Advertisement

Foundations of Physics

, Volume 20, Issue 2, pp 139–158 | Cite as

Maxwell electrodynamics from a theory of macroscopically extended particles

  • J. W. G. Wignall
Article

Abstract

It is shown that an approach to quantum phenomena in which charged particles are treated as macroscopically extended periodic disturbances in a nonlinear c-number field, interacting with each other via massless excitations of that field, leads almost uniquely to the five basic equations of classical electrodynamics: the Lorentz force law and Maxwell's equations. The fundamental electromagnetic quantity in this approach is the 4-vector potential Aα—interpreted absolutely as a measure of the local shift of each particle off its mass shell—rather than theE andB fields, and it thus provides a new viewpoint on the questions of Aharonov-Bohm phase shifts, the existence of magnetic monopoles, and the role of gauge invariance.

Keywords

Phase Shift Charged Particle Basic Equation Lorentz Force Gauge Invariance 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J. C. Maxwell,Philos. Trans. R. Soc. London 155, 459 (1865);A Treatise on Electricity and Magnetism (Clarendon Press, Oxford, 1873).Google Scholar
  2. 2.
    J. D. Jackson,Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975).Google Scholar
  3. 3.
    A. Einstein,Ann. Phys. 49, 769 (1916); W. Pauli,The Theory of Relativity (translation by G. Field of 1921 article) (Pergamon, London, 1958).Google Scholar
  4. 4.
    J. W. G. Wignall,Found. Phys. 18, 591 (1988).Google Scholar
  5. 5.
    For a collection of key papers see J. A. Wheeler and W. H. Zurek,Quantum Theory and Measurement (Princeton University Press, Princeton, 1983); for annotated bibliographies see B. S. Dewitt and R. N. Graham,Am. J. Phys 39, 724 (1971) and L. E. Ballentine,Am. J. Phys. 55, 785 (1987).Google Scholar
  6. 6.
    P. A. M. Dirac,Principles of Quantum Mechanics, 4th ed. (Oxford University Press, Oxford, 1958); R. P. Feynman and A. R. Hibbs,Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).Google Scholar
  7. 7.
    J. W. G Wignall,Found. Phys. 15, 207 (1985).Google Scholar
  8. 8.
    J. W. G. Wignall,Found. Phys. 17, 123 (1987).Google Scholar
  9. 9.
    A. Messiah,Quantum Mechanics (North-Holland, Amsterdam, 1961); W. H. Furry,Boulder Lectures in Theoretical Physics, Vol. 5 (Interscience, New York, 1963); H. M. Bradford,Am. J. Phys. 44, 1058 (1976).Google Scholar
  10. 10.
    B. Rossi,High Energy Particles (Prentice-Hall, Englewood Cliffs, New Jersey, 1952).Google Scholar
  11. 11.
    J. W. G. Wignall, “Empirical Limits on the Sizes of Wave Packets in Visual Track Detectors,” University of Melbourne Report UM-P-88/98 (unpublished).Google Scholar
  12. 12.
    Y. Aharonov and D. Bohm,Phys. Rev. 115, 485 (1959).Google Scholar
  13. 13.
    R. G. Chambers,Phys. Rev. Lett. 5, 3 (1960); A. Tonomuraet al., Phys. Rev. Lett. 48, 1443 (1982); N. Osakabeet al., Phys. Rev. A 34, 815 (1986).Google Scholar
  14. 14.
    B. Cabrera,Phys. Rev. Lett. 48, 1378 (1982); B. Cabrera, M. Taber, R. Gardner, and J. Bourg,Phys. Rev. Lett. 51, 1933 (1983); A. D. Caplin, M. Hardiman, M. Koratzinos, and J. C. Schouten,Nature (London)321, 402 (1986); D. E. Groom,Phys. Rep. 140, 323 (1986).Google Scholar
  15. 15.
    P. A. M. Dirac,Proc. R. Soc. London A 133, 60 (1931),Phys. Rev. 74, 817 (1948).Google Scholar
  16. 16.
    T. T. Wu and C. N. Yang,Phys. Rev. D 12, 3845 (1975).Google Scholar

Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • J. W. G. Wignall
    • 1
  1. 1.School of PhysicsUniversity of MelbourneParkvilleAustralia

Personalised recommendations