I've always been curious -- how can two helium atoms enter the same quantum state when their constituent particles can't? What is happening to the spin-1/2 electrons, for example?
This may be a bit mangled from the last time I took a relevant class, but my recollection is that the "real" reason electrons can't share the same state is that they're what's called antisymmetric with respect to exchange.
In general, most particles are fundamentally indistinguishable: if you swap two of them you haven't really changed anything. This leads to most particles being either symmetric (bosons, integer spin) or antisymmetric (fermions, half-integer spin) with respect to exchange. If symmetric then the wave function doesn't change at all; if antisymmetric then exchange reverses the sign of the wavefunction. If we have two electrons in the same place, and arbitrarily swap them (which we're allowed to do since they're identical), then we've reversed the sign on one of the wavefunctions. But since they're in the same place, the wave functions cancel. This would violate conservation of energy, so isn't allowed; instead, we just never let them occupy the same state in the same place, and call it the Pauli exclusion principle.
While a single electron has half-integer spin, a He-4 nucleus has integer spin, so is symmetric to exchange, and it's wavefunction doesn't cancel if you have two in the same place.
If you exchange electron A with A', the wave function changes sign (antisymmetric). But if you exchange A with A' and B with B', nothing is changed (symmetric).
At the lowest temperatures, the flow rate of helium-3 stopped decreasing. It didn’t exhibit super-solid properties, but it also stopped behaving like a normal solid. ... The researchers were not at a low-enough temperature to expect a helium-3 super-solid. But the temperature was low enough that maybe, just maybe, some pairing was occurring, which was allowing some super-solid properties to start to become apparent.
So it's a tantalizing glimpse of the possibility of super-solids, but not yet a hard proof.
It's a bit better than that from my reading: that quote's for He-3, which we don't expect to show any supersolidity (it's a fermion) unless the He-3 nuclei start forming pairs (the pair would have integer spin) -- which isn't really expected until even lower temperatures.
The key part of this experiment as far as I could tell was that at the same temperatures He-3 showed decreasing flow rate with decreasing temperature, He-4 showed increasing flow rate with decreasing temperature. This is exactly what we'd expect since He-4 nuclei are bosonic, while He-3 nuclei are fermionic. That's pretty good IMO
