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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.)

*More*

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: accel1, cme, programs, stei-lab, & wuzzlers.
  • For source, cite URL at http://newton.umsl.edu/infophys/infophys.html
  • Version release date: 04 Mar 1996.