The bet on Christian's experiment

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

Re: The bet on Christian's experiment

Postby Joy Christian » Thu May 01, 2014 11:23 am

In my opinion Richard Gill owes me 10,000 Euros. I have won his challenge fair and square.

I have generated 2 x N vectors, e_k and -e_k, in this simulation: http://rpubs.com/jjc/16415. They produce a very good approximation to the -cosine curve, with neither "a" nor "b" fixed a priori.

Please do check out the last plot of the simulation to recognize that none of the four correlations, namely

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

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

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

and

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

when calculated separately without replacement, deviate by more than 0.2 from the predicted values. This is more than evident from the last plot of the simulation, with both "a" and "b" completely freely chosen. That is all that is needed to recognize the fact that I have won the 10,000 Euros from Richard Gill.
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Re: The bet on Christian's experiment

Postby gill1109 » Thu May 01, 2014 11:47 am

Joy Christian wrote:In my opinion Richard Gill owes me 10,000 Euros. I have won his challenge fair and square.

I have generated 2 x N vectors, e_k and -e_k, in this simulation: http://rpubs.com/jjc/16415. They produce a very good approximation to the -cosine curve, with neither "a" nor "b" fixed a priori.

Please do check out the last plot of the simulation to recognize that none of the four correlations, namely

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

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

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

and

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

when calculated separately without replacement, deviate by more than 0.2 from the predicted values. This is more than evident from the last plot of the simulation, with both "a" and "b" completely freely chosen. That is all that is needed to recognize the fact that I have won the 10,000 Euros from Richard Gill.

We will see.

All that is needed in order to receive 10 000 Euro, and my apologies, and undying fame, and instant recognition, and the withdrawal of half a dozen of - what I thought were - my best papers, is then just to deliver to me the two files. [You said: deviate by more than 0.2; but I suppose you mean by 0.2 or less from the values predicted by you.]
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Re: The bet on Christian's experiment

Postby gill1109 » Thu May 01, 2014 12:00 pm

Here's how to save "e" (transposed: M rows, 2 columns) in a file:


Code: Select all
set.seed(9875)
M <- 10^5  ## Sample size. Next try 10^6, or even 10^7
s <- runif(M, 0, pi)
t <- runif(M, 0, pi)
x <- cos(s)/1.28
y <- (-1 + (2/(sqrt(1 + (3 * t/pi)))))
e <- cxbind(x, y)  ## M x 2 matrix; M *rows* of e represent the
## x and y coordinates of points on a circle; y -> -y => e -> -e.
## Note: cbind instead of rbind (glue columns together, not rows).

write.table(e, "JoyVector1.txt", row.names=FALSE, col.names=FALSE) ## save in a file


Note, the only changes I made to your code are in the last couple of lines.
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Re: The bet on Christian's experiment

Postby gill1109 » Thu May 01, 2014 12:35 pm

And here are some new results, with many thanks to Zen for new ideas and new result: running your program *four* times, to make four separate files, each analysed separately, the four correlations were:

-0.75156, 0.24978, -0.75114, -0.24862

whose absolute values add up to 2.0011. Not exactly 2. But not far off (about 1 / sqrt N off target?).

Not exactly 2. That was because four separate files were made, a different new random seed each time, four separate correlations were calculated, each on a separate file... as Michel advised!!!

OK. We could have calculated four correlations on one file as per our agreement and then they would have added to 2, exactly, I promise you.

So what is the problem with the simulation?

One problem, Joy, is that in your simulation program you only plot a curve. The curve looks good. But there is of course a whole correlation surface and we want four points on that surface, arranged "above" the four corners of a square.

Your programming skills, however, are improving!

I can advise you how to plot the surface so that you can better see what the simulation is doing ...

If you don't believe me, by the way, you can either calculate the correlations yourself, or we can submit the file and call in the adjudicators. But I do have to add one more rule now: if we disagree, and call in the adjudicators in order to decide, then their decision is final .... and you have no second chances. We can't bother them more than once (for this - separate - challenge).

Though by the way, the offer of 10 000 Euro is based on four correlations each computed on the same data-set and an extremely generous allowed error margin for you of +/- 0.2

If you want to follow Michel's advice and create four separate files then I have to revise my offer. N must be at least 10 000 and I can only allow you an error margin of +/- 0.1. Moreover, I will decide which correlation to calculate on which data-set. Four data-sets, four correlations, but I get to choose which a and b pair are combined with which data set.
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Re: The bet on Christian's experiment

Postby Joy Christian » Thu May 01, 2014 12:58 pm

gill1109 wrote:......


Richard,

Save your energy. I have won already. I have generated the "impossible" 2 x N vectors that produce the strong correlations. This adds a further feather in the cap of my local-realistic framework. A further result in the long list of results supporting my framework.
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Re: The bet on Christian's experiment

Postby gill1109 » Thu May 01, 2014 1:11 pm

Joy Christian wrote:
gill1109 wrote:......


Richard,

Save your energy. I have won already. I have generated the "impossible" 2 x N vectors that produce the strong correlations. This adds a further feather in the cap of my local-realistic framework. A further result in the long list of results supporting my framework.


I saved your "e" and calculated:

-0.68418, 0.68382, -0.31326, -0.31874

whose absolute values add to 2.

Exactly.

Sorry, no 10 000 Euro. No feather in your cap. Another in mine...
Or do you want to submit a file and call in the adjudicators?
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Re: The bet on Christian's experiment

Postby Heinera » Thu May 01, 2014 1:16 pm

gill1109 wrote:If you want to follow Michel's advice and create four separate files then I have to revise my offer. N must be at least 10 000 and I can only allow you an error margin of +/- 0.1. Moreover, I will decide which correlation to calculate on which data-set. Four data-sets, four correlations, but I get to choose which a and b pair are combined with which data set.

But then you can safely grant Joy the original error margin of +/- 0.2! And forget about N > 10 000! :D
Last edited by Heinera on Thu May 01, 2014 1:33 pm, edited 1 time in total.
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Re: The bet on Christian's experiment

Postby Joy Christian » Thu May 01, 2014 1:25 pm

gill1109 wrote:Sorry, no 10 000 Euro. No feather in your cap. Another in mine...
Or do you want to submit a file and call in the adjudicators?


Richard,

As I said, save your energy. I have already won. I have generated the "impossible" 2 x N vectors that produce the strong correlations. This adds a further feather in the cap of my local-realistic framework. A further result in the long list of results supporting my framework.
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Re: The bet on Christian's experiment

Postby gill1109 » Thu May 01, 2014 1:44 pm

Your move: submit the file.

I will abide by our agreement.
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Re: The bet on Christian's experiment

Postby gill1109 » Thu May 01, 2014 11:38 pm

If you want to follow Michel's advice and create four separate files, then I do not have to revise my offer.

Four non-empty data-sets, four correlations, but for fairness, obviously I get to choose which a and b pair are combined with which data set.

I allow you the same error-margin +/- 0.2.

The value of N is immaterial and whether it is the same or different for all data-sets is matter of no concern to me whatsoever.

(Thanks to Heinera for his sharp insight).
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Re: The bet on Christian's experiment

Postby Joy Christian » Fri May 02, 2014 12:01 am

gill1109 wrote:If you want to follow Michel's advice and create four separate files, then I do not have to revise my offer.

Four non-empty data-sets, four correlations, but for fairness, obviously I get to choose which a and b pair are combined with which data set.

I allow you the same error-margin +/- 0.2.

The value of N is immaterial and whether it is the same or different for all data-sets is matter of no concern to me whatsoever.

(Thanks to Heinera for his sharp insight).


Richard,

You are a day or two behind. May be you haven't heard. I have already won 10,000 Euros offered by you. I have won your challenge fair and square. The simulation I have produced yesterday adds to the long list of results supporting my local-realistic framework for the quantum correlations: http://libertesphilosophica.info/blog/.

I have generated 2 x N vectors, e_k and -e_k, in this simulation. They produce the -cosine curve to a very good approximation, with neither "a" nor "b" fixed a priori. The correlations E(a, b) are plotted as a function of the relative angle between the measurement directions a and b. This is what you have been demanding. This is what Bell considered "impossible" to achieve. I have achieved it with spectacular success!!!

Please do check out the last plot of the simulation to recognize that none of the four correlations, namely

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

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

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

and

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

when calculated separately without replacement, deviate by more or less than 0.2 from the predicted values. This is more than evident from the last plot of the simulation, with both "a" and "b" completely freely chosen. That is all that is needed to recognize the fact that I have won the 10,000 Euros offered by you.
Joy Christian
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Re: The bet on Christian's experiment

Postby gill1109 » Fri May 02, 2014 12:10 am

Joy Christian wrote:Maybe you haven't heard. I have already won 10,000 Euros offered by you.

No such thing. You announced your imminent winning of the bet. I haven't seen the computer file yet. Seems it was a kind of premature ejaculation, sorry premature announcement, because I still haven't seen the file.

You also single handedly rewrote the rules we had agreed to, thereby proving to the world that you are a liar and a cheat. It was about time that it was said so clearly. I'm glad that this is now completely plain for all to see.

You can email me when you have posted the file on internet.
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Re: The bet on Christian's experiment

Postby Joy Christian » Fri May 02, 2014 12:22 am

gill1109 wrote:
Joy Christian wrote:Maybe you haven't heard. I have already won 10,000 Euros offered by you.

No such thing. You announced your imminent winning of the bet. I haven't seen the computer file yet. Seems it was a kind of premature ejaculation, sorry premature announcement, because I still haven't seen the file.

You also single handedly rewrote the rules we had agreed to, thereby proving to the world that you are a liar and a cheat. It was about time that it was said so clearly. I'm glad that this is now completely plain for all to see.

You can email me when you have posted the file on internet.


Richard,

You are in denial. I have already won. I have won 10,000 Euros offered by you.

There is no point denying the incontrovertible evidence: http://rpubs.com/jjc/16415.
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Re: The bet on Christian's experiment

Postby gill1109 » Fri May 02, 2014 2:11 am

Still no file of directions received. It is now more than 12 hours after dr. Christian's claim that he has won the bet he made with me.

For the time being, here is my answer to Christian:

http://rpubs.com/gill1109/Fail

It is a little R script proving that his claim is false. If he wants this result adjudicated by our board of adjudicators, he is welcome, but we can only bother them once on this particular challenge. So it would be his one and only chance for the 10 000 Euro jackpot.

Other alternatives: he tries again another day; he gives up; ...

My open one-sided offer does remain offer to anyone, up to June 11. After that it is reduced to 5 000.

Claims have to be submitted to me by email. For the time being I have had enough of discussions with dr. Christian. Submissions do not consist of some computer code drawing some pretty pictures. They consist of a link to a text file, posted on internet, containing N directions of angular momentum observed by Alice, and N directions of angular momentum observed by Bob. I will compute the "usual" four correlations E(0, 45), E(0, 135), E(90, 45), E(90, 135) according to the formulas agreed by Joy and myself which can be found in the first posting in this topic. If any of them is off by 0.2 or more from the target values - 0.7071, + 0.7071, - 0.7071, - 0.7071 the claim has failed. If all four are within tolerance, the claim has succeeded and will be honoured by me.

In case of dispute as to whether or not a particular submission is valid or has / has not won the bet, we will jointly approach three wise men Andrei Khrennikov, Hans de Raedt, and Gregor Weihs, and they may adjudicate. I haven't asked them if they are prepared to do this job, so if they are unavailable, we will have to come up with another adjudication procedure. In any case, we are only going to resort to adjudication once, so after one false claim, you are no longer eligible for new tries (unless of course you actually immediately convince me on your n'th submission that you finally got it right).

Any questions about this procedure are to be submitted to me by email. I am happy to give any further necessary clarification. If an issue is raised of general concern I will add a posting here, addressing it.

Here is the R code referred to above:

Code: Select all
## My response to Christian's claim to my prize.
## First I delete all lines from his code except those generating
## the set of directions "e"

set.seed(9875)
N <- 10^5
s <- runif(N, 0, pi)
t <- runif(N, 0, pi)
x <- cos(s)/1.28
y <- -1 + (2/(sqrt(1 + (3 * t/pi))))
e <- rbind(x, y)  ## 2 x N matrix; N columns of e represent the
## x and y coordinates of points on a circle:
## Alice's observed directions of angular momentum.
## Bob's observed directions are -e.


## Now I separately compute four correlations according to the
## formulas agreed by Christian

alpha <- 0 * pi / 180
beta <- 45 * pi / 180
a <- c(cos(alpha), sin(alpha))
b <- c(cos(beta), sin(beta))
(E_0_45 <- mean(sign(colSums(e * a)) * -sign(colSums(e * b))))

alpha <- 0 * pi / 180
beta <- 135 * pi / 180
a <- c(cos(alpha), sin(alpha))
b <- c(cos(beta), sin(beta))
(E_0_135 <- mean(sign(colSums(e * a)) * -sign(colSums(e * b))))

alpha <- 90 * pi / 180
beta <- 45 * pi / 180
a <- c(cos(alpha), sin(alpha))
b <- c(cos(beta), sin(beta))
(E_90_45 <- mean(sign(colSums(e * a)) * -sign(colSums(e * b))))

alpha <- 90 * pi / 180
beta <- 135 * pi / 180
a <- c(cos(alpha), sin(alpha))
b <- c(cos(beta), sin(beta))
(E_90_135 <- mean(sign(colSums(e * a)) * -sign(colSums(e * b))))

## Just for fun
 - E_0_45 + E_0_135 - E_90_45 - E_90_135


Here are the numerical results which I obtained:

Code: Select all
[1] -0.68418
[1] 0.68382
[1] -0.31326
[1] -0.31874
[1] 2


I am now going on a short vacation but will be reading my email from time to time.
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Re: The bet on Christian's experiment

Postby Joy Christian » Fri May 02, 2014 3:05 am

gill1109 wrote:I am now going on a short vacation but will be reading my email from time to time.


Richard,

You are in denial. I have already won. I have won 10,000 Euros offered by you.

There is no point denying the incontrovertible evidence I have presented: http://rpubs.com/jjc/16415.
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Re: The bet on Christian's experiment

Postby gill1109 » Fri May 02, 2014 3:20 am

Final remark: dr. Christian can consider his wonderful colourful exploding balls experiment also cancelled; at least, any participation by myself in it, and any support of its happening, and any bet with me about its outcome. He has proved himself totally untrustworthy.

I'll therefore ask our beloved and respected forum boss to close this topic.

If Christian wants to redeem credibility he had better post the file of directions corresponding to his recent extravagant and unverified claims on internet, and email me their URL. Or apologize. But I'm afraid he has gone too far now.
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Re: The bet on Christian's experiment

Postby Joy Christian » Fri May 02, 2014 4:29 am

Dear All,

Richard Gill has conceded defeat, both regarding his 10,000 Euros offer for generating N vectors as well as his 5,000 Euros bet concerning my proposed experiment.

I won his offer of 10,000 Euros yesterday by producing this simulation: http://rpubs.com/jjc/16415. It generates the 2 x N vectors, e_k and –e_k, which necessitate the strong correlation unambiguously, for any two freely chosen measurement directions “a” and “b”.

It is pretty clear from the incontrovertible evidence presented in this simulation that when my proposed experiment is realized it will undoubtedly produce the same strong correlation, with e_k and -e_k as spin directions observed by Alice and Bob (respectively).

I think Richard Gill is smart enough to recognize the evidence I have presented and wise enough to realize the inevitability of seeing the strong correlation in my proposed experiment. He has therefore backed-off from the bet which he cannot possibly win. It is of course wiser to retreat than to be humiliated.

With my main opponent defeated, it is now time to get on with real physics, in both theoretical and experimental direction. There is much work to be done.

Joy Christian
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Re: The bet on Christian's experiment

Postby Joy Christian » Fri May 02, 2014 12:08 pm

gill1109 wrote:alpha <- 0 * pi / 180
beta <- 45 * pi / 180
a <- c(cos(alpha), sin(alpha))
b <- c(cos(beta), sin(beta))
(E_0_45 <- mean(sign(colSums(e * a)) * -sign(colSums(e * b))))

alpha <- 0 * pi / 180
beta <- 135 * pi / 180
a <- c(cos(alpha), sin(alpha))
b <- c(cos(beta), sin(beta))
(E_0_135 <- mean(sign(colSums(e * a)) * -sign(colSums(e * b))))

alpha <- 90 * pi / 180
beta <- 45 * pi / 180
a <- c(cos(alpha), sin(alpha))
b <- c(cos(beta), sin(beta))
(E_90_45 <- mean(sign(colSums(e * a)) * -sign(colSums(e * b))))

alpha <- 90 * pi / 180
beta <- 135 * pi / 180
a <- c(cos(alpha), sin(alpha))
b <- c(cos(beta), sin(beta))
(E_90_135 <- mean(sign(colSums(e * a)) * -sign(colSums(e * b))))

## Just for fun
- E_0_45 + E_0_135 - E_90_45 - E_90_135
[/code]

Here are the numerical results which I obtained:

Code: Select all
[1] -0.68418
[1] 0.68382
[1] -0.31326
[1] -0.31874
[1] 2



The above calculations by Richard Gill are wrong. Here is how to do them correctly (I have explained these calculations in much greater detail on the FQXi blog):

Image.

Needless to say, my model passes his test with flying colours. It violates the Bell-CHSH inequality just as I would expect it to: http://rpubs.com/jjc/16415.
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