Simplest proof of Bell's theorem ?

[Dirkman]

http://www.johnboccio.com/research/quan ... /paper.pdf

So I was directed to this as a proof of Bell's theorem, and it seems short and simple (starting from page 4) with two coins.

They start with

where the properties A , B , C of the two coins can take values of either 0 or 1 , and the coins are identical, that is if a coin has value 0(or 1) for A, the other coin will have value 0(or 1) for A .



I can almost understand it, right up until they start in page 7 with the quantum math ...


So where would the mistake be in this paper ?

[minkwe]

http://www.johnboccio.com/research/quantum/notes/paper.pdf

So I was directed to this as a proof of Bell's theorem, and it seems short and simple (starting from page 4) with two coins.

They start with

where the properties A , B , C of the two coins can take values of either 0 or 1 , and the coins are identical, that is if a coin has value 0(or 1) for A, the other coin will have value 0(or 1) for A .



I can almost understand it, right up until they start in page 7 with the quantum math ...


So where would the mistake be in this paper ?

There are many mistakes in that paper, but the main one is that they derive an inequality related to three simultaneous properties in a pair of coins, and then make the mistake of applying it to three different pairs of coins. The terms in equation (1) refer to three measurements on the same set of coins. The terms in equation (4) refer to measurements on 3 separate disjoint sets of coins. Here is their crucial argument in the legend of figure 1. Note that the argument fails if A and B are measured on one pair of objects and B and C are measured on a different pair, while A and C are measured on yet a different pair:

If A of the first object is different from both B and C of the second (dotted area), then B and C of the second object must be the same...

They make this mistake, just like many others before them. Note that in probability theory, whenever you add and subtract probabilities, the expression is only meaningful if all the probabilities are from the same sample space. While you can guarantee that a set of triples of measurements A,B,C each on a pair of coins will be able to generate P(A,B), P(A,C) and P(B,C) that are from the same sample space, there is no way to guarantee that the same can be true for 3 separate measurements in which you only measure A,B on one set of coins, A,C on another set of coins and B,C on yet a different set of coins.

Here are some articles in which the issue is explained with more mathematical rigor than I've done above:
http://mdpi.muni.cz/entropy/papers/e10020019.pdf "Bell-Boole Inequality: Nonlocality or Probabilistic Incompatibility of Random Variables?"
http://arxiv.org/abs/0901.2546: "Extended Boole-Bell inequalities applicable to quantum theory"
https://hal.archives-ouvertes.fr/hal-00824124/document: "The irrelevance of Bell inequalities in Physics"
http://arxiv.org/abs/0907.0767: "Possible Experience: from Boole to Bell"

[Mikko]

http://www.johnboccio.com/research/quantum/notes/paper.pdf

So I was directed to this as a proof of Bell's theorem, and it seems short and simple (starting from page 4) with two coins.

They start with

where the properties A , B , C of the two coins can take values of either 0 or 1 , and the coins are identical, that is if a coin has value 0(or 1) for A, the other coin will have value 0(or 1) for A .



I can almost understand it, right up until they start in page 7 with the quantum math ...


So where would the mistake be in this paper ?

One way to check the part you did understand is to try yourself. Take for example a deck of cards. Each card is either black or red, even or odd, and big or small -- three properties. Draw cards one by one, recording two of these three properties of each card. The two properties should be selected either systematically or randomly so that each possibility is covered roughly the same number of times, for eaxample choosing the same two for every third card. Then compute as in the article. Doing the same again some more times gives you an idea how much the result can vary. If your result exceeds the bound more than by the variation from one time to another, you may say that paper is in error; otherwise you have confirmed their result.

If you want to check the quantum math you need a book of (at least) elementary quantum mechanics. Most book present the basic theory and discuss harmonic oscillators and other stuff before the methods that are useful here. However, Feynman Lectures on Physics volume III covers the relevant methods near the beginning, before attacking anything more complicated.

[minkwe]

One way to check the part you did understand is to try yourself. Take for example a deck of cards. Each card is either black or red, even or odd, and big or small -- three properties. Draw cards one by one, recording two of these three properties of each card.

Quantum particles are not cards. They are dynamic with many more degrees of freedom.

Note that nobody has yet produced the QM predictions for the terms in Bells inequality. They always produce different terms and pretend it's all the same. They are wrong.

[Mikko]

One way to check the part you did understand is to try yourself. Take for example a deck of cards. Each card is either black or red, even or odd, and big or small -- three properties. Draw cards one by one, recording two of these three properties of each card.

Quantum particles are not cards. They are dynamic with many more degrees of freedom.

I tried to make sure that what can be observed with a deck of cards is only relevant to the part before the discussion of the quantum stuff. Quantum mechanics is different math and must be studied (if understanding is desred) separately and differenly.

Note that nobody has yet produced the QM predictions for the terms in Bells inequality. They always produce different terms and pretend it's all the same. They are wrong.

We are not interested in predictions of terms in any inequality. We are interested in predictions of results of eperiments that could be performed, and whether different theories predict different results. Quantum mechanics makes definite predictions for the experiments discussed by Bell.

An important question is not whether cards are quantum particles. An important question is whether an experiment with cards is analogous to an experiment with particles. Bell's inequality shows that it is not, at least not perfectly.

[minkwe]

We are not interested in predictions of terms in any inequality. We are interested in predictions of results of eperiments that could be performed, and whether different theories predict different results. Quantum mechanics makes definite predictions for the experiments discussed by Bell.
An important question is whether an experiment with cards is analogous to an experiment with particles. Bell's inequality shows that it is not, at least not perfectly.

Then you are out of luck, because contrary to popular belief, the experiment embodied in Bell's inequality, can not be performed. Instead, the experiment that can be performed, and for which QM makes predictions, is subtly different from the one in the inequality, and has a different upper bound. It is this subtlety that has escaped (and still escapes) many well meaning people in the age of quantum mysticism.

The fact that cards are different from quantum particles, is obvious, completely uninteresting and not mysterious. That fact can be appreciated without any reference to inequalities designed to confuse and conflate unrelated experiments. Only magicians need a wand to distract the audience.

The simple fact is that there is no mystery/spookiness. I understand that this fact is unfashionable, but it is true. There is an active movement evangelizing spookiness without having done the homework of proper mathematical and logical analysis. It will be a subject of psychology one day why "scientists" were so quick to prefer mysticism and superstition over logic. Some actually believe that logic does not apply to QM!

[FrediFizzx]

We are not interested in predictions of terms in any inequality. We are interested in predictions of results of eperiments that could be performed, and whether different theories predict different results. Quantum mechanics makes definite predictions for the experiments discussed by Bell.
An important question is whether an experiment with cards is analogous to an experiment with particles. Bell's inequality shows that it is not, at least not perfectly.

Then you are out of luck, because contrary to popular belief, the experiment embodied in Bell's inequality, can not be performed. Instead, the experiment that can be performed, and for which QM makes predictions, is subtly different from the one in the inequality, and has a different upper bound. It is this subtlety that has escaped (and still escapes) many well meaning people in the age of quantum mysticism.

And that subtly is pretty well addressed in this thread. I am wondering if one could use Hardy's logical inequalities to express the (different) inequality used to get the bound of ?
http://arxiv.org/abs/1203.1352