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Assume two entangled particles, two synchronized atomic clocks, and two observers. Each observer has agreed to measure the state of their particle at a predetermined time, relative to their atomic clock. Assume one observer/clock/particle is on a spaceship that has been traveling near the speed of light for some time.
What happens when the particles are observed? Will the results be the same, because somehow time is "linked" even though it seems to pass differently for each observer? Will the results be different, because the particles are somehow linked "instantaneously?" (What does that even mean in this context?)
If the former, what happens if the particle is brought back to Earth? We should find the atomic clocks were no longer synchronized. (This part has been tested, right?) If so, wouldn't that mean the particles were permanently out of sync, and that by observing one of them, one could predict the future state of the other? As in, predicting the future?
IANAP, just pointing out some apparent paradoxes that for all I know have been solved.