To be clear: it can't be explained by locally deterministic mechanisms, assuming a nondeterministic universe.
1) If you ask Alice and Bob about the same coin, their answers always agree.
2) If you ask Alice about coin 1 and Bob about coin 2, they are different about 5% of the time.
3) If you ask Alice about coin 2 and Bob about coin 3, they are different about 5% of the time.
4) If you ask Alice about coin 1 and Bob about coin 3, they are different about 20% of the time!
Why is it shocking you ask? Well, if coin 1 is different from coin 3, then at least one of them must be different from coin 2, which you didn't ask about, but could have. So the probability of the last situation can't be larger than the sum of the previous two. But here it is, almost twice larger. Quantum magic :-)
(A && B && C) || (A && D && C) == (A && B) || (D && C)
How do you get from this line:
(A1Y and B2Y and B3Y) or (A1Y and A2Y and B3Y)
(A1Y and B2Y) or (A2Y and B3Y)
Let's write it differently: Why are these terms equivalent?
(u && v && w) || (u && x && w)
(u && v) || (x && w)Now I also get your previous comment. I've read your => as arrows instead of "equal or greater".
Yes it can, as long as that information is non-local. That's where the EPR "paradox" comes in, because Einstein believed non-locality was impossible due to relativity.
For clarity, is this correct (you are simplifying something) or am I reading what you wrote incorrectly?
> Yet using your rules 2 and 3, you could manipulate the odds of Bob's response by asking Alice different questions.
Can you explain in more detail? Assume that the odds of Bob's response are 50/50 at the start.
The following statement is true, correct?
Even though the probability that Alice and Bob's chance of both answering yes varies, the individual chance that either of them answers yes without any other information does not change.
That's not paradoxical, that's just two objects with the same random shape and the same random color. Quantum entanglement is stranger than that, it can't be explained by hidden correlated information about both objects.
Here's an example of quantum entanglement. Imagine that Alice and Bob live far from each other and can't communicate. There are three possible yes/no questions you can ask them, but each person can only answer one question. These facts are known:
1) If you ask Alice and Bob the same question, they always give opposite answers.
2) If you ask Alice question 1 and ask Bob question 2, the probability that both will say yes is 5%.
3) If you ask Alice question 2 and ask Bob question 3, the probability that both will say yes is 5%.
4) If you ask Alice question 1 and ask Bob question 3, the probability that both will say yes is 20%.
Under classical assumptions, there's no way for Alice and Bob to prepare a strategy beforehand that would lead to such probabilities. The reason is that case 4 is completely covered by cases 2 and 3, but has higher probability than the two of them combined. Here's a proof:
Now, as strange as it sounds, in a quantum world Alice and Bob can defeat that proof and prepare a strategy beforehand. When you ask Alice a question, she will consult her prepared photon in a box, and measure it in a way that depends on which question you asked. The measurement will mess up the photon's state, so you don't get to ask another question. Elsewhere, Bob will do the same with his photon. The two photons were prepared together, but are completely separated at the time of the game.Before you ask, it's provable that such tricks cannot be used to send information faster than light. Quantum "spooky action" is somehow more powerful than hidden correlations, but less powerful than outright communication. It's pretty subtle and most popular accounts don't get it right.