Advertisement

Foundations of Physics

, Volume 41, Issue 2, pp 242–260 | Cite as

Electrodynamics of Balanced Charges

  • Anatoli Babin
  • Alexander FigotinEmail author
Open Access
Article

Abstract

We introduce here a new “neoclassical” electromagnetic (EM) theory in which elementary charges are represented by wave functions and individual EM fields to account for their EM interactions. We call so defined charges balanced or “b-charges”. We construct the EM theory of b-charges (BEM) based on a relativistic field Lagrangian and show that: (i) the elementary EM fields satisfy the Maxwell equations; (ii) the Newton equations with the Lorentz forces hold approximately when b-charges are well separated and move with non-relativistic velocities. When the BEM theory is applied to atomic scales it yields a hydrogen atom model with a frequency spectrum matching the Schrodinger model with desired accuracy. An important feature of the theory is a mechanism of elementary EM energy absorption established for retarded potentials.

Keywords

Electromagnetic theory Lagrangian Wave-corpuscle Elementary absorption 

References

  1. 1.
    Babin, A., Figotin, A.: Wave-corpuscle mechanics for electric charges. J. Stat. Phys. 138, 912–954 (2010) zbMATHCrossRefMathSciNetADSGoogle Scholar
  2. 2.
    Babin, A., Figotin, A.: Wave-corpuscle mechanics for elementary charges. e-print available online at arXiv:0812.2686
  3. 3.
    Babin, A., Figotin, A.: Some mathematical problems in a neoclassical theory of electric charges. Discrete Contin. Dyn. Syst. A 27(4), 1283–1326 (2010) zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Bialynicki-Birula, I., Mycielski, J.: Nonlinear wave mechanics. Ann. Phys. 100, 62–93 (1976) CrossRefMathSciNetADSGoogle Scholar
  5. 5.
    Corduneanu, C.: Almost Periodic Oscillations and Waves. Springer, Berlin (2009) zbMATHCrossRefGoogle Scholar
  6. 6.
    Einstein, A.: Über die Entwicklung unserer Anschauungen über das Wesen und die Konstitution der Strahlung. Phys. Z., vol. 10 (1909). English translation: On the development of our view concerning the nature and constitution of radiation. In: The Collected Papers, vol. 2, The Swiss Years Writings 1900–1909, Princeton (1989) Google Scholar
  7. 7.
    Goldstein, H., Poole, C., Safko, J.: Classical Mechanics, 3rd edn. Addison-Wesley, Reading (2000) Google Scholar
  8. 8.
    Griffiths, D.: Introduction to Electrodynamics, 3rd edn. Prentice Hall, New York (1999) Google Scholar
  9. 9.
    Jackson, J.: Classical Electrodynamics, 3rd edn. Wiley, New York (1999) zbMATHGoogle Scholar
  10. 10.
    Kiessling, M.: Quantum Abraham models with de Broglie-Bohm laws of quantum motion. e-print available online at arXiv:physics/0604069v2
  11. 11.
    Mead, C.: Collective Electrodynamics—Quantum Foundations of Electromagnetism. MIT Press, Cambridge (2000) Google Scholar
  12. 12.
    Pauli, W.: Relativistic field theories of elementary particles. Rev. Mod. Phys. 13, 203–234 (1941) zbMATHCrossRefADSGoogle Scholar
  13. 13.
    Pearle, P.: Classical Electron Models. In: Teplitz, D. (ed.) Electromagnetism Paths to Research, pp. 211–295. Plenum, New York (1982) Google Scholar
  14. 14.
    Rohrlich, F.: Classical Charged Particles, 3rd edn. World Scientific, Singapore (2007) zbMATHGoogle Scholar
  15. 15.
    Schiff, L.: Quantum Mechanics. McGraw-Hill, New York (1949) Google Scholar
  16. 16.
    Schwinger, J.: Electromagnetic mass revisited. Found. Phys. 13(3), 373–383 (1983) CrossRefMathSciNetADSGoogle Scholar
  17. 17.
    Spohn, H.: Dynamics of Charged Particles and Their Radiation Field. Cambridge University Press, Cambridge (2004) zbMATHCrossRefGoogle Scholar
  18. 18.
    van Bladel, J.: Electromagnetic Fields, 2nd edn. IEEE Press, New York (2007) CrossRefGoogle Scholar
  19. 19.
    Wentzel, G.: Quantum Theory of Fields. Dover, New York (2003) zbMATHGoogle Scholar
  20. 20.
    Wheeler, J., Feynman, R.: Interaction with the absorber as the mechanism of radiation. Rev. Mod. Phys. 17(2–3), 157–181 (1945) CrossRefADSGoogle Scholar
  21. 21.
    Wheeler, J., Feynman, R.: Classical electrodynamics in terms of direct interparticle action. Rev. Mod. Phys. 21(3), 425–433 (1949) zbMATHCrossRefMathSciNetADSGoogle Scholar
  22. 22.
    Yaghjian, A.: Relativistic Dynamics of a Charged Sphere: Updating the Lorentz-Abraham Model, 2nd edn. Springer, Berlin (2006) Google Scholar
  23. 23.
    Zeh, H.: The Physical Basis of the Direction of Time, 5th edn. Springer, Berlin (2007) zbMATHGoogle Scholar

Copyright information

© The Author(s) 2010

Authors and Affiliations

  1. 1.Department of MathematicsThe University of California at IrvineIrvineUSA

Personalised recommendations