Bell's Theorem looks like Monty Hall problem in reverse

[Scott Mayers]

TL;DR

Trying to determine how the 'hidden' factor(s) in the Monty Hall problem compares to the use of Bell's theorem in asserting just the opposite for quantum entanglement.

Hi, I want to discuss what and IF others have noted the comparison of the Monty Hall problem (or identical ones in different form) to Bell's Theorem because I understood that it was used to argue that quantum entanglement exists by showing no hidden factor yet the puzzle requires a hidden factor. ?

 

[.Scott]

In the Monty Hall problem, there is a correct door and with Monty's inadvertent help you are improving your chance of ending up with that correct choice.

With Bell's inequality, you have two measurement stations and for each particle pair, each station randomly selects one those three possible measurements.

After repeating the Monty Hall experiment 9000 times, you will either end up with 3000 goats and 6000 Cadillacs or 6000 goats and 3000 Cadillacs.

After repeating Bell's experiment 9000 times, you will have:
3000 measurements that were made at the same angle and they all showed the particle pairs with opposite spins (0% the same);
2000 measurements that were made at angles 30 degrees apart with 268 with the same spin (13.4%); and
4000 measurements that were made at angles 15 degrees apart with 136 with the same spin (3.4%).

After Monty carefully examined the results of your Bell experiment, he would deduce:
1) From the 3000 measurements at the same angle, he would discover that the particles in any particle pair had opposite spins;
2) That a 15-degree change in the measurement would result in a 3.4% difference in the measuring result;
3) That two 15-degree changes could not possibly result in more than double that difference, ie 6.8%;
4) That since your 30 degree measurements showed 13.4% (large than 6.8%), you are a chronic cheater and must be banned from winning any goats or Cadillacs.

 

[Scott Mayers]

I am already familiar with the logical means to determine this but never heard anyone but myself comparing the paradoxical riddles to the determination process of quantum entanglement not to mention that perhaps Bell got his idea from these very puzzles but doesn't want anyone to think his idea was not so unique. [Appears as the inverse to the puzzle]

 

[PeroK]

I am already familiar with the logical means to determine this but never heard anyone but myself comparing the paradoxical riddles to the determination process of quantum entanglement not to mention that perhaps Bell got his idea from these very puzzles but doesn't want anyone to think his idea was not so unique. [Appears as the inverse to the puzzle]

I can see no relationship between Monty Hall and Bell's theorem.

 

[.Scott]

I am already familiar with the logical means to determine this but never heard anyone but myself comparing the paradoxical riddles to the determination process of quantum entanglement not to mention that perhaps Bell got his idea from these very puzzles but doesn't want anyone to think his idea was not so unique. [Appears as the inverse to the puzzle]

Did Bell get his idea from "these very puzzles"?
Although the Game Show "Let's Make a Deal" (1963) predates Bell's Scientific American article (1964), the "Monty Hall problem" is attributed to Steve Selvin who described it in a letter in 1975.
But "these very puzzles" might include the "3 Prisoners problem", an equivalent problem published in 1959.

I would doubt that Bell got any inspiration from those puzzles. The task he set himself to was to describe an experiment based on then-available technology (or soon-to-be available technology) that would show the cosine function at work in a way that was impossible with simple hidden variable models.

At the time, QM predictions were very good. But, there was no solid, simple, and "plain" example of an effect that could not be explained by hidden values - ie, particle or environmental states that affected the results in just right way to yield QM-predicted result.

Clearly, Bell latched onto the cosine function that describes the distribution of measured spins as something that would be problematic for any hidden-value model. Without that cosine revelation, the "three door" concept is irrelevant. But with the cosine revelation, lining up three equally-spaced target measurement angles would be an experimental design that most Physicists or technicians who work with those instruments would naturally adopt.

 

[quintinmorrow Refer]

Funny comparison, but I think the similarity kind of breaks once you dig into what’s actually being conditioned on. Monty Hall is all about updating probabilities after new classical information is revealed. Bell’s theorem isn’t about hidden doors, it’s about whether local hidden variables can reproduce quantum correlations. The “reversal” analogy is clever, though I’d be careful not to stretch it too far.