B People-Safe Event Horizon: Can Alice & Bob Experiment?

[Swamp Thing]

Is is possible for Alice and Bob to find themselves on opposite sides of an event horizon and go about their experiments, without the fear that one of them might be mangled to death by tidal / differential gravitation effects?

 

[DaveC426913]

By "opposite sides", do you mean one inside and one outside?
By "go about their experiments", do you mean "together"? Or separately?
They would have to be in a hovering spacelab. It is possible to hover near a SMBH (though not at or inside the EH). The gravitational gradient is what kills you, and SMBHs have a small gradient.

 

[Nugatory]

Is is possible for Alice and Bob to find themselves on opposite sides of an event horizon and go about their experiments, without the fear that one of them might be compacted to death by tidal / differential gravitation effects?

Yes, as long as they're in free fall instead of trying to hover, and (somewhat counterintuitively) the larger the black hole the better. When you're falling into a black hole, what tears you apart is the difference between the force on your feet and your head - the absolute strength of those forces is irrelevant as long as you're in free fall. You could fall through the event horizon of a supermassive black hole without even noticing.

Of course if they're in free fall they don't have very long to perform their experiments. And the outer experimenter won't be able to receive any signals from the inner experimenter until he has also fallen through the horizon.

 

[Nugatory]

It is possible to hover near a SMBH. The gravitational gradient is what kills you,

The gradient is what will kill you if you're free-falling. If you're hovering, it's the proper acceleration needed to hover that will kill you, and that tends towards infinity no matter the size of the black hole.

 

[Swamp Thing]

the outer experimenter won't be able to receive any signals from the inner experimenter until he has also fallen through the horizon.

If they do an entaglement experiment, and then they compare notes after Bob has caught up with Alice on the same side of the horizon, will their results be as per expected correlations?

 

[DaveC426913]

If they do an entaglement experiment, and then they compare notes after Bob has caught up with Alice on the same side of the horizon, will their results be as per expected correlations?

Whether or not it does, that information will never leave the black hole.

But I don't see why entanglement would be affected by an event horizon.

The event horizon is only a mathematical object; not a real object. A person falling toward the EH will pass that point without any changes. The only way they would now they've crossed it is to calculate where it is, knowing the mass of the BH.

Nothing special happens there. The only thing that happens is that light, emitted from anything inside that point won't eventually make its way out into the universe. The scientist inside the EH will never know that either.

 

[Nugatory]

If they do an entaglement experiment, and then they compare notes after Bob has caught up with Alice on the same side of the horizon, will their results be as per expected correlations?

No one has actually done that experiment because we don't have any convenient black holes to try it... but according to our current understanding of the physics, we'd get the predicted quantum mechanical correlations. Consider that we have done Bell tests with spacelike-separated measurements, and we can imagine putting our observers on opposite sides of a Rindler horizon so that we're a coordinate transformation away from that case.

 

[Ibix]

No one has actually done that experiment because we don't have any convenient black holes to try it... but according to our current understanding of the physics, we'd get the predicted quantum mechanical correlations.

Would it be possible to do the experiment in any useful way even if we did have a handy black hole? Presumably you wouldn't be able to test the correlation without meeting up, so the outer observer would have to fall into the hole, and publication of the results would be problematic. Otherwise there'd have to be a way to communicate two ways across an event horizon.

 

[pervect]

Is is possible for Alice and Bob to find themselves on opposite sides of an event horizon and go about their experiments, without the fear that one of them might be mangled to death by tidal / differential gravitation effects?

With a large enough black hole the tidal effects at the horizon can be made small. But the observer inside the black hole has a finite proper time to live before being destroyed in the singularity, and it's most likely that the tidal forces will mangle the one on the interior before they reach the singularity. How long it takes to reach the signularity depends on the size of the black hole, the larger the better. For some representative numbers, IIRC a galactic mass black hole (1 billion solar masses) gives times on the order of a few hours to reach the central singularity from the horizon.

 

[Vanadium 50]

Would it be possible to do the experiment in any useful way even if we did have a handy black hole?

Sure. You just can't publish the results.

 

[Swamp Thing]

Sure. You just can't publish the results.

So it's publish or perish, eh?

 

[Ibix]

So it's publish or perish, eh?

Literally, so I understand, which is why I was asking whether I was misunderstanding something.

 

[Swamp Thing]

If they do an entaglement experiment, and then they compare notes after Bob has caught up with Alice on the same side of the horizon, will their results be as per expected correlations?

The event horizon is only a mathematical object; not a real object.

I'm beginning to wonder -- if Alice and Bob started out on different sides of the EH, can Bob ever get across to Alice's "side" merely by coasting/falling, without having to accelerate a lot? Perhaps there would always be "a" horizon (as opposed to "the") horizon between Alice and Bob?

To avoid existential anxieties and unpleasant images, maybe let's forget about Alice and Bob but just consider particles participating in events. So two particles that start out timelike separated, as they coast along, can they evolve into a spacelike separated configuration?

 

[DaveC426913]

I'm beginning to wonder -- if Alice and Bob started out on different sides of the EH, can Bob ever get across to Alice's "side" merely by coasting/falling, without having to accelerate a lot? Perhaps there would always be "a" horizon (as opposed to "the") horizon between Alice and Bob?

The answers would be just as valid as at any other radius.
Ultimately, they could, if they were of a mind, calculate at what radius they would need to exceed some velocity (such as c) in order to not be able to catch up to each other, and decide that that is a defining radius, but again, it's not a "real" boundary. Nothing happens there, all it does is rule out some of your future paths.

I'm trying to think of some other examples of boundaries - perhaps the point of no-return for a rocket trying to go to Mars and back. You can certainly compute a distance for any trajectory it might take, and graph that to make a 2D boundary in space that shows its limit before it can't return, but it's not like the rocket knows where the boundary is. All it does is rule out some future paths of the rocket (such as any that eventually get it back to Earth orbit).

 

[Nugatory]

I'm beginning to wonder -- if Alice and Bob started out on different sides of the EH, can Bob ever get across to Alice's "side" merely by coasting/falling, without having to accelerate a lot?

Yes, as long as they don't start too far apart.
(Some care is needed to properly define "too far apart" here because there's no sensible way of specifying both positions at the same time. We need to make a statement about their respective worldlines instead of initial positions).

To avoid existential anxieties and unpleasant images, maybe let's forget about Alice and Bob but just consider particles participating in events. So two particles that start out timelike separated, as they coast along, can they evolve into a spacelike separated configuration?

As asked, that question doesn't make sense because the interval (whether timelike, spacelike, or lightlike) is between two events, while a particle defines an entire worldline. You can't speak about the interval between two particles; you have to pick a particular event on each worldline and then calculate the interval between those two events.

 

[Swamp Thing]

As asked, that question doesn't make sense

How about this... At some moment in Bob's proper time, he is able to receive Alice's light cone as they both fall towards the black hole. At a later moment in his own proper time, he sees Alice's light cone red-shifting and disappearing altogether, so he knows that Alice has crossed the event horizon. (It may not make sense to ask exactly "when" she, er, passed over).

Question now is, if Bob continues to fall freely, will there be a third moment in his proper time when Alice's light cone fades back in through the spectrum and becomes visible again? Or would he have to actively chase Alice by accelerating himself towards the BH in order to have a chance of glimpsing her again?

 

[Nugatory]

How about this... At some moment in Bob's proper time, he is able to receive Alice's light cone as they both fall towards the black hole. At a later moment in his own proper time, he sees Alice's light cone red-shifting and disappearing altogether, so he knows that Alice has crossed the event horizon. (It may not make sense to ask exactly "when" she, er, passed over).

Question now is, if Bob continues to fall freely, will there be a third moment in his proper time when Alice's light cone fades back in through the spectrum and becomes visible again? Or would he have to actively chase Alice by accelerating himself towards the BH in order to have a chance of glimpsing her again?

Alice does not fade out and disappear. If Bob were hovering, then light he received from Alice would be increasingly red-shifted as she neared the horizon, and she would fade to invisibility at the horizon. But Bob isn't hovering, he's free-falling along with Alice so the red-shift between them is negligible.

This is the same situation as if Bob were falling feet-first through the event horizon. There is a time (using coordinates in which he is at rest, appropriate for any free-faller) when his feet have passed through the horizon and his head hasn't yet done so. He's looking down, watching his feet. Is there ever a time when he can't see his feet? No.