The bet on Christian's experiment

[gill1109]

OK. Here are the two files:

AliceDirections.txt: vector e_k := ( cost(s_k), -1+(2.08/(sqrt(1+(3 x t_k/pi))), 0), where s_k is randomly picked from [0, pi] and t_k is randomly picked from [0, pi].

BobDirections.txt: vector -e_k := ( cost(s_k), +1-(2.08/(sqrt(1+(3 x t_k/pi))), 0), where s_k is randomly picked from [0, pi] and t_k is randomely picked from [0, pi].

Here k is an integer from [1, 2, 3, ..., 10^7].

So there you have it. These are the two files you are asking for, with the explicit simulation provided here: http://rpubs.com/jjc/16415

Please have one of your friends make the two files for you. If I make them, and if they then fail the test, then you will blame me, right? (Algebraically challenged, third rate statistician, not even a mathematician, probably less than fourth rate programmer!). Michel is a splendid programmer, believe me! Chantal too!

BTW so you are going to give me x, y and z coordinates instead of spherical coordinates? It's not a problem, but I need to know in advance. You first give me two files, and I then tell you a pair of directions such that E(a, b) is 0.2 or more off your prediction. a and b chosen, as agreed, by me, from the usual set of four "CHSH" pairs. I will calculate E(a, b) according to the recipe which we agreed together (the recipe in your experimental paper, indeed). Everyone will be able to check who's right.

[Joy Christian]

OK. Here are the two files:

AliceDirections.txt: vector e_k := ( cost(s_k), -1+(2.08/(sqrt(1+(3 x t_k/pi))), 0), where s_k is randomly picked from [0, pi] and t_k is randomly picked from [0, pi].

BobDirections.txt: vector -e_k := ( cost(s_k), +1-(2.08/(sqrt(1+(3 x t_k/pi))), 0), where s_k is randomly picked from [0, pi] and t_k is randomely picked from [0, pi].

Here k is an integer from [1, 2, 3, ..., 10^7].

So there you have it. These are the two files you are asking for, with the explicit simulation provided here: http://rpubs.com/jjc/16415

Please have one of your friends make the two files for you. If I make them, and if they then fail the test, then you will blame me, right? (Algebraically challenged, third rate statistician, not even a mathematician, probably less than fourth rate programmer!). Michel is a splendid programmer, believe me! Chantal too!

BTW so you are going to give me x, y and z coordinates instead of spherical coordinates? It's not a problem, but I need to know in advance. You first give me two files, and I then tell you a pair of directions such that E(a, b) is 0.2 or more off your prediction. a and b chosen, as agreed, by me, from the usual set of four "CHSH" pairs. I will calculate E(a, b) according to the recipe which we agreed together (the recipe in your experimental paper, indeed). Everyone will be able to check who's right.

Actually, I am not going to ask anyone. I am satisfied that the simulation speaks for itself. It does what you claimed to be impossible to do. If someone wants to help me to do what you are asking for, then I will happily accept their help. But, as I said, the simulation speaks for itself, so I don't see the point. It is pretty clear from the second plot that none of the four E(a, b) are off by more than 0.02, even with just 10^7 trials. So there is no way you are going to get your 0.2 or more deviation.

As for the choice of coordinates, I have no idea which coordinates will be convenient for the experimentalists. To me this is a trivial issue. Translation from one coordinate system to another shouldn't be an issue at all.

By the way, the accuracy of this simulation can be improved in several different ways. I will just have to play around with it a bit more to get some improvements.

[Heinera]

I have already dumped Joy's list of vectors to file. Just let me finsih dinner preparations, then I'll put them in a publicly available place.

[Joy Christian]

I have already dumped Joy's list of vectors to file. Just let me finsih dinner preparations, then I'll put them in a publicly available place.

OK. Thanks.

[Heinera]

The file is here:

JoyVector.txt

It is a dump of the 2*10^7 matrix e in Joy's program. Since he fixes seed in his program, it is the same matrix for every run.

Warning: The file is HUGE. Right click on the link and chose save; don't left click on it, because your browser will crash when trying to display it.

Alternative: It is much easier to regenerate the matrix in R (with the same seed as Joy uses) and do computations in there.

[Joy Christian]

For the benefit of those not familiar with my proposed experiment, let me spell out what this ugly looking simulation is all about. Mimicking quantum mechanical predictions, my proposed experiment makes the following four predictions for a macroscopic EPR-Bohm experiment:

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

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

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

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

These are the well known "Bell test" correlations involving the four pairs of the "Bell test" angles, each to be calculated separately.

Now, because of his deep-seated belief in the Bell's so-called theorem, Richard Gill claims that one of these four correlations would be off target by at least 0.2 (i.e., the absolute value of the difference between the observed and predicted correlation would be 1/5 or more) in my proposed experiment. He has therefore offered 10,000 Euros to anyone who can simulate the hidden variables involved in my experiment which do not exhibit deviation from the correlations by more than 0.2.

In the above simulation, however, I have accomplished just that. It is easy to see from the last plot of the simulation that none of the four corrections deviate by more than 0.02 from the values predicted by my local model. So the net deviation cannot even add up to 0.2. Therefore Richard Gill now owes me 10,000 Euros.

[Heinera]

Therefore Richard Gill now owes me 10,000 Euros.

Did you check E(90, 135)?

[Joy Christian]

Therefore Richard Gill now owes me 10,000 Euros.

Did you check E(90, 135)?

Did you?

[Heinera]

Therefore Richard Gill now owes me 10,000 Euros.

Did you check E(90, 135)?

Did you?

Oh, yes.

[Joy Christian]

Did you check E(90, 135)?

Did you?

Oh, yes.

Good.

[Joy Christian]

Did you check E(90, 135)?

In case anyone else is wondering, the deviation in E(90, 135) is 0.02 --- ten times smaller than what Richard would need to win the bet.

[jreed]

Joy, if I'm not mistaken your simulation is using the detector loophole to obtain the desired curve. The R code statement: good <- ca & cb selects products of the correlations where both the correlations are non-zero. I've seen this several times before in the Gisin & Gisin, Minkwe and Roth simulations when I coded them up in Mathematica.

[Joy Christian]

Joy, if I'm not mistaken your simulation is using the detector loophole to obtain the desired curve. The R code statement: good <- ca & cb selects products of the correlations where both the correlations are non-zero. I've seen this several times before in the Gisin & Gisin, Minkwe and Roth simulations when I coded them up in Mathematica.

Hi John,

The detection loophole is irrelevant both in my model and in the proposed experiment. In the model the complete or initial state of the system is a pair (e, theta), not just the vectors e by themselves. This is explained in more detail in this one page document. Therefore there is 1-to-1 correspondence between the initial state of the system and what is observed. Every state (e, theta) is detected and every detection corresponds to a state. Ultimately what appears as a detection loophole is a manifestation of the topology of the 3-sphere---i.e., the topology of the physical space we live in.

Now in my proposed experiment, the way it is set up, there cannot be any loss of detection, because we are not actually observing the "particles" along the directions a and b. What is being observed are the actual spin directions, without any reference to measurement directions a and b. So no question of detection loophole arises.

I have used the argument good <- ca & cb simply because I don't know much programming. I am certain that one can calculate correlation in the latest simulation without using the "good" line. I do not believe it will change anything. In fact it might improve the accuracy of the simulation. I am working on such improvements.

[gill1109]

The detection loophole is irrelevant both in my model and in the proposed experiment.
...

I have used the argument good <- ca & cb simply because I don't know much programming. I am certain that one can calculate correlation in the latest simulation without using the "good" line. I do not believe it will change anything. In fact it might improve the accuracy of the simulation. I am working on such improvements.

Unfortunately the detection loophole (or if you prefer to interpret it differently, the conspiracy loophole) is an important component in the Pearle model and all known variants.

Try leaving out the line "good <- ca & cb" and the subsequent selection according to the subset defined by good. It is a different subset of all the runs which have been performed for each different value of a and b, so you don't want it here, because you want to end up with just one set of runs.

You could alternatively just work with the settings which we are interested, and do something like good <- "ca1 & ca2 & cb1 & cb2" to select the same subset for all four correlations (a1,b1) etc.

[gill1109]

Zen asked me to post this code here:

Code: Select all

N <- 10^6
e <- matrix(nrow = 2, ncol = N, byrow = FALSE, data = scan("/tmp/JoyVector.txt", nlines = N))
alpha <- 90 * pi / 180
beta <- 135 * pi / 180
a <- c(cos(alpha), sin(alpha))
b <- c(cos(beta), sin(beta))
mean(sign(colSums(e * a)) * -sign(colSums(e * b)))
-cos(alpha - beta)


[Joy Christian]

Zen asked me to post this code here:

Code: Select all

N <- 10^6
e <- matrix(nrow = 2, ncol = N, byrow = FALSE, data = scan("/tmp/JoyVector.txt", nlines = N))
alpha <- 90 * pi / 180
beta <- 135 * pi / 180
a <- c(cos(alpha), sin(alpha))
b <- c(cos(beta), sin(beta))
mean(sign(colSums(e * a)) * -sign(colSums(e * b)))
-cos(alpha - beta)


Richard,

I have no idea what this code is for.

By the way, you may have noticed that the list of vector directions from my latest simulation has been made public since yesterday: angular momentum diections.

[gill1109]

Zen asked me to post this code here:

Code: Select all

N <- 10^6
e <- matrix(nrow = 2, ncol = N, byrow = FALSE, data = scan("/tmp/JoyVector.txt", nlines = N))
alpha <- 90 * pi / 180
beta <- 135 * pi / 180
a <- c(cos(alpha), sin(alpha))
b <- c(cos(beta), sin(beta))
mean(sign(colSums(e * a)) * -sign(colSums(e * b)))
-cos(alpha - beta)


Richard,
I have no idea what this code is for.
By the way, you may have noticed that the list of vector directions from my latest simulation has been made public since yesterday: angular momentum diections.

Hadn't noticed, sorry, till this morning. And now the file is taking a bloody long time to download.

I suspect that Zen is helping out with code for calculating the correlations.

So there is just one file, not two? The directions for Bob are exactly the negatives of those for Alice? The file contains x and y coordinates of vectors in the equatorial plane? Do the vectors have length 1 or are they unnormalised?

I can't do anything with your data set if you don't tell me how you mean it to be interpreted.

[Joy Christian]

Unfortunately the detection loophole (or if you prefer to interpret it differently, the conspiracy loophole) ....

As I explained to John, detection loophole or conspiracy loophole, or any loophole for that matter, is of no relevance to my model, or to my proposed experiment.

Try leaving out the line "good <- ca & cb" and the subsequent selection according to the subset defined by good. It is a different subset of all the runs which have been performed for each different value of a and b, so you don't want it here, because you want to end up with just one set of runs.

You could alternatively just work with the settings which we are interested, and do something like good <- "ca1 & ca2 & cb1 & cb2" to select the same subset for all four correlations (a1,b1) etc.

Thanks. I plan to improve my latest simulation in this and several other ways. I just wanted to submitted the crude version for 10,000 Euros from you, because it is good enough for that purpose. Without the "good" line there will be no more talk of "detection loophole." No "good line", no "detection loophole."

[gill1109]

I just wanted to submitted the crude version for 10,000 Euros from you, because it is enough for that purpose. Without the "good" line there will be no more talk of "detection loophole." No "good line", no "detection loophole."

How you create two files of the same length representing directions of vectors in R^3 is not of any concern in deciding whether or not you have won our bet. You can create two big files first and later trim then down, if that helps.

[Joy Christian]

So there is just one file, not two? The directions for Bob are exactly the negatives of those for Alice? The file contains x and y coordinates of vectors in the equatorial plane? Do the vectors have length 1 or are they unnormalised?

I can't do anything with your data set if you don't tell me how you mean it to be interpreted.

Fair enough. Ask away, and I will explain:

"So there is just one file, not two?"

As far as I understand it, yes.

"The directions for Bob are exactly the negatives of those for Alice?"

Yes, theoretically, but not necessarily in the same run (I will check the file to see if it can be split into two).

"The file contains x and y coordinates of vectors in the equatorial plane?

Yes.

"Do the vectors have length 1 or are they unnormalised?"

The vectors a and b are normalized, but the vectors e_k and -e_k are unnormalized (although they are extremely close to having length 1).