Is the wavefunction ontological or epistemological? 

A quantum Randi challenge for Bell's theorem 

 Who is James Randi (http://en.wikipedia.org/wiki/James_Randi)? He is a former magician who started debunking charlatans and who offers $1M for anyone able to replicate supernatural activities under test conditions. His You Tube clips are most funny. See for example a classic one:

Now physics is by its very nature against supernatural, but and in particular the quantum mechanics area with its counter-intuitive phenomena attracts lots of attention from general public and people espousing their own theories. These days perpetual motion machines are out of favor, and there is surprising interest in "proving Bell theorem wrong". Those "proofs" are in the same category with bending spoons with your mind, unicorns, and Santa Claus. To recap, Bell theorem proves that there is no local realism and there are no causal explanations possible for quantum correlations. 

Some time ago Sascha Vongehr introduced the idea of a "Quantum Randi Challenge" asking the wannabe disprovers to demonstrate their theories on a computer program. Since I have extensive experience in both worlds of physics and computer programming, I tried to simplify the computer program part and this work resulted in the script presented in the prior post. And now I will explain how it can be changed by anyone to their heart's content.

The Bell theorem pedagogical script can be downloaded from: http://www.florinmoldoveanu.org/Math_Philosophy.html as Bell1.html.txt. Save it locally and remove the .txt ending in the name. The script is written in Java Script language. Here are some key points about the syntax:

For illustration please refer to this part of the code:

//Dot is the scalar product of 2 3D vectors
function Dot(a, b)
{
 return a[0]*b[0] + a[1]*b[1] + a[2]*b[2];
};

• Comments begin with double slash //
• All coding lines end with a semicolon ;
• Code is indented for readability but additional white spaces have no effect
• Array index are represented by square brackets []
• Array indexes start at zero a[0]
• Curly brackets are scope qualifiers { }: all variables declared inside them are not visible outside
• The language is based on C/C++/Java basic syntax

Now the part that the user is allowed and encouraged to change in order to test different ideas is the following:

function GenerateAliceOutputFromSharedRandomness(direction, sharedRandomness3DVector) {
    //replace this with your own function returning +1 or -1
    if (Dot(direction, sharedRandomness3DVector) > 0)
        return +1;
    else
        return -1;
};

function GenerateBobOutputFromSharedRandomness(direction, sharedRandomness3DVector) {
    //replace this with your own function returning +1 or -1
    if (Dot(direction, sharedRandomness3DVector) < 0)
        return +1;
    else
        return -1;
};

I mentioned previously that any local realistic model should respect 3 requirements:

1. Outputs to be +1 or -1 and the correlation should be computed using the actual experimental values
2. Outcome independence: Alice outcome should be independent from Bob's outcome
3. Parameter independence: Alice's measurement direction should be independent from Bob's measurement direction

By code construction parameter and outcome independence are automatically fulfilled. Also Alice and Bob are allowed to share a random sharedRandomness3DVector variable which corresponds to a hidden variable. This hidden variable can be generated by the script when pressing this button:



or the user can manually erase the data and enter it by hand or according to their own "hidden variable theory".

Once that is done, all that remains is to replace the simple model I came up with:

    if (Dot(direction, sharedRandomness3DVector) > 0)
        return +1;
    else
        return -1;

with your own method. Save the file locally and try to reproduce the minus cosine curve in the limit of large numbers. If you can do it without changing the rest of the script, the Nobel prize for you is most likely just a formality at that point (and I'll eat my hat).

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