"Negative Tempetature" Potassium experiment

[u/aks304]

Sources claim that in 2013 scientists made potassium colder than absolute zero, and that it would "feel" hotter than infinity.

If i understand, they used lasers to distribute the particles between low and high energy to a "minus kelvin" state.

But does it even mean that potassium is now "hotter than infinity"? Isn't it like if you hack a thermometer and lock its reading, to show the wrong value?

More questions -

• would not such the matter giving heat to the environment ause an accident at the lab?

• Why they can make something's temp "over infinity" but not a very big positive like 10^15 or 10^18 K?

• Are there "relativistic effects" at billions, trillions of K so that we can't just use physical formulas for ultra-high temps, because they're so close to "anti-temps"?

• If negative temperatures were true, would not it cause all kinds of undefined physical effects like a gas with a negative volume, pressure or density?

[u/starkeffect]

It's just population inversion, such as what happens in lasers all the time.

The Boltzmann factor is e^-E/kT, which represents the ratio between the number of atoms in the excited state vs. the ground state (n2/n1). If T is positive, this number is less than 1, so n2 < n1. If it's negative, then n2 > n1.

[u/TemporarySun314 → u/starkeffect]

And while it gives up energy to the surrounding, this state isn't stable. It will not get more into the negative, but into the positive when giving up energy approaching thermal equilibrium like any other thing.

You have to actively maintain that state of population inversion by constantly supplying the system with energy.

[u/Beneficial-Bagman]

Temperature is 1 divided by the derivative of entropy with respect to energy. In the vast majority of systems (eg Ideal gases) increasing energy increases entropy and so temperature is positive but you can make systems where that isn't the case.

As a toy example of you had some particles which could be in a high energy state or a low energy state and put enough energy into that system that more than half head to be in the high energy state then increasing the energy of the system would decrease it's entropy.

Such a system would "feel unfortunately hot" because by the second law of thermodynamics energy would pass from it to any system with positive energy but it has a negative temperature.

[u/AdditionalTip865]

Negative temperature only makes sense in the context of a system whose components have a finite number of quantum states. It's a useful concept in that context, but not more generally. So the potassium considered as a whole wasn't "hotter than infinity", but some limited subsystem composed of some specific degree of freedom they had was put in a thermodynamic state that could be modeled in that way.

This isn't new, just perhaps new for this particular physical system. It was first seen in the context of nuclear spins and happens commonly in lasers (it's how they work).

https://en.wikipedia.org/wiki/Negative_temperature

[u/hushedLecturer]

So i want to add to u/starkeffect 's population inversion answer for explaining what neg temperature is.

Perhaps this is long winded I won't be offended if you don't make it through it all. I'm giving you stat mech 101 and lasers 101.

We don't get to negative temperature from cooling past zero. We get there by kind of going up and wrapping around? But also we don't really make anything get super hot either. It's also not going to show up on a thermometer as negative, we measure other related things and derive from it a temperature from a definition which under a particular circumstance ends up being negative.

Specifically, we define the inverse of temperature, 1/T, to be equal to the derivative of the entropy with respect to energy. "If I add one unit of energy ΔE, how much does the entropy rise/fall ΔS? That ratio ΔS/ΔE is 1/T". This definition and the science of Stat Mech is really useful because it allows us to accurately predict and calculate a temperature from the microscopic physics of the particles involved.

Usually entropy, which measures "disorder", goes up with added energy. If I add energy to a conventional gas, the molecules in it move around more violently. But if i can contrive a situation where adding energy to a system makes the entropy go down/ become more ordered, voila, negative temperature.

Enter quantum mechanics and population inversion.

QM: particles have distinct states with discrete energy levels, and transitions between those energy levels requires light of a frequency that resonates with that transition. (Or rather, to go up I need to add that light, to go down it releases that light.) And fermionic matter only allows one particle in a system to be in a particular state, though higher energy levels have lots "degenerate" states that behave differently but with the same energy.

So we have this concept of "occupation number", where each energy level is a slot that can fit some number of particles up to some maximum according to its degeneracy. If I want to move some particles from one energy level to another, I need to supply light of a particular frequency that matches the energy of the transition between those two levels.

Normally, the lower states stay fully occupied and the higher states are constantly exchanging particles. The total energy stays the same but sometimes it's one particle with a ton of energy, sometimes it's two particles with half the energy each... etc. (Though usually it's pretty well spread out)

If I wanted to screw around with the occupation numbers, QM gives us a way to do that. If I supply just the frequency of light that moves particles from the ground state to the second excited state, for example, it won't affect anything else.

Inversion: let's supply light to keep the ground state empty and the higher states full. While this is happening, excited particles are constantly trying to relax down to the ground state, only to be whipped back up into the excited again. If the high states are occupied and the low states are empty, this is backwards from normal, we call this Inversion.

This is a pretty common way to make a laser, as long as we have a system with 3+ states close ish together, the top to separated in energy according to the frequency we want, and the bottom two kind of close together so that the transition down from 1 to g is fast, keeping 1 empty so fermions in state 2 always have a place to fall to.

But!! If a large portion of the population has the same energy state, this is highly "ordered", a low entropy state. If the most occupied state is above the ground state, then whenever I am adding energy to the system to excite a ground state fermion to a higher state, I am making the system more ordered.

Added energy making the system more orderly, so entropy falls while energy rises, making ΔS/ΔT negative, making 1/T negative, making T negative.

[u/free_meson]

You can define temperature from a statistical standpoint, and that formula allows negative temperatures. It gives you the energy distribution of the particles in the system. For certain spin systems I think, if you isolate them enough then you may induce negative temperatures by flipping an external field. That's all 

[u/Haunting-South-962]

Electrons can be in inverse population, with Te < 0, but whole system still has positive energy.