That's not Brownian motion. That's not even physically accurate. Molecules in a solid don't move. If they do, it's a fluid, not a solid. Likewise, atoms in a molecule can't move relative to one another. A solid particle is essentially inert.
Atoms or molecules in a fluid are constantly moving. They bounce around but crucially they don't change direction unless they hit something or are interfered with by, say, a magnetic field. It is all these particles in the fluid that cause the Brownian motion. As all the particles move around they strike the solid particles (lipids in your video on page 1) and the net effect of the countless collisions causes a net movement in the solid, which constantly varies over time as all the fluid particles bounce around.
You appear to be suggesting that a particle could change direction on its own dependent on the vibrations of it's molecules. This is impossible, per Newton's laws of motion, specifically law number one, which states that a body remains at rest or at constant velocity unless acted upon by an
external unbalanced force. The motion of the individual molecules in a particle, were such a thing even possible, couldn't cause it to move or change direction as that is internal to the particle. Any resultant motion would be akin to one pulling oneself up by one's bootstraps - impossible.
My point with the antiparticles business was that you cannot have Brownian motion without a fluid. If it is occurring in a vacuum it is not Brownian motion. It could be like Brownian motion, but it is not caused by Brownian motion in the solid itself - the glass bead in the quantum vacuum - because you can't have Brownian motion in a solid. The reason I brought up the anti-particles business is because it could be that the observed motion is due to anti-particle pairs striking the glass bead and causing it to move, thus appearing tongi e the same effect as Brownian motion.
Seriously, go read the wikipedia article on Brownian motion, particularly the part where it describes the motion as:
wikipedia said:
the assumably random movement of particles suspended in a fluid