Advertisement

Foundations of Physics

, Volume 21, Issue 2, pp 125–148 | Cite as

Explicit mathematical construction of relativistic nonlinear de Broglie waves described by three-dimensional (wave and electromagnetic) solitons “piloted” (controlled) by corresponding solutions of associated linear Klein-Gordon and Schrödinger equations

  • Jean-Pierre Vigier
Part V. Invited Papers Dedicated To John Stewart Bell

Abstract

Starting from a nonlinear relativistic Klein-Gordon equation derived from the stochastic interpretation of quantum mechanics (proposed by Bohm-Vigier, (1) Nelson, (2) de Broglie, (3) Guerra et al. (4) ), one can construct joint wave and particle, soliton-like solutions, which follow the average de Broglie-Bohm (5) real trajectories associated with linear solutions of the usual Schrödinger and Klein-Gordon equations.

Keywords

Soliton Quantum Mechanic Linear Solution Mathematical Construction Real Trajectory 
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.
    D. Bohm and J. P. Vigier,Phys. Rev. 96, 208 (1954).Google Scholar
  2. 2.
    E. Nelson,Phys. Rev. 150, 1079 (1966).Google Scholar
  3. 3.
    L. de Broglie,Nonlinear Wave Mechanics (Elsevier, Amsterdam, 1960); F. Guerra and R. Marra,Phys. Rev. D 28, 1916 (1988).Google Scholar
  4. 4.
    L. de Broglie,C. R. Acad. Sci. (Paris) 277B, 71 (1973).Google Scholar
  5. 5.
    D. Bohm,Phys. Rev. 85, 186 (1952).Google Scholar
  6. 6.
    J. Schwinger,Found. Phys. 13, 373 (1983).Google Scholar
  7. 7.
    F. Guerra, “Quantum field theory and probability theory,” inTrends and Developments in the Eighties (World Scientific, Singapore, 1985).Google Scholar
  8. 8.
    N. Namsrai,Non-Local Quantum Field Theory and Stochastic Quantum Mechanics (Reidel, Dordrecht, 1986).Google Scholar
  9. 9.
    P. A. M. Dirac,Nature (London) 168, 906 (1951);169, 702 (1952).Google Scholar
  10. 10.
    K. P. Sinha, E. C. G. Sudarshan, and J. P. Vigier,Phys. Lett. 114A, 298 (1986).Google Scholar
  11. 11.
    A. Einstein,Sitz-Preuss. Akad. Wiss. 606 (1917);Verhandl. Dtsch. Phys. Ges. 19, (1917).Google Scholar
  12. 12.
    P. N. Kaloyerou and J. P. Vigier,J. Phys. A. Math. Gen. 22, 663 (1989).Google Scholar
  13. 13.
    J. P. Vigier,Astr. Nach. 303, 5 (1982).Google Scholar
  14. 14.
    J. P. Vigier, inProceedings, Third International Symposium.Foundations of Quantum Mechanics (in Physical Society of Japan, Tokyo, 1989).Google Scholar
  15. 15.
    J. P. Vigier, inEinstein Centenarium (Akademie-Verlag, Berlin, 1979); F. Guerra, “A nonlinear Schrödinger equation and its relativistic generalization from basic principles,”Lett. Nuovo Cimento 34, 351 (1982).Google Scholar
  16. 16.
    L. de Broglie and J. P. Vigier, La physique quantique restera-t-elle indéterministe? (Gauthier-Villars, Paris, 1953).Google Scholar
  17. 17.
    J. P. Vigier,IEEE Trans. Plasma Sci. 18, 64 (1990).Google Scholar
  18. 18.
    M. Born,Ann. Phys. (Leipzig) 30, 1 (1909).Google Scholar
  19. 19.
    J. R. Pounder,Commun. Dublin. Inst. Adv. Stud. A 11, 233 (1954).Google Scholar
  20. 20.
    J. P. Vigier,Lett. Nuovo Cimento 24, 258 (1979).Google Scholar
  21. 21.
    A. Einstein and L. Infeld,Can. J. Math. 1, 455 (1949).Google Scholar
  22. 22.
    A. Einstein,J. Franklin Inst. 221, 313 (1936).Google Scholar
  23. 23.
    A. O. Barut,Phys. Lett. A 143, 349 (1990).Google Scholar
  24. 24.
    N. Cufaro-Petroni, Z. Maris, A. Sardelis, A. Kyprianidis, and J. P. Vigier,Phys. Lett. A 101, 4 (1984).Google Scholar
  25. 25.
    N. Cufaro-Petroni, A. Sardelis, A. Kyprianidis, and J. P. Vigier,Phys. Lett. 106, 368 (1988).Google Scholar
  26. 26.
    J. P. Vigier, to be published.Google Scholar
  27. 27.
    H. Rauch and J. P. Vigier, “Proposed neutron interferometry test of Einstein's Einweg experiment in the Bohr-Einstein controversy,Physics Lett. A (1990), in press.Google Scholar
  28. 28.
    A. Kyprianidis and J. P. Vigier, inQuantum Mechanics Versus Local Realism, F. Selleri, ed. (Plenum, New York, 1988).Google Scholar

Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • Jean-Pierre Vigier
    • 1
  1. 1.CNRS/UA 769, Laboratoire de Physique ThéoriqueUniversité Pierre et Marie CurieParisFrance

Personalised recommendations