Below Absolute Zero?

So via the magic of Twitter, I spied this link: http://www.nature.com/news/quantum-gas-goes-below-absolute-zero-1.12146#/ref-link-1

The article, as you can see is entitled “Quantum Gas Goes Below Absolute Zero”…. I hate to be the harbinger of doom, but, well, it hasn’t. Absolute zero has NOT been broken. Sorry 🙁

Don’t get me wrong, the work is clever and interesting (and can be found here: http://www.sciencemag.org/content/339/6115/52). It’s more that the reporter has slightly gotten the wrong end of the stick.

We live in a world of jiggling atoms – the temperature of a gas is basically related to the average energy of the particles making up the gas. Increase the energy = hotter gas. So a gas with hugely jiggling atoms (technical term!) can be defined as hot, with a high temperature. On the other end of the scale, you have absolute zero (defined as = 0 K, zero Kelvin), which is the temperature predicted when the atoms have “no energy” – where they are so cold, they have stopped jiggling entirely.

So, given this definition of temperature, the concept of a temperature BELOW absolute zero doesn’t make any sense. Once the atoms have stopped jiggling, what’s left?

However, this isn’t really the full story of the definition of temperature. There is also something called ENTROPY (shudder), which defines the amount of disorder in a system.

In a typical gas, by increasing the temperature (by increasing the energy in the system), you also increase the entropy. I could talk about the “arrow of time” etc, but I prefer to think about it in terms of children. Think of a room full of (low energy) children sitting quietly at their desks. Here, there is some semblance of order (low entropy). Now get those children up, show them cartoons, feed them sugar (increasing their energy), and what do you get? Disorder = high entropy.

Most traditional systems, like gases, or collections of small children, cannot achieve so-called negative temperatures, because adding energy = increase in entropy = positive temperatures.

BUT…In a quantum state, it is possible to achieve “negative Kelvin temperatures”, where adding energy actually DECREASES the entropy- this breaks the laws of classical thermodynamics, but is theoretically allowed under quantum mechanics – the laws of physics that defines the very very VERY small.

Negative temperatures are actually what this work refers to, and is not quite the same as “below absolute zero” temperatures. Negative temperatures can only exist when you use a different definition of temperature, in a system where there are a limited number of energy states, a so-called quantum state. Increasing the temperature in a quantum gas causes the particles in the gas move to higher energy states until the number of particles in the lower energy states and in the higher energy states is almost equal. However in quantum systems it is possible to design a system where there are more particles in the higher energy states than in the lower ones. This gas can then be said to have a “negative temperature”. This flies in the thermodynamic face of classical gases, where particles will always try to occupy the lowest energy state they can, so there will always be more particles at lower energy states.

So, negative temperatures are only found in quantum systems, like the ultra-cold quantum gas made up of potassium atoms reported in this work. I’ll hand over to the reporter at this point…..

“Using lasers and magnetic fields, they kept the individual atoms in a lattice arrangement. At positive temperatures, the atoms repel, making the configuration stable. The team then quickly adjusted the magnetic fields, causing the atoms to attract rather than repel each other. “This suddenly shifts the atoms from their most stable, lowest-energy state to the highest possible energy state, before they can react,” “

There is a great Wikipedia entry on this concept of negative temperature – found here – which says that….

A substance with a negative temperature is not colder than absolute zero, but rather it is hotter than infinite temperature. As Kittel and Kroemer (p. 462) put it, “The temperature scale from cold to hot runs:

+0 K, . . . , +300 K, . . . , +∞ K, −∞ K, . . . , −300 K, . . . , −0 K.”

So, recap…. the temperature of a system is defined by the kinetic (jiggling) energy of its particles – when we measure temperature, we’re really measuring the average energy of the particles.

In a normal system, most particles have energies hovering about this average temperature, with a just few particles at a higher energy state. From what I can understand from reading this article and having a head-scratching-look through the sections of the paper I could understand, it seems that, using a combination of laser trapping and a flip of a magnetic field, the researchers reversed this situation so that most of the particles now existed in a high energy state, with only a few at lower energies…….. Thus producing a gas with a “negative temperature”, not a gas with a temperature below absolute temperature.

So as far as I can see, it’s all about how you DEFINE temperature, rather than smashing a “constant” of thermodynamics – I can’t help thinking of the x-ray mode on a Kindle (stay with me on this). Most of us define temperature as black text on a white background. This research group has flipped this definition so it’s now described by white text on a black background.

Actually, maybe that Kindle metaphor is pants. And reading back, I really did waffle. A lot….. Anyway, that’s the best I can do at this point on a Friday afternoon. Hopefully I didn’t lose too many of you!

PS: Feel free to argue with / correct me – I am not, in any way, a temperature expert. The only way I can attempt to understand something is by either doing it myself (not possible in this case) or spewing everything I know about it on paper…. Which is what I’ve done here.

PPS: So I’ve been thinking about this a bit… The concept of “negative temperatures” is a very odd one in that they don’t REALLY exist – the concept only holds (as I said earlier) if you accept a complete reversal of the definition of temperature.

Say that for a particular gas, for it to have a temperature of 300K*, this actually equates that 5000* particles at an energy level equivalent to that temperature with a tiny minority, say another 10 particles, at higher energy levels.

What this research seems to have done is found a way to flip the relative positions of the particles so that now the 10 particles find themselves in a LOWER energy state than the 5000 other ones. Therefore the temperature is “reversed” – hence their assertion that they’ve produced a NEGATIVE temperature. BUT, it’s not really negative! If you have a gas with most of its particles in a high energy state, doesn’t that mean its HOT? Well, yes basically! This is what the excerpt from the Wikipedia article above meant by saying “a substance with a negative temperature is not colder than absolute zero, but rather it is hotter than infinite temperature”.

*PLEASE NOTE THESE NUMBERS MEAN NOTHING, they’re just for show