Foundations of Physics

, Volume 13, Issue 11, pp 1101–1119 | Cite as

Stochastic electrodynamics. I. On the stochastic zero-point field

  • G. H. Goedecke


This is the first in a series of papers that present a new classical statistical treatment of the system of a charged harmonic oscillator (HO) immersed in an omnipresent stochastic zero-point (ZP) electromagnetic radiation field. This paper establishes the Gaussian statistical properties of this ZP field using Bourret's postulate that all statistical moments of the stochastic field plane waves at a given space-time point should agree with their corresponding quantized field vacuum expectations. This postulate is more than adequate to derive the Planck spectrum classically via Boyer's and Theimer's methods, but it requires that the stochastic amplitude of each linearly polarized plane wave in the field contain two independent Gaussian random variables, not just a random phase as has sometimes been assumed. In the succeeding papers in the series, the total motion of a charged HO is described by a fully renormalized dipole-approximation Abraham-Lorentz equation. This leads without further approximation to the following major results concerning this stochastic electrodynamics (SED) of the HO: i) The ensemble-average Liouville equation for the oscillator-ZP field system in the presence of an arbitrary applied classical radiation field is exactly equivalent to the usual time-dependent Schrödinger equation supplemented by an explicit radiation reaction vector potential similar to that of the Crisp-Jaynes-Stroud theory; ii) this SED Schrödinger equation for the HO is incomplete, insmuch as there exists a companion equation that restricts initial conditions such that the corresponding Wigner phase-space distribution is always positive; iii) the wave function of the SED Schrödinger equation has thea priori significance of position probability amplitude; iv) first-order transition rates predicted for the HO by this theory agree with those predicted by quantum electrodynamics for resonance absorption and spontaneous emission, which occurs with no triggering necessary; and v) if SED is taken seriously, then the concepts of quantized energies and photons must be abandoned.


Plane Wave Harmonic Oscillator Electromagnetic Radiation Gaussian Random Variable Total Motion 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    P. Braffort and C. Tzara,Compt. Rend. 239, 1779 (1954); P. Braffort, C. Tzara, and M. Spighel,239, 157 (1954).Google Scholar
  2. 2.
    T. W. Marshall,Proc. R. Soc. London A 276, 475 (1963);Proc. Cambridge Philos. Soc. 61, 537 (1975);Nuovo Cimento 38, 206 (1965);Phys. Lett. A 75, 265 (1980).Google Scholar
  3. 3.
    R. Bourret,Phys. Lett. 12, 323 (1964);Can. J. Phys. 44, 2519 (1966).Google Scholar
  4. 4.
    M. Surdin,Int. J. Theor. Phys. 4, 117 (1971);Ann. Inst. H. Poincaré 15, 203 (1971); M. Surdin, P. Braffort, and A. Taroni,Nature (London) 210, 405 (1966).Google Scholar
  5. 5.
    T. H. Boyer,Phys. Rev. 182, 1374 (1969).Google Scholar
  6. 6.
    T. H. Boyer,Phys. Rev. D 11, 790 (1975); 809 (1975).Google Scholar
  7. 7.
    T. H. Boyer,Phys. Rev. A 18, 1228 (1978); 1238 (1978).Google Scholar
  8. 8.
    T. H. Boyer,Phys. Rev. D 17, 1112 (1979);D 19, 3635 (1979).Google Scholar
  9. 9.
    O. Theimer,Phys. Rev. D 4, 1597 (1971).Google Scholar
  10. 10.
    O. Theimer and P. R. Peterson,Phys. Rev. D 10, 3962 (1974);A 16, 2055 (1977).Google Scholar
  11. 11.
    E. Santos,Nuovo Cimento B 19, 57 (1974);B 22, 201 (1974);J. Math. Phys. 15, 1954 (1974).Google Scholar
  12. 12.
    L. de Peña-Auerbach and A. M. Cetto,J. Math. Phys. 18, 1612 (1977);20, 469 (1979);Found. Phys. 8, 191 (1978)3.Google Scholar
  13. 13.
    L. de la Peña,Am. J. Phys. 48, 1080 (1980);Phys. Lett. A 81, 441 (1981).Google Scholar
  14. 14.
    T. W. Marshall and P. Claverie,J. Math. Phys. 21, 1819 (1980).Google Scholar
  15. 15.
    T. H. Boyer, A Brief Survey of Stochastic Electrodynamics, inFoundations of Radiation Theory and Quantum Electrodynamics, A. O. Barut, ed. (Plenum Press, New York, 1980).4 Google Scholar
  16. 16.
    T. H. Boyer,Phys. Rev. A 20, 1246 (1979);A 21, 66 (1980),D 21, 2137 (1980).Google Scholar
  17. 17.
    M. Surdin,Nuovo Cimento C 3, 626 (1980).Google Scholar
  18. 18.
    L. de la Peña,Phys. Lett. A 81, 441 (1981).Google Scholar
  19. 19.
    G. Cavalleri,Phys. Rev. D 23, 363 (1981).Google Scholar
  20. 20.
    Steven M. Moore,J. Math. Phys. 22, 765 (1981).Google Scholar
  21. 21.
    M. D. Crisp and E. T. Jaynes,Phys. Rev. 179, 1253 (1969);185, 2046 (1969); C. R. Stroud, Jr., and E. T. Jaynes,Phys. Rev. A 1, 106 (1970); E. T. Jaynes,Phys. Rev. A 2, 260 (1970).Google Scholar
  22. 22.
    C. Kittel,Elementary Statistical Physics (Wiley, New York, 1958), pp. 118 ff.Google Scholar
  23. 23.
    J. F. Clauser,Phys. Rev. D 9, 853 (1974).Google Scholar
  24. 24.
    U. Frisch and R. Bourret,J. Math. Phys. 11, 364 (1970).Google Scholar
  25. 25.
    K. Furutsu, On the Statistical Theory of Electromagnetic Waves in a Fluctuating Medium,Natl. Bur. Stand. Monogr., Vol. 79 (National Bureau of Standards, Washington, D.C., 1964).Google Scholar
  26. 26.
    I. E. Segal,Lectures in Applied Mathematics, Vol. 2,Mathematical Problems of Relativistic Physics (American Mathematical Society, 1963).Google Scholar
  27. 27.
    T. W. Marshall,Phys. Rev. D 24, 1509 (1981).Google Scholar
  28. 28.
    Jon Mathews and R. L. Walker,Mathematical Methods of Physics (Benjamin/Cummings, New York, 1970), 2nd edn., Chapter 14.Google Scholar
  29. 29.
    S. O. Rice, Mathematical Analysis of Random Noise, inSelected Papers on Noise and Stochastic Processes, N. Wax, ed. (Dover, New York, 1954);Bell Syst. Tech. J., Vols. 23, 24.Google Scholar

Copyright information

© Plenum Publishing Corporation 1983

Authors and Affiliations

  • G. H. Goedecke
    • 1
  1. 1.Physics DepartmentNew Mexico State UniversityLas Cruces

Personalised recommendations