Foundations of Physics

, Volume 32, Issue 9, pp 1399–1417 | Cite as

The Nature of Information in Quantum Mechanics

  • Rocco Duvenhage


A suitable unified statistical formulation of quantum and classical mechanics in a *-algebraic setting leads us to conclude that information itself is noncommutative in quantum mechanics. Specifically we refer here to an observer's information regarding a physical system. This is seen as the main difference from classical mechanics, where an observer's information regarding a physical system obeys classical probability theory. Quantum mechanics is then viewed purely as a mathematical framework for the probabilistic description of noncommutative information, with the projection postulate being a noncommutative generalization of conditional probability. This view clarifies many problems surrounding the interpretation of quantum mechanics, particularly problems relating to the measuring process.

measurement projection postulate noncommutative conditional probability noncommutative information 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    W. Heisenberg, The Physical Principles of the Quantum Theory (University of Chicago Press, Chicago, 1930).Google Scholar
  2. 2.
    J. Bub, “Von Neumann's projection postulate as a probability conditionalization rule in quantum mechanics,” J. Phil. Logic 6, 381–390 (1977).Google Scholar
  3. 3.
    C. A. Fuchs, “Quantum foundations in the light of quantum information,” in Proceedings of the NATO Advanced Research Workshop on Decoherence and Its Implications in Quantum Computation and Information Transfer, A. Gonis, ed. (Plenum, New York, 2001); quant-ph/0106166, quant-ph/0205039.Google Scholar
  4. 4.
    C. M. Caves, C. A. Fuchs, and R. Schack, “Quantum probabilities as Bayesian probabilities,” Phys. Rev. A 65, 022305 (2002).Google Scholar
  5. 5.
    O. Bratteli and D. W. Robinson, Operator Algebras and Quantum Statistical Mechanics 1, 2nd edn. (Springer, New York, 1987).Google Scholar
  6. 6.
    G. J. Murphy, C*-Algebras and Operator Theory (Academic, San Diego, 1990).Google Scholar
  7. 7.
    W. Rudin, Real and Complex Analysis, 3rd edn. (McGraw-Hill, New York, 1987).Google Scholar
  8. 8.
    B. O. Koopman, “Hamiltonian systems and transformations in Hilbert space,” Proc. Natl. Acad. Sci. U.S.A. 17, 315–318 (1931).Google Scholar
  9. 9.
    M. Born, Physics in My Generation (Pergamon, London, 1956).Google Scholar
  10. 10.
    D. Petz, “Conditional expectation in quantum probability,” in Quantum Probability and Applications III, L. Accardi and W. von Waldenfels, eds. (Springer, Berlin, 1988), pp. 251–260.Google Scholar
  11. 11.
    R. Duvenhage, “Recurrence in quantum mechanics,” Int. J. Theor. Phys. 41, 45–61 (2002).Google Scholar
  12. 12.
    C. A. Fuchs and A. Peres, “Quantum theory needs no ‘interpretation’,” Phys. Today 53(3), 70–71 (2000).Google Scholar
  13. 13.
    S. Straătilaă and L. Zsido´, Lectures on von Neumann algebras (Editura Academiei, Bucures¸ti and Abacus Press, Tunbridge Wells, 1979).Google Scholar
  14. 14.
    R. Haag, Local Quantum Physics: Fields, Particles, Algebras, 2nd edn. (Springer, Berlin, 1996).Google Scholar
  15. 15.
    J. Schwinger, Quantum Mechanics: Symbolism of Atomic Measurements (Springer, Berlin, 2001).Google Scholar
  16. 16.
    J. von Neumann, Mathematische Grundlagen der Quantenmechanik (Springer, Berlin, 1932); English transl. Mathematical Foundations of Quantum Mechanics by R. T. Beyer (Princeton University Press, Princeton, New Jersey, 1955).Google Scholar
  17. 17.
    T. Sudbery, “Continuous state reduction,” in Quantum Concepts in Space and Time, R. Penrose and C. J. Isham, eds. (Oxford University Press, Oxford, 1986), pp. 65–83.Google Scholar
  18. 18.
    A. S. Holevo, “Limit theorems for repeated measurements and continuous measurement processes,” in Quantum Probability and Applications IV, L. Accardi and W. von Waldenfels, eds. (Springer, Berlin, 1989), pp. 229–255.Google Scholar
  19. 19.
    B. Misra and E. C. G. Sudarshan, “The Zeno's paradox in quantum theory,” J. Math. Phys. 18, 756–763 (1977).Google Scholar
  20. 20.
    C. Cohen-Tannoudji, B. Diu, and F. Laloe¨, Quantum mechanics, Volume I (Hermann, Paris, and Wiley, New York, 1977).Google Scholar
  21. 21.
    A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?,” Phys. Rev. 47, 777–780 (1935).Google Scholar
  22. 22.
    C. J. Isham, Lectures on Quantum Theory: Mathematical and Structural Foundations (Imperial College Press, London, 1995).Google Scholar
  23. 23.
    D. Finkelstein, “Space-time code,” Phys. Rev. 184, 1261–1271 (1969).Google Scholar
  24. 24.
    S. Doplicher, K. Fredenhagen, and J. E. Roberts, “The quantum structure of spacetime at the Planck scale and quantum fields,” Commun. Math. Phys. 172, 187–220 (1995).Google Scholar
  25. 25.
    J. Marsden, Application of Global Analysis in Mathematical Physics (Carleton Mathematical Lecture Notes, No. 3, 1973).Google Scholar
  26. 26.
    D. R. Finkelstein, Quantum Relativity: A Synthesis of the Ideas of Einstein and Heisenberg (Springer, Berlin, 1996).Google Scholar
  27. 27.
    R. F. Streater, “Classical and quantum probability,” J. Math. Phys. 41, 3556–3603 (2000).Google Scholar

Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • Rocco Duvenhage
    • 1
  1. 1.Department of Mathematics and Applied MathematicsUniversity of PretoriaPretoriaSouth Africa

Personalised recommendations