Can time dilation be transfered between entangled particles? In other words, if one has two particles that are entangled (based on quantum non-locality) and one particle is placed in a deep gravity well while the other is in deep space, will the particle that experiences time dilation (in the gravity well) relative to an outside observer "transfer" its time dilation to the second particle that is in deep space? So that BOTH of the particle's clocks run "slow"? If so, why? If not, why not? Thank you so much for your help!
Good question! General relativity as it currently exists is not capable of dealing with quantum mechanics in any way. The two theories are simply incompatible. This means, obviously, that at least one if not both of the two theories has to be wrong, at least on the spatial and temporal scales where quantum processes are important. This inconsistency is perhaps the single largest unsolved problem in physics right now (the alternative being the mysterious dark matter and dark energy that make up most of the universe). I guarantee you that whoever unravels this one, he or she is going to get the Nobel Prize.