In one minute

Timothy Boyer shows that a classical charged linear oscillator in classical electromagnetic zero-point radiation has a stable ground state and resonant excited states analogous to the quantum oscillator's. Because zero-point radiation is Lorentz invariant, any system reaching equilibrium in it must be at least approximately Lorentz invariant, and few potentials qualify. Finite wave speed means the charge must feel the full field at its actual position, not just the dipole approximation. In the resonant excited states, dipole radiation is balanced by energy absorbed from zero-point radiation at odd multiples of the oscillator frequency. The Bohr frequency condition appears naturally, giving a classical electromagnetic basis for the old quantum picture of electrons in classical orbits.

The classical linear oscillator in classical electrodynamics with classical zero-point radiation