- #36
Galteeth
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apeiron said:Again, the basis of the argument is that a microstates approach to modelling entropy cannot give you a global arrow of time. And that is really no surprise is it? The arrow is the emergent property of an entropy gradient. For a system at equilbrium, there is no gradient, and so no global macrostate change, and so no global property of "time" in a meaningful sense.
What Greene is arguing is that the Boltzmann ensemble model of entropy (and so interpretations of the second law made in those terms) only predicts what is the most probable state of a system - the maximum entropy of a system gone to general equilibrium. Now if we just take that statement in isolation, then we feel justified in saying that it is most probable that a systems is always at equilibrium. This in turn justifies us to say it is most probable that any system not yet at equilbrium is more likely to be a local fluctuation of some global state of equilibrium than that it is a global state of disequilbrium (lower entropy) still on its way to maximum entropy equilibrium.
What justifies all this is that no direction to time and change is wired into the Newtonian mechanical model of action. So even despite the observational evidence of everyday life and the big bang, we must look on this as most likely a story of local fluctuations from global equilibriums. Hence the Boltzmann brain if we just consider the occurence of our conscious awareness. Or various cosmological views which see the whole big bang as such a local fluctuation.
There is certainly a problem here about how to explain the observation that the universe originated in a state of low entropy. But philosophically, the extrapolation of micro-physical models to arrive at patent paradoxes like "fake memories" is not really getting us anywhere (except to show that this line of thinking is indeed pathologically self-defeating).
The message really is that we should look to what the models are omitting, which again is the macro-physical features of reality. We observe gradients and an arrow of time (that is what the second law actually talks about) and so why not extrapolate from them?
That was well put, but I still don't quite understand what Greene's point is as you've described it.
Statement A: that the Boltzmann ensemble model of entropy (and so interpretations of the second law made in those terms) only predicts what is the most probable state of a system - the maximum entropy of a system gone to general equilibrium.
Statement B:
Now if we just take (Statement A) in isolation, then we feel justified in saying that it is most probable that a systems is always at equilibrium.
Why?