No Way Back

Lubos takes on the second law, once again. Suppose we have a current state which we identify with an ensemble of compatible physical systems [UPDATE: Lubos points out that the usual term is macroscopically indistinguishable microstates - I had forgotten that]. If we evolve that ensemble of states forward in time, entropy increases for all but a tiny fraction of the systems making up the ensemble. What if we use the time symmetric laws of physics to evolve that same ensemble backwards, in the opposite time direction?

Once again, entropy increases for most of the systems of the ensemble. Lumo's paradoxical sounding explanation: that other way isn't really backwards in time, it's forward too!

This was a major brain warp for me, so I had to try rephrasing it. My version: representing a system by an ensemble of compatible states and identifying the future state of the system with the typical evolution of states in the ensemble is a good way to predict the future but a lousy way to retrodict the past. The asymmetry is not so glaring if we remember that the ensemble is not the real physical system, it's just a representation of our current knowledge of the state of the system. Forward or backward evolution of the microstates doesn't matter, since each gives a possible future.

In short, I'm pretty much a convert.

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