Quantum mechanics of the Einstein–Hopf model

The Einstein–Hopf model for the thermodynamic equilibrium between the electromagnetic field and dipole oscillators is considered within the framework of quantum mechanics. Essential to the consistency of the theory is the fluctuation–dissipation theorem connecting the radiation reaction with the zero-point electromagnetic field. The well-known ’’particle’’ term in the Einstein fluctuation formula is shown to be aconsequence of the quantum-mechanical zero-point oscillations of the field and the dipole radiators. Both the wave and particle aspects of the fluctuation formula are interpreted in terms of the fundamental absorption and emission processes.