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 ... But in the
primordial plasma, there were no atoms or molecules.
As you suspected, this is covered by what I wrote. Note that I was
careful to say "Temperature ... measures how the total energy in a
system is divided up among its parts"[-1]. Concretely, atoms and
molecules are typical parts of typical systems, and they store energy
in their wiggling around[0]. Abstractly, however, all that matters
is defining the whole system and how it is divided into parts[1,2].
"temperature"...to me, it is ... the level of mercury in a nice old-
fashioned thermometer!
The catch is, as soon as you try to calculate with it, you'll
discover this view is not so useful. Take two disparate objects with
nice old-fashioned thermometers on them, and then put them together.
Knowing just the level of the mercury on each part beforehand isn't
enough to tell us at what level the two thermometers will eventually
come to agreement[3,4]. Keeping track of energy, one can do the
bookkeeping, and furthermore, with a bit more information about the
composition of these parts, one could then calculate either the
resulting temperature or the level of mercury.
In the case of a thermometer at an everyday temperature, John's
wiggling of atoms and molecules is a decent picture. The wiggling
means that they're constantly bumping into each other, and with the
atoms and molecules neighboring the thermometer, exchanging energy.
So if it's hotter outside, more energetic outside atoms are more
likely, and the thermometer gains energy; if it's colder outside, the
opposite occurs; and in between ("at equilibrium"), it's pretty much
a wash.
This wiggling has two effects. Remember how we said that they're
bumping into each other as well as the neighbors? The energy
statistically overwhelmingly spreads out within the thermometer so
that the observed ratio of probabilities of higher- vs. lower- energy
subsystems (faster/bigger vs. slower/smaller wiggles) is constant,
which means a physical chemist would be able to tell you what the
temperature is[5]. However, the energy spreading out means that the
wiggling has spread out as well, and as mercury with bigger wiggles
takes more space than mercury with smaller wiggles, its volume
increases. Because the diameter of the thermometer is constant, we
see this volume increase as a level increase, which means (if the
scale is still legible) any mother of a child can tell you what the
temperature is.
-Dave
[-1] somewhat like the Gini coefficient, except that temperature has
useful equations.
[0] and, in fact, the wiggling of atoms within molecules shows up on
a spectroscope at wavelengths which in everyday experience we would
associate with heat lamps. Go a little further, and you get microwaves.
[1] in effect, when abstracting, we treat the 10'000 things as straw
dogs.
[2] hence, I maintain that any mill with a mill-pond can claim to be
an structure engineered to create and exploit a negative-temperature
situation.
[3] anyone who says here that they will come to agreement at the
ambient temperature will be sent home with Diogenes' plucked chicken
[4] Kipling can tell you "fire will burn"; he can't tell you how much
firewood you'd need to produce 1 kg of fertilizer via Haber-Bosch.
(cf "the Sons of Martha")
[5] if this ratio were >1 (the reverse of the normal situation), the
p-chemist would, making the same calculation, tell you the
temperature was negative (the reverse of the normal situation)
