Wouldn't the entanglement just break? The preassure would rip the electron apart to begin with. I'm not sure if that erases entanglement already or if the quarks needed to be annihilated. Either way, are the known laws of physics applicable inside a black hole at all? I don't think so.
The entanglement does not break. The entire black hole becomes entangled with the electron left outside (which is less exciting than it sounds).
Sure, plenty of thing break if we start talking about unknowns, like the black hole evaporation for instance, but today's physics has a pretty good idea what happens if we just drop one of the electrons in the black hole and measure the other one. We just learn the spin of both of them at the same time, but we can not choose the value (it is random) hence there is no communication and no "weird peeking into the black hole".
> if one entangled electron flies into a black hole then we would be able to know its spin by measuring the other one even if light from it won't reach us
All the arguments here mention what happens under SR but wouldn't GR be more appropriate? If an electron flies into a black hole, from the frame of reference of the observer doesn't it appear to get closer and closer to the black hole event horizon over time, but never actually enter? It only enters a black hole from its own frame of reference, doesn't it? So the outside observer would never see it enter the black hole, and light from the electron would always reach us.
Or is my understanding of General Relativity effects near a black hole event horizon wrong?
Thanks, I wanted to add that, too, but wasn't sure about it. I still am not, because this opens another can of worms. Can a black hole then not grow if from our POV nothing ever enters?
It is the other way around. From the POV of the object falling they just fall in. Look up Preskill's work for explanation of how it works when entanglement comes into play.
Then how is it different than just splitting a coin, throwing the other half far away and then looking whether you have heads or tails? There is never any spooky action at a distance.
This is a pretty great question with a fairly subtle answer. It is not much more than just flipping a coin, indeed!
See section "4. Relativistic Causality" of http://www.scottaaronson.com/democritus/lec11.html for the best explanation I know of. This entire book "Quantum Computing Since Democritus" is absolutely great if you want to understand these topics.
Think of it this way: We've got two players, Alice and Bob, and they're playing the following game. Alice flips a fair coin; then, based on the result, she can either raise her hand or not. Bob flips another fair coin; then, based on the result, he can either raise his hand or not. What both players want is that exactly one of them should raise their hand, if and only if both coins landed heads. If that condition is satisfied then they win the game; if it isn't then they lose.
They can win 75% of the time if they just never raise their hands. Using a shared entangle state they can "cheat" and win 85.3% of the time by using a specific protocol, because they rely on some new form of correlation. But they still can not use this correlation to send messages (see the no communication theorem). Naively (this naive intuition does break!), you can imagine them having two slightly correlated coins - sure, after Alice flips hers she knows Bob's result, but she did not decide the result of her coin so she can not use it to send information to Bob.
But here you have two independent coins. My question is, how is entanglement fundamentally different than having two sides of the SAME coin but not looking until later?
Let's forget how this looks like two correlated coins and focus on your question.
Yes, if Alice and Bob just measure the spin of their corresponding electron, indeed it just looks like half of a precut coin. But if they want to win the game they will do something more complicated. (side note: To use the typical physicist terminology, this precut coin is a hidden variable - something set inside of the electron even before its measurement.)
But Alice and Bob can do something more interesting, something that permits them to win the game we described more often than 75% of the time. This involves Alice measuring the spin of the electron in a projection different than the one in which Bob is measuring (this is part of the "specific protocol" that I mentioned in the previous post). So while Alice is checking whether the result is h=Heads or t=Tails, Bob is checking whether the result is h+t or h-t. Now the two electrons seize to behave like the two parts of the same coin (and this is what permits them to win the game more often than 75% of the time). Explaining how exactly they use this protocol would take too much space, but you can look it up in the link to the book I provided.
P.S. However, as explained in the previous post, this does not permit them to send messages to each other.
P.P.S. Again, Section 4 of the linked page explains this in details!
