Dynamics Underlying the Gaussian Distribution of the Classical Harmonic Oscillator in Zero-Point Radiation
Figure 7
Sampled oscillation amplitude and the reconstructed Gaussian probability distribution. Top: the oscillation amplitudes (red dot) are sampled from a steady-state trajectory (black) with a sampling time-step equal to , where is the coherence time. Middle: a magnified section of the trajectory shows that the sampling time-step (red dot) is . Bottom: using the amplitude distribution (red bar), a probability distribution (blue line) is constructed and shown to agree with the simulated Gaussian probability distribution (black dot). The simulated probability distribution (black dot) is offset by for better visualization. This result confirms that the underlying mechanism for the Gaussian probability distribution is the addition of a series of double-peak probability distributions according to the amplitude distribution given by the vacuum field. It is also worth noting that the most frequent oscillation amplitude in the amplitude distribution is at the half-maximum of the position distribution (black dot).
