[rprospero]

You're a couple of abstraction levels lower than where I aimed my post :-)

You're absolutely right that everything breaks down after a measurement. However, I'd begun my hypothetical by assuming that we had some magical technique for getting the complete wave function. If our measurements again give us the complete wave function, then we just use the time evolution operator on that again.

I guess what I'm trying to say is that we should be okay after N-1 measurements, as long as we're allowed to see the result of that final measurement. You're right, though, that we rapidly lose the ability to make any predictions if some jerk keeps measuring the system. I think that there's also an Everettian argument that, if you haven't given me the complete wave function for the jerk making the measurements, then you didn't really give me the the complete wave function of the system. However, that's pushing outside my area of expertise.