Skip to main content
SpringerLink
Log in

A quantum mechanical theory of local observables and local operations

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

Local operators are characterized mathematically by means of projection operators on the Banach space of bounded operators. The idea of microlocality, as opposed to macrolocality, is implemented into the theory so as to enable us to define operations that are strictly local. Necessary and sufficient conditions are investigated in order that the interaction of a local measurement instrument with a local quantum field is such a strictly local (or microlocal) operation. Application of the theory to quantum electrodynamics reveals that this theory violates microlocality as defined here. Implications which our theory may have on the issue of quantum nonlocality as studied in relation to the Bell inequalities are discussed.

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.

Similar content being viewed by others

References

  1. A. Einstein, B. Podolsky, and N. Rosen,Phys. Rev. 47, 777 (1935).

    Google Scholar 

  2. J. S. Bell,Physics 1, 195 (1964).

    Google Scholar 

  3. J. F. Clauser and A. Shimony,Rep. Prog. Phys. 41, 1881 (1978).

    Google Scholar 

  4. A. Aspect, P. Grangier, and G. Roger,Phys. Rev. Lett. 47, 460 (1981).

    Google Scholar 

  5. B. d'Espagnat,Found. Phys. 11, 205 (1981).

    Google Scholar 

  6. N. Cufaro-Petroni and J.-P. Vigier,Lett. Nuovo Cimento 25, 151 (1979).

    Google Scholar 

  7. F. Selleri and G. Tarozzi,Riv. Nuovo Cimento 4, 1 (1981).

    Google Scholar 

  8. C. D. Cantrell and M. O. Scully,Phys. Rep. 43, 499 (1978).

    Google Scholar 

  9. G. C. Ghirardi, A. Rimini, and T. Weber,Lett. Nuovo Cimento 27, 293 (1980).

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  12. W. M. de Muynck and J. P. H. W. van den Eijnde,Found. Phys. 14, 111 (1984).

    Google Scholar 

  13. G. C. Hegerfeldt and S. N. M. Ruijsenaars,Phys. Rev. D 22, 377 (1980).

    Google Scholar 

  14. A. Peres,Ann. Phys. (N.Y.)37, 179 (1966).

    Google Scholar 

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

    Google Scholar 

  16. S. N. M. Ruijsenaars,Ann. Phys. (N.Y.)137, 33 (1981).

    Google Scholar 

  17. B. Robertson,Am. J. Phys. 41, 678 (1973).

    Google Scholar 

  18. N. I. Greenberg and S. Raboy,Am. J. Phys. 50, 148 (1982).

    Google Scholar 

  19. W. N. Mathews, Jr., and M. A. Esrick,Am. J. Phys. 48, 782 (1980).

    Google Scholar 

  20. J. M. Knight,J. Math. Phys. 2, 459 (1961).

    Google Scholar 

  21. G. Ludwig, “Measuring and Preparing Processes,” inFoundations of Quantum Mechanics and Ordered Linear Spaces, A. Hartkämper and H. Neumann, eds. (Lecture Notes in Physics, Vol. 29) (Springer, New York, 1973), p. 122.

    Google Scholar 

  22. G. G. Emch,Algebraic Methods in Statistical Mechanics and Quantum Field Theory (Wiley Interscience, New York, 1972), p. 119.

    Google Scholar 

  23. G. G. Emch,Algebraic Methods in Statistical Mechanics and Quantum Field Theory (Wiley-Interscience, New York, 1972), p. 277.

    Google Scholar 

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

    Google Scholar 

  25. R. F. Streater and A. S. Wightman,PCT, Spin and Statistics, and All That (Benjamin, New York, 1964).

    Google Scholar 

  26. B. de Facio and D. C. Taylor,Phys. Rev. D 8, 2729 (1973).

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  29. R. Haag and J. Swieca,Commun. Math. Phys. 1, 308 (1965).

    Google Scholar 

  30. M. I. Shirokov,Theor. Math. Phys. 42, 134 (1980).

    Google Scholar 

  31. J. Hilgevoord,Dispersion Relations and Causal Description (North Holland, Amsterdam, 1960).

    Google Scholar 

  32. S. Schlieder, inQuanten und Felder, H. P. Dürr, ed. (Vieweg, Braunschweig, 1971), p. 145.

    Google Scholar 

  33. H. J. Borchers,Commun Math. Phys. 4, 315 (1967).

    Google Scholar 

  34. A. O. Barut and J. Nagel,J. Phys. A 10, 1233 (1977).

    Google Scholar 

  35. M. Reed and B. Simon,Methods of Modern Mathematical Physics (Academic Press, New York, 1972), Vol.I, p. 297.

    Google Scholar 

  36. F. Mandl,Introduction to Quantum Field Theory (Interscience, London, 1959), Chapter 14.

    Google Scholar 

  37. W. M. de Muynck,Int. J. Theor. Phys. 14, 327 (1975).

    Google Scholar 

  38. W. M. de Muynck and G. P. van Liempd, “On the Relation between Indistinguishability of Identical Particles and (Anti)symmetry of the Wave Function,” Report Eindhoven University of Technology.

  39. B. d'Espagnat,Conceptual Foundations of Quantum Mechanics (Benjamin, Reading, Massachusetts, 1976), Parts 3 and 5.

    Google Scholar 

  40. A. Aspect,Phys. Rev. D 1944, 14 (1976).

    Google Scholar 

  41. A. Shimony,Epistemol. Lett. 1, 47.0, June 1980.

    Google Scholar 

  42. K. Popper, A. Garuccio, and J.-P. Vigier,Epistemol. Lett. 21, 51.5, July 1981.

    Google Scholar 

  43. J.-P. Vigier,Epistemol. Lett. 25, 57.1, October 1981.

    Google Scholar 

  44. A. Aspect, J. Dalibard, and G. Roger,Phys. Rev. Lett. 49, 1804 (1982).

    Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Willem M. de Muynck

Authors
  1. Willem M. de Muynck
    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. A quantum mechanical theory of local observables and local operations. Found Phys 14, 199–253 (1984). https://doi.org/10.1007/BF00730210

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00730210

Keywords

Search

Navigation