
Bell's Theorem: No EPR “Reality” - apsec112
http://lesswrong.com/lw/q1/bells_theorem_no_epr_reality/
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cousin_it
Sometime ago I came up with a very simple reformulation of this.

Imagine that your friend Alice has a set of three fair coins, numbered from 1
to 3. If you ask her to flip one of the coins, the other two will disappear.
Also imagine that your other friend Bob, who lives far away from Alice, has an
identical set of coins that are somehow "mysteriously connected" to Alice's.
The whole setup can be repeated as many times as you want. You do a few
experiments and find out this:

1) If you ask both Alice and Bob to flip the same numbered coin, their answers
always agree.

2) If you ask Alice to flip coin 1 and Bob to flip coin 2, their answers
differ 5% of the time.

3) If you ask Alice to flip coin 2 and Bob to flip coin 3, their answers
differ 5% of the time.

4) If you ask Alice to flip coin 1 and Bob to flip coin 3, their answers
differ 20% of the time.

Why is that weird? Well, if coin 1 differs from coin 3, then at least one of
them would've differed from coin 2, so the 20% case must be completely covered
by two 5% cases, which seems impossible. But you can't use it for faster-than-
light communication between Alice and Bob, because all coins are individually
fair no matter what.

This setup actually happens in our world, it can be easily reproduced in a lab
to 1 digit of precision. This kind of quantum "spooky action at a distance"
sits strictly between what's possible in a classical universe and what would
be possible with FTL communication. More precisely, it allows two distant
players to jointly win some games that wouldn't be winnable in a classical
universe (even with arbitrary communication beforehand), but not all games
that would've been winnable with FTL.

~~~
mrfusion
So experiment one could be explained by a hidden variable right?

I'm guessing somehow the other experiments rule out a hidden variable but I'm
not seeing why.

~~~
strmpnk
I don't think that explanation is clear.

It takes a bit more work to get something which proves the experimental
difference. One of the better explanations I've seen is regarding measuring
spin with three state detectors: [https://www.youtube.com/watch?v=ZuvK-
od647c](https://www.youtube.com/watch?v=ZuvK-od647c)

This would give specific probabilities to certain outcomes (not just 50/50) IF
there were a local hidden variable. (Note: the word local is important there.
It means information encoded and carried by or with the particles themselves.)

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smaddox
EPR doesn't rule out a non-local hidden variables theory, e.g. pilot wave
theory. Ontologically, non-local hidden variables is the only workable
solution, since otherwise the universe would need uncountably infinite
computing power to advance each instant. With non-local hidden variables, our
universe can be advanced with finite (though mind-blowingly large) computing
resources (whether an actual computer or just a system that naturally
computes).

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kobeya
2008

