Advertisement

Communications in Mathematical Physics

, Volume 357, Issue 1, pp 407–420 | Cite as

The Measurement Process in Local Quantum Physics and the EPR Paradox

Article
  • 101 Downloads

Abstract

We describe in a qualitative way a possible picture of the Measurement Process in Quantum Mechanics, which takes into account the finite and non zero time duration T of the interaction between the observed system and the microscopic part of the measurement apparatus; the finite space size R of that apparatus; and the fact that the macroscopic part of the measurement apparatus, having the role of amplifying the effect of that interaction to a macroscopic scale, is composed by a very large but finite number N of particles. The Schrödinger evolution of the composed system can be expected to deform into the conventional picture of the measurement, as an instantaneous action turning a pure state into a mixture, only in the limit \({N \rightarrow \infty, T \rightarrow 0, R \rightarrow \infty}\). Our main point is to discuss this picture for the measurement of local observables in Quantum Field Theory, where the dynamics of the theory and the measurement itself are described by the same time evolution complying with the Principle of Locality. We comment on the Einstein Podolski Rosen thought experiment, reformulated here only in terms of local observables (rather than global ones, as one particle or polarization observables).The local picture of the measurement process helps to make it clear that there is no conflict with the Principle of Locality.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Araki H.: Mathematical Theory of Quantum Fields. Oxford University Press, Oxford (1999)MATHGoogle Scholar
  2. 2.
    Araki H., Yanase M. M.: Measurement of quantum mechanical operators. Phys. Rev. 120, 622–626 (1960)ADSMathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Aspect A.: Bell’s theorem: the naive view of an experimentalist. In: Bertlmann, R.A., Zeilinger, A. (eds) Quantum (Un)speakables—From Bell to Quantum Information, Springer, (2002)Google Scholar
  4. 4.
    Auletta G., Fortunato M., Parisi G.: Quantum Mechanics. Cambridge University Press, Cambridge (2009)CrossRefMATHGoogle Scholar
  5. 5.
    Borchers H.J.: Energy and momentum as observables in algebraic quantum field theory. Commun. Math. Phys. 2, 49 (1966)ADSCrossRefMATHGoogle Scholar
  6. 6.
    Buchholz D., Doplicher S., Longo R.: On Noether’s theorem in quantum field theory. Ann. Phys. 170, 1 (1986)ADSMathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Buchholz D., D’Antoni C., Fredenhagen K.: The universal structure of local algebras. Commun. Math. Phys. 111, 123–135 (1987)ADSMathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Daneri A., Loinger G.M., Prosperi A.: Quantum theory of measurement. Nucl. Phys. 33, 297–319 (1962)CrossRefMATHGoogle Scholar
  9. 9.
    Doplicher, S.: Quantum field theory on quantum spacetime. J. Phys. Conf. Ser. 53, 793–798 (2006). arXiv:hep-th/0608124
  10. 10.
    Doplicher, S.: Spin and Statistics and First Principles, Talk delivered at the Meeting Spin and Statistics 2008, Trieste. arXiv:0907.5313
  11. 11.
    Doplicher, S.: The principle of locality: effectiveness, fate, and challenges. J. Math. Phys. 51, 015218, 50th anniversary special issue (2010)Google Scholar
  12. 12.
    Doplicher S., Longo R.: Local aspects of superselection rules II. Commun. Math. Phys. 88, 399–409 (1983)ADSMathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Doplicher S., Longo R.: Standard and split inclusions of von Neumann algebras. Invent. Math. 75, 493–536 (1984)ADSMathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Doplicher S., Roberts J.E.: Why there is a field algebra with a compact gauge group describing the superselection structure in particle physics. Commun. Math. Phys. 131, 51–107 (1990)ADSMathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Doplicher S., Haag R., Roberts J. E.: Local Observables and Particle statistics I. Commun. Math. Phys. 23, 199–230 (1971)ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    Doplicher S., Haag R., Roberts J. E.: Local Observables and Particle statistics II. Commun. Math. Phys. 35, 49–85 (1974)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    Einstein A., Podolsky B., Rosen N.: Can quantum-mechanical description of physical reality be considered complete?. Phys. Rev. 47, 777 (1935)ADSCrossRefMATHGoogle Scholar
  18. 18.
    Haag R.: Local Quantum Physics: Fields, Particles, Algebras. Springer, Berlin (1994)MATHGoogle Scholar
  19. 19.
    Hellwig K. E., Kraus K.: Formal description of measurement in local quantum field theory. Phys. Rev. D 1, 566–571 (1970)ADSCrossRefGoogle Scholar
  20. 20.
    Sewell G.: On the mathematical structure of quantum measurement theory. Rep. Math. Phys. 56, 271 (2005)ADSMathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Summers, S. J.: Subsystems and independence in relativistic microscopic physics. Stud. Hist. Philos. Sci. B 40(2), 133–141 (2009). arXiv:0812.1517v2
  22. 22.
    Takesaki M.: Theory of Operator Algebras. III, Encyclopedia of Mathematical Sciences. Springer, Berlin (2003)MATHGoogle Scholar
  23. 23.
    von Neumann J.: Mathematical Foundations of Quantum Mechanics. Princeton University Press, Princeton (1955)MATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversity of Rome “La Sapienza”RomeItaly

Personalised recommendations