What is the purpose of the analogies and equations used in the QM TV program?

[airydisc]

Hi

I was watching a TV program about QM on BBC4 given by Jim Khalili. I am a little confused by two aspects. First, he attempted to draw an analogy about polarisation of entangled particles always being opposite when measured, by using a card game where a dealer deals cards in pairs. I think it was in order to discover whether Einstein and his (spooky action at a distance) was right, or Bohr was right. The rule is, when overturned, if the pairs of cards are opposite in colour, then the player wins, if not the dealer wins. The first six pairs the dealer wins. The conclusion is that the pack is rigged. The rules are changed to same colour, player wins, and again the first six pairs are opposite in colour. Same conclusion, the dealer wins because he has rigged the pack. So the new rule is that the rule is not decided until after the pair of cards is dealt. In this way the dealer can't rig the deck as he doesn't know the rule until after he has dealt a pair. He goes on to say that if the player wins as many hands as the dealer, then Einstein was right and the decks previously were rigged, but if the dealer still wins the hands, or consistently a greater percentage of hands, then some other mechanism is at work, which corresponds to Bohr's argument. However, Khalili doesn't then go on to show whether the player wins or loses, so the point is not made. Why use an analogy of playing cards to make a point, and then not make the point? Can anyone enlighten me on what the point of this analogy is supposed to have shown?
Secondly, he shows a lab experiment where beam splitters and prisms are used to split photo pairs so that it can be checked whether polarisation is correct or not when the pairs arrive back at the detectors. He has written an equation on the board which is in four parts i.e. A value, plus another value, minus another value, plus another value. Khalili states that the experimental results should add up to >2 if Bohr is right and <2 if Einstein is right. The first result is 0.56, the second is 0.82, the third is minus 0.81 (I think) and the fourth is 0.56. The first two values are positive and are added together, the third is negative and is minus instead of added, and the fourth is positive and added. He did not mention anything about why one part of the equation value was negative, or why four identical experiments should produce one negative result when the other three were positive, and importantly, why the negative result happens to correspond to the negative part of the equation. Again, the point is not made, in this case because the rule of the equation and experiment is not stated. Can anyone enlighten me here, am I missing something obvious? Remember this was a program on general TV for the layman, who is presumed to have no prior knowledge of QM.

Thanks
AD2004

 

[Nugatory]

Hi
He goes on to say that if the player wins as many hands as the dealer, then Einstein was right and the decks previously were rigged, but if the dealer still wins the hands, or consistently a greater percentage of hands, then some other mechanism is at work, which corresponds to Bohr's argument. However, Khalili doesn't then go on to show whether the player wins or loses, so the point is not made.

Einstein's argument does apply to classical objects such as cards, so there's no way of demonstrating pairs of cards that support Bohr's argument. Say that we decide whether to use the "same color means dealer wins" or "same color means player wins" rule based on the toss of an honest coin; the only way that one player or the other could consistently win would be if the already dealt cards were changing their color to favor that player after the result of the coin toss was known. Obviously no real-world deck of cards can behave that way - but subatomic particles appear to. (Warning - there is a world of subtlety hidden behind those innocent-sounding words "appear to").

Secondly, he shows a lab experiment where beam splitters and prisms are used to split photo pairs so that it can be checked whether polarisation is correct or not when the pairs arrive back at the detectors. He has written an equation on the board which is in four parts...

That is almost certainly the CHSH inequality. Google for "CHSH inequality" and "Bell's theorem" will find many references, but you might best start with our own DrChinese's web page: http://www.drchinese.com/Bells_Theorem.htm