I had recently the privilege to enjoy Nicolas Gisin’s book “Quantum Chance: Non-locality, Teleportation, and Other Quantum Marvels”. It was a tough reading (as promised by the author), but a very eye opening experience!
Here, I’d like to focus on the non-locality aspect, and investigate especially the (in)famous Bell’s Game: It’s rather a mind-boggling thought experiment, which has later on been tested successfully by physicists.
Quite frankly, I don’t want to claim to have fully understood the whole book. I’m merely a computer scientist, who is interested in grasping what these crazy physicists have been up to recently: The whole point of this post is to clarify my own mind by forcing myself to go through the experiment point by point, while not committing blatant mistakes.
Bell’s Game: gorilla or girl?
So, what is this whole game about? Well, it’s not your everyday game; that I can promise you. But to have a more everyday approach to the whole experiment, let’s think of it as a pair of very special gambling devices in a casino:
One day the brothers Ahmed and Mehmed enter the casino, with the strong determination to enjoy a sinful night and get rich in the process. They check Roulette, Black Jack and all the other fancy games, but since they painfully know from experience that somehow the house seems to always win – despite strong claims of fair play – they refuse to play those games.
Then Ahmed discovers a pair of floating spheres - both of them translucent - in the corner of the casino: Neither of them seems to be connected to the ceiling nor to each other, but they simply seem to be suspended in midair! How can this be? Ahmed asks Mehmed: “Yaw, how come that these orbs are floating midair without falling down? Tell me, you’re the physicist here!”
Dr. Mehmed explains to Ahmed with a grin on his face: “Aah, my silly brother: You may have graduated from the number one Computer Science department in the world”, which by the way would be at ETH Zurich in Switzerland, “but when it comes to matters of reality you are utterly lost! Don’t you see that these spheres are made of glass and kept in place thanks to a strong and absolutely steady stream of air from below?”
Ahmed responds: “I see, now I get it! But my cherished brother, I’m not as much of an idiot as you would like to think of myself, alright? Look, there is a scanner embedded into the orbs and when I put my hand onto one it either turns pitch black or marble white. Isn’t that interesting?”
Mehmed is confused: “Indeed very much so! But how do you win or lose this game? Look, independent of which hand I use, the right or the left one, the sphere seems to turn completely randomly black or white. What is the point?”
Ahmed confirms: “You’re right! My orb is acting exactly the same way. But why would they put such a useless game in a casino?” But then he has an idea: “Just wait a minute. What if we touch the orbs at the same time? Maybe then something will happen!”
So, they both touch their respective orbs with their left hands. Ahmed’s orb turns black, while Mehmed’s sphere turns also black. The whole casino starts flashing, and a ravishing girl materializes between the orbs. The brothers cannot believe their eyes and Mehmed asks her: “Amaneen! What’s going on? Who are you?”
The girl responds: “My name is Hooriyeh, and I came to congratulate both of you: You just won one golden ruby. Her you go!” And flip, she’s gone.
Ahmed cheers: “Uy uyyyh, can you believe that? Let’s try it again. Maybe next time she’ll come with a sister of hers and we’ll force them to stay!”
So with greed they touch the spheres again, both of them again with their left hands. But this time one of the orbs turns black, while the other one turns white: Immediately a huge and hairy gorilla materializes and groans: “My name is Hanumaan, and I came to punish you for your sins!” and it starts immediately to whip them without mercy. After some time, which feels like an eternity to the poor brothers, the gorilla vanishes into thin air, but does not take the golden ruby away!
Both brothers get very upset, and complain to the casino manager Zoltaan: “What kind of a violent game is this? We’ll sue you!” But the manager is unmoved, and points out: “When the girl appeared, you were not so upset! I’m going to explain to you now the rules of the game, and then you can decide yourself if you want to continue playing:”
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Rule #1: “If at least one of you two brothers touches the orbs with a left hand, and both orbs turn the same color, Hooriyeh will appear and give you a golden ruby.”
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Rule #2: “If both of you brothers touch the orbs with your right hands, and the orbs color themselves differently, again Hooriyeh will appear with a golden ruby.”
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Rule #3: “In all other cases you will be whipped by Hanumaan. But the gorilla will never take your golden rubies away. If after 400 trials you manage to collect 300 or more rubies, you can marry Hooriyeh and her sister. Otherwise, you’ll be enslaved by Hanumaan for life!”
The brothers are terrified by the possibility of serving a gorilla and potentially be whipped for the rest of their lives. Ahmed speaks: “Come Mehmed, this game is very weird! Let’s switch to roulette.”
However, Mehmed – still a bachelor – cannot silence the masochistic physicist inside himself, and starts unconsciously to calculate the probabilities of winning and losing…
What do you think? Will they stop playing the game, or will they risk everything and potentially get married to two ravishing sisters? It’s a tough choice to make!
