Advertisement

On the Quantum Measurement Problem

  • Časlav Brukner
Chapter
Part of the The Frontiers Collection book series (FRONTCOLL)

Abstract

In this paper, I attempt a personal account of my understanding of the measurement problem in quantum mechanics, which has been largely in the tradition of the Copenhagen interpretation. I assume that (i) the quantum state is a representation of knowledge of a (real or hypothetical) observer relative to her experimental capabilities; (ii) measurements have definite outcomes in the sense that only one outcome occurs; (iii) quantum theory is universal and the irreversibility of the measurement process is only “for all practical purposes”. These assumptions are analyzed within quantum theory and their consistency is tested in Deutsch’s version of the Wigner’s friend gedanken experiment, where the friend reveals to Wigner whether she observes a definite outcome without revealing which outcome she observes. The view that holds the coexistence of the “facts of the world” common both for Wigner and his friend runs into the problem of the hidden variable program. The solution lies in understanding that “facts” can only exist relative to the observer.

Keywords

Quantum State Quantum Theory Lyapunov Exponent Measurement Problem Definite Outcome 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

This work has been supported by the Austrian Science Fund (FWF) through CoQuS, SFB FoQuS, and Individual Project 2462. I would like to acknowledge discussions with Mateus Araujo, Borivoje Dakić, Philippe Grangier, Richard Healey, Johannes Kofler, Luis Masanes, Jaques Pienaar and Anton Zeilinger.

References

  1. 1.
    J. Bub, I. Pitowsky, Two dogmas about quantum mechanics, in Many Worlds? Everett, Quantum Theory, and Reality, ed. by S. Saunders, J. Barrett, A. Kent, D. Wallace (Oxford University Press, 2010), pp. 431–456Google Scholar
  2. 2.
    I. Pitowsky, Quantum mechanics as a theory of probability, in Festschrift in honor of Jeffrey Bub, ed. by W. Demopoulos, I. Pitowsky (Springer, Western Ontario Series in Philosophy of Science, New York, 2007)Google Scholar
  3. 3.
    T. Maudlin, Three measurement problems. Topoi 14(1), 7–15 (1995)MathSciNetCrossRefGoogle Scholar
  4. 4.
    C. Brukner, A. Zeilinger, Information and fundamental elements of the structure of quantum theory, in Time, Quantum, Information, ed. by L. Castell, O. Ischebeck (Springer, 2003)Google Scholar
  5. 5.
    C.A. Fuch, R. Schack, Quantum-Bayesian coherence. Rev. Mod. Phys. 85, 1693 (2007)ADSCrossRefGoogle Scholar
  6. 6.
    C. Rovelli, Relational quantum mechanics. Int. J. Theor. Phys. 35, 1637–1678 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    R. Colbeck, R. Renner, No extension of quantum theory can have improved predictive power. Nat. Commun. 2, 411 (2011)ADSCrossRefGoogle Scholar
  8. 8.
    G.C. Ghirardi, A. Rimini, T. Weber, Unified dynamics for microscopic and macroscopic systems. Phys. Rev. D 34, 470 (1986)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    L. Diosi, Models for universal reduction of macroscopic quantum fluctuations. Phys. Rev. A 40, 1165–1174 (1989)ADSCrossRefGoogle Scholar
  10. 10.
    R. Penrose, On gravity’s role in quantum state reduction. Gen. Relat. Gravit. 28, 581–600 (1996)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    J.S. Bell, Speakable and Unspeakable in Quantum Mechanics, Collected Papers on Quantum Philosophy (Cambridge University Press, 2004)Google Scholar
  12. 12.
    M. Zukowski, Č. Brukner, Quantum non-locality—it ain’t necessarily so.., Special issue on 50 years of Bell’s theorem. J. Phys. A: Math. Theor. 47, 424009 (2014)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    C.A. Fuchs, R. Schack, QBism and the Greeks: why a quantum state does not represent an element of physical reality. arXiv:1412.4211 (2014)
  14. 14.
    S. Osnaghi, F. Freitas, O. Freire Jr., The origin of the Everettian heresy. Stud. Hist. Philos. Mod. Phys. 40(2), 97–123 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    K. Camilleri, M. Schlosshauer, Niels Bohr as philosopher of experiment: does decoherence theory challenge Bohr’s doctrine of classical concepts? Stud. Hist. Philos. Mod. Phys. 49, 73–83 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    P. Heelan, Heisenberg and radical theoretical change. Z. Allgemeine Wissenschaftstheorie 6, 113–138 (1975)CrossRefGoogle Scholar
  17. 17.
    AHQP, Archives for the History of Quantum Physics—Bohr’s Scientific Correspondence, 301 microfilm reels (American Philosophical Society, Philadelphia, 1986)Google Scholar
  18. 18.
    N. Harrigan, R.W. Spekkens, Einstein, incompleteness, and the epistemic view of quantum states. Found. Phys. 40, 125 (2010)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    S. Malin, What are quantum states? Quantum Inf. Process. 5, 233–237 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    A. Peres, When is a quantum measurement?. Ann. New York Acad. Sci. 480, New Tech. Ideas Quantum Meas. Theory 438 (1986)Google Scholar
  21. 21.
    E. Wigner, Symmetries and Reflections (Indiana University Press, 1967), p. 164Google Scholar
  22. 22.
    W. Pauli, Wissenschaftlicher Briefwechsel mit Bohr, Einstein, Heisenberg, vol. 2, ed. by K. von Meyenn, A. Hermann, V. F. Weisskopf (Springer, Berlin, 1985), pp. 1930–1939. For the English translation of Heisenberg’s manuscript with an introduction and bibliography see E. Crull, G. Bacciagaluppi. http://philsci-archive.pitt.edu/8590/
  23. 23.
    G. Chiribella, G. D’Ariano, P. Perinotti, Informational derivation of quantum theory. Phys. Rev. A 84, 012311 (2011)ADSCrossRefGoogle Scholar
  24. 24.
    M.P. Mueller, L. Masanes, Three-dimensionality of space and the quantum bit: an information-theoretic approach. New J. Phys. 15, 053040 (2013)ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    B. Dakic, Č. Brukner, The classical limit of a physical theory and the dimensionality of space, in Quantum Theory: Informational Foundations and Foils, ed. by G. Chiribella, R. Spekkens. (Springer, 2016) pp. 249–282. arXiv:1307.3984
  26. 26.
    J. Kofler, Č. Brukner, Classical world arising out of quantum physics under the restriction of coarse-grained measurements. Phys. Rev. Lett. 99, 180403 (2007)ADSCrossRefGoogle Scholar
  27. 27.
    W.H. Zurek, Decoherence, einselection, and the quantum origins of the classical. Rev. Mod. Phys. 75, 715 (2003)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    J. Kofler, Č. Brukner, Conditions for quantum violation of macroscopic realism. Phys. Rev. Lett. 101, 090403 (2008)ADSCrossRefGoogle Scholar
  29. 29.
    A. Peres, Quantum Theory: Concepts and Methods (Kluwer Academic Publishers, New York, 1995)zbMATHGoogle Scholar
  30. 30.
    A. Peres, Stability of quantum motion in chaotic and regular systems. Phys. Rev. A 30, 1610 (1984)ADSMathSciNetCrossRefGoogle Scholar
  31. 31.
    H.-J. Stöckmann, Q. Chaos, An Introduction (Cambridge University Press, Cambridge, 1999)CrossRefGoogle Scholar
  32. 32.
    P. Jacquod, I. Adagideli, C.W.J. Beenakker, Decay of the Loschmidt echo for quantum states with sub-Planck-scale structures. Phys. Rev. Lett. 89, 154103 (2012)ADSCrossRefGoogle Scholar
  33. 33.
    A. Peres, Recurrence phenomena in quantum dynamics. Phys. Rev. Lett. 49, 1118 (1982)ADSMathSciNetCrossRefGoogle Scholar
  34. 34.
    A.E. Allahverdyan, R. Balian, T.M. Nieuwenhuizen, Understanding quantum measurement from the solution of dynamical models. Phys. Rep. 525, 1 (2013)Google Scholar
  35. 35.
    D. Deutsch, Quantum theory as a universal physical theory. Int. J. Theor. Phys. 24, I (1985)Google Scholar
  36. 36.
    E.P. Wigner, Remarks on the mind-body question, in The Scientist Speculates, ed. by I.J. Good (London, Heinemann, 1961)Google Scholar
  37. 37.
    X.Y. Zou, T.P. Grayson, L. Mandel, Observation of quantum interference effects in the frequency domain. Phys. Rev. Lett. 69, 3041 (1992)ADSCrossRefGoogle Scholar
  38. 38.
    C. Bennett, Private CommunicationGoogle Scholar
  39. 39.
    N. Bohr, Discussion with Einstein on epistemological problems in atomic physics, in Albert Einstein: Philosopher-Scientist, ed. by P.A. Schilpp (The Library of Living Philosophers, Evanston, Illinois, 1949)Google Scholar
  40. 40.
    L. Hardy, Quantum theory from five reasonable axioms. arXiv:quant-ph/0101012 (2001)
  41. 41.
    B. Dakic and C. Brukner, Quantum theory and beyond: is entanglement special?, in Deep Beauty: Understanding the Quantum World through Mathematical Innovation, ed. by H. Halvorson (Cambridge University Press, 2011), pp. 365–392Google Scholar
  42. 42.
    L. Masanes, M. Müller, A derivation of quantum theory from physical requirements. New J. Phys. 13, 063001 (2011)ADSCrossRefGoogle Scholar
  43. 43.
    A. Aufféves, P. Grangier, Contexts, systems and modalities: a new ontology for quantum mechanics. arXiv:1409.2120 (2014)
  44. 44.
    N. Bohr, The Philosophical Writings of Niels Bohr 3 (Ox Bow Press, Woodbridge, Conn., 1987)Google Scholar
  45. 45.
    N. Bohr, On the notions of causality and complementarity. Dialectica 2, 312–319 (1948)CrossRefzbMATHGoogle Scholar
  46. 46.
    As quoted in “The philosophy of Niels Bohr” by Aage Petersen, in the Bull. Atom. Sci. 19(7) (1963); “The Genius of Science: A Portrait Gallery” (2000) by Abraham Pais, p. 24, and “Niels Bohr: Reflections on Subject and Object” (2001) by Paul. McEvoy, p. 291Google Scholar

Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Institute for Quantum Optics and Quantum Information (IQOQI)Austrian Academy of SciencesViennaAustria
  2. 2.Faculty of PhysicsUniversity of ViennaViennaAustria

Personalised recommendations