Foundations of Physics

, Volume 28, Issue 6, pp 881–911 | Cite as

New Trajectory Interpretation of Quantum Mechanics

  • P. R. Holland


It was shown by de Broglie and Bohm that the concept of a deterministic particle trajectory is compatible with quantum mechanics. It is demonstrated by explicit construction that there exists another more general deterministic trajectory interpretation. The method exploits an internal angular degree of freedom that is implicit in the Schrödinger equation, in addition to the particle position. The de Broglie-Bohm model is recovered when the new theory is averaged over the internal freedom. The model exhibits a strong form of entanglement which implies a primary role for the wavefunction of the Universe. The conditions of autonomy are examined, and the viability of the theory is established by application to the measurement problem.


Quantum Mechanic Primary Role Particle Trajectory Strong Form Particle Position 
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  1. 1.
    L. de Broglie, J. Phys. 8, 225 (1927).Google Scholar
  2. 2.
    D. Bohm, Phys. Rev. 85, 166, 180 (1952).Google Scholar
  3. 3.
    P. R. Holland, The Quantum Theory of Motion (Cambridge University Press, Cambridge, 1993), Sec. 3.2.Google Scholar
  4. 4.
    If we extend the question beyond deterministic theories, the answer is surely yes-it is well known that there exist stochastic models describing motion that deviates from (1.1) but which reproduces quantum statistics (and (1.1) ) on the average. See, e.g., E. Nelson, Quantum Fluctuations (Princeton University Press, Princeton, 1985).Google Scholar
  5. 5.
    D. Dürr, S. Goldstein, and N. Zanghi, J. Stat. Phys. 67, 843 (1992). E. Squires, in Bohmian Mechanics and Quantum Theory: An Appraisal, J. T. Cushing et al. eds. (Kluwer, Dordrecht, 1996) 131. R. J. Sutherland, Found. Phys. 27, 845 (1997).Google Scholar
  6. 6.
    E. Deotto and G. C. Ghirardi, Bohmian mechanics revisited, quant-ph/9704021.Google Scholar
  7. 7.
    See, e.g., S. T. Epstein, Phys. Rev. 89, 319 (1952); 91, 965 (1953). D. Bohm, Phys. Rev. 89, 319 (1952). H. Freistadt, Suppl. Nuovo Cimento 5, 1 (1957). G. GarcõÂ a de Polavieja, Phys. Lett. A 200, 303 (1996).Google Scholar
  8. 8.
    We emphasize that we are simply rewriting the usual complex Hilbert space formalism in terms of real functions. This is not the same as so-called “real” quantum mechanics which uses only the first term on the right-hand side of the scalar product (2.6) and has different physical content. See S. L. Adler, Quaternionic Quantum Mechanics and Quantum Fields (Oxford University Press, Oxford, 1995), p. 44.Google Scholar
  9. 9.
    V. Heine, Group Theory in Quantum Mechanics (Pergamon Press, London, 1960), Chap. 7.Google Scholar
  10. 10.
    In what follows the definition of the Euler angles and the relevant results from the quantum theory of rotators are drawn from Ref. 3, Chap. 10, and references therein.Google Scholar
  11. 11.
    Ref. 3, Sec. 3.9.Google Scholar
  12. 12.
    Ref. 3, Chap. 8.Google Scholar
  13. 13.
    P. R. Holland, in Bohmian Mechanics and Quantum Theory: An Appraisal, J. T. Cushing et al., eds. (Kluwer, Dordrecht, 1996), p. 99.Google Scholar
  14. 14.
    For details, see J. T. Cushing, Quantum Mechanics: Historical Contingency and the Copenhagen Hegemony (University of Chicago Press, Chicago, 1994), Chap. 8.Google Scholar
  15. 15.
    A. Einstein, Dialectica 2, 120 (1948).Google Scholar

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© Plenum Publishing Corporation 1998

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  • P. R. Holland

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