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The triangle inequality in CHSH, where is the triangle?

  1. Sep 9, 2014 #1
    http://en.wikipedia.org/wiki/CHSH_inequality#Bell.27s_1971_derivation

    The last step of the CHSH inequality derivation is to apply the triangle inequality. I see there are relative polarization angles, but I don't see any sides have defined length to make up a triangle. Where is the triangle?
     
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  3. Sep 9, 2014 #2

    DrChinese

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  4. Sep 9, 2014 #3
    The triangle inequality, a theorem about distances for any one single triangle, where the sum of the lengths of any two sides must be greater than the length of the remaining side.

    330px-TriangleInequality.svg.png


    On the other hand CHSH inequality is combined from four relative angles between four polarization axis, each pair in their own separate planes a,a' and b,b'. Here we see all of them projected as if they were in the same plane:

    bases.png

    |X-Y|<=|X| + |Y|

    What does X and Y from the triangle inequality correspond to in this CHSH setup?


    26a56c0d3c312cf050f75a4e3ade5126.png

    Instead of one triangle with two sides of certain length, we have four different some things which are called "expectation value". What does X and Y from the triangle inequality correspond to here? How many meters in length is expectation value E(0, 22.5)?
     
  5. Sep 9, 2014 #4

    DrChinese

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    Left is left, right is right. Just look at the equations and I think you can make the correspondence. Note that on the right side, the absolute value is not made because the specification is given that the result of each component is non-negative and therefore >=0.
     
  6. Sep 9, 2014 #5

    DrChinese

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    Now ask yourself, why I am worrying about the CHSH inequality if I don't understand Bell's Theorem? The purpose of the inequality is to make it easy to conduct Bell tests. Nothing more. There is no new theory involved.

    The CHSH barrier of S=2 is completely arbitrary. You can see how arbitrary these numbers are by looking at my page called "Bell's Theorem and Negative Probabilities."

    http://www.drchinese.com/David/Bell_Theorem_Negative_Probabilities.htm

    It shows a specific example whereby the probability for a specific set of outcomes is as follows:

    a. Local realistic expectation: >=0%
    b. QM expectation: -10.36%

    Which do you think is correct, a or b? Please note that there is nothing magical about the -10.36% prediction of QM, it is simply a function of how I set up the equation.
     
  7. Sep 9, 2014 #6

    Nugatory

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    I'm locking this thread. As DrChinese points above, there's no point in going around in circles on the CHSH inequality until we have a basic understanding of the EPR problem and Bell's theorem and inequality.
     
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