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Foundations of Physics

, Volume 26, Issue 8, pp 1055–1068 | Cite as

Maxwell electromagnetic theory, Planck's radiation law, and Bose—Einstein statistics

  • H. M. FranÇa
  • A. MaiaJr.
  • C. P. Malta
Article

Abstract

We give an example in which it is possible to understand quantum statistics using classical concepts. This is done by studying the interaction of chargedmatter oscillators with the thermal and zeropoint electromagnetic fields characteristic of quantum electrodynamics and classical stochastic electrodynamics. Planck's formula for the spectral distribution and the elements of energy hw are interpreted without resorting to discontinuities. We also show the aspects in which our model calculation complement other derivations of blackbody radiation spectrum without quantum assumptions.

Keywords

Radiation Model Calculation Electromagnetic Field Quantum Statistic Spectral Distribution 
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.

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References

  1. 1.
    J. Tersoff and D. Bayer, “Quantum statistics for distinguishable particles,”Phys. Rev. Lett. 50, 553 (1983).Google Scholar
  2. 2.
    H. M. FranÇa and T. W. Marshall, “Excited states in stochastic electrodynamics”.Phys. Rev. A 38, 3258 (1988). See also K. Dechoum and H. M. FranÇa. “Non-Heisenberg states of the harmonic oscillator,”Found. Phys. 25, 1599 (1995).Google Scholar
  3. 3.
    T. W. Marshall, “Random electrodynamics”,Proc. R. Soc. (London) 276A, 475 (1963). See also T. H. Boyer, “General connection between random electrodynamics and quantum electrodynamics for free electromagnetic fields and for dipole oscillator systems”,Phys. Rev. D 11, 809 (1975) and T. H. Boyer, in “Foundations of Radiation Theory and Quantum Electrodynamics”, A. O. Barut, ed. (Plenum, New York, 1980), pp. 49–63.Google Scholar
  4. 4.
    L. de la Peña. “Stochastic electrodynamics: its development, present situation and perspectives,” in “Stochastic Processes Applied to Physics and Other Related Fields” B. Gomes, S. M. Moore, A. M. Rodrigues-Vargas, and A. Rueda, eds. (World Scientific, Singapore, 1982), p. 428. See also P. W. Milonni, “Semiclassical and quantumelectrodynamical approaches in nonrelativistic radiation theory,”Phys. Rep. 25, 1 (1976).Google Scholar
  5. 5.
    A. V. Barranco, S. A. Brunini, and H. M. FranÇa, “Spin and paramagnetism in classical stochastic electrodynamics,”Phys. Rev. A 39, 5492 (1989), and H. M. FranÇa, T. W. Marshall, and E. Santos, “Spontaneous emission in confined space according to stochastic electrodynamics,”Phys. Rev. A 45, 6436 (1992).Google Scholar
  6. 6.
    J. Dalibard. J. Dupont-Roc, and C. Cohen-Tannoudji, “Vacuum fluctuations and radiation reaction: identification of their respective contributions.”J. Phys. 43, 1617 (1982). See also P. W. Milonni, “Different ways of looking at the electromagnetic vacuum”.Phys. Scrip. T21, 102 (1988).Google Scholar
  7. 7.
    P. W. Milonni,The Quantum Vacuum: an Introduction to Quantum Electrodynamics, (Academic Press, Boston. 1994). Chaps. 1, 2, and 8. L. de la Peña and A. M. Cetto,The Quantum Dice. An Introduction to Stochastic Electrodynamics (Kluwer, Dordrecht, 1996).Google Scholar
  8. 8.
    A. Pais, “Einstein and the quantum theory,”Rev. Mod. Phys. 51, 863 (1979).Google Scholar
  9. 9.
    A. V. Barranco and H. M. FranÇa, “Einstein-Ehrenfest's radiation theory and Compton-Debye's kinematics,”Found. Phys. Lett. 5, 25 (1992); and “Stochastic electrodynamics and the Compton effect”.Phys. Essays 3, 53 (1990).Google Scholar
  10. 10.
    See Refs. 3 and 4 and also the papers by R. Schiller and H. Tesser, “Note on fluctuations,”Phys. Rev. A 3, 2035 (1971) and A. A. Sokolov and Tumanov, “The uncertainty relation and fluctuation theory”.Sov. Phys. (JETP) 3, 958 (1957).Google Scholar
  11. 11.
    S. Bergia, P. Lugli, and N. Zamboni. “Zeropoint energy, Planck's law and the prehistory of stochastic electrodynamics, part 2: Einstein and Stern's paper of 1913”.Ann. Found. Louis de Broglie 5, 39 (1980).Google Scholar
  12. 12.
    H. M. FranÇa and G. C. Santos, “The extended charge in stochastic electrodynamics”,Nuovo Cimento 86B, 51 (1985). See the Appendix.Google Scholar
  13. 13.
    T. H. Boyer, “Classical statistical thermodynamics and electromagnetic zero-point radiation”.Phys. Rev. 186(5), 1304 (1969).Google Scholar
  14. 14.
    S. Chandrasekhar, “Stochastic problems in physics and astronomy,”Rev. Mod. Phys. 15, 1 (1943). See Appendix IV, p. 83.Google Scholar
  15. 15.
    S. Bose, “Planck's law and the light quantum hypothesis”.Am. J. Phys. 44, 1056 (1976). This is an English translation of the original 1924 paper.Google Scholar
  16. 16.
    R. Blanco. H. M. FranÇa, and E. Santos, “Classical interpretation of the Debye law for the specific heat of solids.”Phys. Rev. A 43, 693 (1991).Google Scholar
  17. 17.
    D. Cole, “Reviewing and extending some recent works on stochastic electrodynamics.” inEssays on the Formal Aspects of Electromagnetic Theory, A. Lakhtakia, ed., (World Scientific Publ. Co., Singapore, 1993), pp. 501–532. See also D. Cole, “Possible thermodynamic law violations and astrophysical issues for secular acceleration of electromagnetic particles in vacuum.”Phys. Rev. E 51, 1663 (1995).Google Scholar
  18. 18.
    M. J. Klein, in “Paul Ehrenfest”. Vol. 1 (North-Holland, Amsterdam, 1985). See Chap. 10, “The essential nature of the quantum hypothesis”.Google Scholar
  19. 19.
    M. O. Scully and M. Sargent III, “The concept of the photon,”Phys. Today, March 1972, p. 38. See also W. E. Lamb, Jr., “Anti-photon,”Appl. Phys. B. 60, 11 (1995).Google Scholar
  20. 20.
    R. Kidd, J. Ardini. and A. Anton, “Evolution of the modern photon,”Am. J. Phys. 57, 27 (1989): “Compton effect as a double Doppler shift,”Am. J. Phys. 53, 641 (1985).Google Scholar
  21. 21.
    P. Grangier, G. Roger, and A. Aspect, “Experimental evidence for a photon anticorrelation effect on a beam splitter: a new light on single-photon interferences,”Europhys. Lett. 1, 173 (1986).Google Scholar
  22. 22.
    T. W. Marshall and E. Santos. “Comment on ‘Experimental evidence for a photon anticorrelation effect on a beam splitter: a new light on single-photon interferences’”.Europhys. Lett. 3, 293 (1987): “Stochastic optics: a reaffirmation of wave nature of light.”Found. Phys. 18, 185 (1988): “The myth of the photon,” preprint. University of” Manchester. October. 1995.Google Scholar
  23. 23.
    R. Lange, J. Brendel, E. Mohler, and W. Martiensen, “Beam splitting experiments with classical and with quantum particles,”Europhys. Let. 5, 619 (1988). See also J. Brendel, S. Schütrumpf, R. Lange, W. Martienssen. and M. O. Scully, “A beam splitting experiment with correlated photons,”Europhys. Lett. 5, 223 (1988): F. De Martini and S. Di Fonzo, “Transition from Maxwell Boltzmann to Bose Einstein partition statistics by stochastic splitting of degenerate light.”Europhys. Lett. 10, 123 (1989).Google Scholar
  24. 24.
    W. Nernst, “An attempt to return, from the quantum considerations, to the hypothesis of continuous changes in energy.”Verh. Dtsch. Phys. Ges. 18, 83 (1916).Google Scholar
  25. 25.
    T. H. Boyer, “Derivation of blackbody radiation spectrum without quantum assumptions.”Phys. Rev. 182, 1374 (1969).Google Scholar
  26. 26.
    T. H. Boyer, “Derivation of the Planck radiation spectrum as an interpolation formula in classical electrodynamics with classical electromagnetic radiation.”Phys. Rev. D 27, 2906 (1984). See also “Reply to ‘Comment on Boyer's derivation of the Planck spectrum’”.Phys. Rev. D 29, 2477 (1984).Google Scholar
  27. 27.
    T. H. Boyer, “Derivation of the blackbody radiation spectrum from the equivalence principle in classical physics with classical electromagnetic zeropoint radiation,”Phys. Rev. D 29, 1096 (1984).Google Scholar
  28. 28.
    O. Theimer and P. R. Peterson, “Statistics of classical blackbody radiation with ground state,”Phys. Rev. D 10, 3962 (1974).Google Scholar
  29. 29.
    M. Surdin, P. Braffort, and A. Taroni, “Black-body radiation law deduced from stochastic electrodynamics,”Nature 23, 405 (1966).Google Scholar
  30. 30.
    J. L. Jiménez, L. de la Peña, and T. A. Brody, “Zero-point term in cavity radiation.”Am. J. Phys. 48, 840 (1980).Google Scholar
  31. 31.
    A. M. Cetto and L. de la Peña, “Continuous and discrete aspects of blackbody radiation.”Found. Phys. 19, 419 (1989).Google Scholar
  32. 32.
    A. Rueda, “Behavior of classical particles immersed in the classical zeropoint field,”Phys. Rev. A 23, 2020 (1981): see Sec. IV-B.Google Scholar
  33. 33.
    R. Payen, “Champs electromagnétiques aléatories: formalisme général et obtention de la loi de radiation de Planck.”J. Phys. 45, 805 (1984).Google Scholar
  34. 34.
    R. H. Koch, D. J. Van Harlingen, and J. Clarke, “Observation of zero-point fluctuations in a resistively shunted Josephson tunnel junction”,Phys. Rev. Lett. 47, 1216 (1981).Google Scholar
  35. 35.
    S. Haroche and J. M. Raimond, “Cavity quantum electrodynamics”.Sci. Am. 26, April 1993.Google Scholar
  36. 36.
    P. W. Milonni and M. L. Shih, “Casimir forces”.Contemp. Phys. 33, 313 (1993). See also T. H. Boyer, “Quantum zeropoint energy and long-range forces.”Ann. Phys. 56, 474 (1970).Google Scholar
  37. 37.
    Armin Hermann,The Genesis of the Quantum Theory (1899–1913) (MIT Press, Cambridge, 1971). See the Introduction and Chapter 1.Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • H. M. FranÇa
    • 1
  • A. MaiaJr.
    • 2
  • C. P. Malta
    • 1
  1. 1.Instituto de FisicaUniversidade de SÃo PauloSÃo Paulo, SPBrazil
  2. 2.Instituto de Matemática. Estatistica e CiÊncia da ComputaÇÃoUniversidade Estadual de CampinasCampinas, SPBrazil

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