system
Given the following post, respond as if you're commenting on Reddit:
human
Is it possible to slow down a particle until its momentum is 0 if the universe has a finite size?

I was just wondering about Heisenberg's Δx * Δp ≥ h/4π. If you can make p (and therefore Δp) arbitrarily low, then its Δx gets infinitely big.  
But if the universe is finite, then so is Δx, meaning p can't be 0.

Does that make any sense, or it it stupid?
gpt
If the Universe is finite (i.e. it is a 3-sphere) there exist a zero-momentum state where the wavefunction is simply a constant. Since the volume of the Universe is finite, this is a normalizable wavefunction. This is called a zero mode.

The spectrum of momentum in this Universe is discrete, because it's given by the hyperspherical harmonics*. The first excited value of momentum is relative to the wavefunction with wavelength equal to the total circumference. This is more what you meant and what you could guess heuristically with the HUP, as you did. This momentum is of order hbar/radius which is of course ridiculously small.

A precise formulation of the HUP is not really possible here btw because, just to mention one thing, Δx doesn't make a lot of sense if x is not a vector.

\* in general, solving the free Schroedinger equation, which is just the Helmholtz equation, on a compact space will yield a discrete spectrum.