Everyday analogy why hidden variables can’t explain entanglement

[dyb]

Everyday analogy why hidden variables can’t explain entanglement

I tried to come up with an everyday “obvious” analogy that explains why a hidden variable theory cannot explain quantum entanglement.

Here’s the story: There are two guests and one moderator on a stage. The moderator explains to the two guests that they will be separated from one another and then be given each a red or green card. He says that they will be asked to randomly write “head” or “tail” onto the card and return it to the moderator. He also asks them to please give the same answer as the other guest if they are given the same colored cards, and uncorrelated answers if they are given differently colored cards.

Before being separated the guests are allowed to talk to each other and take notes, share all their history, but quite obviously that does not help a bit at meeting the moderator’s request. This “talking, taking notes and knowing each other’s history” are all possible “hidden variables” that the guests – or electrons – could carry with them but it does not help. Only if the guests can call each other on the cell phone they can meet the moderator’s request. And that is exactly what the “spooky action at a distance” is.

Is this analogy physically accurate?

PS: The guests can meet the moderator’s request by taking along an entangled electron/positron. When given a green card, they measure the spin in x direction; when given a red card, they measure the spin in y direction. If the measurement yields a positive spin, the answer should be “head”, if negative, “tail”.

 

[Amok]

In the only hidden variables theory that I know of (Bohmian Mechanics), there's indeed ''action at a distance'', through the quantum potential. It is the price it pays for having the localized and separable physical systems. I think your analogy is good.

 

[mfb]

Hidden variables would be part of the cards itself - something that tells the guests which word to write.
Every classical system can be modeled with hidden variables, I think.

 

[Demystifier]

Dyb, your analogy is OK, but it should be added that it is an analogy for LOCAL hidden variables. By contrast, the spooky action at a distance corresponds to NON-LOCAL hidden variables.

 

[Sonderval]

I think this is very similar to the game used in this paper:
Jonathan Oppenheim, & Stephanie Wehner (2010). The uncertainty principle determines the non-locality of quantum
mechanics Science 19 November 2010: Vol. 330 no. 6007 pp. 1072-1074 arXiv: 1004.2507v2

 

[dyb]

Thanks for all the replies. Yes, I meant local hidden variable. The story is derived more or less from the proof of Bell's theorem.