On Thu, 7 Jun 2001, Michael H. Warfield wrote:

> 	A "population inversion" (a condition where the energized states
> are more likely to be populated than the ground states) is at the heart
> of many things we take for granted today such as lasers, masers, leds,
> NMR (Nuclear Magnetic Resonance) and MRI (the medical use of NMR).
> 
> 	Those "population inversions" represents an "energized state"
> that is more energetic than the state that would be present in a steady
> state infinite temperature.
> 
> 	Mathematically, those states can actually be treated as negative
> absolute temperatures.  IOW, negative absolute temperatures are actually
> hotter than infinite.
> 
> 	It's true that these are not STEADY STATE conditions or in
> equilibrium (which is how we take advantage of populations inversions -
> by their actions in returning to equilibrium), but the math still works.
> Just check out a few issues of Scientific American from the mid 1970's
> on "Negative Absolute Temperatures in Nuclear Magnetic Resonance" and
> to the scientific journals they reference.  I won an argument with
> a physics prof (PhD in high energy physics) over that very issue when
> I did the same thing in a 400 level senior level physics lab on NMR back
> then.  It's actually pretty damn simple, once you work the math, and it
> agravated him that he didn't believe it but couldn't argue with the math
> till he saw the work and publication from someone else.  Then he conceeded
> that I had him and I had been right.

Nobody is doubting that population inversions do exist. And you also can
do all kind of mathematics with it if you like and even calculate a
temperature. But I think you shouldn't interprete this kind of temperature
as something that is macroscopically existant or even measurable. You
also wouldn't say quantum wave functions do exist, would you ?

> 	IAC...  Negative absolute temperatures are about as meaningless
> to this particular discussion as is expressing the temperature in 1/100s
> of a Kelvin which would have a precision than exceeds the accuracy of
> the measuring chips by two orders of magnitude.  IOW...  Both are silly
> and meaningless to this case.  One is out of range in magnitude and one
> is out of the range of accuracy.

I agree and I think we shouldn't get too out of topic ...

--
Thomas

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