# Entanglement and GR

Let's say you have two entangled particles. Is it possible for one of them to fall into the event horizon of a black hole and the particles still be entangled? Or say the two particles are far apart and the universe undergoes extreme expansion (just after the Big Bang, say) such that they are still entangled but no longer in each other's light cones?

If this were so, does the entanglement mean you now have some information about part of the universe which GR says you can't? Also, how can you even tell if the particles are still entangled?

DrChinese
Gold Member
Let's say you have two entangled particles. Is it possible for one of them to fall into the event horizon of a black hole and the particles still be entangled? Or say the two particles are far apart and the universe undergoes extreme expansion (just after the Big Bang, say) such that they are still entangled but no longer in each other's light cones?

If this were so, does the entanglement mean you now have some information about part of the universe which GR says you can't? Also, how can you even tell if the particles are still entangled?

What "forbidden" information is going to be transmitted exactly? I think you will see there is none. Also, you should know that ordering of measurements on entangled particles is generally not meaningful to the outcomes. You cannot say that the one in the black hole "causes" the other one to take a value any more than you can say the reverse.

tom.stoer
The particles are still entangled but there is no local experiment which distinguishes this non-local entanglement from local randomness.

In case of inflation one could do the following: create pairs of entangled particles, wait for inflation to start such that the light cones do no longer intersect, perform some local experiments and store the data. Now wait long enough such that the light cones do again intersect, exchange the data and compare the results. I think via such an experiment long after inflation you can detect entanglement prepared prior to inflation.

What "forbidden" information is going to be transmitted exactly? I think you will see there is none. Also, you should know that ordering of measurements on entangled particles is generally not meaningful to the outcomes. You cannot say that the one in the black hole "causes" the other one to take a value any more than you can say the reverse.

From Wikipedia: "When a measurement is made and it causes one member of such a pair to take on a definite value (e.g., clockwise spin), the other member of this entangled pair will at any subsequent time be found to have taken the complementary value (e.g., counterclockwise spin)."

So isn't the "forbidden" information which is transmitted, the spin value? If no information was transmitted, wouldn't it be just as likely that randomness could produce the same, noncomplementary, spin, as opposed to what I am calling the information transmittal which will invariably result in the complementary spin?

And isn't the measurement, say performed on particle A while particle B is not measured, the cause of the taking on of values?

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My point wasn't that forbidden information was being transmitted. My understanding of these two situations is that you can't know anything about the state of the other side of a event horizon (whether you happen to be inside it or outside it), or anything that's not in your light cone.

But with the case of an entangled pair of particles separated in either of these two ways, you can know there is one particle in a state you know about by looking at the local entangled particle to which you have access. It doesn't matter whether or not you happened to look at the particles' state before they got separated. What does matter is that you can deduce the state of a particle which you can't directly observe by looking at its entangled opposite. What I'm wondering is if you've got a tiny bit of information that GR says you can't have.

tom.stoer
By looking at one particle you can't decide if it belongs to an entangled pair or not (regardless where the partner particle may be)

My point wasn't that forbidden information was being transmitted. My understanding of these two situations is that you can't know anything about the state of the other side of a event horizon (whether you happen to be inside it or outside it), or anything that's not in your light cone.

But with the case of an entangled pair of particles separated in either of these two ways, you can know there is one particle in a state you know about by looking at the local entangled particle to which you have access. It doesn't matter whether or not you happened to look at the particles' state before they got separated. What does matter is that you can deduce the state of a particle which you can't directly observe by looking at its entangled opposite. What I'm wondering is if you've got a tiny bit of information that GR says you can't have.

It depends on your definition of information. No one owns the word.

I say that it is information, but others say it is not information because the measurement can't be used to send a signal. I would be happier if they were to say "electromagnetic information" or "signaling information" or some such.

Let's say you have two entangled particles. Is it possible for one of them to fall into the event horizon of a black hole and the particles still be entangled? Or say the two particles are far apart and the universe undergoes extreme expansion (just after the Big Bang, say) such that they are still entangled but no longer in each other's light cones?

If this were so, does the entanglement mean you now have some information about part of the universe which GR says you can't? Also, how can you even tell if the particles are still entangled?

If you are using GR (a classical theory) then there is not entanglement possible. If you are using QM (a non-geometrical theory) then there is not event horizon possible. You cannot mix both.

One of the basic requirements of a scientific model of nature is its internal consistency.

You do not need to go to such extremes. We have already done experiments on earth where the two measurements are both started and completed before the light cones of the two locations intersect. We already know "if" information is going from one to the other it is going at a rate >1E6 times the speed of light.

This leads people to say "it" is non local. Not sure what is non local. Not sure what non local means. For myself I am still stuck back with Newton and Einstein for A to effect B, A must touch B. Fields are OK, A effects the field, the field propagates the impulse with finite speed (=< c), the field effects B.

Demystifier
Gold Member
Let's say you have two entangled particles. Is it possible for one of them to fall into the event horizon of a black hole and the particles still be entangled?
Yes.

Or say the two particles are far apart and the universe undergoes extreme expansion (just after the Big Bang, say) such that they are still entangled but no longer in each other's light cones?
That's possible too.

If this were so, does the entanglement mean you now have some information about part of the universe which GR says you can't?
If by "you" you mean "a local observer", then the answer is - no. The local observer does not have this information.

Also, how can you even tell if the particles are still entangled?
Experimentally, you can't. But physics is not only about experiments. For example, even without quantum mechanics, GR says that there is something beyond the horizon, and yet it says that you cannot measure it.

If by "you" you mean "a local observer", then the answer is - no. The local observer does not have this information.

Experimentally, you can't. But physics is not only about experiments. For example, even without quantum mechanics, GR says that there is something beyond the horizon, and yet it says that you cannot measure it.

I understand that normally (without entanglement) when either of these cases happens and something disappears "over the horizon" you no longer have any idea of what happened to it. But if you are dealing with one-half of an entangled pair and you still have local access to the other half, why can't you tell the state of the particle over the horizon by looking at the local half? Isn't this possible with entangled pairs that are light years apart but not over the horizon? Why does this aspect of entanglement break down when one of the pair is over the horizon?

My point is that I am wondering if there is an inherent contradiction between QM and GR here. Nothing I know of in QM says you can't tell the state of one of a pair of entangled particles by looking just at the other one of the pair. There's nothing I know of in QM that says there's an exception to entanglement for something over the horizon (does QM even have a concept of "over the horizon"?). Yet as you say, GR says there's no way you can know anything about something over the horizon.

According to you GR rules, but isn't the argument behind QM just as strong?

I understand that normally (without entanglement) when either of these cases happens and something disappears "over the horizon" you no longer have any idea of what happened to it. But if you are dealing with one-half of an entangled pair and you still have local access to the other half, why can't you tell the state of the particle over the horizon by looking at the local half? Isn't this possible with entangled pairs that are light years apart but not over the horizon? Why does this aspect of entanglement break down when one of the pair is over the horizon?

My point is that I am wondering if there is an inherent contradiction between QM and GR here. Nothing I know of in QM says you can't tell the state of one of a pair of entangled particles by looking just at the other one of the pair. There's nothing I know of in QM that says there's an exception to entanglement for something over the horizon (does QM even have a concept of "over the horizon"?). Yet as you say, GR says there's no way you can know anything about something over the horizon.

According to you GR rules, but isn't the argument behind QM just as strong?

QM and GR are irreconcilable in some respects, which is partly why the search is on for a theory that will somehow contain both of them or for a deeper theory that will supersede them. As for whether an entangled particle beyond the horizon would still have a property opposite to its twin here, or not, it seems like it would be a little difficult to find out.

Demystifier
Gold Member
I understand that normally (without entanglement) when either of these cases happens and something disappears "over the horizon" you no longer have any idea of what happened to it.
But that's wrong. You do have a very good idea. Of course, you cannot measure it, but to "have an idea" is not about measuring. "To have an idea" is to have a theory, and the theory (general relativity) says very clearly what happens there.

But if you are dealing with one-half of an entangled pair and you still have local access to the other half, why can't you tell the state of the particle over the horizon by looking at the local half?
But you can, provided that you trust your theory (general relativity and quantum mechanics).

Isn't this possible with entangled pairs that are light years apart but not over the horizon?
Yes, it's possible.

Why does this aspect of entanglement break down when one of the pair is over the horizon?
It doesn't break down.

My point is that I am wondering if there is an inherent contradiction between QM and GR here.
Here, there is no such contradiction. Perhaps somewhere else (e.g., there is a black-hole information paradox for the case when the black hole EVAPORATES), but definitely not here.

Nothing I know of in QM says you can't tell the state of one of a pair of entangled particles by looking just at the other one of the pair. There's nothing I know of in QM that says there's an exception to entanglement for something over the horizon (does QM even have a concept of "over the horizon"?).
And you are right.

Yet as you say, GR says there's no way you can know anything about something over the horizon.
Please read carefully what I say. I never said you cannot KNOW it. You can, by theory. I said you cannot MEASURE it.

According to you GR rules, but isn't the argument behind QM just as strong?
According to me, they both rule and there is no contradiction.

DrChinese
Gold Member
My point wasn't that forbidden information was being transmitted. My understanding of these two situations is that you can't know anything about the state of the other side of a event horizon (whether you happen to be inside it or outside it), or anything that's not in your light cone...