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Q: Two entangled particles approach a black hole, one falls in and the other escapes. Do they remain entangled? What about after the black hole evaporates?
In practice (reality), entangled particles don’t have any kind of connection with each other, they’re just correlated in a funny way. In quantum physics things can be in multiple states, such as being in multiple places or multiple energy levels. You have to include states that involve multiple particles that are in multiple states. A black hole, in addition to all of its other weird properties, does a really good job doing exactly that. This has lead to some new ideas like black hole entropy, Hawking radiation, holography theory, and black hole computation (this last one is a little more far-fetched than the others).
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