Entangled particles in black hole decay?

[nomadreid]

TL;DR Summary

Discussions about the firewall paradox and the black hole information paradox rely on the existence of entangled particles, but unless one accepts the popular (but apparently way oversimplified) picture of “virtual particles becoming real”, it is not clear to me where the entanglement comes from.

First, I was not sure whether this should go into the Relativity or the Quantum Physics rubric, but since the central question is about entanglement, I opted for the Quantum.

I do not have the necessary sophistication to follow string theory arguments, and even most explanations in thermodynamics are difficult for me, so this is a “broad-strokes” question.

The following article for the layperson:
https://www.forbes.com/sites/starts...-about-how-black-holes-decay/?sh=3e5d98aa4e63
explains Hawking radiation thus:
(1) "…the difference in the zero-point energy in quantum fields from the curved space around a black hole to the flat space infinitely far away.,,, the curved space around the black hole is constantly emitting radiation due to the curvature gradient around it… the energy is coming from the black hole itself… the energy emitted by this Hawking radiation is slowly reducing the curvature of space in that region.”

Opposing this to the popular
(2) “emission of particles and antiparticles from the event horizon.”

OK, (1) sounds more reasonable, but then I am unsure how to deal with Wiki’s explanation https://en.wikipedia.org/wiki/Firewall_(physics)#The_motivating_paradox of the firewall paradox , as the explanation seems to be based on (2), stating “a single emission of Hawking radiation involves two mutually entangled particles”. Also the explanation of some of the proposed solutions to the black hole information paradox https://en.wikipedia.org/wiki/Black_hole_information_paradox#Recent_developments seem to rest on the existence of such entangled particles.

So, the main question: Where would an entanglement between particles inside and particles outside the black hole come from, using (1)?
Similar question: How would a firewall appear using (1)?

This brings me to a related question about the above-mentioned proposed solutions to the information paradox. The latest (2019) one of them is explained in greater length, albeit still for the layman (and with a silly title), besides also using the explanation of (2) in its diagram, also has the information escaping such that “ …when the black hole gets to be extremely old… Not only does information spill out, anything new that falls in is regurgitated almost immediately.” https://www.quantamagazine.org/the-black-hole-information-paradox-comes-to-an-end-20201029/
But if this is supposed to be headed towards a solution, doesn’t GR imply that an observer falling into a black hole should not notice anything (beyond tidal forces) before getting to the singularity?

Finally, is it correct to say that these explanations concerning information leaving the black hole refer not only to forms of Hawking radiation but also to other means?

I realize that a full answer to my questions is impossible here because (a) some of them don’t exist yet, (2) the answers would be many volumes, and (3) they would require more of a mathematics and physics background than I have. However, any clarification would be highly appreciated.

 

[DennisN]

Hi, I have got only two comments at the moment:

doesn’t GR imply that an observer falling into a black hole should not notice anything (beyond tidal forces) before getting to the singularity?

That's correct.

How would a firewall appear using (1)?

The only comment I have at the moment is that as far as I understand, the existence of firewalls is an open question in theoretical physics.

 

[nomadreid]

Thank you, DennisN.

That's correct.

OK, next step -- why isn't this considered a problem in the proposed solution I cited?

as far as I understand, the existence of firewalls is an open question in theoretical physics.

Yes, this is why I used "would" in my question, as in "if a theory of a firewall exists or were to exist using (1) instead of the widespread explanation using (2), how would a firewall appear in this theory?".
Alternative formulation: if a theory (as of yet unproven) of a firewall already exists using (1), then what form does it take? If not, then could the (as of yet unproven) theory of a firewall be formulated in terms of (1), and if so, how?

 

[DennisN]

As far as I understand:

According to the firewall hypothesis, objects that pass the event horizon get disintegrated at the horizon, which is in direct contradiction to "GR imply that an observer falling into a black hole should not notice anything (beyond tidal forces) before getting to the singularity".
So GR alone isn't capable of describing firewalls, other physics is needed for this, e.g. quantum physics.

That's about as much as I am comfortable saying, since I'm not well acquainted with firewalls.

Maybe someone who knows more about these things will chime in.

 

[PeterDonis]

According to the firewall hypothesis, objects that pass the event horizon get disintegrated* at the horizon, which is in direct contradiction to "GR imply that an observer falling into a black hole should not notice anything (beyond tidal forces) before getting to the singularity".
So GR alone isn't capable of describing firewalls, other physics is needed for this, e.g. quantum physics.

Not just "quantum physics", but quantum physics over and above ordinary quantum field theory in curved spacetime, which only predicts ordinary Hawking radiation from a black hole that is otherwise just like a classical GR black hole--i.e., no firewall.

 

[PeterDonis]

Where would an entanglement between particles inside and particles outside the black hole come from, using (1)?

A particle-antiparticle pair gets created just outside the horizon. The pair is entangled when it's created. Then one of the pair falls into the hole and the other escapes to infinity. So you now have a particle at infinity entangled with a particle inside the hole.

Similar question: How would a firewall appear using (1)?

It wouldn't. (1) by itself doesn't predict a firewall; it just predicts ordinary Hawking radiation from a black hole that can still be fallen into just like in classical GR.

You need something extra in your model to predict a firewall; just ordinary quantum field theory in curved spacetime won't do it.

 

[PeterDonis]

Opposing this to the popular
(2) “emission of particles and antiparticles from the event horizon.”

This is not opposed to (1); they are both part of the same overall picture, the "standard" Hawking radiation picture where you have Hawking radiation coming from a black hole that is otherwise just like a classical GR black hole (i.e., no firewall).

 

[PeterDonis]

A particle-antiparticle pair gets created just outside the horizon. The pair is entangled when it's created. Then one of the pair falls into the hole and the other escapes to infinity. So you now have a particle at infinity entangled with a particle inside the hole.

It's worth noting, btw, that this description is highly heuristic, and doesn't actually match up well with the underlying math. It is also somewhat questionable, IMO, because it seems to imply that a quantum degree of freedom is being added to the hole, when in fact, since Hawking radiation causes the hole to lose mass, each emission of a Hawking radiation particle should cause a quantum degree of freedom to be removed from the hole (and added to the outgoing radiation).

I'm not entirely clear how the above is addressed in the various arguments in the "firewall" debate.

 

[Demystifier]

Summary:: Discussions about the firewall paradox and the black hole information paradox rely on the existence of entangled particles, but unless one accepts the popular (but apparently way oversimplified) picture of “virtual particles becoming real”, it is not clear to me where the entanglement comes from.

You can think of it this way. At the horizon some complicated entangled quantum state is created. This complicated state is not simply a "particle-antiparticle" pair. Nevertheless, a part of this complicated state falls into the black hole, while another part escapes far from the black hole. So eventually you have entanglement between two parts of the complicated state, one part in the black hole, the other far from the black hole. That's where entanglement comes from.

But were do particles come from? It turns out that the part far from the black hole looks like a mixed thermal state of particles. But it looks so only when it is far from the black hole. When it is close to the horizon, it does not look like particles at all.

 

[nomadreid]

All those who have answered: thanks very much for the very helpful replies.

I would be interested in leaving the firewall question but pursuing the posts #8 & #9 (PeterDonis & Demystifier) a step further (keeping it in the realm of limited (not necessarily zero) mathematics -- thus still superficial, but perhaps a little less "highly heuristic") -- especially what this"complicated state" and this "part" is in Demystifier's "...a part of this complicated state falls into the black hole, while another part escapes far from the black hole..." , and how a degree of freedom gets subtracted as per PeterDonis's remark. If this is possible.

(If any references are given, it would be nice if they were Internet sites which are freely accessible.)

 

[Demystifier]

Unfortunately, I don't know a suitable reference with limited math.

 

[nomadreid]

Unfortunately, I don't know a suitable reference with limited math.

Thanks for answering, Demystifier.

I am not completely without such sources (see next paragraph), but the more ways I see of explaining the same thing, the better chance I have to understand it. But if not, I will concentrate on what I have.

[Here are the sources that I am working through in order to try to understand this; I
(1) John Baez's explanation on https://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/hawking.html
(2) Whereas this does not specifically mention Hawking radiation (but it does mention Unruh radiation), and although I do not follow all the equations, nonetheless Sections 10.0-10.4 (pages 267-277 of the Second Edition, Dec. 2013 /Sandtrove Press) of "Student Friendly Quantum Field Theory" by Robert K. Klauber is helpful
(3) https://en.wikipedia.org/wiki/Bogoliubov_transformation and similar Google-searches for some of the individual concepts. ]