3 ms·

Thanks! I had a chat with a mathematician friend today, and we came up with a fairly simple resolution actually that I'm pretty satisfied with: the trick here i

Thanks! I had a chat with a mathematician friend today, and we came up with a fairly simple resolution actually that I'm pretty satisfied with: the trick here is to stop thinking of particles as T-symmetric billiard balls, and just to assume that there exists microscopic T-asymmetric interactions. If we assume molecular chaos hypothesis (independent particle velocities prior to collision) and take into account probabilistic collisions occurring at the 2-particle microscopic level, then post-collision velocities are now dependent, thereby imposing an ordering to time. I have to think more about this though, and I'm still struggling with understanding the circular dependency between entropy "being time" and entropy being "caused" by "motion" (with respect to ... time?)

erostrate 7y ago
Why can't you assume time symmetric billiard balls? If you take a lot of them, black and white, put all the black ones on one side and the white on the other, give them random velocities, and wait a bit, you will end up with them all mixed together. The entropy has increased even though all interactions are reversible. The macroscopic transformation is time asymmetric (the balls will not sort themselves back again) even though the microscopic transformations are time symmetric (elastic collisions and frictionless movement). The way I think about this (from Feynman) is that entropy measures "how special" a macroscopic state is, on average. When you apply many microscopic independent fluctuations to a given state you are unlikely to end up with a "more special" state. That's how states are ordered at the macroscopic level giving the arrow of time a clear direction.
- ericjang 7y ago
  The macroscopic transformation is time asymmetric (the balls will not sort themselves back again) even though the microscopic transformations are time symmetric (elastic collisions and frictionless movement). I agree with your observation of what happens to the black and white billiards. My question is - if the interactions are all time-symmetric (implies conservation of entropy), where does the entropy come from in the macroscopic system? My belief is that the microscopic model is flawed; if we simply introduce some randomness into the collision dynamics of two particles (which is believable given particle accelerator experiments / QM), then microscopic interactions are no longer T-symmetric. It comes down to a philosophical interpretation of whether you can treat a system of two particles probabilistically (i.e. thermodynamically in aggregate) or not.

erostrate 7y ago

Why can't you assume time symmetric billiard balls? If you take a lot of them, black and white, put all the black ones on one side and the white on the other, give them random velocities, and wait a bit, you will end up with them all mixed together. The entropy has increased even though all interactions are reversible. The macroscopic transformation is time asymmetric (the balls will not sort themselves back again) even though the microscopic transformations are time symmetric (elastic collisions and frictionless movement). The way I think about this (from Feynman) is that entropy measures "how special" a macroscopic state is, on average. When you apply many microscopic independent fluctuations to a given state you are unlikely to end up with a "more special" state. That's how states are ordered at the macroscopic level giving the arrow of time a clear direction.

ericjang 7y ago
The macroscopic transformation is time asymmetric (the balls will not sort themselves back again) even though the microscopic transformations are time symmetric (elastic collisions and frictionless movement). I agree with your observation of what happens to the black and white billiards. My question is - if the interactions are all time-symmetric (implies conservation of entropy), where does the entropy come from in the macroscopic system? My belief is that the microscopic model is flawed; if we simply introduce some randomness into the collision dynamics of two particles (which is believable given particle accelerator experiments / QM), then microscopic interactions are no longer T-symmetric. It comes down to a philosophical interpretation of whether you can treat a system of two particles probabilistically (i.e. thermodynamically in aggregate) or not.