This just started to bother me after reading yet another entangled particle question, so I hate to ask one myself, but...
If we have two entangled particles and take a measurement of one, we know, with certainty, what the outcome of same measurement of the other particle will be when we measure it. But, as with all fundamental QM, we also say the second particle does not have a definite value for the measurement in advance of making it.
Of course, the particle pairs are always described by an appropriate wave function, and measurement of half the pair changes the probabilities associated with each term. But, and this is the part that bothers me, with knowledge of the first measurement, we know the outcome of the second measurement. There's nothing strange or forbidden or anything about this, no non-local affects, no FTL communication, etc.
But does it still make sense to talk about the second particle not being in a definite state prior to the measurement? Or can we consider a local measurement of one half of an entangled pair to be a measurement of the other half? The latter option feels distasteful because it implies communication between the particles when communication is possible, which is obviously wrong, but I find it hard to pretend the second particle in the pair, whose state I know by correlation, is somehow not in that state before I confirm it by measurement.
I should clarify that my uneasiness comes from a comparison with the usual "large separation" questions of entangled particles, where our ignorance of the first measurement leads us to write an "incorrect" wavefunction that includes a superposition of states. Although this doesn't affect the measurement outcome, it seems there is a definite state the second particle is in, regardless of our ignorance. But in this more commonly used scenario, it seems more fair to say the second particle really isn't in a definite state prior to measurement.
As a side note, I realize there's no contradiction in two different observers having different descriptions of the same thing from different reference frames, so I could accept that a local measurement of half the pair does count as a measurement of the other half, while a non-local measurement doesn't, but the mathematics of the situation clearly point to the existence of a definite state for the second particle, whereas we always imply it doesn't have a well-defined state (at least in the non-local case) before measurement.
At this point, my own thinking is that the second particle is in a definite state, even if that state could, in the non-local separation case, be unknown to the observer. But that answer feels too much like a hidden variables theory, which we know is wrong. Any thoughts?