Skip to main content
SpringerLink
Log in

Measurement theory in the Lax-Phillips formalism

  • Part I. Invited Papers Dedicated to Constantin Piron
  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

It is shown that the application of the Lax-Phillips scattering theory to quantum mechanics provides a natural framework for the realization of the ideas of the “Many-Hilbert-Space” theory of Machida and Namiki to describe the development of decoherence in the process of measurement. We show that if the quantum mechanical evolution is pointwise in time, then decoherence occurs only if the Hamiltonian is time-dependent. If the evolution is not pointwise in time (as in Liouville space), then the decoherence may occur even for closed systems. These conclusions apply as well to the general problem of mixing of states.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. For a review, seeQuantum Theory and Measurement, J. A. Wheeler and W. H. Zurek, eds. (Princeton University Press, Princeton, 1993).

    Google Scholar 

  2. S. Machida and M. Namiki,Prog. Theor. Phys. 63, 1457 (1980);63, 1833 (1980); see also, M. Namiki,Found. Phys. 18, 29 (1988).

    Google Scholar 

  3. M. Namiki and S. Pascazio,Phys. Lett. A 147, 430 (1990);Phys. Rev. A 44, 39 (1991).

    Google Scholar 

  4. M. Namiki and S. Pascazio,Phys. Rep. 232, 301 (1993) and references therein.

    Google Scholar 

  5. P. D. Lax and R. S. Phillips,Scattering Theory (Academic Press, New York, 1967).

    Google Scholar 

  6. C. Flesia and C. Piron,Helv. Phys. Acta 57, 697 (1984).

    Google Scholar 

  7. L. P. Horwitz and C. Piron,Helv. Phys. Acta 66, 693 (1993).

    Google Scholar 

  8. E. Eisenberg and L. P. Horwitz,Adv. Chem. Phys., to be published (1994).

  9. C. George,Physica 65, 277 (1973); I. Prigogine, C. George, F. Henin, and L. Rosenfeld,Chem. Scr. 4, 5 (1973); T. Petrosky and I. Prigogine,Physica A 175, 146 (1991); I. Prigogine,Proceedings, Quantum Physics and the Universe, M. Namikiet al., eds.;Vistas in Astronomy 37, 7 (1993), and references therein.

    Google Scholar 

  10. C. Piron,Foundations of Quantum Physics (Benjamin/Cummings, Reading, Massachusetts, 1976).

    Google Scholar 

Download references

Author information

Author notes

  1. S. Tasaki

    Present address: Institute for Fundamental Chemistry, 34-4 Takano-Nishihiraki-cho, Sakyo-ku, 606, Kyoto, Japan

  2. L. P. Horwitz

    Present address: School of Physics, Tel Aviv University, Ramat Aviv, Isreal

Authors and Affiliations

  1. International Solvay Institutes for Physics and Chemistry, Campus Plaine ULB, Boulevard de Triomphe, CP 231, 1050, Brussels, Belgium

    S. Tasaki

  2. Department of Physics, Bar-Ilan University, 52900, Ramat-Gan, Israel

    E. Eisenberg & L. P. Horwitz

  3. Institute for Advanced Study, School of Natural Sciences, 08540, Princeton, New Jersey

    L. P. Horwitz

Authors
  1. S. Tasaki
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. Eisenberg
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. L. P. Horwitz
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tasaki, S., Eisenberg, E. & Horwitz, L.P. Measurement theory in the Lax-Phillips formalism. Found Phys 24, 1179–1194 (1994). https://doi.org/10.1007/BF02057863

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02057863

Keywords

Search

Navigation