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If quantum teleportation is performed into a black hole (by an electron for example), what happens to that electron?

Let's say a hydrogen atom is very close to a black hole and the electron jumps into the next level of energy, which collides with the black hole, is the electron stuck forever? Is it prevented from entering the black hole? Is it free to enter and leave?

EDIT [More precision about my train of thoughts, feel free to either answer or discuss about my why of thinking if not appropriate for the concern] :

I understand that we do not know enough about the QFT and black hole interaction, but I would like to try to narrow a bit the question, to see if there is a way to actually answer the question with a relative precision.

Theoretically, at the moment the electron jumps and his electron cloud conflicts with the black hole, I believe the only possibilities are :

  • The electrons "enters" the black hole at one point (quantum teleports its state into it) and is free to leave the part of the cloud that is in the black hole, resulting in a paradox in the fact that no information can enter then leave the black hole. So not possible ?

  • The electron does NOT enter the black hole and is trapped into a electron cloud which is a part of the real cloud, resulting in a disorder in the electromagnetic stability of the atom, and making the electron "drop" into the atom. (what could that imply? is it possible ?)

  • The electron enters the black hole, and is trapped in it, breaking the link between the nucleus and the electron. ( what could that imply ? Is it possible ? Breaking the link requires energy, so the black is loosing energy/mass, while also earning energy because of the mass gained by the absorption ?). But that would mean that the nucleus "sees" the electron entering the black hole because of the link broken or would that mean that the nucleus still considers itself a hydrogen atom ?

I know this is very theoretical, and my train of thoughts is probably really bad, but I found it interesting to think about.

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  • $\begingroup$ It depends on frame of reference, for example if someone is going into black hole and his friend is watching him, he will never see him crossing 'event horizon' while that someone will think that he has already passed event horizon (If he's still alive of course). This phenomenon is called Gravitational Time dilation $\endgroup$ – Gigi Butbaia Apr 28 '14 at 14:47
  • $\begingroup$ To expand on Gigi's point, see: arxiv.org/abs/0712.0689 which provides a "derivation" of this phenomenon using the Schwarzschild metric. $\endgroup$ – JamalS Apr 28 '14 at 15:05
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I think there are two separate issues here. The first is quantum teleportation, and the second is about an electron entering a black hole.

To address the first issue: remember that quantum teleportation does not teleport the electron, it teleports the quantum state of the electron. So you can't teleport an electron into a black hole. You can, in principle, teleport the quantum state of a distant electron to an electron near a black hole event horizon, though I'm not sure that quantum teleportation is thoroughly understood in curved spacetimes.

As for the electron entering the black hole: you use the example of exciting an electron in a hydrogen atom. The problem is that the electron in a hydrogen atom is a fuzzy object without a precise position. In the $1s$ ground stat it's a fuzzy blob centred on the nucleus and extending out in principle to infinity, though the probability of finding the electron falls rapidly with distance from the nucleus and it effectively zero within a few nanometres. When you excite the electron, e.g. into the $2p$ orbital, you expand the fuzzy blob a bit.

If you have a hydrogen atom within a nanometre or so of the event horizon then I guess the electron cloud would overlap the event horizon and there would be a finite probability that the electron is within it. Exciting the electron from the $1s$ to $2p$ orbital would increase this probability a bit. However I don't think quantum mechanics in the curved spacetime at an event horizon is well enough understood for us to say with any certainty exactly what would happen.

Both Gigi and Jamal mention in their comments that for any observer outside the event horizon it takes an infinite time for anything to reach the horizon. This has been discussed on this site before, see: for example Can matter really fall through an event horizon?. However this is the result of a classical treatment, and it's not clear to me how this conclusion would be modified by quantum effects very close to the event horizon.

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  • $\begingroup$ Thanks for the element of answer, see my edit for more precision on my concerns. It'll probably be, as you said, not understood enough to bring a precise answer, but I can hope :) $\endgroup$ – Saffron Apr 29 '14 at 8:17

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