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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.

Keywords

Dynamical Variable Hide Variable Probability Interpretation Quantum Formalism Bohmian Mechanics 
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.

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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)zbMATHGoogle 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)zbMATHGoogle 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)zbMATHCrossRefADSGoogle Scholar
  11. 11.
    A. M. Gleason: Measures on the Closed Sub-spaces of Hilbert Space. J. Math. Mechs. 6, 885– 893 (1957)zbMATHMathSciNetGoogle Scholar
  12. 12.
    J. M. Jauch, C. Piron: Can Hidden Variables be Excluded from Quantum Mechanics. Helv. Phys. Acta 36, 827–837 (1963)zbMATHMathSciNetGoogle Scholar
  13. 13.
    S. Kochen, E. P. Specker: The Problem of Hidden Variables in Quantum Mechanics. J. Math. Mech. 17, 59–87 (1967)zbMATHMathSciNetGoogle 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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