Hidden Variables

  • Basil J. Hiley

Standard quantum mechanics, in the hands of von Neumann, makes the assumption that the ► wave function, ψ(r, t), provides the most complete description of state of an evolving system. It then uses the Born probability postulate (► Born rule) and assumes that the probability of finding the system at position r at time t is given by P = |ψ(r, t)|2. This gives an essentially statistical theory, ► probability interpretation but a statistical theory unlike those found in classical situations where all the dynamical variables such as position, momentum, angular momentum etc., are well defined but unknown.

The dynamical variables of a quantum system are determined by the eigenvalues of operators called ► ‘observables’. Given a quantum state, not all the dynamical variables have simultaneous values. For example, if the position is sharply defined, then the momentum is undefined and vice-versa. In other words there exist sets of complementary variables such that if one set are well defined, the other set are completely undefined. This is the feature that underlies the ► Heisenberg uncertainty principle.


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Primary Literature

  1. 1.
    M. Born: Zur Quantenmechanik der Strossvorgänge. Z. Phys. 37, 863–867 (1927)ADSGoogle Scholar
  2. 2.
    J. von Neumann: Mathematical Foundations of Quantum Mechanics (Princeton University Press, Princeton 1955, p. 324)MATHGoogle Scholar
  3. 3.
    N. Wiener: The Role of the Observer. Phil. Sci. 3, 307–319 (1936)CrossRefGoogle Scholar
  4. 4.
    D. Bohm: A Suggested Interpretation of the Quantum Theory in Terms of Hidden Variables, I and II. Phys. Rev. 85, 166–179; 180–193 (1952)CrossRefADSMathSciNetGoogle Scholar
  5. 5.
    L. de Broglie: La méchanique ondulatoire et la structure atomique de la matiére et du rayon-nement. J. Phys. Radium, 6e series 8, 225–241 (1927)Google Scholar
  6. 6.
    L. de Broglie: Non-linear Wave Mechanics: a Causal Interpretation (Elsevier, Amsterdam 1960)MATHGoogle Scholar
  7. 7.
    W. Pauli: Reports on the 1927 Solvey Congress (Gauthiers-Villars et Cie, Paris 1928, p. 280)Google Scholar
  8. 8.
    D. Bohm, B. J. Hiley: The Undivided Universe: an Ontological Interpretation of Quantum Theory (Routledge, London 1993)Google Scholar
  9. 9.
    P. R. Holland: The Quantum Theory of Motion (Cambridge University Press, Cambridge 1993)CrossRefGoogle Scholar
  10. 10.
    J. S. Bell: On the Problem of Hidden Variables in Quantum Theory. Rev. Mod. Phys. 38, 447– 452 (1966)MATHCrossRefADSGoogle Scholar
  11. 11.
    A. M. Gleason: Measures on the Closed Sub-spaces of Hilbert Space. J. Math. Mechs. 6, 885– 893 (1957)MATHMathSciNetGoogle Scholar
  12. 12.
    J. M. Jauch, C. Piron: Can Hidden Variables be Excluded from Quantum Mechanics. Helv. Phys. Acta 36, 827–837 (1963)MATHMathSciNetGoogle Scholar
  13. 13.
    S. Kochen, E. P. Specker: The Problem of Hidden Variables in Quantum Mechanics. J. Math. Mech. 17, 59–87 (1967)MATHMathSciNetGoogle Scholar
  14. 14.
    N. Bohr: Atomic Physics and Human Knowledge (Science Editions, New York 1961, p. 39)Google Scholar
  15. 15.
    D. Bohm, B. J. Hiley: On the Intuitive Understanding of Nonlocality as Implied by Qauntum Theory. Found. Phys. 5, 93–109 (1975)CrossRefADSGoogle Scholar
  16. 16.
    J. S. Bell: On the Einstein-Podolsky-Rosen paradox. Physics 1, 195–200 (1964)Google Scholar
  17. 17.
    D. Bohm, B. J. Hiley, P. N. Kaloyerou: An Ontological Basis for the Quantum Theory: II - A Causal Interpretation of Quantum Fields. Phys. Reports 144, 349–375 (1987)CrossRefMathSciNetGoogle Scholar

Secondary Literature

  1. 18.
    F. J. Belinfante: A Survey of Hidden-Variables Theories (Pergamon Press, Oxford 1973)Google Scholar
  2. 19.
    M. Jammer: The Philosophy of Quantum Mechanics (Wiley-Interscience, New York 1974)Google Scholar
  3. 20.
    J. S. Bell: Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge 1987)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Basil J. Hiley

There are no affiliations available

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