Entanglement inside a black hole

[Kostik]

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.

 

[Nugatory]

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.

 

[Kostik]

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.

 

[Dale]

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.

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

 

[Kostik]

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.

 

[Nugatory]

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.

 

[Kostik]

Of course it does not matter, except if both spins turns out to be the same.

 

[phinds]

Why did you ask the question if you don't want to know the answer? Seems like you just want to argue, not learn.

 

[Kostik]

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.

 

[phinds]

The paradox

is all in your head

 

[Kostik]

Hoping for a more useful reply.

 

[Vanadium 50]

Hoping for a more useful reply.

What could be more useful than being told where the mistake is?

 

[phinds]

What could be more useful than being told where the mistake is?

Read the answers you've already gotten.

 

[DrClaude]

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.

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.

 

[PeterDonis]

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.