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 [1] 0.9921147 0.9921147 0.0000000 0.9921147 0.9921147 0.0000000 0.9921147 0.9921147 0.9921147
  [10] 0.0000000 0.9921147 0.9921147 0.9921147 0.9921147 0.9921147 0.0000000 0.0000000 0.0000000
  [19] 0.9921147 0.9921147 0.0000000 0.9921147 0.9921147 0.9921147 0.0000000 0.0000000 0.9921147
  [28] 0.9921147 0.9921147 0.0000000 0.9921147 0.0000000 0.9921147 0.0000000 0.0000000 0.9921147
  [37] 0.0000000 0.0000000 0.9921147 0.9921147 0.9921147 0.9921147 0.9921147 0.9921147 0.0000000
  [46] 0.9921147 0.9921147 0.9921147 0.9921147 0.9921147 0.9921147 0.0000000 0.9921147 0.9921147
  [55] 0.0000000 0.0000000 0.9921147 0.0000000 0.9921147 0.9921147 0.9921147 0.9921147 0.0000000
  [64] 0.0000000 0.0000000 0.9921147 0.0000000 0.9921147 0.9921147 0.9921147 0.9921147 0.9921147
  [73] 0.9921147 0.9921147 0.0000000 0.0000000 0.9921147 0.9921147 0.9921147 0.0000000 0.0000000
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  [91] 0.0000000 0.9921147 0.0000000 0.9921147 0.9921147 0.0000000 0.9921147 0.9921147 0.9921147

FrediFizzx wrote:Something very strange is going on with the R simulation. If I take the sign function off so that we have,

A = cos(alpha)*g(a,e1)
B = -cos(beta)*g(b,e2)

I still get 1, -1 and 0 for A and B outputs. ??? The g-function is just doing the regular complete states selection and outputting 1 or 0. It is like alpha and beta get stuck at 0 or 2pi for every iteration.

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 [1] 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 0 1 0 1 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 0 1 0 1 0
  [48] 0 1 1 1 0 1 1 0 1 0 1 1 0 0 1 0 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 0 1 1 0 0 1 1 1 0 1 1 1 0 1 0 0
  [95] 0 1 0 1 1 0 0 1 1 1 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0 1 1 0 0 1 1 0 0 1 0 1 0
 [142] 1 0 0 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 0 0 1 0 1 0 1 0 1 1 1
 [189] 1 1 1 0 1 1 1 1 1 1 0 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1 1 0 1 0 1 1 0 0 0 1 0 1 1 0 0 1 1 0 0 0
 [236] 0 1 0 1 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 1 1 1
 [283] 1 0 1 1 0 1 0 1 1 0 1 1

FrediFizzx wrote:

Joy Christian wrote:

FrediFizzx wrote:OK, new interpretation for modelling the "real EPR-Bohm scenario". That "e" is zero always is correct since the polarizers take "e" --> +/-a and "e' " --> +/-b. Then the sign function is simply the polarizer action. Simple is usually better.

Fred,

With the limits s1 --> +/-a and s2 --> +/-b you have been suggesting, what is the prediction for the product A(n, h)B(n, h) with those limits included in the GA model?

In other words, what is AB for the a = b case?

***

A(n, h)B(n, h) = -1 as it should be. What has changed is that now the polarizer action is just determined by cos(a) and cos(b) by the sign function of those. I kind of like the other way better but this more simple way works also. At least it works in the Mathematica simulation. I am waiting to see if it also works in Michel's Python sim. I am currently trying to get it to work in your R sim without much success yet.
.

Joy Christian wrote:

FrediFizzx wrote:OK, new interpretation for modelling the "real EPR-Bohm scenario". That "e" is zero always is correct since the polarizers take "e" --> +/-a and "e' " --> +/-b. Then the sign function is simply the polarizer action. Simple is usually better.

Fred,

With the limits s1 --> +/-a and s2 --> +/-b you have been suggesting, what is the prediction for the product A(n, h)B(n, h) with those limits included in the GA model?

In other words, what is AB for the a = b case?

***

FrediFizzx wrote:OK, new interpretation for modelling the "real EPR-Bohm scenario". That "e" is zero always is correct since the polarizers take "e" --> +/-a and "e' " --> +/-b. Then the sign function is simply the polarizer action. Simple is usually better.

minkwe wrote:In that simulation, since you are using angle subtractions instead of vectors, cos( angle) is the same as cos(angle-0). Thus, it doesn't mean you omit "e". It just means you set e to always 0.

minkwe wrote:

FrediFizzx wrote:OK, I get it now. So say we have 5 degree increments instead of 7.2 then in the matrix the 9th column is 45 degrees and the 18th row is 90 degrees so the difference there is 45 degrees. So it is possible to extract (beta - alpha) from the matrix.

I am just still trying to figure out why sign(cos(angle*pol)) works in Mathematica with random angles but does not work in R. It is like cos(angle) is already in the R functions for the complete state and polarizer.

How do you know it doesn't work with random angles in R?

FrediFizzx wrote:New discovery with the Mathematica simulation. Here is a PDF of the Mathematica notebook file.

EPRsims/EPRsim_MF_JR_JC_pol4.pdf

Note that it works with no original polarization angle (vector), "e". And "no" polarizer function. All it needs is complete state selection and the random angle.

Michel was sort of right. The polarizer function must be contained in the sign function by itself but there is now no projection of "e" to "angle". Michel, this should work in your Python sim.

FrediFizzx wrote:

FrediFizzx wrote:

FrediFizzx wrote:OK, I get it now. So say we have 5 degree increments instead of 7.2 then in the matrix the 9th column is 45 degrees and the 18th row is 90 degrees so the difference there is 45 degrees. So it is possible to extract (beta - alpha) from the matrix.

Ok, so the 18th column is 90 degrees and the 9th row is 45, so is the difference there 45 or -45 degrees?
.

I guess it doesn't matter. It looks like it is completely arbitrary as to whether the columns or rows are alpha or beta so if one is +45 the other is -45.

FrediFizzx wrote:

minkwe wrote:

FrediFizzx wrote:How does this line of code for the fourth plot,

QM = matrix(nrow = K, ncol = K, data = sapply(Angles, function(t) -cos(t - Angles)), byrow = TRUE)

have (beta - alpha) in it?

Fred, for each angle in Angles, sapply constructs a new array of 51 differences between the angle and all the rest. Theta is not always zero. Theta is a 51 by 51 matrix with zero on the diagonal.

OK, I get it now. So say we have 5 degree increments instead of 7.2 then in the matrix the 9th column is 45 degrees and the 18th row is 90 degrees so the difference there is 45 degrees. So it is possible to extract (beta - alpha) from the matrix.

I am just still trying to figure out why sign(cos(angle*pol)) works in Mathematica with random angles but does not work in R. It is like cos(angle) is already in the R functions for the complete state and polarizer.

FrediFizzx wrote:

FrediFizzx wrote:OK, I get it now. So say we have 5 degree increments instead of 7.2 then in the matrix the 9th column is 45 degrees and the 18th row is 90 degrees so the difference there is 45 degrees. So it is possible to extract (beta - alpha) from the matrix.

Ok, so the 18th column is 90 degrees and the 9th row is 45, so is the difference there 45 or -45 degrees?
.

FrediFizzx wrote:OK, I get it now. So say we have 5 degree increments instead of 7.2 then in the matrix the 9th column is 45 degrees and the 18th row is 90 degrees so the difference there is 45 degrees. So it is possible to extract (beta - alpha) from the matrix.

minkwe wrote:

FrediFizzx wrote:How does this line of code for the fourth plot,

QM = matrix(nrow = K, ncol = K, data = sapply(Angles, function(t) -cos(t - Angles)), byrow = TRUE)

have (beta - alpha) in it?

Fred, for each angle in Angles, sapply constructs a new array of 51 differences between the angle and all the rest. Theta is not always zero. Theta is a 51 by 51 matrix with zero on the diagonal.

FrediFizzx wrote:

Joy Christian wrote:

FrediFizzx wrote:Well... theta = 0 always in the R version of the simulation so how can it be a valid simulation for -a.b = -cos(b - a)? The 3D plot is showing alpha on one side and beta on the other instead of (beta -alpha). The middle is theta which is always zero.

In this simulation the third plot is for S^3 model and the fourth plot is for the quantum mechanical prediction E(a, b) = -a.b. The plots match exactly for all angles.

***

How does this line of code for the fourth plot,

QM = matrix(nrow = K, ncol = K, data = sapply(Angles, function(t) -cos(t - Angles)), byrow = TRUE)

have (beta - alpha) in it?

FrediFizzx wrote:

Joy Christian wrote:

FrediFizzx wrote:Well... theta = 0 always in the R version of the simulation so how can it be a valid simulation for -a.b = -cos(b - a)? The 3D plot is showing alpha on one side and beta on the other instead of (beta -alpha). The middle is theta which is always zero.

In this simulation the third plot is for S^3 model and the fourth plot is for the quantum mechanical prediction E(a, b) = -a.b. The plots match exactly for all angles.

***

How does this line of code for the fourth plot,

QM = matrix(nrow = K, ncol = K, data = sapply(Angles, function(t) -cos(t - Angles)), byrow = TRUE)

have (beta - alpha) in it?

Joy Christian wrote:

FrediFizzx wrote:Well... theta = 0 always in the R version of the simulation so how can it be a valid simulation for -a.b = -cos(b - a)? The 3D plot is showing alpha on one side and beta on the other instead of (beta -alpha). The middle is theta which is always zero.

In this simulation the third plot is for S^3 model and the fourth plot is for the quantum mechanical prediction E(a, b) = -a.b. The plots match exactly for all angles.

***

FrediFizzx wrote:

FrediFizzx wrote:I just realized that in the R version simulation, there is never theta = (b - a) produced where it is produced in the Mathematica version. Hmm...

Well... theta = 0 always in the R version of the simulation so how can it be a valid simulation for -a.b = -cos(b - a)? The 3D plot is showing alpha on one side and beta on the other instead of (beta -alpha). The middle is theta which is always zero.