On Sun, 06 Jan 2013 07:49:27 -0800, Paul Brandon wrote:
That's the problem with treating 'infinity' as if it were a number (it's
not).
Literally, it means 'unmeasureable -- beyond limit'.
Well, that depends upon how one defines infinity and what context it is
used. In explaining "negative absolute temperature", it has been shown
that if one starts at 0 degree Kelvin and increases the energy under the
right circumstances, the temperature in degrees Kelvin will increase until
it reaches positive infinity Kelvin at which point it switches over to
negative infinity Kelvin and the negative degrees Kelvin decrease to
zero degrees Kelvin. See the Wikipedia entry on "Negative Temperature"
which use Kittel and Kroemer's (1980) "Thermal Physics" as their source:
http://en.wikipedia.org/wiki/Negative_absolute_temperature
An older reference that helps to establish the concept of negative
absolute temperature is by Ramsey and can be obtained here:
http://www.physics.umd.edu/courses/Phys404/Anlage_Spring11/Ramsey-1956-Thermodynamics%20and%20S.pdf
An interesting point made by Ramsey is that if we use a transform of
temperature T, namely -1/T, then infinite temperature is zero. I'm
not a physicist but maybe Allen Esterson can explain how infinity is
used in physics calculations (one can also look at the Wikipedia entry
on infinity which has a section on this; see:
http://en.wikipedia.org/wiki/Infinity )
Another interesting concept is "Absolute Hot" (not a social comment)
which it the highest possible temperature, which is around 10**32 Kelvin
according to one framework; see:
http://en.wikipedia.org/wiki/Absolute_hot
But consider the following. Quoting from this entry:
|Quantum physics formally assumes infinitely positive or negative
temperatures
|in descriptions of spin system undergoing population inversion from the
|ground state to a higher energy state by excitation with electromagnetic
|radiation. The temperature function in these systems exhibits a
singularity,
|meaning the temperature tends to positive infinity, before discontinuously
|switching to negative infinity.[5] However, this applies only to specific
|degrees of freedom in the system, while others would have normal
|temperature dependency
The footnote/reference is to Kittel & Kroemer's (1980) "Thermal Physics".
Like I said: Busy, busy, busy.
-Mike Palij
New York University
[email protected]
On Jan 6, 2013, at 7:36 AM, Mike Palij wrote:
One example that is used to represent Stevens' conception of a ratio
scale, that is, a constant interval scale with an absolute zero, is the
Kelvin temperature scale which, unlike the Fahrenheit and Celsius
scales, has a absolute zero point representing the coldest temperature
that can be achieved.
But who knew that you could have "negative absolute" temperatures,
temperatures below absolute zero? But instead of being cold, these
temperature are hot, theoretically, hotter than infinity.
These are strange ideas but experimentally confirmed ones. For
popular accounts of the research showing negative absolute temps,
here is one from HuffPost:
http://www.huffingtonpost.com/2013/01/04/absolute-zero-record-setting-negative-temperature_n_2404666.html
To appreciate the weirdness associated with this research, consider
the following quote from the HuffPost article:
|To comprehend the negative temperatures scientists have now devised,
|one might think of temperature as existing on a scale that is actually a
|loop, not linear. Positive temperatures make up one part of the loop,
|while negative temperatures make up the other part. When temperatures
|go either below zero or above infinity on the positive region of this
scale,
|they end up in negative territory.
Science Daily has the following article:
http://www.sciencedaily.com/releases/2013/01/130104143516.htm
And the Max Planck Institute where the research was done has provided
this press release:
http://www.mpq.mpg.de/cms/mpq/en/news/press/13_01_04.html
The research was published in "Science" and the article can be accessed
here:
http://www.sciencemag.org/content/339/6115/52
Busy, busy, busy.
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