Following up on this question "Does a diatomic molecule falling into a black hole dissociate?", if a diatomic molecule is falling into a black hole (BH) with the bond connecting the atoms oriented normal to the event horizon (EH), there will be some time period when to a distant observer the bond straddles the EH - that is, one atom is outside the EH, the other is within.
During that time, it seems in the molecular frame of reference the atoms in the molecule can interact for example they could still undergo harmonic motion, repel/attract each other, exchange electronic excitation energy etc. However a distant observer can still make observations about the atom exterior to the EH and this would seem to violate the transfer of information across the EH, since by extension the distant observer now knows what is happening to the atom within the EH. How does one resolve this apparent paradox?
To push this further one can imagine a polymer chain of N atoms crossing the EH and then observing the motion of the effects of the entire chain on the last atom exterior to the EH. How long could the chain be and still have communication between the atoms at the opposite ends of the chain?
Note this does not have to be a quantum mechanical phenomenon, you could choose heavy atoms, or even a macroscopic system of 2 (or more) devices that communicate with each other falling into the BH with orientation perpendicular to the EH.
If the answer is best/easiest done by referring to technical papers etc., then I'm happy to have references provided and dig into those myself.