Average Randomness Thought experiment

1. Jul 23, 2012

ImaBeast

"Average Randomness" Thought experiment

Please bear with my explanation, I am, by no means a Physicist.

During a recent theoretical thought experiment, I thought of a strange factor that I feel I should let out before it becomes forgotten by the constant wave of thought experiments that flow through my mind.

Lets say we have an object, that is being acted upon, by a random force.
For example a particle, in space, and the force would be someone pushing it slightly in any & all given (random) directions....
Just assume the force to be equal on each push.

So the particle would kind of wobble in a three dimensional "sphere".

Now, if this happens for billions100 of "pushes" per second, for billions100 of years, and each movement were documented, wouldn’t it average out (statistically) eventually? Ultimately becoming predictable?

2. Jul 23, 2012

Mark M

If the pushes were totally random, then by definition, you would never be able to predict the exact push. You could, however, begin to predict the probability that a certain push occurs.

Similarly, in quantum mechanics, the most information you can give about a particle prior to your observation is the probability of the particle being in a certain state, since wavefunction collapse is totally random.

3. Jul 23, 2012

rorix_bw

Re: "Average Randomness" Thought experiment

In computer [STRIKE]programming[/STRIKE] science this is called a "random walk".

Simulating it results in the particle moving from its starting place and on average, increasing its distance from its starting location as time continues. (Because if two events combine to move it, it takes an exact combination of the same 2 events to put it back, and that doesn't likely happen).

All you can really predict is that "after N seconds, the ball is somewhere between X and Y distance of its start point" edit: Where X and Y are proportional to N.

Maybe the mathematicians on here can do better than me.

4. Jul 23, 2012

Staff: Mentor

Re: "Average Randomness" Thought experiment

This actually happens in what is called "diffusion" or "Brownian motion". Yes, although the path of an individual particle at a given time is unpredictable, averaged out over a long time for one particle or over a shorter time for a lot of particles the average becomes predictable.

5. Jul 23, 2012

Staff: Mentor

Re: "Average Randomness" Thought experiment

The total integrated movement based on all "pushs" is linear with time, but the average (expected) distance from the original position grows with the square root of time. This is the "predictable" part: Give it 10^1000 pushs, and you can expect to find it somewhere within 10^500 push-distances from the origin with a high probability.