A Crystal Clear illustration of the Bell illusion

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

Re: A Crystal Clear illustration of the Bell illusion

Postby Ben6993 » Mon Apr 21, 2014 8:12 am

Hi Richard

I have read more on counterfactual reasoning and agree that my example was as you said.

Thank you very much for the link to your statistical paper on historical demography, which I will read.

I had seen the video of your TEDx talk a few days earlier than your post. A nurse was charged yesterday concerning three death at Stepping Hill hospital, Stockport, which is not much more than ten miles from me. I don't know the details of this case and whether probabilty calculations played any part in the accusation.


If I read it correctly, Joy's recent post on FQXi is a stunner. He doesn't need your, nor anybody's, computer programs. He probably doesn't even need a computer, spreadsheet or calculator. He just needs the back of an envelope to record the four numbers in categories 00, 01, 10 and 11. Just to be calculated for one pair of a and b values. He is probably correct!
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Re: A Crystal Clear illustration of the Bell illusion

Postby Ben6993 » Mon Apr 21, 2014 10:32 am

I should have written: categories --, -+, +-, ++ rather than 00, 01, 10 and 11.
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Re: A Crystal Clear illustration of the Bell illusion

Postby gill1109 » Mon Apr 21, 2014 1:40 pm

Ben6993 wrote:If I read it correctly, Joy's recent post on FQXi is a stunner. He doesn't need your, nor anybody's, computer programs. He probably doesn't even need a computer, spreadsheet or calculator. He just needs the back of an envelope to record the four numbers in categories 00, 01, 10 and 11. Just to be calculated for one pair of a and b values. He is probably correct!

Of course one can count four kinds of outcomes on the back of an envelope. But if you are making a bet with someone, you need to agree in advance who is going to count what.

If you only use one value of a and one value of b, known in advance, you prove absolutely nothing. There is nothing remarkable about a correlation of +/- 0.7. The remarkable thing is the pattern of four correlations, three - 0.7, and one + 0.7. In fact the whole mystery revolves around the joint distribution of four binary variables - Alice setting, Alice outcome, Bob setting, Bob outcome.

Which is too complicated a concept for anyone to understand intuitively.

Sounds to me that Joy's stunning post yet again exhibits his total lack of understanding what the whole thing is about.... but then I read Heinera's recent post on the forum here, with a stunningly original idea.

Brilliant!

We do the experiment.
Joy hands me over the two files of N directions of angular momentum, u_k and -u_k, k=1, ..., N.
I will then produce a pair of measurement directions a and b such that the computed correlation differs from the QM correlation by at least +/- 0.2!
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Re: A Crystal Clear illustration of the Bell illusion

Postby gill1109 » Tue Apr 22, 2014 7:48 am

Ben6993 wrote:If I read it correctly, Joy's recent post on FQXi is a stunner. He doesn't need your, nor anybody's, computer programs. He probably doesn't even need a computer, spreadsheet or calculator. He just needs the back of an envelope to record the four numbers in categories 00, 01, 10 and 11. Just to be calculated for one pair of a and b values. He is probably correct!


Dear Ben

Yes it is a stunner. Well, we do need computer programs, but they are so simple there is no need to discuss coding issues now.

Speaking metaphorically, I need the back of four envelopes. Joy will only need one, to check my finding.

The experiment (N exploding balls, and analysis of a a lot of video footage of those explosions) generates two computer files each containing N directions of angular momentum. Spherical coordinates theta (azimuth), phi (zenith).

Let's call the directions of angular momentum in Alice's file u_k, k=1, ..., N, and in Bob's file v_k, k = 1, ..., N

In theory one would have v_k = - u_k, but in practice that might not be exactly the case.

If I pick measurement directions a and b, then according to Joy's experimental paper the outcomes left and right are

A_k = sign(a . u_k) and
B_k = sign(b . v_k),

and the estimated (observed, sample, experimental ...) correlation is

E(a, b) = 1/N sum_k A_k B_k
= ( N(++) + N(--) - N(+-) - N(-+) ) / ( N(++) + N(--) + N(+-) + N(-+) )

in the obvious notation.

Joy predicts the theoretical (population, large N limit, ensemble) correlation rho(a, b) = - a . b = - cos(angle between a and b)

Now we are going to look at two possible directions for Alice and two for Bob. They are all in the equatorial plane so they can be described just by azimuthal angles alpha = 0 and 90 for Alice and beta = 45 and 135 for Bob.

Joy predicts

E(0, 45) = - 0.7071...,

E(0, 135) = + 0.7071...,

E(90, 45) = - 0.7071...,

E(90, 135) = - 0.7071....

I will win my bet if I show him that one of these four predictions has failed, by an amount 0.2 or more.

He will give me two computer files "AliceDirections.txt" and "BobDirections.txt"
I'll claim that I'll be able to show him that one of his predictions has failed by a large amount (0.2 in either direction, or more).

I am actually certain that I will win. Notice that I even generously went to 0.2 whereas in my old proposal (when we randomly sampled subsets of the runs) I only went to 0.1
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Re: A Crystal Clear illustration of the Bell illusion

Postby Ben6993 » Wed Apr 23, 2014 3:53 pm

Hi Richard

I had noticed that you had mentioned 0.2 rather than 0.1. I would have stayed with a symmetric cutoff correlation coefficient of 0.6, but never mind.

Don't feel guilty about being certain that you will win the bet. You seem to me to have been scrupulously fair at all times in this forum wrt the bet. A number of times you have suggested different versions of the bet which would have meant that you were less sure of winning and possibly that is because you do not want it to be too easy for yourself. But on the other hand you said the experiment should be done without the need for a complex probability judgement to determine the winner. And you now have that. You are sure, Joy is sure. That seems ideal.
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Re: A Crystal Clear illustration of the Bell illusion

Postby gill1109 » Wed Apr 23, 2014 11:01 pm

The reason I can generously go to 0.2 rather than the symmetric cut-off 0.1 is because all chance has been totally eradicated. My "spread-sheet argument" (the math core of CHSH) says that -E (0, 45) + E(0, 135) - E(90, 45) - E(90, 135) is less than or equal to 2. No probability. This is certain. Just substitute the four expressions for E and merge the four sums over k = 1 to N into one sum. You don't have to actually do it, and Joy has forbidden it to be actually done, but unfortunately in a thought experiment nothing is forbidden. And pure mathematics is pure thought experiment.

If each of the four terms is within 0.2 of 0.7071, then the smallest that that thing can be is 4 * (0.7071 - 0.2) = 4 * 0. 5071 = 2 + 4 * 0.071 = 0.284 > 2. Contradiction. So at least one must be within 0.2 of 0.7071.

It's very neat. (This was Heinera's brilliant idea).
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Re: A Crystal Clear illustration of the Bell illusion

Postby Joy Christian » Wed Apr 23, 2014 11:13 pm

gill1109 wrote:The reason I can generously go to 0.2 rather than the symmetric cut-off 0.1 is because all chance has been totally eradicated. My "spread-sheet argument" (the math core of CHSH) says that -E (0, 45) + E(0, 135) - E(90, 45) - E(90, 135) is less than or equal to 2. No probability. This is certain.


And yet Nature says -E (0, 45) + E(0, 135) - E(90, 45) - E(90, 135) = 2.828427125...

And that is what we shall observe.
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Re: A Crystal Clear illustration of the Bell illusion

Postby gill1109 » Wed Apr 23, 2014 11:44 pm

Joy Christian wrote:
gill1109 wrote:The reason I can generously go to 0.2 rather than the symmetric cut-off 0.1 is because all chance has been totally eradicated. My "spread-sheet argument" (the math core of CHSH) says that -E (0, 45) + E(0, 135) - E(90, 45) - E(90, 135) is less than or equal to 2. No probability. This is certain.


And yet Nature says -E (0, 45) + E(0, 135) - E(90, 45) - E(90, 135) = 2.828427125...

And that is what we shall observe.


And that is why we are doing the experiment: to learn from Nature!
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