Skip to main content
SpringerLink
Log in

A derivation of local commutativity from macrocausality using a quantum mechanical theory of measurement

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

A theory of the joint measurement of quantum mechanical observables is generalized in order to make it applicable to the measurement of the local observables of field theory. Subsequently, the property of local commutativity, which is usually introduced as a postulate, is derived by means of the theory of measurement from a requirement of mutual nondisturbance, which, for local observables performed at a spacelike distance from each other, is interpreted as a requirement of macrocausality. Alternative attempts at establishing a deductive relationship between relativistic causality and local commutativity are reviewed, but found wanting, either because of the assumption of an unwarranted objectivity of the object system (algebraic approach) or because of the use of a projection postulate (operational approach). Finally, the quantum mechanical nonobjectivity is related to certain features of nonlocality which are present in the formalism of quantum mechanics.

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. W. M. de Muynck, P. A. E. M. Janssen, and A. Santman,Found. Phys. 9, 71 (1979).

    Google Scholar 

  2. R. Haag and D. Kastler,J. Math. Phys. 5, 848 (1964).

    Google Scholar 

  3. G. G. Emch,Algebraic Methods in Statistical Mechanics and Quantum Field Theory (Wiley-Interscience, New York, 1972).

    Google Scholar 

  4. K. Kraus,Ann. Phys. (N.Y.) 64, 311 (1971).

    Google Scholar 

  5. M. D. Srinivas,J. Math. Phys. 20, 1593 (1979).

    Google Scholar 

  6. J. von Neumann,Mathematical Foundations of Quantum Mechanics (Princeton University Press, Princeton, New Jersey, 1955).

    Google Scholar 

  7. J. L. Park and H. Margenau,Int. J. Theor. Phys. 1, 211 (1968).

    Google Scholar 

  8. G. Lüders,Ann. Phys. 8, 322 (1951).

    Google Scholar 

  9. E. B. Davies and J. T. Lewis,Commun. Math. Phys. 15, 305 (1969).

    Google Scholar 

  10. M. D. Srinivas,J. Math. Phys. 16, 1672 (1975).

    Google Scholar 

  11. J. von Neumann,Mathematical Foundations of Quantum Mechanics (Princeton University Press, Princeton, New Jersey, 1955), VI.2.

    Google Scholar 

  12. K.-E. Hellwig and K. Kraus,Commun. Math. Phys. 11, 214 (1969).

    Google Scholar 

  13. K.-E. Hellwig and K. Kraus,Commun. Math. Phys. 16, 142 (1970).

    Google Scholar 

  14. K. Kraus, “Operations and Effects in the Hilbert Space Formulation of Quantum Theory,” inFoundations of Quantum Mechanics and Ordered Linear Spaces, A. Hartkämper H. Neumann, eds. (Springer, New York, 1974), p. 206.

    Google Scholar 

  15. C. M. Caves, K. S. Thorne, R. W. P. Drever, V. D. Sandberg, and M. Zimmermann,Rev. Mod. Phys. 52, 341 (1980).

    Google Scholar 

  16. Z. Vager,Phys. Lett. A 84, 163 (1981).

    Google Scholar 

  17. R. Mercer,Commun. Math. Phys. 84, 239 (1982).

    Google Scholar 

  18. L. E. Ballentine,Rev. Mod. Phys. 42, 358 (1970), and literature cited therein.

    Google Scholar 

  19. M. Reed and B. Simon,Methods of Modern Mathematical Physics (Academic Press, New York, 1972), Vol. I.

    Google Scholar 

  20. N. N. Bogolubov, A. A. Logunov, and I. T. Todorov,Introduction to Axiomatic Quantum Field Theory (Benjamin, Reading, Massachusetts, 1975), p. 588.

    Google Scholar 

  21. N. Bohr and L. Rosenfeld,K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 12, 258 (1933) [reprinted inBoston Studies in the Philosophy of Science, R. S. Cohen and J. J. Stachel, eds., Vol. XXI (Kluwer, Boston, 1979), p. 357]; N. Bohr and L. Rosenfeld,Phys. Rev. 78, 794 (1950).

    Google Scholar 

  22. W. M. de Muynck,Found. Phys. 14, 199 (1984).

    Google Scholar 

  23. P. Havas,Synthese 18, 75 (1968).

    Google Scholar 

  24. H. Roos,Commun. Math. Phys. 16, 238 (1970).

    Google Scholar 

  25. Y. Avishai and H. Ekstein,Found. Phys. 2, 257 (1972).

    Google Scholar 

  26. S. Schlieder,Commun. Math. Phys. 13, 216 (1969).

    Google Scholar 

  27. B. DeFacio and D. C. Taylor,Phys. Rev. D 8, 2729 (1973).

    Google Scholar 

  28. H. Ekstein,Phys. Rev. 184, 1315 (1969).

    Google Scholar 

  29. B. DeFacio,Found. Phys. 5, 229 (1975).

    Google Scholar 

  30. K. Kraus,Z. Phys. 181, 1 (1964).

    Google Scholar 

  31. B. DeFacio,Found. Phys. 6, 185 (1976).

    Google Scholar 

  32. S. Schlieder,Commun. Math. Phys. 7, 305 (1968).

    Google Scholar 

  33. K.-E. Hellwig and K. Kraus,Phys. Rev. D 1, 566 (1970).

    Google Scholar 

  34. Y. Aharonov and D. Z. Albert,Phys. Rev. D 21, 3316 (1980).

    Google Scholar 

  35. P. Benioff and H. Ekstein,Phys. Rev. D 15, 3563 (1977).

    Google Scholar 

  36. J. G. Cramer,Phys. Rev. D 22, 362 (1980).

    Google Scholar 

  37. B. d'Espagnat,Conceptual Foundations of Quantum Mechanics (Benjamin, Menlo Park, Calif., second edition, 1976).

    Google Scholar 

  38. J. L. Park, W. Band, and W. Yourgrau,Ann. Phys. 37, 189 (1980).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Theoretical Physics, Eindhoven University of Technology, Eindhoven, The Netherlands

    W. M. de Muynck & J. P. H. W. van den Eijnde

Authors
  1. W. M. de Muynck
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. P. H. W. van den Eijnde
    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

de Muynck, W.M., van den Eijnde, J.P.H.W. A derivation of local commutativity from macrocausality using a quantum mechanical theory of measurement. Found Phys 14, 111–146 (1984). https://doi.org/10.1007/BF00729970

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00729970

Keywords

Search

Navigation