The discussion centers on Hawking radiation and the entanglement of virtual photons, highlighting the complexities surrounding the black hole information paradox. Participants clarify that Hawking's derivation of radiation properties does not rely on virtual particles but rather on quantum field theory in non-inertial reference frames. The conversation emphasizes that entanglement persists even when one particle crosses the event horizon, challenging traditional notions of information transfer in quantum mechanics. Ultimately, the discussion reveals a fundamental misunderstanding of entanglement and its implications in the context of black holes.
PREREQUISITESPhysicists, quantum mechanics enthusiasts, and anyone interested in the intersection of black hole physics and quantum theory will benefit from this discussion.
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 said:
I am perhaps wandering into areas I really do not understandsDemystifier said:
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!Demystifier said:
Thanks for your comment. I guess trying to analyse a layman explanation will lead to anomalies...stevendaryl said:
The particles remain entangled even when one of them crosses the horizon.Zaphodpsi said:
So that means that information can cross the horizon in both directions...! ?Demystifier said:
Zaphodpsi said:
You say they do not exist and yet they can influence 'real' systems...how do you define existence?weirdoguy said:
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 said:
So how do you explain the Lamb shift?phinds said:
Zaphodpsi said:
The same goes with Cassimir effect.Guess that's told me! You should consider a career in teaching...weirdoguy said:Using mathematics of QFT with proper understanding and not some pop-sci heuristics
Zaphodpsi said:
Zaphodpsi said:
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.Zaphodpsi said:
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.Zaphodpsi said:
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 said:
Derek P said:
Thanks for thanking the time to write your replies. I am clearly out of my depth but will remain an interested layman.Derek P said:
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.Zaphodpsi said:
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 asZaphodpsi said:
phinds said:
akvadrako said: