I know "Random motion" is non-deterministic unpredictable motion of a particle. But it seems "Brownian motion" has some form of determinism as we can predict the pattern created by path taken by particle in long term.
What's the main difference between these two kinds of motion?
Best Answer
Brownian motion has a very specific meaning: the motion of small particles suspended in a fluid. The motion is due to the random collisions between the molecules of fluid with the particles in suspension. So Brownian motion does not refer to the thermal motion of the molecules but is an effect of this molecular motion on particles much larger than one molecules. However the particles have to be small enough so that the effects of collisions with many molecules do not average to zero (or to values to small to matter). Both molecular motion and Brownian motion can be called "random" (or not) depending of the meaning we associate with this concept of "randomness". Ideally, if ones knows the positions and velocities of all molecules at a given time, we could in principle predict next configuration for both molecules and particles in suspension.
But if you consider thermal motion as an example of random motion, then Brownian motion is a more specific example of the general term "random motion".