Foundations of Physics

, Volume 19, Issue 11, pp 1371–1383 | Cite as

Scaling symmetry and thermodynamic equilibrium for classical electromagnetic radiation

  • Timothy H. Boyer
Article

Abstract

At present classical physics contains two contradictory groups of derivations of the equilibrium spectrum of random classical electromagnetic radiation. One group of derivations finds Planck's spectrum based upon the use of classical electromagnetic zero-point radiation and fundamental ideas of thermodynamics. The other group of derivations finds the Rayleigh-Jeans spectrum from scattering equilibrium for non-linear mechanical systems in the limit of small charge coupling to radiation. Here we examine the scaling symmetries of classical thermal radiation. We find that, in general, classical mechanical systems do not share the scaling symmetries of thermal radiation. In particular, this is true for the mechanical scattering systems used in the derivations of the Rayleigh-Jeans law. Indeed, relativistic hydrogenlike systems with Coulomb potentials of fixed charge are the only mechanical potential systems which do share the scaling symmetries of thermal radiation. We propose that only these last mechanical systems are allowed in a classical electromagnetic description of nature.

Keywords

Mechanical System Thermal Radiation Classical Physic Fixed Charge Scatter System 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M. Born,Atomic Physics, 7th edn. (Hafner, New York, 1966), Chap. 8, Sec. 1; R. Eisberg and R. Resnick,Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles (Wiley, New York, 1974), Chap. 1.Google Scholar
  2. 2.
    T. H. Boyer,Phys. Rev. 182, 1374 (1969).Google Scholar
  3. 3.
    T. H. Boyer,Phys. Rev. 186, 1304 (1969).Google Scholar
  4. 4.
    T. H. Boyer,Phys. Rev. D 27, 2906 (1983);29, 2418 (1984).Google Scholar
  5. 5.
    T. H. Boyer,Phys. Rev. D 29, 1089, 1096 (1984);30, 1228 (1984).Google Scholar
  6. 6.
    T. H. Boyer,Phys. Rev. D 13, 2832 (1976).Google Scholar
  7. 7.
    T. H. Boyer,Phys. Rev. A 18, 1228 (1978).Google Scholar
  8. 8.
    L. Pesquera and P. Claverie,J. Math. Phys. 23, 1315 (1982).Google Scholar
  9. 9.
    R. Blanco, L. Pesquera, and E. Santos,Phys. Rev. D 27, 1254 (1983);29, 2240 (1984); R. Blanco and L. Pesquera,Phys. Rev. D 33, 421 (1986);34, 1114 (1986); R. Blanco, L. Pesquera, and J. L. Jimenez,Phys. Rev. D 34, 452 (1986).Google Scholar
  10. 10.
    H. A. Lorentz,The Theory of Electrons (Dover, New York, 1952). This is a republication of the 2nd edition of 1915. Note 6, p. 240, gives Lorentz's explicit assumption on the boundary conditions.Google Scholar
  11. 11.
    T. H. Boyer,Phys. Rev. D 11, 790, 809 (1975).Google Scholar
  12. 12.
    In ref. 11, p. 798.Google Scholar
  13. 13.
    H. A. Kastrup,Ann. Phys. (Leipzig) 9, 388 (1962).Google Scholar
  14. 14.
    H. A. Kastrup,Phys. Lett. 3, 78 (1962). See the remarks and footnote on page 78.Google Scholar
  15. 15.
    A. Sommerfeld,Thermodynamics and Statistical Mechanics (Academic Press, New York, 1956). See pages 140–145.Google Scholar

Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • Timothy H. Boyer
    • 1
  1. 1.Department of PhysicsCity College of the City University of New YorkNew York

Personalised recommendations