Thursday, September 15, 2016

Playing with Bell's theorem

In this post I'll write just a little text because editing is done straight in the HTML view which is very tedious. Below I have a Java script program which illustrates Bell's theorem. If you want to play with this code just right click on the page to view the source and extract it from there. If you do not know how to do that then you are not going to understand it in a few sentences. Next time I'll describe the code and how to experiment with various hidden variable models.
This is about an EPR-B Alice-Bob experiment where each ("measurement") generate a deterministic +1 or -1 outcome for a particular measurement direction using a shared piece of information: a random vector. Then the correlations are computed and plotted. No matter what deterministic model you try the correlation near the origin you generate a straight line vs. a curve of zero slope in the case of quantum mechanics. For this particular program, given a measurement direction specified as a unite vector in Cartesian coordinates I am computing the scalar product and I return +1 if positive I and -1 if negative. The experiment is repeated a number of times on various random measurement directions.
If you do not trust the randomly generated data, you can enter you own random Alice-Bob shared secret and your own measurement directions. Part of the credit for this program goes to Ovidiu Stoica.

Number of experiments:
Number of directions:




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

  1. Luboš MotlSeptember 18, 2016 at 1:59 AM

    These are good JavaScript skills. I've played with similar JavaScript calculators and similar things 20 years ago and then nothing. Would you be able and willing to write a similar code doing some other things, e.g. an interactive evaluation of some limited climate data?

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  2. Luboš MotlSeptember 18, 2016 at 1:59 AM

    These are good JavaScript skills. I've played with similar JavaScript calculators and similar things 20 years ago and then nothing. Would you be able and willing to write a similar code doing some other things, e.g. an interactive evaluation of some limited climate data?

    ReplyDelete
    Replies
    1. Florin MoldoveanuSeptember 18, 2016 at 7:32 PM

      My PhD thesis included numerical modeling for light propagation in optical fibers and I wrote that in C (for the algorithm I used Numerical Recipes in C). I know Java Script and C and I used to know Fortran. I also know R to some degree (Richard Gill forced me to learn it). Java performs poorly with large datasets: it uses too much memory and it is too slow, but it is very easy to code in it. The program above was developed during my fight with Joy. Cristi provided the graph part which I did not know how to do. The program is very easy to change to test different ideas.

      Thank you for the offer, but I have no time: I am focusing now on deriving Born rule in the category theory framework.

      Delete
  3. kashyap vasavadaSeptember 19, 2016 at 11:06 AM

    Hi Florin,
    I posted the following comment on the previous blog on Mother Teresa! Before it gets lost,I would like to see an answer to the question posed in the last line.Thanks.

    QM has been known to be non-realistic since 1925. So let us forget about Bohmian interpretation.Since all of us agree on Lorentz invariance, perhaps the debate is only about semantics. Locality and non-locality are just two words in the english dictionary, with whatever meaning we like to assign them.So why not just call it "non-factorizability" which will emphasize that the system has a non-factorizable wave function and nothing else. Does your word non-locality mean anything more than non-factorizability?



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