# Question about measurement and unitary dynamics

This is a question that's been in the back of my mind since I first learned quantum mechanics.

There seems to me to be some tension between the postulates of unitary evolution and state reduction upon measurement: basically, any quantum system ought to evolve unitarily; so in principle, every observer is a quantum system, so it ought to be possible to take the composite of the observer and the system she observes, treat it as a quantum system, and have it evolve unitarily. But then, where does the non-unitary reduction (i.e. the 'wave-function collapse') entailed by measurement come from?

Is it just that, if you have the system $\rho_{OS}$, i.e. the system made from the combination of the observer O and the observed system S, this will in general be highly entangled, since observation necessitates interaction, so the observer 'sees' the reduced system $\mathrm{Tr}_O(\rho_{OS})$, with herself 'traced out', which typically will have some von Neumann entropy -- which will tend to grow over time, as the entanglement grows with further observation, and since only non-unitary dynamics lead to rising entropy, the observer will tend to see non-unitary dynamics, even though the system made of herself and the observed system evolves unitarily?

Ugh, this turned into a bit of a run-on sentence. To be more clear, the observer is part of the system made out of the observer herself, and the observed system, described by the density operator $\rho_{OS}$. However, she 'sees', from the inside, only the reduced system $\rho_S = \mathrm{Tr}_O(\rho_{OS})$. As the system $\rho_{OS}$ evolves unitarily, as all (closed) quantum systems do, the observer 'sees' a nonunitary evolution of $\rho_{S}$, since entanglement between herself and the system she observes tends to grow, and thus, so does the von Neumann entropy of $\rho_{S}$. Is that where the nonunitarity of measurement comes from?