Skip to main content
Log in

Constraint on collapse models by limit on spontaneous x-ray emission in Ge

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

The continuous spontaneous localization (CSL) model modifies Schrödinger's equation so that the collapse of the state vector is described as a physical process (a special interaction of particles with a universal fluctuating field). A consequence of the model is that an electron in an atom should occasionally get “spontaneously” knocked out of the atom. The CSL ionization rate for the 1s electrons in the Ge atom is calculated and compared with an experimental upper limit for the rate of “spontaneously” generated x-ray pulses in Ge. This gives, for the first time, an experimental constraint on the parameters which characterize this model (the GRW parameters and the relative collapse rate of electrons and nucleons). It is concluded that the values assigned to the GRW parameters by GRW may be maintained only if the coupling of electrons to the fluctuating field is 0.35% or less than the coupling of nucleons, suggestive of a mass-proportional (and therefore gravitational) collapse mechanism. For other allowed values of the GRW parameters, it is still argued that nucleons should collapse more rapidly than electrons.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. D. Bohm and J. Bub,Rev. Mod. Phys. 38, 543 (1966).

    Google Scholar 

  2. P. Pearle,Phys. Rev. D 13, 857 (1976).

    Google Scholar 

  3. For further references to this pre-GRW work, see P. Pearle inSixty-Two Years of Uncertainty, A. Miller, ed. (Plenum, New York, 1990), p. 193.

    Google Scholar 

  4. G. C. Ghirardi, A. Rimini, and T. Weber,Phys. Rev. D 34, 470 (1986);Phys. Rev. D 36, 3287 (1987);Found. Phys. 18, 1 (1988).

    Google Scholar 

  5. J. S. Bell, inSchrödinger-Centenary Celebration of a Polymath, C. W. Kilmister, ed. (Cambridge University Press, Cambridge, 1987);Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1987), p. 167.

    Google Scholar 

  6. For a review, see G. C. Ghirardi and A. Rimini, inSixty-Two Years of Uncertainty, A. Miller, ed. (Plenum, New York, 1990), p. 167.

    Google Scholar 

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

    Google Scholar 

  8. G. C. Ghirardi, P. Pearle, and A. Rimini,Phys. Rev. A 42, 78 (1990).

    Google Scholar 

  9. See reviews in Refs. 3 and 6; G. C. Ghirardi and P. Pearle, inProceedings of the Philosophy of Science Foundation 1990, Vol. 2, A. Fine, M. Forbes, and L Wessels, eds. (PSA Association, Michigan, 1992), pp.19, 35; G. C. Ghirardi inQuantum Chaos-Quantum Measurement, P. Cvitanovicet al., eds. (Kluwer, Dordrecht, 1992), p. 305.

    Google Scholar 

  10. See Ref. 6 and E. J. Squires,Phys. Lett. A 158, 432 (1991).

    Google Scholar 

  11. H. S. Miley, F. T. Avignone, III, R. L. Brodzinski, J. I. Collar, and J. H. Reeves,Phys. Rev. Lett. 65, 3092 (1990).

    Google Scholar 

  12. P. Pearle and E. J. Squires,Phys. Rev. Lett. 73, 1 (1994). This paper also points out that a relativistic CSL (which unfortunately is not yet in completely satisfactory shape) should be highly constrained by the proton lifetime experiments.

    Google Scholar 

  13. P. M. Morse and H. Feshbach,Methods of Theoretical Physics, Part II (McGraw-Hill, New York, 1953), p. 1665. Because of different normalization, this expression differs from ours by an extra factor 2k/√2π.

    Google Scholar 

  14. I. S. Gradshteyn and I. M. Rhyzik,Table of Integrals, Series, and Products (Academic Press, New York, 1965), p. 860 (Eq. 7.621, Sec. 4).

    Google Scholar 

  15. H. Bateman,Higher Transcendental Functions, A. Erdélyi, ed. (McGraw-Hill, New York, 1953), p. 105. (Equation (2) expressesF in terms of anF with −1 as one of the first two indices, whose series truncates at two terms).

    Google Scholar 

  16. D. R. Hartree,Proc. Cambridge Philos. Soc. 24, 89, 111 (1928).

    Google Scholar 

  17. W. Barth, R. S. Martin, and J. H. Wilkinson,Numer. Math. 9, 386 (1967).

    Google Scholar 

  18. Linear Alegbra, J. H. Wilkinson and C. Reinsch, eds. (Springer, Heidelberg, 1971), pp. 418–439.

    Google Scholar 

  19. J. C. Slater,Phys. Rev. 98, 1039 (1955).

    Google Scholar 

  20. L. Diosi,Phys. Rev. A 40, 1165 (1989) and G. C. Ghirardi, R. Grassi, and A. Rimini,Phys. Rev. A 42, 1057 (1990), have already discussed such a model.

    Google Scholar 

  21. L. L. Light, D. Lavoie, D. Valencia-Laver, S. A. A. Owens, and G. Mead,J. Exp. Psychol.: Learning, Memory and Cognition 18, 1284 (1992).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Collett, B., Pearle, P., Avignone, F. et al. Constraint on collapse models by limit on spontaneous x-ray emission in Ge. Found Phys 25, 1399–1412 (1995). https://doi.org/10.1007/BF02057460

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02057460

Keywords

Navigation