Observation of Super-ballistic Brownian Motion in Liquid

Brownian motion is a foundational physical process characterized by a mean squared displacement that scales linearly in time in thermal equilibrium, known as diffusion. At short times, the mean squared displacement becomes ballistic, scaling as t^2. This effect was predicted by Einstein in 1907 and recently observed experimentally. We report that this picture is only true on average; by conditioning specific initial velocities, we predict theoretically and confirm by experiment that the mean squared displacement becomes super-ballistic, with a power scaling law of t^(5/2). This result is due to the colored noise of incompressible fluids, resulting in a non-zero first moment for the thermal force when conditioned on non-zero initial velocities. These results are a step towards the unraveling of nonequilibrium dynamics of fluids.