A classical harmonic oscillator radiates energy as it oscillates, spiraling to rest. This is the textbook prediction of classical electrodynamics: accelerating charges radiate, and radiation carries energy away. The oscillator should die.
Add classical zero-point radiation — a background electromagnetic field with energy (1/2)ℏω per mode — and the oscillator reaches equilibrium. It absorbs energy from the background at the same rate it radiates. The equilibrium energy levels are quantized: J = (n + 1/2)ℏ, where n is an integer. The ground state has energy (1/2)ℏω, matching the quantum result exactly.
No quantum mechanics was used. The oscillator is classical. The electromagnetic field is classical. The zero-point radiation is classical — it is simply a boundary condition on the electromagnetic field, specifying the spectral energy density of the background. The quantization arises from the balance between radiative loss and resonant absorption, which selects discrete energy levels as the only stable equilibria.
This is stochastic electrodynamics (SED): classical mechanics plus classical electrodynamics plus classical zero-point radiation. The program has been pursued since the 1960s, and this particular result — quantized action for a linear oscillator — has been known since Cole and Zou's numerical work. The contribution here is the explicit analytical demonstration of the equilibrium balance and the identification of the mechanism: the oscillator's radiation reaction creates a natural linewidth, and the zero-point radiation's spectral density at that linewidth determines the discrete energy levels.
The structural point is not that classical physics can reproduce quantum results — it can, for this system, and the limits of the correspondence are well known (anharmonic oscillators and multi-particle entanglement remain problematic). The point is that quantization is not inherently a statement about the nature of matter. It is a statement about equilibrium with a structured background. Change the background's spectrum, and you change the quantization. The discrete energy levels are a property of the relationship between system and environment, not of the system alone.