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Puzzler: Most people agree that the absolute zero of temperature is impossible to reach. But few know that it is possible to attain minus absolute temperatures, and thus in a way to "approach absolute zero" from the negative as well as the positive direction. Moreover, you can begin to do so with a set of dominoes in the living room of your very own home. How so? (Hint: Part of the paradox here is related to the strange way, historically, that temperature was defined.)
Dominos when more than half are standing on end, atoms in excited states prior to
photon release in the pulsed emission of a laser, and nuclear spins
can all find themselves in
inverted population states -- in other words states with an
uncertainty slope dS/dE (i.e. reciprocal temperature or coldness) which has
decreased until it is below zero. Although these inverted states have been
described as "non-thermal" because they only occur in systems with an
upper limit on the energy they can accomodate, thermal
"equilibration" between systems in sub-zero coldness states happens as
one might expect (cf. Kittel & Kroemer, Thermal Physics, W. H. Freeman 1980, p. 463).
This would result in little confusion
at all if we considered coldness alone. Coldness in practice decreases with
added energy, so that the fact that with some systems it dips below zero
would hardly raise an eyebrow.
However, calculating historical temperature from such negative
uncertainty slopes (by taking their reciprocal) yields a negative
absolute temperature, which in reality (e.g. if you watch how it gets
that way) is "higher" than all positive absolute temperatures. The
historical temperature scale, thus unfortunately, creates the illusion
that the more dominos one puts on end, the closer one gets to absolute
zero from the negative side. As one can see easily from the coldness
scale below, there are in fact two absolute zero's of temperature, one at each
end of the coldness scale. Standing dice and other inverted population
states in reality take you closer only to the negative (high energy) one.
Given the foregoing, what would you estimate for the "spin temperature" of the dominos in the image above? *Yet More*
Copyright (1970-95) by Phil Fraundorf
Dept. of Physics & Astronomy, University of Missouri-StL, St. Louis MO 63121-4499
Phone: (314)516-5044, Fax:(314)516-6152
At UM-StLouis see also:
For source, cite URL at http://newton.umsl.edu/infophys/infophys.html
Version release date: 04 Mar 1996.