Your final quote was the sense I'm familiar with; the term 'infinitely positive or negative ....' uses the term as a modifier, not a noun. See: http://scienceblogs.com/goodmath/2008/10/13/infinity-is-not-a-number/
On Jan 6, 2013, at 11:52 AM, Mike Palij wrote: > 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. > > > --- > You are currently subscribed to tips as: [email protected]. > To unsubscribe click here: > http://fsulist.frostburg.edu/u?id=13438.3b5166ef147b143fedd04b1c4a64900b&n=T&l=tips&o=22716 > or send a blank email to > leave-22716-13438.3b5166ef147b143fedd04b1c4a649...@fsulist.frostburg.edu Paul Brandon Emeritus Professor of Psychology Minnesota State University, Mankato [email protected] --- You are currently subscribed to tips as: [email protected]. 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