I still don't get it, but that's not for lack of clarity on your part, Dave, for your write-up is excellent.
Rather, it's like when you try to explain to somebody that "one plus one equals two" and they say "I don't get it." At some point you just have to give up. I do think that if I study this and think about it, I will eventually get it. But have a related question. I read recently about new theories of infinitely or nearly infinitely hot plasma existing in the picoseconds after the big bang. I have a hard time understanding what temperature even means in this context, since I've always thought of temperature as a measure of the wiggling around of atoms & molecules ( which understanding is to be emended by your explanation below, as soon as I've understood it). But in the primordial plasma, there were no atoms or molecules. So what does temperature even mean in this context. I expect that your explanation below covers this, but maybe not, ergo, this post. jrs On Jan 5, 2013, at 4:16 AM, Dave Long wrote: >> I don't understand this, at least as it is explained here. Somebody care >> to explain? > > Temperature is not (as we tend to think of it) a level, like the level of > water in a lake. > > Instead, it measures how the total energy in a system is divided up among its > parts. > > Statistically speaking, it's overwhelmingly likely that there's a > self-similar distribution of energies, with the ratio of higher energy > subsystems to lower constant. > > This constant[0] is related to the temperature[1], and in normal experience, > it goes between absolute zero, where there is "no" energy in the system and > hence all subsystems are in their lowest energy state, so there is no chance > to find any higher states; and an infinite temperature, where the energy in > the system is evenly divided between all possibilities and so it's equally > likely to find a higher energy subsystem as a lower. > > If, however, one locally prepares a system so that there are more higher > energy subsystems than lower ones, the probability of getting a higher-energy > subsystem is higher than that of a lower, and, because of the way we've > defined temperature[1] the math works out such that we see a *negative* > temperature. > > In fact, this is not "colder" than zero, it's "hotter"[2]. > > But it's not that unusual: the lasers in CD-players or laser pointers (we are > all old enough to remember these, right?) work because of a population > inversion[3], and anyone with a hydroelectric plant, or for that matter a > traditional dam-powered sawmill[4], also created negative temperature > situations. > > -Dave > > [0] it's possible to prepare systems that, strictly speaking, don't have a > "temperature" in this sense, because they have unusual distributions; but one > can usually come up with a "closest temperature" to a given distribution. > [1] the inverse of the logarithm of the constant, more or less > [2] a very rough rule of thumb is that chemical reactions double their speed > with each 10 degree (C or K) increase in temperature, because it's > increasingly likely to find molecules with sufficient activation energy > (think of this as an "up-front cost" or "barrier to entry") as temperature > increases, and is why chemists are commonly pictured with hot plates and > bunsen burners. > [3] working lasers have a negative temperature component all the frickin' time > [4] where locally there is more water above the turbine or grindstone than > below it, even though globally more water is in the oceans than above... > >
