Of course, quantum mechanics has all kinds of things to say about what an observer would measure if measuring the position, momentum, etc., of some particle, or of some set of particles. But I have never heard anyone discuss what would happen if two independent observers (i.e. each having their own apparatus and not communicating with each other until after all measurements have taken place) were to attempt a measurement on one particle. If they were each trying to measure, say, the position of a proton somewhere, it's not hard to imagine that the classical aspects of their respective devices and the quantum mechanical aspects of the proton would all conspire to produce a proton definitely (kind of sort of) located at some place that the observers could agree on.
But let's say both observers try to measure the angular momentum of that proton about their own two individual locations. What happens to the proton, and to their measurements then?
EDIT: I want to head off an objection that this is a repeat of this question. That question also has multiple observers, but it deals with position and momentum, accurate (beyond a certain extent) measurements of both being impossible because of the Heisenberg uncertainty relation. So that question was pretty readily answered. In my question, there is no obvious recourse to that line of argument. (If there is some subtle recourse, I will be glad to hear it!)
