I’ve only gotten round to reading a Science journal article from a few months back that caused a lot of media buzz. It was about negative absolute temperatures, which sounds like presumably going below absolute zero (an impossibility in all senses of the word). Anyway, here’s the full-text PDF on arXiv.org for anyone interested. HIGHLY recommended reading, this is, since it’s a beautiful piece of experimental physics that will blow your mind!
As it turns out, it actually has nothing to do with going below absolute zero! Instead, it’s a symmetric matter of inverting the sign of temperature in Boltzmann factor so that more particles occupy higher energy states than lower energy states. In essence, it’s a question of how can more energy be packed into a thermodynamic system after it has reached infinite temperature? Because at that point every energy state is occupied with equal probability such that the same average number of particles would be found in every energy state. Hence, the total energy is finite despite the infinite temperature :\ My head hurts :’(
But this finite total energy is still not the maximum possible! So the theory then goes that if the probabilities can be pushed such that fewer particles occupy lower energy states and more particles occupy higher energy states, then the total energy will be larger than what it was before at infinite temperature! And the way to do this (in theory at least) is to invert the sign of Boltzman factor so that the probability distribution now exponentially grows, as opposed to exponentially decaying before.
Anyway, what all of this means is that negative absolute temperatures are HOT because a system with negative temperature has humongous amount of energy stored inside (relatively speaking, of course). So the authors of this paper devised clever ways to trap bosons into a negative temperature zone so that they have greater probability of being in a higher energy state than in the relatively lower energy states. Thus the total energy is increased to more than what would be possible if one were to simply heat up the bosons (so to speak) until they reached infinite temperature the old fashioned way :P
It’s amazing to ponder the role of symmetry in all of physics (and consequently, all of nature). We didn’t evolve to grasp such beauty intuitively/quickly. It takes a lot of thinking to appreciate the shear simplicity with which the universe goes about its business. The idea that total energy can be finite despite a system having infinite temperature is mind blowing to say the least. And thanks to symmetry, the temperature can then turn around to be negative just so that the finite total energy still has a chance to increase further. In fact, the maximum energy obtainable in theory happens to be when this negative temperature rolls all the way around to absolute zero - from the other side :P