What happens if you make an observation of the spins of two entangled, far apart electrons at exactly the same time? If we consider the spins of two, far apart, entangled electrons, what will happen if we make a measurement on both spins at exactly the same time (let's assume time is not discrete)? I see it as a problem because if you measure one spin the other one pops instantaneously in the opposite spin state, depending on what the observed spin of the other electron is. But that's the same the other way round. Isn't the system in some state of not to "know" (I don't know how to phrase it differently) which spin pair will emerge? Is this a paradox? Do the measurements adapt to each other?  
I can't see a problem if you consider the wavefunction as a pilot wave, in which case the particles have well-defined positions, energies, and spins (which are always opposite and have already before the measurement well defined opposite values). By the way, I see that the uncertainty principle has nothing to do with this (as I presumed in the earlier formulation of this question). The locations of the two particles are not spooky connected.
 A: Nothing special happens.  What you end up is making two measurements, which confirm that one particle spins one way and the other particle spins the other, just like you expected to see.
There's no paradox here unless you presume a naive version of causality.  If you are worried about whether Measurement 1 caused the results of Measurement 2, or whether Measurement 2 caused the results of measurement 1, you could end up in a bit of a bind.  However, what you find is that no paradox occurs because the observable results of the two measurements is unaffected by this existential crisis.  If necessary, you can break this issue down by saying "The simultaneous measurements of Measurement 1 and Measurement 2 caused the particle to be in a particular state."
A: First problem you have with that is, what do you mean by exactly the same time? Both observers in the same rest frame? So lets exclude different rest frames.
There is still a problem with pilot wave theory. If one of the observers changes which direction he wants to measure (entanglement is only interesting if you allow for different non compatible measurements), then something has to change immediately at the other observers place (if you believe in realism, which seems you do). This is because Bell-inequalities (and CHSH) show that local realism is not compatible with experimentally confirmed QM. So how does a superluminal change of the pilot wave help there in any way?
