Quizatzhaderac wrote:While scientists have a tendency to define the the macro-states in terms of the micro-states, knowledge ultimately goes the other way: We know the macro system first, and we learn the micro system through careful analysis/ experimentation with the macro system. So when we find a disjoint between the two, we have to throw out the micro-system, not the macro-system. It's unlikely that statistical mechanics is wrong, it's much more ridiculous to say that classical thermodynamics is anything but close to right for common occurrences. (You put something in the oven to make it hotter? Don't you know they proved that's impossible?)Post by Eebster the Great wrote:since the variables that we use simply would not be macroscopic variables
What are you talking about? On the one hand, you say we throw out the microstate, not the macrostate. On the other hand, you say that because of the UV catastrophe, classical thermodynamics is useless. I don't get it. Can you be more specific abut what you mean?
Classical thermodynamics actually does make extremely good predictions within its domain of validity. It's just that high frequency radiation isn't in that domain. It can still explain why your oven heats your food, and it can even do it to a high degree of accuracy, as long as you only integrate up through visible light.
As for "throwing out the microstate," well you don't know the microstate, so there is nothing to throw out. Microstates are not observable, only macrostates. My contention was that in a universe in which the set of variables we use to define our macrostate would result in a definition of entropy that could decrease, such a universe would not use our variables, because they would not define a macrostate according to subjective experience.
I'm not sure what you mean by this. A object with negative temperature can be arbitrarily large.This is I think an example of a failure of the continuum limit.
But it cannot have arbitrarily many available energy levels. It is a fundamentally quantum phenomenon.
Not really, no. Naively counting motive degrees of freedom gets us to a good approximation; counting game of life microstates won't get you within an order of magnitude.Isn't that a practical reality anyway?
The game of life is discrete and doesn't really have macrostates. It is also not random. Most states are impossible, at least after a single generation. But of the states that are possible, how do you know that at the largest scales they don't all seem essentially uniform and random? It is only when you look at the finer details of just exactly how all the persistent elements work together to maintain their shape that you can distinguish between one microstate and another.