Question

At absolute zero, all particle motion does what?

Answer 1

Stops (at least, for atoms... not for molecules). This can be related back to the third law of thermodynamics:

There exists an arbitrary condition called absolute zero in which the entropy of a perfect crystal is chosen to be zero.

That is, at absolute zero, there is perfect order in the system, and it is defined that only one microstate is supposedly available: stillness.

Each ensemble of microstates must be consistent with a given macrostate, but with only one microstate, there is only one macrostate. So we'd be able to observe (in the macrostate) as well that there is no motion (theoretically).

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We could have also realized that temperature is defined as the average kinetic energy (or at least directly proportional to it, which is good enough), and at absolute zero, temperature is `"0 K"`.

Thus, the average kinetic energy is `0` at `"0 K"` and it is said that there is no motion in the system, unless it is a molecule. Then it can vibrate with a zero-point energy of about `1/2hnu`.