A comparison between the harmonic oscillators with and without the vacuum field. Top: without any external force except for the vacuum field, the SED harmonic oscillator undergoes a motion that results in a Gaussian probability distribution. This motion is investigated with our simulation. Bottom: in the absence of the vacuum field or any external drive, a harmonic oscillator that is initially displaced from equilibrium performs a simple harmonic oscillation with constant oscillation amplitude. The resulting probability distribution has peaks at the two turning points.