I have looked at
- Helium Nucleus as boson
- How can multiple fermions combine to form a boson?
- Why are He-4 nuclei considered bosons, and He-3 nuclei considered fermions? but I still feel like saying "superfluid helium is a boson" is an oversimplification.
I don't have a problem with the rules of adding fermions to make bosons, I have a problem reconciling the behaviour of superfluid Helium like the one seeing at
with the sentence "superfluid helium is a boson". Pure bosons like photons can occupy the same time-space, you can in principle pack as many photons as you want in a light pulse, but in the video you can clearly see that the helium still occupies volume and drips into drops, the atoms do not collapse into a single atom sized box that then moves at unison. To me this makes it clear that whatever bosonic condensation happens in superfluid helium is not "the atom becomes a boson" but rather some degrees of freedom of the atoms become bosonic and all the atoms start hitting the ground state of these degrees of freedom. Indeed, a basic introductory quantum mechanics course will take a simple wave function over one spacial dimension (or better, the tensor product of n spacial dimensions, where each dimension is one "particle") and simply show than when it is anti-symmetric it becomes zero when the position of any of the "particles" are equal, so only symmetric ones can have equal positions and thus occupy the same space.
Can we compile a list of which degrees of freedom stay fermionic or bosonic, and which ones change from fermionic to bosonic? Or am I wrong and is there a way for an object with fully bosonic degrees of freedom to occupy cumulative amounts of volume?
This question is maybe a more specific version of
The answer there is very vague, but it sounds like it confirms my guess even if maybe it is not fully correct: there are still degrees of freedom/variables that are fermionic and stop the atoms to overlap with the container or themselves.
