On BBC episode The Secrets of Quantum Physics (Part 1) Jim Al-Khalili explains quantum mechanics for the layman. In the first half, he does a very good job; in the second half, either he thought his explanations/analogies were clear but were not, or I terribly missed something. Here is a summary of the part on “entanglement”.
Let me try and explain this by imagining the two particles are
spinning coins. Imagine these coins are two electrons created from the
same event and then moved apart from each other. Quantum mechanics
says that, because they're created together, they're entangled. And
now many of their properties are for ever linked, wherever they are.
The Copenhagen interpretation says that until you measure one of the
coins, neither of them is heads or tails. In fact, heads and tails
don't even exist. And here's where entanglement makes this weird
situation even weirder. When we stop the first coin and it becomes
heads; because the coins are linked through entanglement, the second
coin will simultaneously become tails. And here's the crucial thing: I
can't predict what the outcome of my measurement will be, only that
they will always be opposite. Einstein believed there was a simpler
interpretation: Quantum particles were nothing like spinning coins;
they were more like, say, a pair of gloves, left and right, separated
into boxes. We don't know which box contains which glove until we open
one, but when we do, and find, say, a right-handed glove, immediately,
we know that the other box contains the left-handed glove.
[To compare these two theories, Jim Al-Khalili devises a semi-analogous card game.]
The card game is against a mysterious quantum dealer. The cards he
deals represent any subatomic particles, or even quanta of light,
photons. And the game we'll play will ultimately tell us whether
Einstein or Bohr was right. Now, the rules of the game are deceptively
simple. The dealer's going to deal two cards face down: If they're the
same color, I win; if they're different colors, I lose.
[He loses each game.]
I know what the dealer's doing here. ,Clearly, the deck has been
rigged in advance so that every pair came out as opposite colors. But
there's a simple way to catch the dealer out. So what we can do now is
change the rules of the game. This time, if they are the opposite
color, I win.
[He loses each game.]
I'm now not going to tell the dealer which game I want to play, same
colors wins, or different color wins, until after he's dealt the
cards. Now, because he can never predict which rules I'm going to play
by, he can never stack the deck correctly. Now he can't win…or can
he? This gets to the very heart of Bell's idea. If we now start
playing and I win as many as I lose, then Einstein was right. The
dealer is just a trickster with a gift for slight of hand.
[He loses each game.]
Assuming that the analogy is correct (who am I to judge him), how does the third card game relate to the Einstein-Bohr debate? Specifically, his conclusion, “This gets to the very heart of Bell's idea. If we now start playing and I win as many as I lose, then Einstein was right”.
Continuing, Jim Al-Khalili performs an experiment, which supposedly proves that Bell's Equation was right. Is there a nontechnical explanation of how the truthfulness of Bell's inequality confirms/proves Bohr's interpretation on “entanglement”?
Best Answer
Bells inequality doesn't prove that Bell or Einstein are right, it only shows (mathematically) that there is a difference (an inequality) in the predicted outcomes of Quantum Mechanics and Classical Mechanics even before an experiment is done. Classical mechanics relies on local hidden variables and Quantum mechanics more on Spooky action at a distance so to say. Bell's theorem on the other hand states that no real or physical local hidden variable theory can reproduce all the predictions of quantum mechanics. The third card game is an analogy to represent some of the actual experiments where two entangled particle (which are very hard to produce) are tested for correlation. Two entangled photons fired are at two separate detectors but along the way they go through a slit that can be set in three different positions 120 degrees apart. The photons will (Y) or will not (N) go through the slits. Bell's theory was that no matter how you set the slit settings there will only be eight different outcomes. Depending on the photon and the settings the photon may not go through (theoretically) any of the slits NNN or all of the slits YYY. Then there are six other combinations of NNY, NYN, NYY, YNY, YYN, or YNN. The other entangled photon at the other detector has the same odds and when you compare the outcomes Bell's math claims that the matching corelation will be no more than 33%. On the other hand quantum mechanics experiments test 25%. Sorry I may be off on the way I'm remembering the percentages but I think that's the basics.