So an initially factorizable distribution, evolved into an “entangled system”—a joint amplitude distribution that is not viewable as a product of distinct factors over subspaces.
Actually, that’s still factorizable. You just need to change basis to the diagonal. Effectively, you’re treating them as one particle. The other dimension is their relative motion, and ‘being a particle’ corresponds to one value in that dimension.
The ability to make this transformation is why we can speak of protons and neutrons and atoms and quasiparticles. And bricks.
Actually, that’s still factorizable. You just need to change basis to the diagonal. Effectively, you’re treating them as one particle. The other dimension is their relative motion, and ‘being a particle’ corresponds to one value in that dimension.
The ability to make this transformation is why we can speak of protons and neutrons and atoms and quasiparticles. And bricks.