Please see below. -- Russ
> But my underlying point still stands: that when > characterizing a physical system (with concepts like entropy and > thermodynamics as a whole), one has to choose the layers or aspects they > want to pay attention to. If the characterization is intended to > capture the details of every particular element (boson, lepton, virtual > particle pair, etc. in its position, velocity, spin, etc.), then the > description _would_ be as large as the universe, itself. There could be > no abstraction in such a characterization, making it useless as a model. > If all the particles were arrayed in a regular lattice, the description could be smaller than the universe itself. I thought that was the point of entropy. > When talking about an > increase in entropy for a single system, we compare the system at time > t_0 to that same system at time t_1. Even in that case, entropy is a > measure applied to 2 different systems. We often choose to call it the > same system and refer to it as changing state; but in practice, it's the > same measure used to compare 2 separate systems (non-causally derived > from measures of heat and causally derived from measures of the states > of its constituents). > > The observer is necessary to do the measuring. If the observer is > _inside_ the system, then that results in an infinite regress. So, an > observer measuring the entropy of the universe from inside can, at best, > approximate (or show a bound for) the total entropy. And the only point > in placing the whole universe in that metric space (the entropy > quantity) is to compare it to other systems, subsets of itself or the > whole universe at different times. > > Whether it's one system or two, a messy arrangement takes more work to describe than a neat one. This is a perspective from outside the system, but it would seem to be a perspective in which entropy makes sense without having to say anything special about an observer. Of course whenever we say anything about anything there is an implied observer, but we don't complain about that in other contexts.
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