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We were dealing with the Third Law of Thermodynamics in class, and my teacher mentioned something that we found quite fascinating:

It is physically impossible to attain a temperature of zero kelvin (absolute zero).

When we pressed him for the rationale behind that, he asked us to take a look at the graph for Charles' Law for gases:

enter image description here

His argument is, that when we extrapolate the graph to -273.15 degrees Celsius (i.e. zero kelvin), the volume drops down all the way to zero; and "since no piece of matter can occupy zero volume ('matter' being something that has mass and occupies space), from the graph for Charles' Law, it is very clear that it is not possible to attain the temperature of zero kelvin".

However, someone else gave me a different explanation: "To reduce the temperature of a body down to zero kelvin, would mean removing all the energy associated with the body. Now, since energy is always associated with mass, if all the energy is removed there won't be any mass left. Hence it isn't possible to attain absolute zero."

Who, if anybody, is correct?

Edit 1: A note-worthy point made by @Loong a while back:

(From the engineer's perspective) To cool something to zero kelvin, first you'll need something that is cooler than zero kelvin.

Edit 2: I've got an issue with the 'no molecular motion' notion that I seem to find everywhere (including @Ivan's fantastic answer) but I can't seem to get cleared.

The notion:

At absolute zero, all molecular motion stops. There's no longer any kinetic energy asscoiated with molecules/atoms.

The problem? I quote Feynman:

As we decrease the temperature, the vibration decreases and decreases until, at absolute zero, there is a minimum amount of motion that atoms can have, but not zero.

He goes on to justify this by bringing in Heisenberg's Uncertainity Principle:

Remember that when a crystal is cooled to absolute zero, the atoms do not stop moving, they still 'jiggle'. Why? If they stopped moving, we would know were they were and that they had they have zero motion, and that is against the Uncertainity Principle. We cannot know where they are and how fast they are moving, so they must be continually wiggling in there!

So, can anyone account for Feynman's claim as well? To the not-so-hardcore student of physics that I am (high-schooler here), his argument seems quite convincing.

So to make it clear; I'm asking for two things in this question:

1) Which argument is correct? My teacher's or the other guy's?

2) At absolute zero, do we have zero molecular motion as most sources state, or do atoms go on "wiggling" in there as Feynman claims?

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    $\begingroup$ Both are utter nonsense. Absolute zero is physically possible (not that we can attain it, though). $\endgroup$
    – Ivan Neretin
    Commented Oct 13, 2016 at 18:18
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    $\begingroup$ Since systems can only approach it logarithmically, one would have to seriously question if it is physically possible. $\endgroup$
    – Jon Custer
    Commented Oct 13, 2016 at 18:54
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    $\begingroup$ Both explanations are wrong. (a) It is quite possible nowadays to obtain temperatures in the milli-kelvin range. This is done to remove thermal noise on very sensitive instruments. (b) very briefly, temperature is a measure of motional energy, molecule still have what is called zero-point vibrational energy at zero K, and crystals have lattice motion (phonons) that also have zero point energies, so it is not true that the total energy is zero at zero K. Atoms still have the same electronic energy as at room temperature. $\endgroup$
    – porphyrin
    Commented Oct 13, 2016 at 21:13
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    $\begingroup$ @porphyrin Temperature is not a measure of motional energy. All it is is a ratio between dU and dS at constant V and N. That's how it can be negative in many exotic systems and (effectively) in some that have become quite familiar, for example. You can perfectly have motion at $T=0$. A harmonic oscillator does. $\endgroup$
    – The Vee
    Commented Oct 15, 2016 at 23:05
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    $\begingroup$ I think that what I wrote is correct in the context of the question but not complete in a general sense. The average energy, translation, vibration, rotation is $<E>=k_BT/2$ for each 'squared' energy term with $k_B$ being Boltzmann's constant. This assumes that a Boltzmann distribution applies, i.e. that each energy level has a smaller population than the one immediately below it in energy and that the number of levels is infinite. A population inversion as in the laser or in nuclear spin pulsed NMR experiments is then described as having a negative temperature but just for those levels. $\endgroup$
    – porphyrin
    Commented Oct 20, 2016 at 8:08

8 Answers 8

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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.

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    $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. If anyone needs any content from them to be incorporated into the answer, I can undelete those as needed, or you can copy them back from the chatroom. $\endgroup$
    – jonsca
    Commented Oct 17, 2016 at 23:22
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    $\begingroup$ Of course I did simplify things a lot; so did Feynman. True, at absolute zero the atoms still have some uncertainty of position, which can't be further diminished because of Heisenberg's principle. Whether or not it constitutes a motion is a philosophical (that is, pointless) question. $\endgroup$
    – Ivan Neretin
    Commented Oct 25, 2016 at 19:45
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    $\begingroup$ I just said that a matter at absolute zero is not forbidden by physical laws; I never said we can reach it. On the contrary, see "the closer you get to it, the more effort it takes" part? $\endgroup$
    – Ivan Neretin
    Commented Mar 8, 2018 at 12:20
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    $\begingroup$ @IvanNeretin Can you separate never being able to do something from a physical law? How does one know something can never be done unless one argues from other physical laws, or in essence, discovers a new law? $\endgroup$
    – Linear Christmas
    Commented May 19, 2018 at 18:41
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    $\begingroup$ @LinearChristmas Why, of course we can. An ideal vacuum is probably the simplest example. Or imagine a 100% pure crystal of NaCl, without any impurities or defects. For all we know, it would persist just fine. Good luck trying to obtain it in real life, though. Same thing with absolute zero. $\endgroup$
    – Ivan Neretin
    Commented May 19, 2018 at 22:20
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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!

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    $\begingroup$ Nice answer! Thanks for posting, and welcome to Chem.SE! $\endgroup$
    – hBy2Py
    Commented Oct 13, 2016 at 23:15
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    $\begingroup$ I'd prefer to state the uncertainty argument as: observing, in any way, that the object is in a particular place, is an interaction that imparts some momentum to it, and after that interaction there's a 0% chance that the object is at absolute zero. It goes together with the first paragraph. Even if we theoretically have an object at absolute zero, it only exists there as long as it's never observed or interacted with. $\endgroup$
    – hobbs
    Commented Oct 14, 2016 at 19:35
  • $\begingroup$ @hobbs That is true. I was being a bit cagey about that way of wording it. Given that I'm starting with a hypothetical approach to reach absolute zero, I wanted to stay as close to the raw mathematical limits as I could manage. I wanted to avoid the natural loophole of developing a hypothetical measurement approach which could do the job. $\endgroup$
    – Cort Ammon
    Commented Oct 14, 2016 at 19:49
  • $\begingroup$ @CortAmmon fair enough. I just feel that the "if you know momentum perfectly, then position could be anywhere!" argument is one of those that causes more confusion than it's worth. People don't understand it as a mathematical bound on the possible information gained from all possible measurements, they imagine all kinds of mystical things going on :) $\endgroup$
    – hobbs
    Commented Oct 14, 2016 at 19:57
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    $\begingroup$ I think you misused the term "metastable", what you describe is highly unstable. It has zero resistance to any perturbation. A metastable state is a local minimum in potential energy, what you describe is a local maximum, and I believe it's called a saddle point. $\endgroup$
    – luk32
    Commented Oct 15, 2016 at 20:13
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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.

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    $\begingroup$ "To cool something down, its heat must be transferred to something cooler than it" is plain wrong. E.g. the freezer is by far the coolest object in my apartment, yet it has no trouble working. $\endgroup$
    – Dmitry Grigoryev
    Commented Oct 14, 2016 at 11:37
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    $\begingroup$ @DmitryGrigoryev On a macro level, yes. However, at each physical stage within it, heat is moving from hotter to colder. What is hotter and what is colder is manipulated by pressure. There can be no colder than absolute zero, no matter how much you pressurize, depressurize, or otherwise mess with a substance; by definition the closest you can get is the same temperature, so there is never a heat sink available to reach abs 0. $\endgroup$
    – user7652
    Commented Oct 14, 2016 at 17:08
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    $\begingroup$ @WilliamKappler Heat doesn't have to move to something colder. If you expand a gas it cools. An example of another effect is a common method for reaching ~0.3 mK. You draw a vacuum on liquid He3 causing some to evaporate and cool down the remaining liquid He3. It obviously isn't the case that the only way to get colder is to have heat move to something colder, otherwise a refrigerator would need some sort of "cold source". But that isn't the case, they use a compressor to cool down the refrigerant without the need for something colder. $\endgroup$
    – Matt
    Commented Oct 14, 2016 at 18:55
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    $\begingroup$ @Matt No matter how much you decompress something, it will retain the exact same thermal energy. Absolute zero has no thermal energy. You might get closer to absolute zero, but you cannot reach it by playing with pressure. And that's ignoring that you're not going to have gas phase (or indeed any of the 4 common phases) near absolute 0. $\endgroup$
    – user7652
    Commented Oct 14, 2016 at 19:08
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    $\begingroup$ @Matt The refrigerator's cold source is the room, because the temperature of the coolant can be increased above room temperature by raising the pressure. You can never create a relative temperature difference that will cool something to absolute zero, which is required for heat transfer, unless you have something below absolute zero. Which does not meaningfully exist. $\endgroup$
    – user7652
    Commented Oct 14, 2016 at 19:09
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The usual answer is that it actually is possible because even though the ground state of spacetime itself has non-zero energy, it is not kinetic energy, which is the very definition of temperature.

Due to the discrete nature of bound states, it is possible and has been achieved to bring single particles or even ensembles to their ground states or common ground state. If you define your system as just that and ignore the fact that very soon it'll get hit by something and suddenly no longer been at zero, goal achieved.

Macroscopic systems or timespans, though: no dice. As a single kinda random example, you have lots of neutrinos everywhere, which you need to count, and 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.

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    – ManishEarth
    Commented Oct 16, 2016 at 6:58
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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 $0\ \mathrm{K}$

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    $\begingroup$ Like the uncertainty principle, this is not about observation but way more fundamental. $\endgroup$
    – yeoman
    Commented Oct 15, 2016 at 11:47
  • $\begingroup$ @yeoman how is observation not fundamental and why is this not about observation? $\endgroup$
    – Andrei
    Commented Oct 16, 2016 at 7:20
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    $\begingroup$ In quantum mechanics, a particle is not a dot flying through space. Instead, it's a blob in space-time, described by the Schrödinger / Dirac equation. The blob can either be very focused around a specific position, then it implicitly is very fuzzy about its momentum. Or the other way round. or something in between. It's a fundamental property of its state, thus a fundamental property of the particle itself that exists with or without measurement. $\endgroup$
    – yeoman
    Commented Oct 16, 2016 at 7:36
  • $\begingroup$ To put it simply, when something isn't measurable it can't exist. When you can't measure the exact position without interfering with the momentum then the particle just doesn't have definite momentum. There are no hidden variables that just can't be measured. To put it in an analogy, even God wouldn't know the exact momentum. $\endgroup$
    – user36079
    Commented Oct 16, 2016 at 19:48
  • $\begingroup$ @JannikPitt then the whole concept of observation for me is completely blown off. How can you observe something without any interaction? In my opinion, observation involves a transfer of information. A transfer means that something which used to be somewhere it is not there anymore, but at a position, from which the information can be interpreted for humans to read through one of their senses. Even if the observation does not actively change the object, the object has to change itself for others to be able to observe it. The object though, imo, still exist, even in the absence of observation. $\endgroup$
    – Andrei
    Commented Oct 17, 2016 at 12:44
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Absolute zero is unattainable. You could do it in theory according to classical laws of physics, but it's quantum mechanics (including quantum electrodynamics) which prevents absolute zero to be reached. According to these laws, there is a possibility to have a fluctuation in energy even at zero level, which means that temperature will also fluctuate above zero. And the lower the temperature, the bigger the impact of quantum effects is. Special relativity (things like $E=mc^2$) doesn't matter here.

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    $\begingroup$ If anything, it is classic theory that prevents us from reaching absolute zero, and quantum theory provides a faint hope that it can actually be done, if only in some limited sense. See, if the energy is infinitely divisible, then you may suck out half of the remaining heat, then half of the rest, then again half of the rest, and so on. But if the energy goes in tiny discrete portions, that's another story. $\endgroup$
    – Ivan Neretin
    Commented Oct 14, 2016 at 10:46
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    $\begingroup$ That is true for any temperature, not only absolute zero. Any given temperature value is unattainable exactly due to fluctuations. $\endgroup$
    – Dmitry Grigoryev
    Commented Oct 14, 2016 at 11:40
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    $\begingroup$ Please don't call the ground state "zero level" when the whole point is that it has non-zero energy :D $\endgroup$
    – yeoman
    Commented Oct 15, 2016 at 11:48
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    $\begingroup$ This argument makes no sense. The zero point energy of any QM system is certainly finite, while we can cool any object down infinitesimally close to zero K. $\endgroup$
    – Karl
    Commented Apr 24, 2020 at 21:12
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Two days ago a publication (Ref. 1) appeared proving mathematically that it is impossible to reach Absolute Zero.

This is kinda hard to read but well this is a serious proof.

Have a good read !

Reference

  1. Masanes, L., Oppenheim, J. A general derivation and quantification of the third law of thermodynamics. Nat Commun 8, 14538 (2017). https://doi.org/10.1038/ncomms14538
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Feynman is correct. Stop and think a moment. What does it mean to be "at absolute zero" if we accept the proposition that absolute zero is unobtainable? Assume that absolute zero is unobtainable. Which of these statements is more false:1. At absolute zero, there is no motion. or 2. At absolute zero, there is no mass. Both are equally false; since the predicate is false, the statements are, logically, meaningless. (Which means both statements are equally true, too. But while #1 has often been used, I sure wouldn't use #2 unless I wanted to be pelted with rotten fruit. #1 is "close enough" to be a "useful" (if false) explanation while #2 has no physical justification.). Classically, the Laws of Thermodynamics are empirical. They is what they is because they is. No "why" there. However, we can derive them from classical statistical mechanics (which was invented many years after the acceptance of the 2nd Law) or even better after the invention of quantum mechanics (1925 on) and its application to statistical mechanics. Temperature is a property of large populations of quantum particles, an atom does not have a (classically defined) temperature. So, in order to understand why this population can't have a temperature of 0 K, we need to understand how temperature is derived from the quantum mechanical properties of the particles that the system is composed of. That is a semester course in college, and not an Introductory one! If you understand Feynman's explanation, accept it (although it's not perfect - it was, after all, targeted at college freshmen with no previous exposure to quantum mechanics)

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    $\begingroup$ I'm not sure what Feynman means here. The lowest quantum state of a finite system is definitely reachable. At that point, we cannot remove any more energy from the system, and are at zero thermodynamic temperature. Of course any macroscopic object is practically infinite, in terms of an exact quantummechanical description. $\endgroup$
    – Karl
    Commented Dec 2, 2016 at 1:25

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