...sent one into a black hole?
You don't see it any more.
So the particle that didn't go into the black hole also disappears? ∞
No. Why would it?
No. But it does have one hell of a case of separation anxiety.
So when you observe the particle that didn't go into the black hole nothing odd will happen. I guess i'm asking an impossible questions since its going to be a long time before we can start sending stuff into black holes :)
No, we already know what will happen. It doesn't matter that we haven't been to a black hole yet, the rules still work the same.
Well, in theory, as we don't have any experimental evidence specifically for throwing entangled particles into black holes, the actual laws unifying QM and GR (if they do exist) could have a small correction causing the other entangled particle to instantaneously turn into a television playing 2001: A Space Odyssey. But, I agree, we have no reason to think our current rules break down when throwing entangled particles into black holes. Assuming that was your point.
There is no reason to believe that nonlocality, if it exists, can be affected by mass and gravity. AFAIK, no experiment so far has shown any such hint. The more interesting question is what happens to the wave packet as it enters the horizon.
Thank you Maui you probably asked the question I should of asked. I'm a Very, Very amateur physics guy and really enjoy watching shows on Nova and Discovery about physics and astronomy. My limited understanding of Black Holes is nothing gets back out once its goes past the horizon, so as you said what does happen to the "wave packet" as it enters the horizon.
The black hole information paradox comes to mind.
You might find this blog interesting, particularly the exhange between Bee and Andrew Thomas in the comments section since your exact question is discussed there:
The Black Hole Information Loss Paradox
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