Entanglement inside a black hole

In summary, the paradox is that Assistant #1 can measure + and also see the Assistant #2 measure +. Hence, he observes that the entanglement was severed by the BH event horizon.
  • #1
Kostik
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TL;DR Summary
A thought experiment involving measuring the spins of entangled electrons.
Suppose two electrons are entangled with opposite spins. Electron #1 passes through the event horizon of a black hole, together with Laboratory Assistant #1. Suppose the assistant measures electron #1's spin after they pass through the event horizon (according to #1's [proper] time) and measures a + spin.

Another laboratory assistant, #2, outside the black hole, watches the Assistant #1 falling into the black hole, but #2 never sees #1 cross the event horizon. After a time, suppose Assistance #2 measure the spin of electron #2. He measures + or −.
If Assistant #2 measures +, then electron #1 must be −. And yet, Assistant #1 (in his proper time) already measured +!

It seems to me the "answer" is probably that when #1 makes his measurement inside the BH, he is no longer within the same spacetime as #2. He is not in #2's universe. Hence, the entanglement is effectively severed once #1 enters the BH (which #2 never sees), since #2 has no access to #1's spacetime.

Therefore, both electrons can have a spin measurement of +.

Assistant #2 never sees #1's measurement, so the issue here is meaningless to him. The interior of the BH is not in #1's spacetime.

HOWEVER, Assistant #1 can see #2's measurement, especially if he has a long time to relax and wait before reaching the BH singularity. #1 can measure +, and then after a while he can observe that #2 also measured +. Therefore, #1 can witness that the entanglement was broken.
 
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  • #2
Kostik said:
How to understand this?
Your black hole is just a more complicated way of setting up an experiment which has been done many times: the two measurements are spacelike-separated so there is no unambiguous way of saying which one happened first. The resolution of your apparent paradox is also the same: Entanglement doesn’t work the way you’re thinking.

Measuring the spin of one particle does not somehow set the spin of the other particle. When I measure one particle and get spin up, that just means that I know that when and if the other particle is measured (and for all I know that’s already happened) it will be spin down. It doesn’t matter which measurement is first.
 
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  • #3
Nugatory said:
Your black hole is just a more complicated way of setting up an experiment in which has been done many times: the two measurements are spacelike-separated so there is no unambiguous way of saying which one happened first. The resolution of your apparent paradox is also the same: Entanglement doesn’t work the way you’re thinking.

Measuring the spin of one particle does not somehow set the spin of the other particle. When I measure one particle and get spin up, that just means that I know that when and if the other particle is measured (and for all I know that’s already happened) it will be spin down. It doesn’t matter which measurement is first.
It’s not just a spacelike separation scenario. I outlined a scenario where both spins are measured with the same direction. Observer #2 never sees #1 make a measurement.
 
  • #4
Kostik said:
It’s not just a spacelike separation scenario. I outlined a scenario where both spins are measured with the same direction. Observer #2 never sees #1 make a measurement.
It is still just a spacelike separation scenario.

Kostik said:
If assistant #2 measures +, then electron #1 must be -. And yet, assistant #1 (in his proper time) already measured +.
This cannot happen according to our current theories. And we don’t have any experimental evidence contradicting the theory for this scenario
 
  • #5
But it can easily happen. It seems to me the "answer" is probably that when #1 makes his measurement, he is no longer within the same spacetime as #2. He is not in #2's universe. Hence, the entanglement is effectively severed once #1 is inside the BH, since #2 has no access to #1's spacetime.
 
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  • #6
Kostik said:
It’s not just a spacelike separation scenario. I outlined a scenario where both spins are measured with the same direction. Observer #2 never sees #1 make a measurement.
You are just repeating your original misunderstanding. In all of these entanglement situations, it is does not matter whether either observer sees the other’s measurement.
 
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  • #7
Of course it does not matter, except if both spins turns out to be the same.
 
  • #8
Why did you ask the question if you don't want to know the answer? Seems like you just want to argue, not learn.
 
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  • #9
The paradox seems to be how Assistant #1 can measure + and also see the Assistant #2 measure +. Hence, he observes that the entanglement was severed by the BH event horizon.
 
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  • #10
Kostik said:
The paradox
is all in your head
 
  • #11
Hoping for a more useful reply.
 
  • #12
Kostik said:
Hoping for a more useful reply.
What could be more useful than being told where the mistake is?
 
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  • #13
Vanadium 50 said:
What could be more useful than being told where the mistake is?
Read the answers you've already gotten.
 
  • #14
Kostik said:
But it can easily happen.
As said above, this has never been observed. Our current best understanding of the universe says it can't happen.

Kostik said:
It seems to me the "answer" is probably that when #1 makes his measurement, he is no longer within the same spacetime as #2. He is not in #2's universe. Hence, the entanglement is effectively severed once #1 is inside the BH, since #2 has no access to #1's spacetime.
We do not allow personal speculation. Thread closed.
 
  • #15
Kostik said:
when #1 makes his measurement, he is no longer within the same spacetime as #2
This is wrong. The entire black hole, interior and exterior, is a single spacetime.
 

FAQ: Entanglement inside a black hole

What is quantum entanglement?

Quantum entanglement is a physical phenomenon that occurs when pairs or groups of particles are generated, interact, or share spatial proximity in ways such that the quantum state of each particle cannot be described independently of the state of the others, even when the particles are separated by a large distance.

How does entanglement work inside a black hole?

Inside a black hole, the extreme gravitational forces and the breakdown of classical spacetime concepts complicate our understanding of entanglement. Theoretical models suggest that entangled particles that fall into a black hole might remain entangled, but the exact nature of their interactions and the influence of the black hole's singularity on the entanglement are still subjects of ongoing research.

Can information about entangled particles escape a black hole?

According to the no-hair theorem and Hawking radiation, information about the particles that fall into a black hole is seemingly lost. However, the black hole information paradox suggests that information might be preserved in some form. Recent theories, such as the holographic principle, propose that information about entangled particles might be encoded on the event horizon, potentially allowing it to escape.

What is the role of the event horizon in entanglement?

The event horizon is the boundary beyond which nothing can escape a black hole. For entangled particles, one particle crossing the event horizon while the other remains outside presents a unique challenge. The event horizon might act as a medium where information about the entangled state is stored or transformed, playing a crucial role in the ongoing debate about information preservation in black holes.

What are the implications of entanglement for the black hole information paradox?

Entanglement is central to the black hole information paradox, which questions whether information that falls into a black hole is lost forever. If entangled particles can somehow preserve information or if the event horizon encodes this information, it might offer a resolution to the paradox. The study of entanglement in black holes could provide insights into quantum gravity and the unification of general relativity and quantum mechanics.

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