  We demonstrate experimentally that a Brownian particle is subject to inertial
effects at long time scales. By using a blinking optical tweezers, we extend
the range of previous experiments by several orders of magnitude up to a few
seconds. The measured mean square displacement of a freely diffusing Brownian
particle in a liquid shows a deviation from the Einstein-Smoluchowsky theory
that diverges with time. These results are consistent with a generalized theory
that takes into account not only the particle inertia but also the inertia of
the fluid surrounding the particle. This can lead to a bias in the estimation
of the diffusion coefficient from finite-time measurements. We show that the
decay of the relative error is polynomial and not exponential and, therefore,
can have significant effects at time scales relevant for experiments.
