossRefGoogle Scholar
  2. 2.
    Omnès, R.: J. Stat. Phys. 53, 893 (1988) ADSMATHCrossRefGoogle Scholar
  3. 3.
    Gell-Mann, M., Hartle, J.: In: Zurek, W. (ed.) Complexity, Entropy and the Physics of Information. Sante Fe Institute Studies in the Science of Complexity, vol. VIII. Addison–Wesley, Reading (1990) Google Scholar
  4. 4.
    Griffiths, R.B.: Consistent Quantum Mechanics. Cambridge University Press, Cambridge (2002) Google Scholar
  5. 5.
    Feynman, R.P.: Rev. Mod. Phys. 20, 367 (1948) MathSciNetADSCrossRefGoogle Scholar
  6. 6.
    Feynman, R.P., Hibbs, A.R.: Quantum Mechanics and Path Integrals. McGraw–Hill, New York (1965) MATHGoogle Scholar
  7. 7.
    Caves, C.M.: Phys. Rev. D 33, 1643 (1986) MathSciNetADSCrossRefGoogle Scholar
  8. 8.
    Hartle, J.B.: Phys. Rev. D 44, 3173 (1991) MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    Hartle, J.B.: Vistas Astron. 37, 569 (1993). arXiv:gr-qc/9210004 MathSciNetADSCrossRefGoogle Scholar
  10. 10.
    Hartle, J.B.: In: Julia, B., Zinn-Justin, J. (eds.) Gravitation and Quantizations: Proceedings of the 1992 Les Houches Summer School. North-Holland, Amsterdam (1995). arXiv:gr-qc/9304006 Google Scholar
  11. 11.
    Feynman, R.P.: Phys. Rev. 76, 749 (1949) MathSciNetADSMATHCrossRefGoogle Scholar
  12. 12.
    Feynman, R.P.: Phys. Rev. 80, 440 (1950) MathSciNetADSMATHCrossRefGoogle Scholar
  13. 13.
    Feynman, R.P.: Phys. Rev. 84, 108 (1951) MathSciNetADSMATHCrossRefGoogle Scholar
  14. 14.
    Teitelboim, C.: Phys. Rev. D 25, 3159 (1982) MathSciNetADSCrossRefGoogle Scholar
  15. 15.
    Hartle, J.B., Hawking, S.W.: Phys. Rev. D 28, 2960 (1983) MathSciNetADSCrossRefGoogle Scholar
  16. 16.
    Hartle, J.B., Kuchař, K.V.: Phys. Rev. D 34, 2323 (1986) MathSciNetADSCrossRefGoogle Scholar
  17. 17.
    Halliwell, J.J.: Phys. Rev. D 64, 044008 (2001) MathSciNetADSCrossRefGoogle Scholar
  18. 18.
    Halliwell, J.J., Thorwart, J.: Phys. Rev. D 64, 124018 (2001) MathSciNetADSCrossRefGoogle Scholar
  19. 19.
    Halliwell, J.J., Thorwart, J.: Phys. Rev. D 65, 104009 (2002) MathSciNetADSCrossRefGoogle Scholar
  20. 20.
    Blencowe, M.: Ann. Phys. (N. Y.) 211, 87 (1991) MathSciNetADSCrossRefGoogle Scholar
  21. 21.
    Isham, C.J., Linden, N., Savvidou, K., Schreckenberg, S.: J. Math. Phys. 39, 1818 (1998) MathSciNetADSMATHCrossRefGoogle Scholar
  22. 22.
    Isham, C.J., Savvidou, K.: Quantising the foliation in history quantum field theory. Tech. Rep. Imperial/TP/00-01/32, Imperial College of Science (2001). arXiv:quant-ph/0110161
  23. 23.
    Griffiths, R.B.: Phys. Rev. A 66, 062101 (2002) MathSciNetADSCrossRefGoogle Scholar
  24. 24.
    Seidewitz, E.: Found. Phys. 37, 572 (2007). arXiv:quant-ph/0612023 MathSciNetADSMATHCrossRefGoogle Scholar
  25. 25.
    Seidewitz, E.: J. Math. Phys. 47, 112302 (2006). arXiv:quant-ph/0507115 MathSciNetADSCrossRefGoogle Scholar
  26. 26.
    Seidewitz, E.: Ann. Phys. 324, 309 (2009). arXiv:0804.3206 [quant-ph] MathSciNetADSMATHCrossRefGoogle Scholar
  27. 27.
    Kent, A.: Int. J. Mod. Phys. A 5, 1745 (1990) MathSciNetADSCrossRefGoogle Scholar
  28. 28.
    Squires, E.J.: Phys. Lett. A 145, 67 (1990) MathSciNetADSCrossRefGoogle Scholar
  29. 29.
    Zurek, W.H.: Philos. Trans. R. Soc. Lond. A 356, 1793 (1998) MathSciNetADSCrossRefGoogle Scholar
  30. 30.
    Zurek, W.H.: Rev. Mod. Phys. 75, 715 (2003) MathSciNetADSMATHCrossRefGoogle Scholar
  31. 31.
    Zurek, W.H.: Phys. Rev. Lett. 90, 120404 (2003) MathSciNetADSCrossRefGoogle Scholar
  32. 32.
    Zurek, W.H.: Phys. Rev. A 71, 052105 (2005) MathSciNetADSCrossRefGoogle Scholar
  33. 33.
    Zurek, W.H.: Phys. Rev. A 76, 052110 (2007). arXiv:quant-ph/0703160 ADSCrossRefGoogle Scholar
  34. 34.
    Zurek, W.H.: Relative states and the environment, einselection, envariance, quantum Darwinism, and the existential interpretation. Tech. Rep. LAUR 07-4568, Los Alamos National Laboratory (2007). arXiv:0707.2832 [quant-ph]
  35. 35.
    Halliwell, J.J., Wallden, P.: Phys. Rev. D 73, 024011 (2006). arXiv:quant-ph/0301117 MathSciNetADSCrossRefGoogle Scholar
  36. 36.
    Peskin, M.E., Schroeder, D.V.: An Introduction to Quantum Field Theory. Addison–Wesley, Reading (1995) Google Scholar
  37. 37.
    Weinberg, S.: The Quantum Theory of Fields. Foundations, vol. 1. Cambridge University Press, Cambridge (1995) Google Scholar
  38. 38.
    Ticciati, R.: Quantum Field Theory for Mathematicians. Cambridge University Press, Cambridge (1999) MATHCrossRefGoogle Scholar
  39. 39.
    Stueckelberg, E.C.G.: Helv. Phys. Acta 14, 588 (1941) MathSciNetMATHGoogle Scholar
  40. 40.
    Stueckelberg, E.C.G.: Helv. Phys. Acta 15, 23 (1942) MathSciNetMATHGoogle Scholar
  41. 41.
    Wichmann, E.H., Circhton, J.H.: Phys. Rev. 132, 2788 (1963) MathSciNetADSCrossRefGoogle Scholar
  42. 42.
    Schlosshauer, M., Fine, A.: Found. Phys. 35, 197 (2005) MathSciNetADSMATHCrossRefGoogle Scholar
  43. 43.
    Fock, V.A.: Phys. Z. Sowjetunion 12, 404 (1937) Google Scholar
  44. 44.
    Nambu, Y.: Prog. Theor. Phys. 5, 82 (1950) MathSciNetADSCrossRefGoogle Scholar
  45. 45.
    Schwinger, J.: Phys. Rev. 82, 664 (1951) MathSciNetADSMATHCrossRefGoogle Scholar
  46. 46.
    Morette, C.: Phys. Rev. 81, 848 (1951) MathSciNetADSMATHCrossRefGoogle Scholar
  47. 47.
    Cooke, J.H.: Phys. Rev. 166, 1293 (1968) ADSCrossRefGoogle Scholar
  48. 48.
    Horwitz, L.P., Piron, C.: Helv. Phys. Acta 46, 316 (1973) Google Scholar
  49. 49.
    Collins, R.E., Fanchi, J.R.: Nuovo Cimento A 48, 314 (1978) ADSCrossRefGoogle Scholar
  50. 50.
    Fanchi, J.R., Collins, R.E.: Found. Phys. 8, 851 (1978) MathSciNetADSCrossRefGoogle Scholar
  51. 51.
    Piron, C., Reuse, F.: Helv. Phys. Acta 51, 146 (1978) MathSciNetGoogle Scholar
  52. 52.
    Fanchi, J.R., Wilson, W.J.: Found. Phys. 13, 571 (1983) ADSCrossRefGoogle Scholar
  53. 53.
    Fanchi, J.R.: Parametrized Relativistic Quantum Theory. Kluwer Academic, Dordrecht (1993) CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.14000 Gulliver’s TrailBowieUSA

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