[VadeRetro]

Naturally, Brownian motion shows that even a classical system is completely non-predictable (even in principle) if molecules exist.

Supposedly the classical physics "arrow of time" is non-reversible, but I always wondered if this isn't still in principle deterministic. In a sealed vaccuum container, you introduce three sealed bottles. Two contain vaccuums themselves, the third is full of gas. You open all the bottles and the gas from one rapidly fills the bigger container. Tah-dah! You cannot tell which bottle the gas came from, so the arrow of time is irreversible, etc.

I tend to think that God or even a really jazzy supercomputer could unravel it. The information is always there at any given time (in the position and momentum of each gas particle) to unravel the previous state of the gas. Never mind how you know the position and momentum of every gas particle. If you do, you know what it last bounced off of and when.

So you can get to the state of the machine a millisecond ago. Then you can use that to go back a millisecond from there. There is no creeping uncertainty in this process since we're using theoretical knowledge rather than physical measurements with error bars. So the information is still there in theory, but it's very much in theory.

Happily, the classical physics of little balls clacking around into each other is dead, so we can stop torturing ourselves over it.

[ahayes]

In a sealed vaccuum container, you introduce three sealed bottles. Two contain vaccuums themselves, the third is full of gas. You open all the bottles and the gas from one rapidly fills the bigger container. Tah-dah! You cannot tell which bottle the gas came from, so the arrow of time is irreversible, etc.

Try reading the labels. ;-)