# Absolute zero and Heisenberg uncertainty principle

I got to read Feynman vol I and there was written that at absolute zero, molecular motion doesn't cease at all, because if so happens, we will be able to make precise determination of position and momentum of the atom. But we do know that Heisenberg uncertainty principle holds for microscopic particle IN MOTION....then what is wrong to consider that all molecular motion ceases at absolute zero...need some help!

-
I've read your question two times. I don't get what you're asking. Can you try to elaborate a bit further? I especially don't get your last sentence. –  lomppi Mar 7 '13 at 8:58
I mean to say that the heisenberg rule holds only 4 microscopic particle in motion...but at absolute zero motion is assumed to be absent...hope this helps... –  idiosincrasia23 Mar 8 '13 at 20:08

Motion does not cease at absolute zero if the system you are looking at has a zero point energy.

In many systems, e.g. crystals, at low temperatures the atoms/molecules behave as harmonic oscillators, and the energy of a harmonic oscillator cannot be reduced to zero: there is always some minimum energy called the zero point energy. This means that at absolute zero the atoms in a crystal will not be stationary. There will be a small vibration corresponding to the zero point energy. This is most obvious for light atoms like Helium where the zero point energy is enough to keep the system liquid, so even at absolute zero Helium will not solidify unless it's put under pressure.

The situation is different for a free particle. In that case, at absolute zero the momentum is zero but then we have no knowledge about where the particle is (i.e. $\Delta x = \infty$). If we want to measure where the particle is we have to put some energy in, but then of course the system is no longer at absolute zero and the momentum is now non-zero.

-
Answer blew my mind –  speeder Dec 18 '13 at 23:31
This is an excellent question, and an equally excellent answer. Thank you. –  Seanosapien Mar 5 '14 at 0:15

The uncertainty principle is a fundamental property of quantum systems, and is not a statement about observational success. No particle either free or in crystal can have zero momentum otherwise a nonsensical infinity is required for the standard deviation of position $\Delta x$, in the uncertainty principle $\Delta x \Delta p \geq \hbar / 2$.

$0 \cdot \infty$ is undefined, so breaks the principle if the product is interpreted as zero. More likely the product should be interpreted as also undefinable, in which case the principle itself becomes undefinable. So all particles must move at least to some extent at all times or the uncertainty principle itself breaks down.

-