`On Thu, Jun 07, 2001 at 09:30:54PM +0000, mirabilos {Thorsten Glaser} wrote:> It was posted by L. K. where I now add my 0.02 EUR...> > On Thu, 7 Jun 2001, Albert D. Cahalan wrote:> > > Negative temperatures do not really exist.> > Are you really sure about this ?> I am. I made Abitur (german degree after 13yrs of school)> with physics being an important course, and there can not> be any temperature less than 0 K (or -273.15°C if you want).> This is because temperature is nothing but the movement of> pieces of materie (and even photons, ergo energy).	Then you must have blown your quantum finals.  Royally.  ESPECIALLYafter that statement about "temperature is nothing but the movement ofpieces of materie".  Not even close, once you get into the quant.	Mathematically and quantum mechanically, negative absolutetemperatures do exist.  In quantum mechanics, temperature is expressed asprobability populations in various quantum states.	Absolute zero is the quantum state were all particles are inthe ground state.  An infinite temperature is, quantum mechanically,the condition where all states, ground and energetic, have an equalprobability of population.	A "population inversion" (a condition where the energized statesare more likely to be populated than the ground states) is at the heartof 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 steadystate infinite temperature.	Mathematically, those states can actually be treated as negativeabsolute temperatures.  IOW, negative absolute temperatures are actuallyhotter than infinite.	It's true that these are not STEADY STATE conditions or inequilibrium (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'son "Negative Absolute Temperatures in Nuclear Magnetic Resonance" andto the scientific journals they reference.  I won an argument witha physics prof (PhD in high energy physics) over that very issue whenI did the same thing in a 400 level senior level physics lab on NMR backthen.  It's actually pretty damn simple, once you work the math, and itagravated him that he didn't believe it but couldn't argue with the mathtill he saw the work and publication from someone else.  Then he conceededthat I had him and I had been right.	IAC...  Negative absolute temperatures are about as meaninglessto this particular discussion as is expressing the temperature in 1/100sof a Kelvin which would have a precision than exceeds the accuracy ofthe measuring chips by two orders of magnitude.  IOW...  Both are sillyand meaningless to this case.  One is out of range in magnitude and oneis out of the range of accuracy.> -mirabilos> -- > C:\>debug> -e100 EA F0 FF 00 F0> -g> --->Enjoy!	Mike--  Michael H. Warfield    |  (770) 985-6132   |  mhw@WittsEnd.com  (The Mad Wizard)      |  (678) 463-0932   |  http://www.wittsend.com/mhw/  NIC whois:  MHW9      |  An optimist believes we live in the best of all PGP Key: 0xDF1DD471    |  possible worlds.  A pessimist is sure of it!-To unsubscribe from this list: send the line "unsubscribe linux-kernel" inthe body of a message to majordomo@vger.kernel.orgMore majordomo info at  http://vger.kernel.org/majordomo-info.htmlPlease read the FAQ at  http://www.tux.org/lkml/`