An important property of matter taught in grade school is that it occupies space (has a volume, whether it's relatively fixed like a solid or liquid, or depends on pressure like a gas), and that matter cannot occupy the same space at the same time.
This is often contrasted with other forms of energy like light or sound, which has no problem occupying the same space at the same time.
The underlying reason given for this in college physics classes is the Pauli exclusion principle. Matter is made of fermions, which have antisymmetric wavefunctions. The spacial probability distributions of two or more fermions are less likely to overlap than you'd expect for classical particles, while the probability distributions for bosons are more likely to overlap.
At low densities or high temperatures, matter molecules stay far enough away for the distinction of fermion/boson not to matter. The distributions are too sharply localized to overlap, so they just behave classically.
But what about a Bose-Einstein condensate of composite bosons such as He-4? It's matter in the sense of being composed of matter molecules. But as a bosonic fluid, the bosons should prefer sharing the same spacial state instead of avoiding it. If so, it would seem to be acting more like light or sound.
On the other hand, each molecule is still composed of individual fermions. And fermions tend to avoid each other.
How can the bosons share the same space while simultaneously the fermions they're composed of avoid the same space? Are these two competing effects, or just different levels of description (as in, an effective field theory) which shouldn't be mixed? And if they do compete, what determines the balance? Which one wins out and why?
