ELi5: How does a laser have “negative temperature” if it’s not cold?
In: Physics
Initially temperature was defined as a measure of how hot things are. Physicists didn’t really understand what heat was.
Later, it was realised that everything is made of atoms and molecules, and so temperature could be defined in terms of the average kinetic energy of those molecules. As you add heat, the average kinetic energy goes up, and the temperature goes up.
Then, along came quantum mechanics, and it was realised that atoms and molecules are better thought of as being in quantum states with energy levels, rather than as having individual amounts of kinetic energy. Now, temperature is defined based on how quickly “entropy” increases as you add heat.
Entropy is, basically, the total possible number of quantum states for all the individual atoms and molecules. If you had three atoms, with quantum states (ie, energy levels) 1, 2, 3, 4, … Then if the total energy was 3, there’s only one state for the three atoms: 1, 1 and 1. If the total energy was 4, there’d be three possible states: (1,1,2) and (1,2,1) and (2,1,1), and there would be even more combinations that add up to 5, or 6, or 7 total energy.
Because the number of states goes up when we add energy, the temperature is positive. Because it goes up faster and faster as we add more energy the temperature keeps rising as we add more energy.
Some weird and unusual systems don’t act like that though. Imagine that each atom had only two possible states, 0 and 1. Eg, maybe they’re like coins, you’ve bet on heads,and the energy is how much you win.
If there’s a lot of coins and only a little bit of energy, then this behaves perfectly normally. The number of combinations goes up and up as you add energy.
Once most of the coins have been flipped to heads, though, the opposite is happening: the more heads there are, the fewer combinations there are. Since the number of states is decreasing as you add energy, the temperature is actually negative. However, this still a very hot system, it has heaps and heaps of energy: most of the coins are heads = most of the atoms are in the high energy state.
It’s as if the “temperature” scale starts at absolute 0, and wraps through infinity into negative numbers, all the way back to “negative 0”. It seems very weird, but it would make a lot more sense if we measured “coldness”, ie, 1/T instead.
Then,
* 0 Kelvin is infinite coldness
* Normal things have coldness approach 0 as they get hotter and hotter.
* Weird systems like these atoms in a laser can smash through “zero coldness” all the way to negative coldness.
But to invent a system like that, we would have had to know a lot more about heat and temperature than we did when we first invented temperature scales. And high school physics and chemistry questions about heat capacity would involve more complicated formulas.
The ELI5 explanation is that it comes down to how we define “temperature” in a physics context.
We have an intuitive idea of what temperature means from every-day life. But for science we want more precise, more technical definitions, that are useful, interesting and consistent with all our other terms.
And it turns out that when we use that definition we can get some weird results where you can have a “negative temperature” in a system (although intuitively that system will be “hotter” in the intuitive sense). It sounds kind of silly, but it works out consistently with a bunch of other areas of physics, so we go with it.
If you want a more detailed explanation there is a decent askscience thread on this [over here](https://np.reddit.com/r/askscience/comments/12wj25/how_does_negative_temperature_work_ex_in_lasers/), which gets into the more technical stuff.
Lasers having a “negative temperature” isn’t a measurable thing. It’s conceptual. The Boltzmann factor does a good job of explaining how there is a probability of temperature increasing when energy increases. It describes a thermal equilibrium where at 0 K, the excited state has a factor of 0 and the gain state has a factor of 1. Lasers aren’t in thermal equilibrium and would theoretically be found to be negative if they did follow this scale. The exited/gain state of lasers is called a “population inversion” referring to how lasers emit exponentially more excited particles than ground state.
Excited particles from certain lasers will transfer energy to objects and produce heat, though. The laser itself is not something that has temperature. The whole “negative temp” thing is just physics mumbo jumbo
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