# Is absolute zero possible?

During a recent conversation about absolute zero with a friend of mine, he claimed that absolute zero had never actually been achieved by scientists. And what’s more, if anyone ever did succeed it would spread outward to affect everything (the walls of the space it’s contained in, the air outside the container, the scientists etc.) stopping everything on the planet and ultimately the universe. Please reassure me I can tell him he’s talking nonsense!

He’s talking half-nonsense; It’s really difficult to make things cold, because cold isn’t a thing, it’s the absence of a thing - heat. You make things cold by letting the heat flow into something colder.
Trouble is that by definition, there’s nothing colder than absolute zero, so it’s hard to find somewhere for that last little bit of heat to escape to.
There are tricks though, involving collapsing magnetic fields and lasers, that can also be used to cool things down, I think.

As regards the second bit about it spreading everywhere; there’s simply no reason to suspect that would happen and lots of reasons to suspect it wouldn’t. He’s talking about a Sci-Fi concept called Ice-9.

In the a little bit of knowledge is a dangerous thing department…

The product of an particle’s momentum and uncertainty of position is a (very, very tiny) constant.

If a particle were to stop moving at all (the classical def. of absolute zero) its uncertainty of position would go towards infinity. Very loosely, it would be “everywhere”.

However, that wouldn’t affect the rest of the Universe in any way.

The problem with ultralow temperatures is that it’s kinda like Zeno’s paradox, in that you can go in steps that take you halfway. But in this case it takes just as much effort for each step, so that as you get closer to absolute zero you put a huge amount of effort into steps that get you closer by smaller and smaller amounts. To get as close as you can these days requires a repertoire of straightforward methods and nifty tricks.

But you can never get all the way to absolute zero, if you define that as the place where all motion completely stops, because that would violate the Heisenberg Uncertainty Theorem – you’d have a particle that was absolutely motionless, which would imply that you should have no idea where it was. But you’d know it was in your apparatus. Even if you didn’t have its position pinned down any better than that, it would be in violation of the HUT. So you’re always going to have some residual uncertainty. (Besides, even the lowest state in a QM harmonic oscillator has a wavefunction that isn’t a delta function – what are you going to do, violate QM?)
The Ice-Nine thing isn’t a low temperature thing, anyway. The point was supposed to be that it was solid at room temperature and pressure.

Just how strict is Heisenberg’ ?

A slight nitpick: I agree that absolute zero can not be achieved, but it is not because of the Heisenberg Uncertainty principle. A more accurate definition of absolute zero is not when all molecular motion stops, but when all of the atoms of the system are in the ground state. The ground state is the lowest permitted energy level, but due to quantum effects, there will still be some vibrational motion. If all of the atoms are in the ground state then no energy can be extracted from the system, for it is at its lowest allowed by QM; therefore, that would be absolute zero.

However, thermodynamics does not permit absolute zero to occur. The third law of thermodynamics states that absolute zero cannot be attainted in a finite number of steps.

Thus, at absolute zero some atomic motion would exist due to quantum effects, but no more energy could be taken from the system. However, getting to such a point would require an infinite number of steps, which is impossible.

The product of thwe uncertainty in position with the uncertainty in momentum must be less than or equal to h/4(pi)
h is the Planck constant, 6.626 x 10[sup]-34[/sup] Joule-seconds , which is pretty damned small, but the point is, it’s not zero.

(h/4(pi) is usually called “h-bar” and designated by the h with a diagonal slash through it. The same uncertainty relation holds for other incomensurate QM quantities like Energy and Time, Angular mementum and angular position, and other pairs that have dimensions of action. If the quantities aren’t commutative, they have an uncertainty relationship. Just another weird feature of the world of the quantum.

I’m uncertain.

I thought that atoms had been observed to ‘smear’ into little puddles of Bose-Einstein condensate (or something) at near-absolute zero - if this is the case, wouldn’t it neatly deal with the Heisenberg issue?

No, [dwl]lekatt[/del] Kozmik, that doesn’t make any sense at all.

:smack:

Nitpick: [del]h[/del] = h/2pi, not h/4pi. And in fact, one almost never actually uses h (rather than [del]h[/del]) in physics, since the latter form shows up a lot more often and more conveniently.

Dammit! That was my recollection, but it’s been years since QM, so I checked, and the book I looked in had 4(pi).
So you won’t use it, it’s the you’d-think-it-was-reliable Penguin Dictionary of Physics.

Here is a thread I started a while back dealing with ABSOLUTE ZERO

This may help.

What’s the lowest temperature that’s been achieved in a laboratory?

*100 pK (2.5 × 10^-10 K) - Lowest temperature ever produced, during an experiment on nuclear magnetic ordering in the Helsinki University of Technology’s Low Temperature Lab. *

That would be only a few billionths of a degree above Absolute Zero.

Can’t quantum states briefly have a negative energy value? If so, could you go from very little energy to lowest ground state in one step?

Not quite certain what you mean by “quantum states briefly have a negative energy value”; regions of space can have a so-called negative energy density (see Casimir Effect), and a particle could have a negative energy relative to a defined reference state, but by definition the ground state for fundamental particles is 0 Kelvin. CalMeacham has it right that there is a fundamental limit for a particle with a given intrinsic mass-energy as to exactly how “cold” (i.e. motionless) it can be, per the Indeterminacy (or Uncertainty) Principle. (Heisengberg, by the way, objected to the christening of that principle after him.) In fact, you can’t even reference the particle to the limit described by the IP; your actual measurement will be somewhat greater because of your own interference in measuring it. You can measure the effect it has on a third body to limit your direct interference, but then you have the greater uncertainty of two particles. You can measure a whole system and cancel out various uncertainties to come to a close average, but in the end it’s always less accurate than the intrinsic uncertainty.

Although this is a result of quantum mechanics, you have a somewhat similar argument from classical thermodynamics, as elucidated by randomlyblanks. To bring the system to the absolute ground state you’d have to make ΔS=0 (zero change in entropy). But the entropy of a system is always changing while you’re moving energy around, and so like a wily fox you can never quite bring it to ground.

This guy lays claim to the idea that QM is all bunk and that you can reduce electrons within an atom to “fractional energy states” (and presumably bring an electron to a ground-reference zero state) but since he’s batshit crazy and hasn’t been able to produce any of the high temperature superconductors, high density batteries, inert hydrogen gas, or miracle cures for cancer, we can probably safely dismiss his claims.

And Sevastopol, I heard Heisenberg was a pretty easy going guy, as long as you stay within his bounds. Outside of there, he’s likely to be pretty flighty.

Stranger

Um kind of. If the atom is bosonic (an integer spin overall), then at low temperatures the atoms will collapse into the ground state. Ground state bosons will bunch into the exact same place at the same time. What you end up with is a “jumbo atom” in which many atoms appear to be sitting all in the same place at the same time. Still even in this state, a significant portion of the sample is not in the ground state and, therefore, not at absolute zero. Looking at this image, one notices that the peak is not a spike, but rather a bit bell shaped. If all the atoms are in the same place at the same time in the condensate, it should appear to be a spike. The spread in the peak is from the Heisenberg Uncertainty Principle; since the momentum is precisely known in the ground state, the position is “smeared” a bit. Nothing gets around uncertainty–its not an error in the equipment or method, it is a fundamental principle that can be mathematically derived fairly easily.