Brownian motion

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Like the Brownian motion in a cup of tea: not only is a spontaneous lurch of all participants in one direction at once unlikely, it is impossible. The Brownian collision that sends one molecule to the left must send another to the right.

For every molecule to go left at once defies the laws of physics. Physics requires independently-interacting particles to move in offsetting directions. Hence the emergent stability of a a stationary cup of tea. Independent events that interact with each other tend to cancel each other out. Interdependent events — at least those propelled by the autonomous, self-aware animal minds don’t. They can void collisions. They can turn and run in the same direction as oncoming traffic. Tea molecules can’t jump out of the tea-cup at the same time. Participants in a securities market can and, from time to time, do.

According to Newton's third law of motion, for every action, there is an equal and opposite reaction. This principle ensures that the total momentum of an isolated system remains constant unless acted upon by external forces.

In the context of collisions between particles, if particle A experiences a force in one direction due to a collision, there must be an equal and opposite force on particle A' as a result of the same collision. This conservation of momentum holds true.

However, it's important to note that while the conservation of momentum is satisfied at the system level, the individual trajectories of particles are still influenced by random thermal motion, Brownian motion, and the probabilistic nature of quantum mechanics. Therefore, while the overall momentum of the system is conserved, the specific paths and velocities of individual particles are subject to statistical uncertainty.

In other words, while it might be improbable for all particles to collectively move in the same way at the same time due to the random nature of individual particle motions, the conservation of momentum ensures that the sum of all these individual motions complies with the laws of physics. So, at a macroscopic level, momentum is conserved even if the individual trajectories are unpredictable.

Yes, you are correct. If we consider a system of randomly colliding particles subject to the laws of physics, including the conservation of momentum, it would be logically impossible for all particles to move in the same direction at the same time. The inherent randomness and probabilistic nature of particle motion, combined with the principles of physics, make such a scenario logically impossible.