If it doesn't allow for transmitting of any information, what was/is "spooky" about it? Is there anything spooky about it at all in the end?
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"Spooky" is of course the subjective term, so the question is really, is anything "spooky" in the entanglement left, or is it more or less figured out? – Łukasz Zaroda Aug 20 '16 at 23:09
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1Also, and more importantly, it violates the speed of light postulate, even if you can't send information. As far as I know, it is not figured out in anything I've read, it's still unexplainable. – Aug 20 '16 at 23:10
3 Answers
The thing people consider interesting/spooky is that even though one cannot transmit information by means of an entangled system, an entangled system does have have information stored in a non-local fashion. This is considered weird because all other physical phenomena can be explained using laws which only act locally and entanglement cannot.
Note that alternative quantum mechanical theories like the many worlds theory of quantum mechanics, there is no need for non-locality to explain entanglement.

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Can you elaborate on the claim that MWI treats entanglement differently? I thought MWI was solely about the measurement problem. – Norbert Schuch Aug 22 '16 at 10:48
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In the Copenhagen interpretation the wave function collapses upon measurement. When one has a pair of electrons in the singlet state, upon measuring the spin of one of them, the wave function of the other will also collapse. This collapse happens instantaneously for both electrons, even if they are separated by a large distance and is thus a non-local effect. – Crimson Aug 23 '16 at 09:59
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In the MWI upon measuring one electron, nothing happens to the other electron, but the observer becomes in a superposition. When traveling to the other electron, both states of the observer will measure that the state of the second electron is what they expect with regard to the entanglement. The observers thus observe the same in both theories. However, in the MWI all interactions are local. – Crimson Aug 23 '16 at 10:00
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So how does this work for, say, a measurement of the CHSH inequality (or, more generally, a measurement by two parties)? – Norbert Schuch Aug 24 '16 at 21:03
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@NorbertSchuch The principle remains the same. When one observer measures the state of one electron, he can be described as being in a superposition. When another observer measures the other electron, he can also be described as being in a superposition. When they performed their measurements in different bases, the total state of the system is best described as a superposition of four states, corresponding to each possible pair of measurement outcomes. An observer not measuring the individual electrons, but only their correlations is measuring in yet another basis. – Crimson Aug 31 '16 at 07:21
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@NorbertSchuch The trick is to precicely keep track of the amplitude of each state and then the probabilites follow automatically. A worked out example for measuring the Bell inequality is given here – Crimson Aug 31 '16 at 07:23
I think that Einstein called it "spooky" because he didn't get it at that moment. People are scared of strange or obscure things! Especially that he thought that this spooky action violates the relativistic upper limit on speed of propagation of information which seemed (to him) faster than the speed of light. But after understanding the quantum entanglement, there is nothing spooky about it.

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Comments are not for extended discussion; this conversation has been moved to chat. – David Z Aug 22 '16 at 14:22