Foundations of Physics

, Volume 45, Issue 2, pp 134–141 | Cite as

Quantum Potential Energy as Concealed Motion

Article

Abstract

It is known that the Schrödinger equation may be derived from a hydrodynamic model in which the Lagrangian position coordinates of a continuum of particles represent the quantum state. Using Routh’s method of ignorable coordinates it is shown that the quantum potential energy of particle interaction that represents quantum effects in this model may be regarded as the kinetic energy of additional ‘concealed’ freedoms. The method brings an alternative perspective to Planck’s constant, which plays the role of a hidden variable, and to the canonical quantization procedure, since what is termed ‘kinetic energy’ in quantum mechanics may be regarded literally as energy due to motion.

Keywords

Potential energy Kinetic energy Hidden variables  Quantum hydrodynamics 

References

  1. 1.
    Thompson, J.J.: Applications of Dynamics to Physics and Chemistry, p. 15. Macmillan, London (1888)Google Scholar
  2. 2.
    Webster, A.G.: The Dynamics of Particles and of Rigid, Elastic, and Fluid Bodies, sec. 48. Teubner, Leipzig (1904)Google Scholar
  3. 3.
    Routh, E.J.: A Treatise on the Stability of Motion, p. 60. Macmillan, London (1877)Google Scholar
  4. 4.
    Macdonald, H.M.: Electric Waves, chap. 5. Cambridge University Press, Cambridge (1902)Google Scholar
  5. 5.
    Whittaker, E.T.: A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, 4th edn, p. 54. Cambridge University Press, Cambridge (1952)Google Scholar
  6. 6.
    Byerly, W.E.: An Introduction to the Use of Generalized Coordinates in Mechanics and Physics, chap. 2. Ginn and Co., Boston (1944)Google Scholar
  7. 7.
    Goldstein, H.: Classical Mechanics, chap. 7. Addison-Wesley, Reading (1950)Google Scholar
  8. 8.
    Pars, L.A.: A Treatise on Analytical Dynamics, chap. 10. Heinemann, London (1965)Google Scholar
  9. 9.
    Lamb, H.: Hydrodynamics, chap. 6., 6th edn. Cambridge University Press, Cambridge (1932)Google Scholar
  10. 10.
    Whittaker, E.T.: From Euclid to Eddington, p. 84. Cambridge University Press, Cambridge (1949)Google Scholar
  11. 11.
    Holland, P.: Computing the wavefunction from trajectories: particle and wave pictures in quantum mechanics and their relation. Ann. Phys. 315, 503 (2005)ADSCrossRefGoogle Scholar
  12. 12.
    Holland, P.: Hydrodynamic construction of the electromagnetic field. Proc. R. Soc. A461, 3659 (2005)ADSCrossRefGoogle Scholar
  13. 13.
    Holland, P.: Quantum field dynamics from trajectories. In: Chattaraj, P. (ed.) Quantum Trajectories, chap. 5. Taylor & Francis, Boca Raton (2010)Google Scholar
  14. 14.
    Holland, P.: Symmetries and conservation laws in the Lagrangian picture of quantum hydrodynamics. In: Ghosh, S. K, Chattaraj, P. K. (eds.) Concepts and Methods in Modern Theoretical Chemistry: Statistical Mechanics, chap. 4. Taylor & Francis, Boca Raton (2013)Google Scholar
  15. 15.
    Holland, P.: Hidden variables as computational tools: the construction of a relativistic spinor field. Found. Phys. 36, 1 (2006)CrossRefMathSciNetGoogle Scholar
  16. 16.
    Holland, P.: Hydrodynamics, particle relabelling and relativity. Int. J. Theor. Phys. 51, 667 (2012)Google Scholar
  17. 17.
    Guerst, J.A.: Variational principles and two-fluid hydrodynamics of bubbly liquid/gas mixtures. Physica A 135, 455 (1986)Google Scholar
  18. 18.
    Holland, P.: Schrodinger dynamics as a two-phase conserved flow: an alternative trajectory construction of quantum propagation. J. Phys. A 42, 075307 (2009)ADSCrossRefMathSciNetGoogle Scholar
  19. 19.
    Holland, P.: What’s wrong with Einstein’s 1927 hidden-variable interpretation of quantum mechanics? Found. Phys. 35, 177 (2005)Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Green Templeton CollegeUniversity of OxfordOxfordEngland, UK

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