Wednesday, August 28, 2013

Bell's Theorem

Is the wavefunction ontological or epistemological?

Charlatans beware! So you think you can beat Bell's theorem?

Number of experiments:
Number of directions:

Legend: Direction index|Data index|Measurement Alice|Measurement Bob

Before I present the problems with all current quantum mechanics interpretation, let me wrap up the discussion on Bell's theorem with this pedagogical tool above.

This is based on the original idea of Sascha Vongehr's Quantum Randi Challenge: either prove you can beat Bell's theorem in a controlled environment or shut up ( and was created with coding help from Cristinel Stoica.

This is a simple Java Script HTML page which illustrates Bell's theorem for the singlet state in an EPR-B experiment and allows the user to try their hand on beating Bell's theorem. The script works fastest on Google's Chrome, and potentially on Internet Explorer 10, but the older IE versions 7,8,9 are very slow (blame Microsoft for that). The page can be also downloaded from:

The advantage of Java script is that it can be modified by anyone and can be tested on any web browser. Next week I will add explanations of how this page works and add a small tutorial on Java script to enable the reader to change the code. Until then, please play with this page. Enjoy!

Let me explain how this program works. The first two boxes allow the user to enter the number of experiments and the number of directions. The number of experiments is how many times the EPR-B experiment is supposed to be repeated (we are after obtaining correlations and they require repeated measurements). The number entered here has to match the number of rows in the first large box. In there we generate a shared randomness element in the form of a random unit vector. The information in each row is shared between Bob and Alice outcome generation program and can be used to enforce a generation strategy. The generate buttons can randomly populate the boxes, or the user can erase all data and enter whatever he/she wants.

In the original Aspect experiment, the detector orientation is randomized and it is arbitrarily changed while the photons are in mid-flight. The number of directions times two has to match the number of rows in the Alice-Bob measurement directions box. The format is 3D Cartesian: the x component, the y component, and the z component with the values being comma separated. The odd entries (1,3,5, etc rows) are for Alice and the even entries (2,4,6, etc rows) are for Bob.

In the next box, the experimental outcomes of +1 or -1 are generated. The first two numbers are control indexes to identify the experiment orientation and the experiment run. The user can play with low numbers in the first two boxes to see how the data is generated and displayed.

Last, the Plot Data button displays the correlations from the prior box in graphical form. The user can check the validity of the data display by manually computing the correlations and verifying that the point on the graph are in the proper place.

Bell theorem states (and this program illustrates) that any local hidden variable model respecting three requirements generate a correlation which is a straight line, while quantum mechanics and nature shows a minus cosine correlation. The three requirements are: parameter independence, outcome independence, and binary outputs. Parameter independence and outcome independence are called Bell locality and next time I will show how the code behind implementation respects them. The experimental outcomes have to be +1 or -1 detector results and the correlations have to be computed using actual outcomes and not in other mathematical representations of the hidden variables.

Next time I will present a brief Java script tutorial and a brief description of the script behind this web page and this hopefully will allow the user to modify the script to his own hidden variable model in an attempt to recover the minus cosine correlation.

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