Hawking radiation and entanglement

[Zaphodpsi]

I have been considering Hawkin radiation and I am puzzled about the capture of a virtual photon. Given that the escaped photon is entangled with the captured photon I do not see how the escaped photon can shed the entanglement. Can anyone help with this?

 

[stevendaryl]

I don’t have an answer, but I have a comment about the question. Hawking’s derivation of the properties of the radiation from black holes was not in terms of virtual particles being captured by the black holes. Instead, it involved applying quantum field theory in a noninertial refererence frame. The virtual particle idea was supposed to be a more intuitive, non-mathematical explanation.

As far as I know, there isn’t a convincing proof that the virtual particle idea is a correct way to explain it.

 

[Demystifier]

I have been considering Hawkin radiation and I am puzzled about the capture of a virtual photon. Given that the escaped photon is entangled with the captured photon I do not see how the escaped photon can shed the entanglement. Can anyone help with this?

Entanglement, indeed, is at the core of the black hole information paradox. But it is not clear to me what exactly do you mean by "shed the entanglement".

 

[Zaphodpsi]

Entanglement, indeed, is at the core of the black hole information paradox. But it is not clear to me what exactly do you mean by "shed the entanglement".

I am perhaps wandering into areas I really do not understands

Entanglement, indeed, is at the core of the black hole information paradox. But it is not clear to me what exactly do you mean by "shed the entanglement".

As I understand it when virtual particles are created they are entangled due to conservation requirements. If one of a pair is captured by the black hole this allows the other to move away as Hawkin radiation and this particle has a lifetime not limited by the uncertainty principle...that is it becomes a persistent particle. Entanglement would require information to cross the event horizon which I would have thought can not happen...so entanglement no longer applies. I am beginning to think. Am out of my depth!

 

[Zaphodpsi]

I don’t have an answer, but I have a comment about the question. Hawking’s derivation of the properties of the radiation from black holes was not in terms of virtual particles being captured by the black holes. Instead, it involved applying quantum field theory in a noninertial refererence frame. The virtual particle idea was supposed to be a more intuitive, non-mathematical explanation.

As far as I know, there isn’t a convincing proof that the virtual particle idea is a correct way to explain it.

Thanks for your comment. I guess trying to analyse a layman explanation will lead to anomalies...

 

[Demystifier]

Entanglement would require information to cross the event horizon which I would have thought can not happen...so entanglement no longer applies.

The particles remain entangled even when one of them crosses the horizon.

 

[Zaphodpsi]

The particles remain entangled even when one of them crosses the horizon.

So that means that information can cross the horizon in both directions...! ?

 

[weirdoguy]

As I understand it when virtual particles are created they are entangled due to conservation requirements. If one of a pair is captured by the black hole this allows the other to move away as Hawkin radiation and this particle has a lifetime not limited by the uncertainty principle...

This is just poor heuristics, since "virtual particle" is just a name w for some math tool used in QFT. They don't exist the way "real" particles does.

 

[Zaphodpsi]

This is just poor heuristics, since "virtual particle" is just a name w for some math tool used in QFT. They don't exist the way "real" particles does.

You say they do not exist and yet they can influence 'real' systems...how do you define existence?

 

[phinds]

You say they do not exist and yet they can influence 'real' systems...how do you define existence?

However you define "existence" is irrelevant. The virtual particles are a mathematical fiction and Hawking said that he developed the heuristic of "virtual particles" to describe in English something that really can only be described with math.

 

[Zaphodpsi]

However you define "existence" is irrelevant. The virtual particles are a mathematical fiction and Hawking said that he developed the heuristic of "virtual particles" to describe in English something that really can only be stated described with math.

So how do you explain the Lamb shift?

 

[weirdoguy]

And some links to read up to on that issue:
https://www.physicsforums.com/insights/physics-virtual-particles/
https://www.physicsforums.com/insights/misconceptions-virtual-particles/

 

[weirdoguy]

So how do you explain the Lamb shift?

Using mathematics of QFT with proper understanding and not some pop-sci heuristics The same goes with Cassimir effect.

 

[Zaphodpsi]

Using mathematics of QFT with proper understanding and not some pop-sci heuristics The same goes with Cassimir effect.

Guess that's told me! You should consider a career in teaching...

 

[Vanadium 50]

I am perhaps wandering into areas I really do not understands

Then maybe you shouldn't take such an aggressive stand about such things.

 

[weirdoguy]

Guess that's told me! You should consider a career in teaching...

Well the main thing that most people (and physicists that do some pop-sci things) should really understand - you can't explain everything to everyone. I am a teacher and I must stay honest to my students. I can't tell them pop-sci lies just because they are more understandable than what really is going on. And guess what - they don't have problems with that! Einstein said: everything should be made as simple as possible, but not simpler.

 

[Mentz114]

I am perhaps wandering into areas I really do not understands

As I understand it when virtual particles are created they are entangled due to conservation requirements. If one of a pair is captured by the black hole this allows the other to move away as Hawkin radiation and this particle has a lifetime not limited by the uncertainty principle...that is it becomes a persistent particle. Entanglement would require information to cross the event horizon which I would have thought can not happen...so entanglement no longer applies. I am beginning to think. Am out of my depth!

This seems to leave two possibilities - either the information does cross an horizon or when one of the pair meets or crosses the horizon this acts as a projection and the entanglement is broken.

[Just noticed you're talking about virual particles so my comment does not apply. Rats]

 

[Derek P]

I have been considering Hawkin radiation and I am puzzled about the capture of a virtual photon. Given that the escaped photon is entangled with the captured photon I do not see how the escaped photon can shed the entanglement. Can anyone help with this?

Entanglement is only a superposition of correlated states. Let's call it |1>|₁0>₂+|0>₁|1>₂ where the subscripts indicate the particles and the "0" and "1" labels are for the states of the two particles. So if your statement is correct, that the particles are entangled - and if the picture of virtual photons is correct too - then being captured by the BH is just another kind of "observation" which automatically breaks the entanglement. If you want to flesh the picture out with standard measurement theory then the entanglement doesn't really disappear, it gets extended to include the "observer", the BH, which has swallowed the particle. (To make any entanglement disappear, you need to assume collapse of the superposition.) So it is then |1>|₁0>_BH+|0>₁|1>_BH. Measurement theory tells us that such a superposition would appear like a simple probability distribution of |1>|₁ and |0>₁| because we have lost any information about the second system. So the entanglement is either actually broken or apparently broken but actually extended. It depends on your interpretation.
So, when it comes to black holes as observers, it all hinges on whether a BH can be treated like a normal quantum system. If it can then normal rules apply. If not - who knows? And I would not like to say whether it can or cannot!

 

[Derek P]

I am perhaps wandering into areas I really do not understands

As I understand it when virtual particles are created they are entangled due to conservation requirements. If one of a pair is captured by the black hole this allows the other to move away as Hawkin radiation and this particle has a lifetime not limited by the uncertainty principle...that is it becomes a persistent particle. Entanglement would require information to cross the event horizon which I would have thought can not happen...so entanglement no longer applies. I am beginning to think. Am out of my depth!

Ah, I see the thread has grown - and now I see what the problem is. You have a fundamental misunderstanding of what entanglement is, I'm afraid. The famous Bell theorem certainly rules out any local, causal, definite model. Non-locality applies even where something at A must cause something at B, so that would mean information moving faster than light even in ordinary EPR experiments - unless our whole idea of things interacting locally is utterly wrong. Likewise causality is not really optional unless you are happy with time-travelling waves (The TI) or such-like. So "crossing the event horizon" is no different from the "faster-than-light" interpretations of ordinary entanglement. In fact that's exactly what it is. But in a no-collapse interpretation - see my other reply - such as MWI, there is no need for any information to be exchanges at all. The observed correlations are just the effect of including the macroscopic observer in the system. One again, using a BH as the observer makes not a blind bit of difference.

 

[Zaphodpsi]

Ah, I see the thread has grown - and now I see what the problem is. You have a fundamental misunderstanding of what entanglement is, I'm afraid. The famous Bell theorem certainly rules out any local, causal, definite model. Non-locality applies even where something at A must cause something at B, so that would mean information moving faster than light even in ordinary EPR experiments - unless our whole idea of things interacting locally is utterly wrong. Likewise causality is not really optional unless you are happy with time-travelling waves (The TI) or such-like. So "crossing the event horizon" is no different from the "faster-than-light" interpretations of ordinary entanglement. In fact that's exactly what it is. But in a no-collapse interpretation - see my other reply - such as MWI, there is no need for any information to be exchanges at all. The observed correlations are just the effect of including the macroscopic observer in the system. One again, using a BH as the observer makes not a blind bit of difference.

Ah, I see the thread has grown - and now I see what the problem is. You have a fundamental misunderstanding of what entanglement is, I'm afraid. The famous Bell theorem certainly rules out any local, causal, definite model. Non-locality applies even where something at A must cause something at B, so that would mean information moving faster than light even in ordinary EPR experiments - unless our whole idea of things interacting locally is utterly wrong. Likewise causality is not really optional unless you are happy with time-travelling waves (The TI) or such-like. So "crossing the event horizon" is no different from the "faster-than-light" interpretations of ordinary entanglement. In fact that's exactly what it is. But in a no-collapse interpretation - see my other reply - such as MWI, there is no need for any information to be exchanges at all. The observed correlations are just the effect of including the macroscopic observer in the system. One again, using a BH as the observer makes not a blind bit of difference.

Thanks for thanking the time to write your replies. I am clearly out of my depth but will remain an interested layman.

 

[Demystifier]

So that means that information can cross the horizon in both directions...! ?

It depends on what do you mean by "information". This is a subtle topic which has more to do with interpretations of quantum mechanics than with black holes and Hawking radiation.

 

[Demystifier]

So how do you explain the Lamb shift?

The Lamb shift can be calculated with the aid of virtual particles. But it doesn't mean that virtual particles really exist. To explain this, I often use the following metaphor. Suppose that you have 1 apple. You can calculate this as

1 apple = 2 apples + (- 1 apple)

but that doesn't mean that 2 apples and -1 apple are real.

 

[akvadrako]

However you define "existence" is irrelevant. The virtual particles are a mathematical fiction and Hawking said that he developed the heuristic of "virtual particles" to describe in English something that really can only be described with math.

And how do you distinguish the virtual particles from so-called "real particles"? How do you know they aren't virtual too?

 

[weirdoguy]

And how do you distinguish the virtual particles from so-called "real particles"? How do you know they aren't virtual too?

Again, everything is explained here:
https://www.physicsforums.com/insights/physics-virtual-particles/
https://www.physicsforums.com/insights/misconceptions-virtual-particles/