Setting of the experiment: Triplets Alice, Bob, and Carla have plenty of entangled electrons when they depart from Earth. Alice stays behind, Bob goes to Zeta Reticuli, and Carla goes to Andromeda. All three continuously make a video of everything around them, assuming they could even see each others clocks. Because of time dilation (including relativistic Doppler-shift) they all see each others clock running slow. However, if Bob returns to Alice she will be older because he accelerated. In Carla her reference frame, she thought that Bob was travelling anti-parallel to the motion of the Milky Way when he was on his way to Zeta Reticuli. The velocity of Alice was greater than Bob's according to Carla, concluding Alice her clock was running slowest. Outside the lightcones of certain events, Carla might even see a different sequence of events than Alice or Bob would.
The experiment: The triplets have distributed entangled pairs of electrons among them so that each pair is separated after departure. They have agreed to make a position measurement at the end of every week (7 days of exactly 24 hours on their own clock). The "collapse of the wavefunction" happens instantaneously, while relativity denies the notions of absolute time: there is no "now-moment".
The question is: when does the other electron collapse, "after" the position measurement? Could the triplets carry out this experiment, and see regularities in the wavefunction collapses caused by their siblings? I know it's correlation rather than causation, but what if the triplets agreed to a secret code? Since they might be able to predict each others clocks, they could agree that a postion measurement between 0-30 min of some hour represents 0 while 30-60 min represents 1.
