I find myself unable to give an “interpretation-independent” account of what a density matrix is that would be any advance on what’s already been said. It is, among other things, a way to represent a probability distribution over quantum states, but you can get the same density matrix from different starting points; but that is less of a problem if you have decided in advance that only certain starting points (e.g. configuration basis, position eigenstates) correspond to reality; that’s what I should have said. And the response of a diehard “positionist” to Scott’s challenge would be, I think, that any density matrix which cannot be reduced to a mixture of position-basis pure states could only have arisen as the reduced density matrix describing some part of a larger pure state.
I suppose the bigger question is whether the formal ability to change basis in Hilbert space, or even to work independently of any basis at all, is a principle which should be accorded the same significance as, say, special relativity. There is a curious argument for the priority of position, utilizing probability currents and “weak-valued measurements”. In that paper it is expressed in the context of Bohm-like hidden variables theories, but I wonder if it can be transposed into a many-worlds perspective.
I find myself unable to give an “interpretation-independent” account of what a density matrix is that would be any advance on what’s already been said. It is, among other things, a way to represent a probability distribution over quantum states, but you can get the same density matrix from different starting points; but that is less of a problem if you have decided in advance that only certain starting points (e.g. configuration basis, position eigenstates) correspond to reality; that’s what I should have said. And the response of a diehard “positionist” to Scott’s challenge would be, I think, that any density matrix which cannot be reduced to a mixture of position-basis pure states could only have arisen as the reduced density matrix describing some part of a larger pure state.
I suppose the bigger question is whether the formal ability to change basis in Hilbert space, or even to work independently of any basis at all, is a principle which should be accorded the same significance as, say, special relativity. There is a curious argument for the priority of position, utilizing probability currents and “weak-valued measurements”. In that paper it is expressed in the context of Bohm-like hidden variables theories, but I wonder if it can be transposed into a many-worlds perspective.