Is Brownian Motion actually random or does it follow determinism?

[Lunct]

If you have enough information could you not determine with certainty the movements of pollen particles in water? In other words, if you were able to measure the movements the particles, then repeat the exact same experiment, with all things controlled, would the particles move in the same way?
I hope I have been able to explain myself well enough here.

 

[stevendaryl]

Brownian motion can be understood classically through statistical mechanics. The idea is that particles have a wide variety of velocities, and their velocities change constantly through collisions. So if a pollen grain is struck by a particle, it will be shoved in one direction or another. And it will seem completely random, because it's about as likely to get shoved in any direction.

Of course, quantum mechanics introduces yet more probability into the microscopic world.

 

[PeroK]

If you have enough information could you not determine with certainty the movements of pollen particles in water? In other words, if you were able to measure the movements the particles, then repeat the exact same experiment, with all things controlled, would the particles move in the same way?
I hope I have been able to explain myself well enough here.

You might to ask what you mean by "determine with certainty"?

And how could you "control" the position of $10^{25}$ water molecules in every litre?

 

[Lunct]

You might to ask what you mean by "determine with certainty"?

And how could you "control" the position of $10^{25}$ water molecules in every litre?

What I mean is that you can calculate the position of where the particles will be with the same certainty as an apple falling to the ground when your drop it.

I mean that you control all the variables so they are the same for each repeat, and it's a hypothetical.

 

[Wes Tausend]

You can determine the outcome to an extent. Think of the particles like pool balls on a table in a game of eight-ball.

So you 'break' the tight 'rack' of pool balls that you opponent has carefully 'racked' for you. The momentum of the cue ball strikes the triangular shaped numbered ball assembly and transfers energy to all of them. The balls then move in varied directions, some striking the rubber banks and perhaps then striking one another. Actually, if one paid close attention to the initial geometry of the rack and initial geometry of the cue ball strike (and spin), the balls do closely follow a predetermined pattern. But how close need you pay attention to the prerequisites for every game that men might play?

Close counts in eight-ball pool because the pockets are so large. Some pool tables do have tighter pockets, billiard tables for instance. Suppose they became extremely tighter. Then tighter yet. One can see that it currently seems to become impossible to find an end to the ultra precision nuances of fine tuning for small enough pockets.

I think that is the crude version of why Brownian Motion is still done with probability and statistics. It doesn't prove that it must be this way, so much as we don't know any better yet and maybe never will. It's not even important as long as our 'games' do not require ever tighter pockets, so tight that we cannot guess at the likely answer with ever smaller probabilities of larger probabilities.

Of course some think the gods do not play pool, and mess with the minds of mortals, but then what would they do for recreation, I ask?

Wes

 

[PeroK]

What I mean is that you can calculate the position of where the particles will be with the same certainty as an apple falling to the ground when your drop it.

If you have a water container that is smaller than an apple, then you'd know where all the water molecules were to within the dimensions of an apple.

To make a better comparison, what about the certainty of where an apple will end up if a) there is a strong wind and b) the ground is rough?

Also, if you drop an apple once, you probably smash it up a bit and it's not available in the same state for a second attempt. Am I looking at this the wrong way?

In general, a lot of people seem to see determinism and predictablity everywhere and are offended when an experiment, such as Brownian motion, seems to go against this. I must admit I see unpredictability everywhere, except in a few simple cases. And even then, in many cases, such as power from a wall socket, it's a statistical predictability.

 

[Lunct]

If you have a water container that is smaller than an apple, then you'd know where all the water molecules were to within the dimensions of an apple.

To make a better comparison, what about the certainty of where an apple will end up if a) there is a strong wind and b) the ground is rough?

Also, if you drop an apple once, you probably smash it up a bit and it's not available in the same state for a second attempt. Am I looking at this the wrong way?

In general, a lot of people seem to see determinism and predictablity everywhere and are offended when an experiment, such as Brownian motion, seems to go against this. I must admit I see unpredictability everywhere, except in a few simple cases. And even then, in many cases, such as power from a wall socket, it's a statistical predictability.

I would much prefer if determinism is incorrect actually, because if it is, it follows that we have no free will, which, at least for me, is an incredibly uncomfortable conclusion. However, I still call into doubt the supposed "randomness" of Brownian motion. If there are specific variables that determine where the particle will end up, impact force, angle ect. then surely it follows that it can't be random.

 

[anorlunda]

Your question is essentially the same as "Why can't we have perfect weather forecasts infinitely far into the future?"

You are also far from the first to ask this philosophical question. See
https://en.wikipedia.org/wiki/Pierre-Simon_Laplace#Laplace's_demon

True, QM refutes that view. But even without QM, we have chaos theory. And even without chaos we have nonlinearities in physics.

I like to think of it like a digital time simulation. As long as our knowledge is imperfect, there will be some inaccuracies in the results of the first time step. Those become the initial conditions for the second step which inevitably magnifies the inaccuracies in the second step, and so on.

Unless there are feedback mechanisms that limit the size of the errors, errors and uncertainties grow without limit until the only tools we have to study them are stochastic; as if they were random. It is not that the process itself is random (like throwing dice), but rather that the results inevitably become randomized.

In many real world simulations (think of a flight simulator) there are many feedback loops that limit the inaccuracies.

The second law of thermodynamics is closely associated with the same kinds of thinking. Thermalized and randomized are two words with associations.

But to complete the loop. If we scratch deeper and deeper, then we do see that QM indeed lies at the bottom of everything, and that is the ultimate answer.

 

[Lunct]

Your question is essentially the same as "Why can't we have perfect weather forecasts infinitely far into the future?"

You are also far from the first to ask this philosophical question. See
https://en.wikipedia.org/wiki/Pierre-Simon_Laplace#Laplace's_demon

True, QM refutes that view. But even without QM, we have chaos theory. And even without chaos we have nonlinearities in physics.

I like to think of it like a digital time simulation. As long as our knowledge is imperfect, there will be some inaccuracies in the results of the first time step. Those become the initial conditions for the second step which inevitably magnifies the inaccuracies in the second step, and so on.

Unless there are feedback mechanisms that limit the size of the errors, errors and uncertainties grow without limit until the only tools we have to study them are stochastic; as if they were random. It is not that the process itself is random (like throwing dice), but rather that the results inevitably become randomized.

In many real world simulations (think of a flight simulator) there are many feedback loops that limit the inaccuracies.

The second law of thermodynamics is closely associated with the same kinds of thinking. Thermalized and randomized are two words with associations.

But to complete the loop. If we scratch deeper and deeper, then we do see that QM indeed lies at the bottom of everything, and that is the ultimate answer.

Surely it doesn't matter what we can know about the particles, as they have determined positions outside of our knowledge.
And yes I am aware of Laplace's Demon. Philosophy and Physics are both equally my main interests.

 

[anorlunda]

Surely it doesn't matter what we can know about the particles, as they have determined positions outside of our knowledge.

It isn't about the particles at all. It is about the tools we have to model their behavior.

We avoid philosophy here at PF, no matter how compelling. So if you really want to discuss free will yes/no, PF is the wrong place to do it.

 

[PeroK]

Surely it doesn't matter what we can know about the particles, as they have determined positions outside of our knowledge.

How do you know that? By definition, if it's outside our knowledge you cannot know it.

 

[Nugatory]

... they have determined positions outside of our knowledge.

That is an assumption, not an experimentally verifiable fact or a conclusion logically derived from universally accepted first principles. It works really well for all the macroscopic objects for which we have direct experience (so well that it would be perverse to reject the assumption) but becomes problematic in several ways when dealing with objects small enough that quantum effects become relevant.

 

[Lunct]

How do you know that? By definition, if it's outside our knowledge you cannot know it.

Yeah that's fare. You're right.