Suppose you take some potassium atoms and put them in a vacuum where you cool them to as close to absolute zero as you possibly can in a lab. What you’ve done is reduced the entropy of this system of atoms because the colder it gets, the less kinetic energy they have, and the less energy they could exchange with each other. Sure there will be some quantum effects that will upset the perfect stillness of these atoms which is why it’s theorized that we’ll never see absolute zero temperatures in the wild, but for all intents and purposes, you’ve hit the coldest that matter can get. Now, with a laser, start heating up the atoms but charge them so they attract each other and stay in their place in the system. Their energy goes up but they can’t exchange it or move in any direction. The overall entropy of the system is now technically less and you’ve just broken a limit we had the gall to preface with the word "absolute." You’ve effectively "cooled" potassium to a billionth of a degree below absolute zero, or at least to a quantum state that seems like it.
This is exactly what a team of scientists recently achieved in the lab and they’re excited about a slew of possible experiments to test the behavior of atoms and molecules in an exotic quantum state, opening new avenues for investigating the nature of dark matter and dark energy. As the media reports it, they managed to chill something below -273.15 °C, but take a moment to note that the word cooled in the description of the experiment is in quote marks. That’s because they didn’t actually go below this temperature. What they really did is way, way more complicated and has actually been long thought possible, just never accomplished. Absolute zero is still important because it marks a point at which injecting energy into a system changes how its distributed. For the positive temperature range, which in this case is anything above absolute zero, more energy brings more atoms to the same energy state. Negative temperatures, however, make exchange of energy much more difficult and can create inequalities between the atoms’ energy states.
Again, seems rather counter-intuitive, doesn’t it? In this setup, positive temperatures should be the low entropy ones, right? Well, in this range, atoms can move and exchange their energy with no limit which means that their possible number of quantum states could be infinite. Atoms which have to deal with negative temperature have a limit to how many energy states they could be in, meaning that you can keep injecting energy into the system but it will be more or less trapped in the atoms and the lattice will remain stable rather than fly apart as the atoms start moving more and more in response. In short, when you go into negative temperatures, you lower entropy as you add energy with the bizarre added twist that as you initially heat up the atoms, they could be in an infinite amount of energy states, then abruptly find themselves trapped in ever fewer. Just another way quantum mechanics makes things fun, and by fun I mean really, really weird.
So what does this all mean? It means that in this case, absolute zero has nothing to do with how cold things are, but how energy states are distributed in a system, and while we thought that this temperature was the dividing line between the two types of energy distribution, this is really the first experimental proof we have that this can happen in nature. If this seems really confusing, it is, because this is just the complicated nature of the beast. But knowing that one can achieve a negative temperature under the right conditions means that you can explore an entire realm of very bizarre quantum states what could explain otherwise seemingly inexplicable behaviors, one of which could offer an explanation for dark energy and give experimentally verifiable answers to one of cosmology’s biggest mysteries. And while yours truly would love to dive deeper into these possibilities, it may be best for everyone just to digest what we have so far and get ready for the imminent flood of Twitter and Facebook posts about cooling things below absolute zero…
See: Braun, S., et al. (2013). Negative absolute temperature for motional degrees of freedom Science, 339 (6115), 52-55 DOI: 10.1126/science.1227831