Foundations of Physics

, Volume 36, Issue 3, pp 369–384

Hidden Variables as Computational Tools: The Construction of a Relativistic Spinor Field

Article

Hidden variables are usually presented as potential completions of the quantum description. We describe an alternative role for these entities, as aids to calculation in quantum mechanics. This is illustrated by the computation of the time-dependence of a massless relativistic spinor field obeying Weyl’s equation from a single-valued continuum of deterministic trajectories (the “hidden variables”). This is achieved by generalizing the exact method of state construction proposed previously for spin 0 systems to a general Riemannian manifold from which the spinor construction is extracted as a special case. The trajectories form a non-covariant structure and the Lorentz covariance of the spinor field theory emerges as a kind of collective effect. The method makes manifest the spin 1/2 analogue of the quantum potential that is tacit in Weyl’s equation. This implies a novel definition of the “classical limit” of Weyl’s equation.

Keywords

hidden variables spinor quantum hydrodynamic trajectories Weyl’s equation Riemannian geometry classical limit Lorentz covariance 

PACS

03.65.Ta 

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References

  1. 1.
    Belinfante F.J. (1973). A Survey of Hidden-Variables Theories. Pergamon Press, OxfordGoogle Scholar
  2. 2.
    d’Espagnat B. (1976). Conceptual Foundations of Quantum Mechanics, 2nd edn. W. A. Benjamin, Reading MAGoogle Scholar
  3. 3.
    Holland P. (2005). Ann. Phys. (NY) 315:503CrossRefADSMathSciNetGoogle Scholar
  4. 4.
    Holland P. (2005). Proc. R. Soc. A 461:3659CrossRefMATHADSMathSciNetGoogle Scholar
  5. 5.
    Bialynicki-Birula I. (1995). Acta. Phys. Pol. B 26:1201MATHMathSciNetGoogle Scholar
  6. 6.
    Holland P.R. (2004). The Quantum Theory of Motion. Cambridge University Press, CambridgeGoogle Scholar
  7. 7.
    Madelung E. (1926). Z. Phys 40: 322ADSGoogle Scholar
  8. 8.
    Holland P. (2003). Ann. Phys. (Leipzig) 12:446CrossRefMATHADSMathSciNetGoogle Scholar
  9. 9.
    Holland P. and Philippidis C. (2003). Phys. Rev. A 67:062105CrossRefADSGoogle Scholar
  10. 10.
    Dahl J.P. (1977). Kon Danske Vid. Selsk Mat-fys. Medd 39:12Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Green CollegeUniversity of OxfordOxfordEngland

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