Blackbody Radiation, Conformal Symmetry, and the Mismatch Between   Classical Mechanics and Electromagnetism
  The blackbody radiation problem within classical physics is reviewed. It is again suggested that conformal symmetry is the crucial unrecognized aspect, and that only scattering by classical electromagnetic systems will provide equilibrium at the Planck spectrum. It is pointed out that the several calculations of radiation scattering using nonlinear mechanical systems do not preserve the Boltzmann distribution under adiabatic change of parameter, and this fact seems at variance with our expectations in connection with derivations of Wien's displacement theorem. By contrast, the striking properties of charged particle motion in a Coulomb potential or in a uniform magnetic field suggest the possiblity that these systems will fit with classical thermal radiation. It may be possible to give a full scattering calculation in the case of cyclotron motion in order to provide the needed test of the connection between conformal symmetry and classical thermal radiation. 
Timothy H. Boyer