Physics noob here. I can't find a good answer to this thought experiment that is consistent with general relativity and It's really bothering me. I'm probably missing something huge but just can't figure it out, so here it goes.
If many particle pairs are entangled on Earth and one particle of each of the pairs of particles is transported to a distant point in space at sub-light speeds using any means, then wouldn't faster than light information transmission be possible between those pairs? The particles on Earth could be measured along a particular spin axis, forcing the other particles to take the opposite spin along that axis. Using "weak measurement" couldn't a measurer at the distant point in space statistically determine the wave function state and therefore when to check for spin axis alignment and therefore a transmitted binary value? I have a feeling the answer may be "weak measurement isn't possible" but I don't know enough to say whether the literature to date has reached a consensus.