Brownian Motion of Atoms: Our limited Approach

Brownian Motion: The Random motion of atoms in space is called Brownian Motion.

We have been taught that atoms are in random motion. I don't say that this is wrong postulation but I also disagree that it is true to be a fact. In the passage below I will take a simple example that will simulate our view of the atoms' motion in space through a limited window (supposedly a microscope).

There is a room with a window that opens towards a playground. You sit in the room facing
the window. There is a table in the room just under the window. So you can not go near the
window.Therefore you can see everything ouside that comes within the area of window.

Now unknown to you, some students are playing a game in the playground.
Suppose 100 students stand to the left of the window and 100 students to the
right of the window. But you cannot see them as they are donot come in your view through the window. Each student has a rubber ball.Each child on left and right are
numbered 1 to 100 . The game they are playing is like this.From left side 1st child will throw the ball towards 1st child on the right.Then 1st child on right will catch the ball and will throw it
back to 1st child on left and so on for each child will continue to throw his ball to his
corresponding counterpart on both sides. The top view of the situation can be like this:
Go to This Link to see a diagram representation of above scenario





Note: You can only see straight through the window, so you cannot see the children, but if they throws balls from left to right or vice versa then you will see the different balls only.


Since while sitting in the room , far from the window, you can only see in line of window,
therefore you cannot see the children.You only see the balls moving from left to right and
right to left. Since the balls follow projectile path in actual but infront of your window
some balls will be in rising phase of their projectile path, some in falling phase of their
projectile path, some in horizontal phase of their projectile path (depending on the
throwing position of child and throwing velocity and angle).
What will appear to you is that some ball are going left, some right, some moving upwards,
some downwards, some horizontal. Although if you had known the complete picture the
projectile path of each ball could be calculated by you but since you only look out of a
small window the paths become random.
When any element has been studied, its atoms paths have either been traced through
microscopes or experiments involving detectors, lasers etc . In both cases we are looking at
the whole system through a hole( a limited window), in which every atom(ball) appears to
move randomly. We have no other choice also to look at the whole of the system at once
because due to large size difference, the velocity of atomic system's frame is different from
our frame's velocity. Even if elements are exchanging atoms in a calculated manner along calculated paths, in our microscope hole we only catch a small part of that path and say that it is
random.
Keeping the above analogy in view isn't it too much of an assumption. While we can
not see the whole path followed by an atom and are unaware of the rest of the motion in the
remaining sample, then also we start believing that atoms have random motion.

Isn't it wonderful that most of our laws assume random motion of atoms and isn't it more
wonderful that they still seem to work in practical situations.