tlb wrote:Consider a box that initially contains only carbon dioxide at room temperature, where the main interaction between molecules is collisions. Seems straight forward, although there can be internal vibrations. Also there might be a possibility of a collision generating an oxygen molecule and two carbon monoxide molecules.
Uhh, no? CO2 is chemically stable at room temperature, it does not degenerate into 2 CO and O.
However, even though the molecules are not in the quantum level, they are light enough that there is a measurement problem. In order to get their initial values, they have to be hit with energy; which means that those initial values cannot be known to great precision. In turn that means the results of collisions cannot be predicted with almost any precision.
So the system (meaning the position and velocity of each molecule) cannot be predicted after any iteration that includes a significant number of collisions. By your definition, that means it is NOT deterministic. Only a probabilistic description can be made of it.
Okay, that's just the Heisenberg uncertainty principle though.
What I posited was a thought experiment: "What if we could know the initial state of a system to arbitrary position?"
As I mentioned upthread:
Leaving aside various proofs that show that a laplacian demon cannot exist due to fundamental limitations of performing computation and things like Heisenberg's uncertainty principle, I believe that in theory, a complete definition of the universe's ruleset can exist - whether or not human science will ever reach that point, who knows.
WE, as in literal actual humans living in this current year, cannot know the initial state of a system at subatomic precision, therefore we can't use that information to predict future iterations of said state.
However, we know that such a state does exist. Atoms and molecules have defined positions, energy states and movement vectors, and the interactions between them are governed by rules that are fairly well known (one such rule being that two CO2 molecules colliding at room temperature does not cause them to lose cohesion).
Therefore, an entirely theoretical observer that has the ability to get around the uncertainty principle could construct an accurate representation of the world state, apply known rules, and arrive at a prediction that - again, leaving aside that this is physically impossible - would allow such an observer to predict what would happen next, which would rule out free will as a concept.