This question arose in the context of another discussion here: https://physics.stackexchange.com/questions/241247/semi-classical-calculation-gives-wrong-answer-for-emission I wanted to analyze the time-varying charge density of a heated tungsten filament, and Pisanty said I couldn't do it because the filament wasn't in a pure state, it was in a mixed state (a thermal state actually) so the chaarge density would be stationary. (Feel free to correct me if I am misrepresenting Pisanty's argument).
That discussion was shut down by the moderators, but it was somewhat continued here: Is there a charge density in quantum mechanics? where Pisanty elaborates on his reasons why you can't analyze the filament as a pure state.
I think he must be wrong. Isn't the whole universe in a pure state? Isn't a mixed state just something we use when we don't have (or don't want) all the detailed information? Pisanty defines the tungsten filament as a mixed state...specifically, a thermal state...and then concludes that the charge density must be stationary in time. I think he's wrong...I think he just threw away the information about the time-varying charge density when he chose to analyze the filament as a thermal state.
Isn't the filament actually in a pure state, with an enormously complicated time varying charge distribution? And if so, what is to stop us (in principle) from using Maxwell's Equations to analyze the resulting emission of radiation? Other than the fact that it might give us the wrong answer.
EDIT: It doesn't look like anyone wants to answer this: a few comments have ridiculed the notion that something as chaotic as a glowing filament could be in a "pure" state. Look, I don't like the terminology either, but I adopted it because it has a precise technical meaning as used by Pisanty in the previous discussions. A "pure" state (correct me if I'm wrong) is simply one for which the wave function is completely specified; that is, it is not a statistical mixture of various pure states. So a beam of silver atoms coming out of an aperture is, for practical purposes, in a "mixed" state of spins...half up and half down. This is different from a single atom being 1/2|up> + 1/2|down>, which is actually pure sideways.
So my question really is: isn't every system in the universe, including my tungsten filament, actually in a "pure" state...except for the fact that we simply aren't in a position to know the precise details of that state? So in cases where it doesn't make a difference, we treat it as a statistical mixture. Even the beam of silver atoms coming out of an aperture...yes, for our purposes it's a statistical mixture, but in fact isn't that beam itself in a pure state?
If no one wants to answer this I'm going to have to answer it myself.