View source for Is Brownian motion really 100 percent random(q)


cobaltfjord@aol.com (CobaltFjord) wrote in message news:<b21nju$t59$1@panther.uwo.ca>...

I will respond in the order of importance
> High entropy randomness is not the same kind of
> randomness as QM randomness, right?  What is
> the difference?
>
No.  Classical randomness is not the same as quantum randomness.

Roughly speaking, classical randomness is a way to account for the unknown  input variables.

For example, classically,  you are 100% allowed to keep track of the particles in a gas.  It's just it is easier to deal with them if you catagorize them random.

For example, think of rolling a ball down the valley. Classically, the more and more you can account for every ups and downs and friction of the cliff, you may be able to predict the 'exact' position where the ball is going to fall.

On the other hand, you can choose a model of the valley by choosing a probabilitistic model of the distribution of the bumps. From that model, you will be to calculate, the average position where the ball stops and the probability that it lands x distance away from that average position.

On the other hand, quantum mechanically, no matter, how hard you try, you will never know all properties of the particle exactly. This knowledge is forbidden by the uncertainty principle. In a way, even though you may be able to build powerful instruments or powerful computational devices, you will never know what will 'exactly' happen in the next instant.

> Couldn't we predict motion of a single molecule over
> some arbitrarily small distance, over some arbitrarily
> small time period?
Within the classical paradigm, this is possible. However,  quantum mechanics tells you this cannot be done.

> Do molecules in Brownian Motion take a 100% random
> walk, or is their motion just causal, but unpredictable,
> deterministic chaos?
Chaos is a good word to describe it. Deterministic systems can also behave compeletely chaotically.

An example is Windows 98. Since Windows 98 runs a computer, the flow of the program is determinstic. However, it does 'randomly' crash from time to time for 'unknown' reasons. It is possible, that with enough variables, you can figure out when it is going to crash. However, it is easier to model it as a random system ;-)

>
> Don't molecules in a liquid or a gas move as a result
> of the forces they encounter?  Or do they move, as if
> Newton's First and Second Laws of Motion did not exist?
> Are Newton's First and Second laws of motion refuted
> by the laws of thermodynamics?

http://scienceworld.wolfram.com/physics/BrownianMotion.html

> Obviously, Newton's
> Laws refer to single bodies, and thermodynamics refers
> to a very large number of bodies, but doesn't there
> need to be any consistency between the two?
>

They are not inconsistant, as far as i know and have come to know. For example, think of the following relation.

1/2 m <v>^2 = 1/2 kT


>
> George Gamow wrote that liquid and gas molecules do,
> in effect, take a random walk and that we can calculate
> the probability of all the air in any room suddenly gathering
> to some random place in the room, in some arbitrarily
> small volume. Do air molecules move contrary to
> Newton's First and Second Laws of Motion, ignoring
> the repellent electrical forces of their atomic shells?
> What am I missing?
>
Not really, George Gamow, carefully chose his words. Remember that he tell that you can calculate the ''''''probability'''''' that all air molecules suddenly gather in arbitarily small volume.

To translate his statement (into some else's statement), giving 1000 monkeys, a 1000 typewriters, for a 1000 000 000 years, there is probability that one of those monkey will have typed 'to be or not to be'.

> Is it theoretically possible for all the matter and
> energy in the universe to suddenly gather into
> some arbitrarily small volume?  If air molecules
> can overcome the repellent electrical forces
> of their atomic shells without any external force
> being applied, can't matter and energy overcome
> the forces that hold things together?

Keyword is 'possible'.

> In fact,
> if I am not mistaken, I think Roger Penrose makes
> this claim.  It seems he looks at matter and
> energy in the universe as being completely
> determined by the laws of chance, that all the
> energy and matter could suddenly find itself in
> the same place, and produce a big bang, this
> possibility occupying a certain position in some
> probabilistic phase space.
>
>
-suresh