# Uncertainty and absolute zero

1. Apr 27, 2004

### Michael2003

RIght, everytime I hear someone define absolute zero lately they say that it is when all of the atoms are in their lowest energy states, which leaves a finite amount of energy because the uncertainty principle does not allow knowing exactly where something is and how fast it is moving, and if there is absolutely no energy (above mass-energy and such) you know the speed exactly and where it is. So, what amount of energy is there left? Is it a range of energys? If so how big is it? And does the energy that you can say is left depend on just how well you know where the atoms all are?

2. Apr 27, 2004

### ZapperZ

Staff Emeritus
Your question has two different aspects to it. The first is that for many quantum systems, there is already a MINIMUM energy state the system can occupy. The clearest example of this is a quantum harmonic oscillator. The lowest energy state is not zero, but rather $$1/2 \hbar\omega$$ simply based on the energy eigenvalues. So for a quantum harmonic oscillator, already one can see that even at T=0, there is still a non-zero energy to the system without explicitly invoking the HUP (even though it is a direct consequence of it).

Secondly, the amount of energy the system has at T=0 depends on the nature of the "confinment" or the potential energy profile. A Lenard-Jones type potential will give a different energy correction than the harmonic oscillator potential, etc. For Noble gasses, such energy corrections have been carefully studied (theoretically and experimentally) and are contained in what is known as the de Boer parameter[1,2]. This will tell you exactly what energy to add as the zero-point state is approached. The correction to "solid" He, for instance (both He4 and He3) is tremendously big that purely classical treatement of it fails spectacularly.

Zz.

[1] Ashcroft and Mermin "Solid State Physics" p.412 (Saunders, 1976).
[2] C.P. Herrero, J. Phys. Condens. Matt., v.15, p.475 (2003).

Last edited: Apr 27, 2004
3. Apr 27, 2004

### LURCH

This has been puzzling me recently, as well. When I was in highschool, I was told that Absolute Zero was the total absence of all energy. Thsi would indeed violate Uncertainty, but I always thought that was why Absolute Zero could never really be achieved.

4. Apr 27, 2004

### Michael2003

Right, I think I sort of understand that.

Just a couple of questions though. Firstly, does this site look fairly informative on quantum harmonic oscillators (I wouldn't want to read something that's wrong and try to understand it). Secondly, you said noble gases were studied. Was this done because they don't react with each other so are easy to observe the effect on. If so, would there be any difference using atoms that reacted together?

And just what stops a system reaching absolute zero? It's one of the laws of thermodynamics, but I thought I read somewhere that they are statistical, so there would still be a chance that absolute zero could be reached, surely?

5. Apr 27, 2004

### Dayle Record

Wouldn't absolute zero be mostly a postulate, since everything is moving, regardless of how we still it? Wouldn't we have to cool something, in a spin counter to the solar system, in fact the galaxy, to to reach a state of non energy like absolute zero? Would it make a hole in time, if we did that? Keep the answer simple, if there is one. I am very interested in motion vs stillness.

6. Apr 27, 2004

### quartodeciman

Scientific American magazine for May 2004, p. 120 [ASK THE EXPERTS] included this question:

Scientific American online > ASK THE EXPERTS > How are temperatures close to absolute zero achieved and measured?

I would love to pepper Professor Ketterle with more questions about his carefully-worded answer, but I zero in on one paragraph (page 2 of online article):

"How do we measure very low temperatures of atoms?"

(my summarization)
1. Extension of the cloud indicates indirectly the kinetic energy opposing the energy of the entrapping magnetic field.
2. Magnetic trap is switched off and cloud expands. The rate indicates directly the average velocity of the previously trapped atoms. Small clouds observed AFTER A FIXED TIME OF EXPANSION indicate previous low temperature.

? ->
If these are practically the only means for estimating extreme small temperatures acheived, then isn't measurement of a former zero temperature automatically excluded from possibility?
<- ?

Hmmm! Maybe if a zero Kelvin temperature were actually attained, the size of the cloud would disappear and no expansion would be detected afterward.

Hmmm! Maybe heating something that is at zero Kelvin is completely futile.