# Novice question about heat, ZPE and HUP

1. Jul 28, 2007

### jackle

Hi,

I was watching a pop-sci TV program on heat recently. Specifically, it was about trying to reach the lowest temperature possible. I was trying to recall something I learnt about the uncertainty principle being a barrier to reaching absolute zero. When I searched on the internet I got some stuff back about zero point energies, but I could not work out how the concepts of heat, zero point energy and uncertainty fit together.

1) Does the uncertainty principle generate heat?

2) Is it theoretically possible to reach absolute zero?

3) Is a system at the zero point energy also at absolute zero?

Thanks

Last edited: Jul 28, 2007
2. Jul 28, 2007

### meopemuk

It would be helpful if you avoid using acronyms as much as possible, unless they are 100% commonly known (like USA). My guess is that you meant

HUP = Heisenberg uncertainty principle
ZPE = zero-point energy

Eugene.

3. Jul 28, 2007

### jackle

You guessed right.

Sorry for being lazy, I have tried to put it right by editing the original post.

4. Jul 28, 2007

### christianjb

1) Not that I'm aware of.

2) No, but you can get asymptotically close.

3) ZPE is defined as the residual energy (potential + kinetic) due to quantum effects at 0 K. If it weren't for quantum effects- the system would have a lower potential energy (with a kinetic energy of zero). The difference between the system's actual energy and its hypothetical classical energy is the zero-point energy. i.e. the zero-point energy would be zero if the system were purely classical (hbar ->0).

5. Jul 28, 2007

### meopemuk

In statistical quantum mechanics, a system is at temperature T if it is in a mixed state where all possible energy levels enter with their weights $\exp(-E/kT)$. In principle, it is possible to prepare a macroscopic system (e.g., a piece of crystal) in a lowest energy pure quantum state. This would effectively mean that T=0. I think that superfluids or Bose-Einstein condensates also formally have T=0.

Eugene.