Dynamics Underlying the Gaussian Distribution of the Classical Harmonic Oscillator in Zero-Point Radiation

Figure 5

Contributions of different oscillation amplitudes in the final probability distribution. Top: several sections (red) of a steady-state trajectory (black) are shown. A section is limited to the duration of the characteristic modulation time. The oscillation amplitude changes significantly beyond the characteristic modulation time, so different sections of the trajectory obtain different oscillation amplitudes. Bottom: the probability distributions of each section of the trajectory are shown. As the oscillation amplitude is approximately constant in each section, the corresponding probability distribution (red bar) is close to the classic double-peak distribution. The probability distributions in different sections of the trajectory contribute to different areas of the final probability distribution (black dashed line). The final probability distribution is constructed from the steady-state trajectory.