Understanding Randomness in Brownian Matter

[EntropicThinker]

TL;DR

Can Brownian motion be predicted with advanced computing, and what implications does quantum mechanics have on its apparent randomness?

Video on Brownian matter that got me thinking

Brownian motion is a fundamental concept in physics, describing the random movement of particles suspended in a fluid. However, the apparent randomness of this motion is largely due to our limited understanding and computational power. As computational capabilities continue to advance, will it be possible to accurately predict the movement of particles in Brownian motion? If so, would this imply that the motion is deterministic, and what role would quantum mechanics play in our understanding of this phenomenon?

 

[Frabjous]

A cubic cm of water weighs about 1 gram.
Water weighs around 18gm/mole.
So there are around 3*10²² molecules of water in a cubic cm.
Computational capabilities are nowhere near this.

 

[FactChecker]

It's not just the computational power that is needed. A completely accurate prediction would require complete knowledge of the type, initial position, and initial velocity of every molecule.
(Water molecules move at over 1,000 mph on average in room-temperature water. So every molecule needs to be considered. There are about 1.5 sextillion molecules in a drop of water. So that is a lot of initial data to determine.)

 

[Nugatory]

Google for “Laplace’s Demon”.
If classical mechanics applied at arbitrarily small scales, and we had unlimited computing power, and we had exact knowledge of all the initial conditions…. Then yes, we could predict the exact trajectory of every particle in a body of fluid. But we don’t have infinite computing power and even if we did classical mechanics doesn’t apply at sufficiently small scales and quantum mechanics says that there is no such thing as exact knowledge of the classical initial conditions.

So no, we cannot and never will be able to exactly predict the trajectories of quantum particles the way that Laplace was imagining.

 

[EntropicThinker]

Google for “Laplace’s Demon”.
If classical mechanics applied at arbitrarily small scales, and we had unlimited computing power, and we had exact knowledge of all the initial conditions…. Then yes, we could predict the exact trajectory of every particle in a body of fluid. But we don’t have infinite computing power and even if we did classical mechanics doesn’t apply at sufficiently small scales and quantum mechanics says that there is no such thing as exact knowledge of the classical initial conditions.

So no, we cannot and never will be able to exactly predict the trajectories of quantum particles the way that Laplace was imagining.

Very insightful , thank you for your answer I appreciate it