Quantum Computing: Myth or Reality?
Bell's Theorem for Dummies or the Collapse of the Wave Function
Take two unmixable elements, try to mix them, then measure each one of them as they leave the mixing area. You will see that they are still the same.
Now do the same thing with two mixable elements, and measure each one of them after they have left the mixing area. You will see that you will need only to measure one of them to know the measure of the other.
Wait, that's not what I meant. In quantum theory you can of course never have 100% certainty, but only probabilities. Still, the idea is valid. Oh, wait again! The results are certain: if one is up, the other will be down. There is nothing probable about this.
But then we are speaking of a deterministic relation, otherwise even hidden variables would make no sense.

Suppose, as is often told, we have as a result of the mixing, the so-called entanglement, an electron and a positron. Both have two states. We have therefore a total of four states. But now it seems like our results only explain two: any time you measure one, you get the opposite of the other. One explanation is that somehow both particles communicate with each other.

Elektra: things are looking up, here, how about you?
Positra: eh, I think I'm feeling kind of down.

And the most remarkable thing is that they chat each other up faster than the light travels. That is why distances between the different parts of the experiment are so essential.
Einstein's gang, the EPR Hood (for Expats, Pollacks and Russians), did not really like the idea. They preferred a neutral boss overseeing the whole thing, like Nature. So they imagined that she had to have spies all over the place. And because a known spy is a dead spy, these little guys preferred to remain hidden.
There was another point of dissension: suppose the whole gang went to see a football match (remember "The Warriors"?). Did their turf still exist while they were gone? EPR's found the whole idea ridiculous, but the BG's (Bohr's Gang) were convinced that at that moment there was no turf at all, so it was all right to create one in the same place and make it their own. That was asking for trouble of course.

Here is how I see it.
Neither the EPR's nor the BG's  could swear on their respective mothers' graves about the state in which both particles were right before they were so cruelly separated. In other words, the lovers could have been both weeping, ecstatic, or just faking it either way.
The only thing that everybody knew for sure was what they saw when they opened the door and looked at one of them.
In other words, what is surprising is that both gangs should be surprised at the results at all.
Try to turn the things around: anytime one is up, the other is down.
And now try to explain it without making a fool out of yourself.
Saying that it should be possible for them to be both up or both down is admitting that your first theory, the classical theory, is not applicable to this case. Unless of course, there was no other way for the particles to be.
Here is now the problem: you will never know, and neither will your counterpart. Even though the EPR's stand a better chance. They believe in an independent reality which they hope one day to uncover, while the BG's  are convinced that it is all in their mind. That means that they do not really need experiments to tell them what to think. They just need to dream them. After all, there is not a single experiment that could prove them wrong.
Like I said, it is all a matter of faith.
Not convinced? Think about it. The only way to prove that the BG's  are wrong, would be to get results that do not comply with the predictions. And that is exactly what everybody agrees about. However you organize the experiment, you will always get the same results. Even the EPR's concede this essential point.
What we need is another kind of test to find out if the theory is any good. Like quantum computing (but see above Is a Mathematical Model of Time Travel Possible?). IBM's spokesmen promise results in the following ten years (see their new public project, "IBM Quantum Experience"). If I am still alive then, and they succeed, I will buy a chocolate hat and eat it! It's the thought that counts, right? Anyway, I don't think they can make recipes for hats.

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