# Chemistry - Why is absolute zero unattainable?

## Solution 1:

There was a story in my days about a physical chemist who was asked to explain some effect, illustrated by a poster on the wall. He did that, after which someone noticed that the poster was hanging upside down, so the effect appeared reversed in sign. Undaunted, the guy immediately explained it the other way around, just as convincingly as he did the first time.

Cooking up explanations on the spot is a respectable sport, but your teacher went a bit too far. What's with that Charles' law? See, it is a **gas** law; it is about gases. And even then it is but an approximation. To make it exact, you have to make your gas ideal, which can't be done. As you lower the temperature, all gases become *less and less ideal*. And then they condense, and we're left to deal with liquids and solids, to which the said law **never** applied, not even as a very poor approximation. Appealing to this law when we are near the absolute zero is about as sensible as ruling out certain reaction mechanism on the grounds that it requires atoms to move faster than allowed by the road speed limit in the state of Hawaii.

The energy argument is even more ridiculous. We don't have to remove all energy, but only the **kinetic** energy. The $E=mc^2$ part remains there, so the mass is never going anywhere.

All that being said, there is no physical law forbidding the existence of matter at absolute zero. It's not like its existence will cause the world to go down with error 500. It's just that the closer you get to it, the more effort it takes, like with other ideal things (ideal vacuum, ideally pure compound, crystal without defects, etc). If anything, we're doing a pretty decent job at it. Using sophisticated techniques like laser cooling or magnetic evaporative cooling, we've long surpassed the nature's record in coldness.

## Solution 2:

Absolute zero is a tricky concept, particularly once you start getting precise about it. Thermodynamics and quantum mechanics is a tricky business! I'll try to avoid the precise parts, and see if I can give you an answer which is more intuitive than a pile of equations.

The first question is what does it mean to "attain a temperature of absolute zero." Typically when we phrase things like this, we are thinking in terms of equilibrium thermodynamics. In this context, we are interested in bulk objects that have a uniform temperature. We can quickly see that if there is any heat transfer between an object "at absolute zero" and any object not at absolute zero, then the first object will be warmed as thermal energy from the warmer object flows into it. This mean our object at absolute zero can only remain there if it is in thermal isolation. There is no known way to do this (especially when it comes to radiative heating), unless your object at absolute zero is completely surrounded by other objects at absolute zero. This forms a sort of tower of babel that eventually falls when some outside objects must be subjected to the 3K background radiation. Empty space is "warmer" than absolute zero.

What if we consider the world of non-equilibrium thermodynamics. This is the study of systems that are not currently at equilibrium. This is a strange place where some things can occur which don't make sense at first sight. One of them is negative temperatures. Negative temperatures occur because of how physicists define temperature: $\frac{1}{T} = \frac{\text{change in entropy}}{\text{change in energy}}$. It's easy to show that in equilibrium situations (the ones we are used to) it is impossible to have a negative temperature (it also points out that if you ever set T=0, you would have an undefined value in your equation). However, in non-equilibrium thermodynamics, we can consider strange compounds that are *metastable*. You can think of them like a ball perfectly at the top of a smooth hill. If the ball is tapped in any direction, it will roll down the hill to the bottom. However, at the top, it can theoretically stay motionless (temporarily).

We have corralled atoms into traps, and cooled them until they were very very cold (a few billionths of a kelvin). Then, we flipped a switch which turned the trap around. Suddenly a position that was very stable became an unstable equilibrium. If you run the math on this weird state, it turns out that this implies a negative temperature!

Now this would suggest that, since a temperature went from positive to negative, it must have crossed through 0K, proving that we created something at absolute zero. However, this is not the case. What actually happens is that the temperature rushes towards positive infinity, reaches a discontinuity, and then wraps around to negative infinity. It then approaches its negative temperature from negative infinity. So even in this case, we can't reach absolute zero.

Quantum mechanics also poses an issue in that you could never prove you attained absolute zero if you tried. Thermal energy is kinetic energy, which is related to momentum. Let's say you found a hypothetical approach to reach absolute zero. When you go to prove your findings, you must prove the momentum is also 0. However, by proving that to be true, with no error, the uncertainty principle states that you can know nothing about the position of those particles. They might be anywhere in the universe!

## Solution 3:

Leaving quantum mechanics aside (it gives me a headache) the second law of thermodynamics prevents absolute zero from being reached in practice. To cool something down, its heat must be transferred to something cooler than it. Since nothing can be cooler than absolute zero, one cannot cool something to absolute zero.

One can sidle right up close to $0\ \mathrm{K}$ and be amazed by its quantum awesomeness, but as Cort explained, at absolute zero, quantum effects make the concept of temperature rather awkward.

Your teacher's explanation is, as Ivan points out, based on the ideal gas law and there is no such thing as an ideal gas, especially not close to absolute zero.

And let's not forget about the physicist who fell into a vat of liquid helium. He's 0K now.

## Solution 4:

The usual answer is that it's unattainable because absolute vacuum is unattainable because the ground state of spacetime itself has non-zero energy. This ground state occasionally condensing is what creates the virtual particles.

Plus, apart from this fundamental reason of the lowest energy level of spacetime itself being non-zero, you have lots of neutrinos everywhere, which you can't really shield yourself from. A massive galaxy-sized sphere of gold might do that to some degree, but unfortunately you can't build such a thing because of general relativity (i.e. it would become a black hole long before).

Numbers extremely close to zero are just as hard to get to as their inverse, i.e. things like massive galaxy-sized golden spheres, so even without the fundamental reason I gave first, it would still be impossible because our universe is full of stuff

## Solution 5:

Absolute zero can definitely exists (see the later edit), and there is at least one theory, that says that absolute zero will kind of be the norm in the universe at one point.

Absolute zero cannot be observed. Observation always implies interaction. Absolute zero implies no movement whatsoever. Observation implies that you somehow either receive a particle from the observed object or you send some particles that somehow get back to you, or you have a device on the other side and you measure the interaction of your particles with the other particles.

If a position in space is $0\ \mathrm{K}$, it means that nothing moves, so nothing from there can reach you, unless:

You send a particle to a position in space, which you expect to have $0\ \mathrm{K}$, but by the time your particle is there, the space will not have $0\ \mathrm{K}$ anymore, because it will have a moving particle that you just sent and in the end you will observe the temperature that you just produced.

**Later Edit:** I suppose it depends on how you define temperature. If you consider that something has to exist for it to have temperature, then $0\ \mathrm{K}$ cannot exist, because any fluctuation in any field means that something exists and that something has a temperature higher than $0\ \mathrm{K}$. But if you extend the definition of temperature to non-existing objects, then such an object should have $0\ \mathrm{K}$