Question from a 5 year old: Bell and Black Holes

[jshrager]

Seriously, a 5 year old asked me whether entanglement information survives/escapes a black hole. Specifically, he asked me (in only slight paraphrase) whether if one of the particles (headed in different directions) fall into black holes on either end, does the other one know it?

 

[DrChinese]

That's some 5 year old! Get him into some advanced physics classes now!

The "free" particle would not evidence any particular trait by having its partner fall into a black hole (as opposed to not). You could say it would "know" it, but that is somewhat a matter of interpretation and semantics. But we wouldn't know it regardless.

Generally speaking, the ordering of measurements on entangled particles is not relevant to the outcome of measurements. No one knows the underlying mechanism past that.

 

[Nugatory]

The effects of entanglement can only be seen when we compare the results of measurements on both particles after the fact. Drop one member of the pair into a black hole before you measure it and there's no way for us outside the event horizon to make that comparison.

In principle I suppose we could drop an experimenter along with one particle into the black hole, do our measurement, and then transmit our result to the other guy, and he would be able to make the comparison. Of course we'd never know what he found... But I would expect the results to be no different than comparisons between any other two space-like separated measurement events.

 

[atyy]

If the black hole is big so that the curvature is small at the event horizon, and the black hole is not evaporating, everything will be the same as outside the black hole, except that the guy inside cannot send his results out. However, for a quantum black hole which is evaporating, we don't know the answer. John Preskill has a write-up about why we don't understand entanglement in the evaporating black hole. http://quantumfrontiers.com/2012/12/03/is-alice-burning-the-black-hole-firewall-controversy/

 

[jshrager]

Thanks, all, for this interesting discussion.

(Lest you think I'm making up that this came from a 5 year old, here's the relevant snippet of the actual conversation:



You'll accuse me of over-interpretation, and that's fair enough. But, over-interpreted or not, it's an interesting question. :-)

 

[bhobba]

That's some 5 year old! Get him into some advanced physics classes now!

Maybe another Terry Tao who used to ask questions like that at 5.

Thanks
Bill

 

[atyy]

At a more basic level than the firewall paradox that Preskill discusses in the blog post I linked to in #4, I should point out that an evaporating black hole is about entangled particles. A classical black hole is truly "black", as it does not radiate and does not have a temperature. However, a black hole in which spacetime is classical but matter is quantum will radiate, and is not "black". The radiation has a thermal spectrum, so the black hole has a temperature. The radiation emitted by the black hole is entangled with particles inside the black hole. This entanglement causes information to appear to be "lost" since we see only the radiated particle, but not its entangled partner inside the black hole. This radiation is known as Hawking radiation. It is one of the big questions as to whether information is truly lost or only appears to be lost, if we also allow spacetime itself to be quantum. This is called the "black hole information paradox". The more modern firewall paradox is a development of the black hole information paradox.

 

[jshrager]

Aren't pretty much all the particles we see entangled all over the place?

 

[atyy]

Aren't pretty much all the particles we see entangled all over the place?

The entanglement is generally weak, because of monogamy of entanglement. To be "maximally entangled", you can do that with one other particle. The Preskill blog post I linked to in #4 talks about monogamy of entanglement.

BTW, here I am loosely talking as if the wave function is real, and entanglement is real. This is not necessarily the case. The wave function, and entanglement are just tools to calculate the probabilities of measurement results. Only the measurement results are real.

 

[naima]

Pati is the author of the no hiding theorem.
Any pure state falling in a black hole is changed into a mixed state by a unitary process.
Look at:
http://www.hri.res.in/~akpati/bh01.pdf
and
http://arxiv.org/abs/1004.5073
Could you comment his conclusions in the first link?

 

[jshrager]

BTW, he also asked me whether, since time dilation increases as you get closer and closer to the speed of light, whether photons, which are actually AT the speed of light, see any time change at all? (Put another way: Is proper time for a photon unchanging?) Alas, I don't have video of that...but anyway, it's a discussion probably more appropriate for a different forum.

 

[naima]

If you have only one book to read about black holes; read https://www.amazon.com/dp/0393312763/?tag=pfamazon01-20
"Black holes and time warps"
You will learn for 10 dollars what an observer sees when she falls in a BH.
And remember that when you buy anything on amazon from this forum (not only books) A part of your money returns to the forum!

 

[harrylin]

BTW, he also asked me whether, since time dilation increases as you get closer and closer to the speed of light, whether photons, which are actually AT the speed of light, see any time change at all? (Put another way: Is proper time for a photon unchanging?) Alas, I don't have video of that...but anyway, it's a discussion probably more appropriate for a different forum.

To elaborate on that question would require a separate thread, even in a different sub forum; however there is no need for a discussion as the short answer is that indeed, if you interpret a photon as a wave packet (in contrast to just a detector "click") then a photon's proper time is "frozen" (and from that immediately follows the impossibility of establishing a co-moving reference system :) ).

 

[Nugatory]

To elaborate on that question would require a separate thread, even in a different sub forum; however there is no need for a discussion as the short answer is that indeed, if you interpret a photon as a wave packet (in contrast to just a detector "click") then a photon's proper time is "frozen" (and from that immediately follows the impossibility of establishing a co-moving reference system :) ).

There's a FAQ in the relativity subforum: https://www.physicsforums.com/threads/rest-frame-of-a-photon.511170/