Thursday, August 11, 2011

Local Hidden Variables Correlations

Number of experiments: Number of tests:
To generate random angular momentum variables, press "Generate Random Data". In this case the correlations will be the classical ones (along the blue line), as it is predicted. To test it on random generated orientations and plot the result, press "Plot Data". Alternatively, if anybody believes that a local hidden variable theory can provide a set of data which gives the correlation of Quantum Mechanics, he or she can paste the data instead of randomly generating it, and then plot it. For example, Joy Christian claims in arxiv:0806.3078v2, page 4, that an experiment he describes can provide a list of angular momenta which gives correlations = -cos of the angle between the two orientations chosen by Alice and Bob (the green curve). He claims by this that his local hidden variables can reproduce the outcomes of the EPR-Bohm experiment.

More exactly, Joy saids that after an experiment involving balls which explode in halves which have total angular momentum 0, a list of angular momenta can be collected. The second part of his experiment is to randomly generate on a computer pairs of directions a and b in space, and calculate the result using equation (16) from his paper, page 4. He then claims that the result will be -cos of the angle between the two orientations (the green curve), rather than the linear function represented in blue.

My application does exactly the second part of Joy's experiment. If Joy Christian or anybody else can produce this kind of data, they he can test it in this application. I already provided a mathematical proof that the only possible correlation depending only on the angle between a and b is the linear one, but there are people who don't trust the mathematical proof. Therefore, I challenge them to produce the data which will contradict my proof by counterexample.

Given that the output of the first part of Joy's experiment is just a list of angular momenta, you can produce it by performing the first part of Joy's experiment. But I will not require anybody to get the data only by actually making the experiment. Joy can produce the list by any means he wants, I will not constrain him to make the experiment. Just to provide a list of angular momenta which give his prediction.

I used JavaScript, so that anyone can easily verify the source code.

P.S. For the moment, there is a problem viewing the results in Internet Explorer, so please use Mozilla, Chrome or Opera instead.

P.P.S. Thanks to Florin Moldoveanu for the uniformization of the random generator.

P.P.P.S. This test may look similar to the Quantum Randi Challenge of Sascha Vongehr, but its purpose was different, as it can be seen from the text. I fully agree with Vongehr, just that my script has a different purpose, although it can be used for the Quantum Randi Challenge too. Vongehr's challenge appeared few months earlier than mine, in connection to J.C.'s claimed disproof of Bell's theorem. Mine refers only to J.C.'s proposed experiment in which he claimed that classical mechanics reproduces Bell's correlations, and appeared from a discussion I had with J.C. on FQXi's blog, where I also gave a proof that the kind of correlations he proposed can't be obtained in that way. The discussion started on Florin Moldoveanu's post, before he turned completely against J.C., and continued here, here, here, and here. For the "disproof", I shown there that J.C.'s proposal works only for singlet state, and it is in fact the quaternion formulation from Peres's book, hence no locality involved; I gave then many other arguments, but I will not repeat the discussion here. The only reason I made the script in this post was to show that the classical proposed experiment of J.C. (also inspired from the same book by Peres) can't give the same correlations as Bell's. He rejected the math proof (both Peres's and mine), so I made this script and asked him to introduce at that time, or after the experiment will be performed, the data he claimed will show the same correlations as Bell's. My point was that no data can give the Bell correlations by using the data as generated in his proposed experiment. I maintain this page only because I said I will wait for him to come with the data, but I am no longer interested in that topic.


Anonymous said...

Question: What do the three columns represent

1. Do they represent 3 *actual* simultaneously real "hidden" variables?


2. Do they represent 3 "outcomes" from *possible* experiments which can not all be measured simultaneously.

If it is (1), What makes you thing such a thing will reproduce correlations of "outcomes" of experimenters which are *actually performed* and not just mutually exclusively *possible*? Or correlations from QM which gives correlations from only experiments which can *actually* be performed?

If it is (2), What makes you think the correlations obtained from such data can be compared to QM or experiments? On what basis do you purport to do such comparisons?

Cristi Stoica said...

Please refer to Peres - Quantum Theory, Concepts and Methods, page 161 to see the description given by Peres to the experiment.

As for Joy's version of the experiment, please refer to his paper

I extracted for you page 4 from Joy's paper, with my annotations showing what I am doing in this scripthere.

My program just calculates the correlations, as it is given in Joy's paper. It is intended to be a mean to test the lists of angular momenta produced by Joy's experiment.

Actually, I don't think that such lists, giving those correlations, exist. But Joy in his article and at FQXi claims that his experiment can provide such a list, giving the correlations -cos.

But hey, we must be open, if he or somebody else can come up with the list, the program will confirm it. The program just computes equation (16) from Joy's article.