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On Gravity's role in Quantum State Reduction

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Abstract

The stability of a quantum superposition of two different stationary mass distributions is examined, where the perturbing effect of each distribution on the space-time structure is taken into account, in accordance with the principles of general relativity. It is argued that the definition of the time-translation operator for the superposed space-times involves an inherent ill-definedness, leading to an essential uncertainty in the energy of the superposed state which, in the Newtonian limit, is proportional to the gravitational self-energyE Δ of the difference between the two mass distributions. This is consistent with a suggested finite lifetime of the order of ħ/E Δ for the superposed state, in agreement with a certain proposal made by the author for a gravitationally induced spontaneous quantum state reduction, and with closely related earlier suggestions by Diósi and by Ghirardiet al.

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References

  1. Anandan, J. (1994).Gen. Rel. Grav. 26, 125.

    Google Scholar

  2. Anandan, J. (1995). "Gravitational phase operator and cosmic strings". To appear inPhys. Rev. D.

  3. Bell, J. S. (1990).Physics World 3, 33.

    Google Scholar

  4. Bialynicki-Birula, I., and Mycielski, J. (1976).Ann. Phys. (NY) 100, 62.

    Article Google Scholar

  5. Bohm, D. (1952).Phys. Rev. 85, 166.

    Article Google Scholar

  6. Bohm, D., and Hiley, B. (1994).The Undivided Universe (Routledge, London).

    Google Scholar

  7. Cartan, É. (1923,1924). "Sur les variétés à connexion affine et la théorie de la relativité generalisée",Ann. École Norm. Sup. 40, 325,41, 1.

    Google Scholar

  8. Christian, J. (1995). "Definite events in Newton-Cartan quantum gravity" Oxford University preprint.

  9. de Broglie, I. (1956).Tentative d'Interpretation Causale et Nonlineaire de la Mechanique Ondulatoire (Gauthier-Villars, Paris).

    Google Scholar

  10. DeWitt, B. S., and Graham, R. D. (eds.) (1973).The Many Worlds Interpretation of Quantum Mechanics (Princeton University Press, Princeton).

    Google Scholar

  11. Diósi, L. (1989).Phys. Rev. A 40, 1165.

    Article Google Scholar

  12. Ehlers, J. (1991). InClassical Mechanics and Relativity: Relationship and Consistency (Int. Conf. in memory of Carlo Cataneo, Elba 1989), G. Ferrarese, ed. (Monographs and Textbooks in Physical Science, Lecture Notes 20, Bibliopolis, Naples).

    Google Scholar

  13. Everett, H. (1957).Rev. Mod. Phys. 29, 454.

    Article Google Scholar

  14. Friedrichs, K. (1927).Math. Ann. 98, 566.

    Article MathSciNet Google Scholar

  15. Gell-Mann, M., and Hartle, J. B. (1993).Phys. Rev. D 47, 3345.

    Google Scholar

  16. Ghirardi, G. C., Rimini, A. and Weber, T. (1986).Phys. Rev. D 34, 470.

    Google Scholar

  17. Ghirardi, G. C., Grassi, R., and Rimini, A. (1990).Phys. Rev. A 42, 1057.

    Google Scholar

  18. Griffiths, R. (1984).J. Stat. Phys. 36, 219.

    Article Google Scholar

  19. Haag, R. (1992).Local Quantum Physics: Fields, Particles, Algebras (Springer-Verlag, Berlin).

    Google Scholar

  20. Károlyházy, F. (1966).Nuovo Cimento A 42, 390.

    Google Scholar

  21. Károlyházy, F. (1974).Magyar Fizikai Polyoirat 12, 24.

    Google Scholar

  22. Károlyházy, F., Frenkel, A., and Lukács, B. (1986). InQuantum Concepts in Space and Time, R. Penrose and C. J. Isham, eds. (Oxford University Press, Oxford), p. 109.

    Google Scholar

  23. Kibble, T. W. B. (1981). InQuantum Gravity 2: a Second Oxford Symposium, C. J. Isham, R. Penrose and D. W. Sciama, eds. (Oxford University Press, Oxford), p.63.

    Google Scholar

  24. Komar, A. B. (1969).Int. J. Theor. Phys. 2, 157.

    Article Google Scholar

  25. Omnès, R. (1992).Rev. Mod. Phys. 64, 339.

    Article Google Scholar

  26. Page, D. N., and Geilker, C. D. (1981).Phys. Rev. Lett. 47, 979.

    Article Google Scholar

  27. Pearle, P. (1985). InQuantum Concepts in Space and Time, R. Penrose and C. J. Isham, eds. (Oxford University Press, Oxford), p.84.

    Google Scholar

  28. Pearle, P. (1989).Phys. Rev. A 39, 2277.

    Google Scholar

  29. Pearle, P., and Squires, E. J. (1995). "Gravity, energy conservation and parameter values in collapse models". Durham University preprint DTP/95/13.

  30. Penrose, R. (1981). InQuantum Gravity 2: A Second Oxford Symposium, C. J. Isham, R. Penrose and D. W. Sciama, eds. (Oxford University Press, Oxford), p.244.

    Google Scholar

  31. Penrose, R. (1986). InQuantum Concepts in Space and Time, R. Penrose and C. J. Isham, eds. (Oxford University Press, Oxford), p.129.

    Google Scholar

  32. Penrose, R. (1987). In300 Years of Gravity, S. W. Hawking and W. Israel, eds. (Cambridge University Press, Cambridge), p. 17.

    Google Scholar

  33. Penrose, R. (1989).The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics (Oxford University Press, Oxford).

    Google Scholar

  34. Penrose, R. (1993). InGeneral Relativity and Gravitation 13. Part 1: Plenary Lectures, R. J. Gleiser, C. N. Kozameh and O. M. Moreschi, eds. (IOPP, Bristol/Philadelphia), p. 179.

    Google Scholar

  35. Penrose, R. (1994). InFundamental Aspects of Quantum Theory, J. Anandan and J. L. Safko, eds. (World Scientific, Singapore), p.238.

    Google Scholar

  36. Penrose, R. (1994).Shadows of the Mind; An Approach to the Missing Science of Consciousness (Oxford University Press, Oxford).

    Google Scholar

  37. Percival, I. C. (1995).Proc. R. Soc. Lond. A 451, 503.

    Google Scholar

  38. Squires, E. (1990).Phys. Lett. A 145, 67.

    Google Scholar

  39. Squires, E. (1992).Found. Phys. Lett. 5, 279.

    Article Google Scholar

  40. Trautman, A. (1965). InLectures on General Relativity (Brandeis 1964 Summer Inst. on Theoretical Physics), vol. I, by A. Trautman, F. A. E. Pirani and H. Bondi (Prentice-Hall, Englewood Cliffs, NJ), p.7.

    Google Scholar

  41. Weinberg, S. (1989).Phys. Rev. Lett. 62, 485.

    Article Google Scholar

  42. Wigner, E. P. (1961). InThe Scientist Speculates, I. J. Good, ed. (Heinemann, London); reprinted in E. Wigner (1967).Symmetries and Reflections (Indiana University Press, Bloomington) and in 1983 in QuantumTheory and Measurement, J. A. Wheeler and W. H. Zurek, eds. (Princeton University Press, Princeton).

    Google Scholar

  43. Zurek, W. H. (1991).Physics Today 44, 36.

    Google Scholar

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Authors and Affiliations

  1. Mathematical Institute, University of Oxford, 24-29 St Giles', OX1 3LB, Oxford, UK

    Roger Penrose

  2. Center for Gravitational Physics and Geometry, Pennsylvania State University, 16801, University Park, Pennsylvania, USA

    Roger Penrose

Authors
  1. Roger Penrose

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Penrose, R. On Gravity's role in Quantum State Reduction. Gen Relat Gravit 28, 581–600 (1996). https://doi.org/10.1007/BF02105068

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  • DOI: https://doi.org/10.1007/BF02105068

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