A real EPR-Bohm scenario

[Joy Christian]

Speaking about a real EPR-Bohm scenario, does any of you have ideas of how to use quaternions or other multivectors (constrained by S3) for an event by event simulation? I know at least in Python there are libraries for this. The currently discussed simulations are the R3 flatlanders versions of Joy's model, and therefore have the if/else then 0 at the polarizer stage, which limits the proving value of the model.
(maybe this post belongs in a new thread)

ajw, my code is using geometric algebra with Cl(0,3) through out. It is a simple tweak to change the algebra to some other layout. Like I mentioned, I can easily test any model by simply defining the two functions so I welcome any suggestions. All I need are:

1) Source: How are the particle pairs represented, and what information should they contain
2) Station: What are the steps involved to produce the detection events (+1, -1) and what other side-effects are caused by the detection (eg, time delays, memory, etc if relevant to the model)

The framework can handle all those.

This sounds great!
I can only guess that for the description of the spin a quaternion should be used and a random variable lambda as hidden variable for the sign of the base to simulate Joys model. I have no clue whether or not the polarizer settings should be described using a quaternion, and how to arrive at the detection events using these objects.

Hi Albert Jan,

You are right to observe that the "currently discussed simulations are the R3 flatlanders versions of [my] model, and therefore have the if/else then 0 at the polarizer stage, which limits the proving value of the model."

Unfortunately my 3-sphere model is based on a non-trivial Mobius-like twist in the Hopf bundle of S^3, as discussed in this post: viewtopic.php?f=6&t=286#p6893.

Very few people have shown understanding of this non-trivial twist. Among them we now also have Jay Yablon, who says that he now understands my model from "top to bottom." But a theoretical understanding of the model still does not help us in simulating it without using some flatland background, added to the fact that I myself know next to nothing about programming. I therefore appreciate that you, Fred and Michel continue to strive towards that goal (and I can also ask Chantal for help).

Happy New Year, everyone!

***

[FrediFizzx]

I therefore appreciate that you, Fred and Michel continue to strive towards that goal (and I can also ask Chantal for help).

***

You're welcome, Joy. Your discovery is in fact a special breakthrough in physics and quite profound. Plus working on it keeps my chops up to use some musician's lingo.

We still need to figure out how to implement correctly what I found in the Mathematica simulation for polarizer separation in the R version. I will still be working on that. Thanks to Michel for figuring out that it actually wasn't working in R. It needs to work using alpha and beta. Now that I know how to program that correctly, we can possibly investigate it further.

[FrediFizzx]

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...

[FrediFizzx]

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.

[Joy Christian]

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.

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]

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]

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?

It is the same plot that Michel has produced with Python: https://drive.google.com/file/d/0B6sZy9 ... RvYWs/view

Just looking at both plots it seems clear to me that they are plots of E(a, b) = -a.b.

***

[minkwe]

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?

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]

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]

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]

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]

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.

[minkwe]

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.

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

[minkwe]

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.

Cos(45) = cos(-45) = cos(360-45)

[minkwe]

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.

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.

[FrediFizzx]

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?

I meant in Joy's R version simulation. I am sure that R could be setup the same way with random angles like in Mathematica to work. But things have changed now since sign(cos(angle)) works without "pol". As you say, "e" is always zero in that scenario as an angle. I'm getting deja vu; seems like we did this before.

[FrediFizzx]

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.

Does that mean that "e" is always zero in the GAViewer simulation?

viewtopic.php?f=6&t=296

[FrediFizzx]

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.

[Joy Christian]

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]

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.
.