Ballistic motion of a Brownian particle

Raizen and Li reply: We are aware of the excellent work by Jixiang Zhu and coauthors, which we referenced in a recent review article. ¹ Zhu and his team used dynamical light scattering to measure the mean square displacement ⟨Δr²(t)⟩ of concentrated particles at short time scales and from it determined the velocity autocorrelation function. A more recent experiment with optical tweezers reported a similar result. ² Neither of those prior experiments could resolve the instantaneous velocity of a Brownian particle, the topic of the 1907 paper by Albert Einstein. We stand by our assertion that the experiments reported in the Quick Study are the first such measurements.

The other work mentioned by Douglas Durian (his reference 2) examined the mechanical motion of a Ping-Pong ball in turbulent airflow. The researchers observed that the ball behaved like a Brownian particle and is a beautiful simulation with a macroscopic system. The effective temperature is on the order 10¹⁷ K, so that clearly is not the case discussed by Einstein, in which the Brownian motion is directly caused by the thermal fluctuations of molecules at the actual temperature of the system.