Smearing effect due to the spread of a probe-particle on the Brownian motion near a perfectly reflecting boundary

Quantum fluctuations of electromagnetic vacuum are investigated in a half-space bounded by a perfectly reflecting plate by introducing a probe described by a charged wave-packet distribution in time-direction. The wave-packet distribution of the probe enables one to investigate the smearing effect upon the measured vacuum fluctuations caused by the quantum nature of the probe particle. It is shown that the wave-packet spread of the probe particle significantly influences the measured velocity dispersion of the probe. In particular, the asymptotic late-time behavior of its $z$-component, $ < \D v_{z}^{2}>$, for the wave-packet case is quite different from the test point-particle case ($z$ is the coordinate normal to the plate). The result for the wave-packet is $<\D v_{z}^{2} > \sim 1/\t^2$ in the late time ($\t$ is the measuring time), in stead of the reported late-time behavior $<\D v_{z}^{2} > \sim 1/z^2$ for a point-particle probe. This result can be quite significant for further investigations on the measurement of vacuum fluctuations.