Observation of the instantaneous velocity of a Brownian Particle

A notable feature of Brownian motion is that it is self-similar for all time scales. However, at short enough time scales, a particle at thermal equilibrium follows straight line trajectories with a well-defined velocity. The time scale at which the transition occurs between ballistic and Brownian motion is set by the momentum relaxation time, $\tau_p$. We have measured the position of an optically trapped particle in air with temporal resolution much faster than $\tau_p$, and have thus observed the transition between ballistic and diffusive Brownian motion and measured the instantaneous velocity of a Brownian particle for the first time. This has allowed us to directly verify the energy equipartition theory for Brownian motion. We are currently working towards observing the instantaneous velocity of a particle in water, for which $\tau_p$ is several orders of magnitude smaller.