Violation of Heisenberg's Uncertainty Principle

That is a good description of classical entanglement - what, in this context, would be called a hidden variable theory (the cards have a certain face value, even if you can't see them).

Let's see if I can expand this analogy. Suppose you had two decks of cards, each with only two cards - say the king of hearts and the king of spades. Off-stage, I shuffle them, so that there is either one deck of 2 hearts, and one of two spades, or one deck of both, and another of both. Say that the chances of either shuffle are the same.

Now, repeat your experiment, except you and your friend only get to pull 1 card each, each from your own deck. Classically, the chances are

- 50%, you pull from 1 spade and 1 heart
- 25%, you pull from 2 spades
- 25%, you pull from 2 hearts.

And, of course, ditto for your friend.

Now, if you pull a spade, then the classical chances are

2/3 the other card is a heart
1/3 the other card is a spade

and the classical chances for your friend are thus

2/3 he has a spade and a heart
1/3 he has 2 hearts

so his (classical) chances on his card are

2/3 he pulls a heart
1/3 he pulls a spade.

(If you pull a spade, you CANNOT have two hearts, while he can.)

So, if you pull a Spade, you can tell your friend he is likely to have a heart. Do this a lot of times, and you should be correct 2/3 of the time. The cards are indeed entangled, but classically. Experimental error (maybe you can't always see your cards well) will lower this, but (for a long enough term average) cannot raise this.

In Quantum Mechanics, however, you can get correlations that you cannot get in classical physics, i.e., greater than 2/3 in this case. That is the essence of Bell's Theorem - you have correlations that you just can't "get there from here," classically. This is a consequence of having a complex amplitude. Again, it's not just having a correlation, it's that you can get correlations you just can't classically.

I saw a lecture from Dick Feynman once where he showed that you could explain all of this by allowing for negative probabilities for intermediate results, and that this was mathematically the same as the normal (i.e., complex) formulation of QM. (Since you cannot actually measure the intermediate results, you never actually measure a negative probability.) In some ways, I find that helps to grasp the weirdness. YMMV.

Source: http://rss.slashdot.org/~r/Slashdot/slashdotScience/~3/3D8QGbzLibo/violation-of-heisenbergs-uncertainty-principle

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