Quaternion simulation no hidden variable

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Re: Quaternion simulation no hidden variable

Post by FrediFizzx » Wed Jan 13, 2021 8:51 am

gill1109 wrote:
FrediFizzx wrote:
jreed wrote:Yes, you've rediscovered the hidden variable simulation. It produces the well known triangle shape that we talk about all the time.

The singlet vector really isn't a hidden variable. The point of that exercise went zoom... right over your head.

Dear Fred

I think that Jim Reed and I are both wondering what the point of your simulations are. Presumably you are trying to simulate some physics experiment. But which? ...

It's John Reed, BTW. No particular experiment. Just investigating the cause of the linearity. It is more than just the linking of A and B by another common vector. It takes a rotation of at least 90 degrees by the common vector to produce the linearity.
.

Re: Quaternion simulation no hidden variable

Post by gill1109 » Wed Jan 13, 2021 7:49 am

FrediFizzx wrote:
jreed wrote:Yes, you've rediscovered the hidden variable simulation. It produces the well known triangle shape that we talk about all the time.

The singlet vector really isn't a hidden variable. The point of that exercise went zoom... right over your head.

Dear Fred

I think that Jim Reed and I are both wondering what the point of your simulations are. Presumably you are trying to simulate some physics experiment. But which?

In your simulations you have random angles a, b and s. You have functions A and B, with arguments as follows: A(a, s) and B(b, s). You use simulation to compute the mean value of A times B for each value of delta = a - b. So your correlation function, let me call it r, is a function of d = delta. But in the literature on EPR-B and on Bell’s theorem, one looks at the correlation as a function of a and b.

In the EPR-B situation (singlet state, usual spin observables for each particle’s spin in different directions in the plane, say) one predicts that r(a, b) = - cos(a -b). Measuring angles in degrees, Bell’s theorem (usual proof, using CHSH inequality) looks only at r(0, 45), r(0, 135), r(90, 45), r(90, 135). Some early experimenters assumed (or experimentally verified) that r(a, b) only depended, in their situation, on d = a - b. They went on to keep one angle fixed, just varied the other, and if they saw the negative cosine they published their paper. That might have been exciting around 1970 but in 2020 it is “not done”; everyone knows that a lot more work needs to be done. You seem to be putting the clock back 50 years. (It’s fun, to be sure).

Re: Quaternion simulation no hidden variable

Post by FrediFizzx » Tue Jan 12, 2021 7:02 pm

jreed wrote:Yes, you've rediscovered the hidden variable simulation. It produces the well known triangle shape that we talk about all the time.

The singlet vector really isn't a hidden variable. The point of that exercise went zoom... right over your head. When the singlet vector is set to zero of course we get,

Image

With the vector expanded to range from 0 to 30 degrees we get,

Image
0 to 60 we get
Image
0 to 90
Image
0 to 120
Image

We can see it went linear at 90 but went slightly non-linear at 120. Interesting. Have to investigate that some more.
.

Re: Quaternion simulation no hidden variable

Post by jreed » Tue Jan 12, 2021 5:19 pm

Yes, you've rediscovered the hidden variable simulation. It produces the well known triangle shape that we talk about all the time.

Re: Quaternion simulation no hidden variable

Post by FrediFizzx » Tue Jan 12, 2021 10:12 am

Of course with the simple addition of the singlet vector added in linking A and B, it straightens out all that mess into near perfect linearity,

e1 = RandomReal[{0, 360}];
s[[j]] = e1;
a = RandomInteger[{1, 360}];
If[Cos[(a - s[[j]]) Degree] < 0, A = -1, A = 1];
b = RandomInteger[{1, 360}];
If[Cos[(b - s[[j]]) Degree] < 0, B = 1, B = -1];

Image
.

Re: Quaternion simulation no hidden variable

Post by gill1109 » Mon Jan 11, 2021 12:28 pm

jreed wrote:Perfect! Thanks for that explanation.

I don't have a proof yet, but I plotted second differences and they look like they are zero up to rounding errors...

Re: Quaternion simulation no hidden variable

Post by jreed » Mon Jan 11, 2021 10:25 am

gill1109 wrote:The curve is, I believe, piecewise quadratic.
Code: Select all
a <- 1:1000
b <- 1:1000
AB <- outer(1 - 2 * ((a > 250) & (a < 750)), 2 * ((b > 250) & (b < 750)) - 1, "*")
d <- outer(a, b, "-")
ABvec <- as.vector(AB)
dvec <- as.vector(d)
out <- aggregate(x = ABvec, by = list(dvec), FUN = mean)
dvals <- out[ , 1]
corrs <- out[ , 2]
plot(dvals, corrs, type = "l", xlim = c(0, 1000)
lines(dvals, -cos(pi * dvals / 500), col = "magenta")

Image


Perfect! Thanks for that explanation.

Re: Quaternion simulation no hidden variable

Post by gill1109 » Mon Jan 11, 2021 7:33 am

The curve is, I believe, piecewise quadratic.
Code: Select all
a <- 1:1000
b <- 1:1000
AB <- outer(1 - 2 * ((a > 250) & (a < 750)), 2 * ((b > 250) & (b < 750)) - 1, "*")
d <- outer(a, b, "-")
ABvec <- as.vector(AB)
dvec <- as.vector(d)
out <- aggregate(x = ABvec, by = list(dvec), FUN = mean)
dvals <- out[ , 1]
corrs <- out[ , 2]
plot(dvals, corrs, type = "l", xlim = c(0, 1000)
lines(dvals, -cos(pi * dvals / 500), col = "magenta")

Image

Re: Quaternion simulation no hidden variable

Post by gill1109 » Sun Jan 10, 2021 11:48 pm

Image
Bit better picture (I'm testing drawing apps...)

Re: Quaternion simulation no hidden variable

Post by gill1109 » Sun Jan 10, 2021 10:14 pm

FrediFizzx wrote:Last time you said I was wrong it was YOU that was wrong. Are ya sure you want to go that route again and look more foolish?

Well, I do make mistakes from time to time, and when I learn about them, I admit them and try to repair any damage found. Close to 70 years old, I make more mistakes now, and I'm slower to "get" things, than when I was 30.

But no matter. This is your model:

Take two large wooden disks and colour half of each black, half white. Fix to a wall. There's a pointer painted on the disks, near the edge, in the middle of the black half of the circumference. Painted on the wall, just above the top of each disk, is another pointer. Around the side of the disk, painted on the wall, equally spaced, are the numbers 1 to 360; 360 on top. Spin each disk. Wait till it stops. The pointers painted *in* the disks each point to a number alpha, beta between 1 and 360, painted on the wall. The pointers at the top of the disk painted *on the wall* point either to black, or to white, *in *the disk. That defines A = +/- 1 and B = +/- 1. You repeat this fairground game many, many times, and average A times B for each value of delta = alpha - beta.

That's the curve you drew.

Exercise: compute it analytically. Probably Mathematica can do it by computer algebra if you are clever with Mathematica! Good luck.

Hint: do the continuous case, and simplify the double integration over alpha and beta by a change of variables to alpha and delta.

Image
Image: two fairground "wheels of fortune" which have come to rest at A = +1 (black on top), B = -1 (white on top), alpha = 330 (approx), beta = 220 (approx)

Re: Quaternion simulation no hidden variable

Post by FrediFizzx » Sun Jan 10, 2021 10:00 pm

Last time you said I was wrong it was YOU that was wrong. Are ya sure you want to go that route again and look more foolish?
.

Re: Quaternion simulation no hidden variable

Post by gill1109 » Sun Jan 10, 2021 9:05 pm

FrediFizzx wrote:When there is enough non-linearity the bounds of CHSH can be exceeded by optimum selection of angles just like they do for experiments. So here we have another example that shoots the heck out of Bell's junk theory and probably Gill's theory also.

Rubbish, Fred, you are not even computing the CHSH bound how real physicists compute it. I also can compute a number and get an answer bigger than two. Look: 4 * 0.7 = 2.8 ! Wow! I violated CHSH, and confirmed QM! Only a tiny bit short of 2 sqrt 2. That’s because of rounding error. Obviously, I need to get Mathematica so as to do it to four decimal places instead of 1.

Your “theory” sure is junk physics.

Re: Quaternion simulation no hidden variable

Post by FrediFizzx » Sun Jan 10, 2021 5:59 pm

jreed wrote:Since my name is on that Mathematica notebook as its author, I went back and looked at it. It has changed considerately since I translated Fodje's Python program. I took my original version (which I still have) and changed the hidden variable so that it no longer sneaks in the detection loophole, and it gives the triangle output waveform. I don't know what the curves that are being shown here represent in terms of physics. ...

Sorry, I should have added to the title that it was modified by me. But of course that should be rather obvious. Some improvements have been made to the original. This particular simulation is an attempt to see what it might take for just the detector angles along with the -1 from singlet to produce -a.b using the event be event outcomes. No hidden variable. Easy to see that something much more sophisticated than the cosine of the angles is required. I too was expecting the striaght line triangle output but got this non-linear output instead. So, this is the physics of that particular operation. Here is an updated notebook file,

EPRsims/abalone2.nb
EPRsims/abalone2.pdf

You may need to clear your browser cache for the PDF to update.
.

Re: Quaternion simulation no hidden variable

Post by jreed » Sun Jan 10, 2021 5:35 pm

gill1109 wrote:
FrediFizzx wrote:CHSH = 2.53315

Which two settings do you let Alice use, and which two settings do you let Bob use?

I find CHSH equal to -2 for some choices, +2 for others, since *all* correlations rho(alpha, beta) = +/- 1

Am I right in thinking that *you* compute each of your four correlations rho(alpha, beta) by *assuming* that rho(alpha, beta) = f(alpha - beta) for some periodic function f, with period 2 pi?

If you want to do that, you must first experimentally verify your assumption. You don’t. It doesn’t hold.

It is true that this is a serious mistake which quite a few experimenters have made in the past.


Since my name is on that Mathematica notebook as its author, I went back and looked at it. It has changed considerately since I translated Fodje's Python program. I took my original version (which I still have) and changed the hidden variable so that it no longer sneaks in the detection loophole, and it gives the triangle output waveform. I don't know what the curves that are being shown here represent in terms of physics.

I have been working on Gull's theorem and took a few days off to check this out. As far as Gull's theorem I have been able to simulate Gill's equation (1), the correlation function. Now I need to understand how to do the Fourier transform. Progress is slow but I want to make sure I'm correct.

Re: Quaternion simulation no hidden variable

Post by FrediFizzx » Sun Jan 10, 2021 7:24 am

When there is enough non-linearity the bounds of CHSH can be exceeded by optimum selection of angles just like they do for experiments. So here we have another example that shoots the heck out of Bell's junk theory and probably Gill's theory also.
.

Re: Quaternion simulation no hidden variable

Post by gill1109 » Sat Jan 09, 2021 8:23 pm

FrediFizzx wrote:CHSH = 2.53315

Which two settings do you let Alice use, and which two settings do you let Bob use?

I find CHSH equal to -2 for some choices, +2 for others, since *all* correlations rho(alpha, beta) = +/- 1

Am I right in thinking that *you* compute each of your four correlations rho(alpha, beta) by *assuming* that rho(alpha, beta) = f(alpha - beta) for some periodic function f, with period 2 pi?

If you want to do that, you must first experimentally verify your assumption. You don’t. It doesn’t hold.

It is true that this is a serious mistake which quite a few experimenters have made in the past.

Re: Quaternion simulation no hidden variable

Post by FrediFizzx » Sat Jan 09, 2021 3:31 pm

CHSH = 2.53315
.

Re: Quaternion simulation no hidden variable

Post by gill1109 » Sat Jan 09, 2021 11:18 am

FrediFizzx wrote:I finally got around to cleaning up the Mathematica code,

EPRsims/abalone.pdf

However, there is a problem with the sign function as A and B are zero too many times so about 10 percent of events are dropped. So, we changed to these A and B functions,

If[Cos[(a) Degree] < 0, A = -1, A = 1];
If[Cos[(b) Degree] < 0, B = 1, B = -1];

Which avoids that problem.

EPRsims/abalone2.pdf

And we still have the same result.

Yes, your result is right. Good to see the code. So ... what does it tell you?
Image
Here’s my code.
https://gill1109.com/2021/01/09/r-stuff/

Alice chooses a setting a, sees outcome A = +/-1 (deterministic function of a)
Bob chooses a setting b, sees outcome B = +/-1 (deterministic function of b).
The mean of AB, identically equal to +/-1 for given (a, b), is a deterministic function of (a, b). The mean of AB given a - b, when you pick a and b independently and uniformly at random, is something else. It's what you see in the plot. But alas, this beautiful plot tells us nothing.

To investigate Bell’s inequality you must pick two values of a, two values of b, and look at the four correlations AB. Each is equal to +/-1. You’ll see that any one, minus the sum of the other three, lies between -2 and +2. That’s because for four numbers +/-1 denoted A1, A2, B1, B2 it is always true that A1B1 - (A1B2 + A2B2 + A2B1) equals +/-2.

Bell's theorem is vindicated yet again, as of course it has to be. There is no counterexample to a true mathematical theorem. You can call it junk physics if you like. Bell does not claim that it is physics. In fact: Bell would conclude that it is *not* true physics. Bell would conclude that the true physical world is not like this, since stringent experiment has shown that the real world does not conform to local realism. Bell already showed that QM did not conform to local realism.

Re: Quaternion simulation no hidden variable

Post by FrediFizzx » Sat Jan 09, 2021 10:01 am

I finally got around to cleaning up the Mathematica code,

EPRsims/abalone.pdf

However, there is a problem with the sign function as A and B are zero too many times so about 10 percent of events are dropped. So, we changed to these A and B functions,

If[Cos[(a) Degree] < 0, A = -1, A = 1];
If[Cos[(b) Degree] < 0, B = 1, B = -1];

Which avoids that problem.

EPRsims/abalone2.pdf

And we still have the same result.

Image
.

Re: Quaternion simulation no hidden variable

Post by gill1109 » Sat Jan 09, 2021 8:32 am

gill1109 wrote:
FrediFizzx wrote:Do the simulation in R and if it doesn't match my plot I will tell you where your mistake is.

I did do it in R, and got the result which I expected.

Have a nice weekend! Keep safe.

No, my code was wrong. I tried again and I got what you got! OK. So what?

Look at the model: Alice chooses a setting a, sees outcome A = +/-1 (deterministic function of a)
Bob chooses a setting b, sees outcome B = +/-1 (deterministic function of b).
The mean of AB = +/-1 for given (a, b) is a deterministic function of (a, b). Plot it as a function of b - a and you see the curve you drew. This curve is pretty but not particularly interesting.

To investigate Bell’s inequality you must pick two values of a, two values of b, and look at the four correlations AB. Each is equal to +/-1. You’ll see that any one minus the sum of the other three lies between -2 and +2. That’s because for four numbers +/-1 denoted A1, A2, B1, B2 it is always true that A1B1 - (A1B2 + A2B2 + A2B2) equals +/-2.

Code: Select all
a <- 1:360
b <- 1:360
AB <- outer(-sign(cos(pi * a / 180)), sign(cos(pi * b / 180)), "*")
d <- outer(a, b, "-")
ABvec <- as.vector(AB)
dvec <- as.vector(d)
out <- aggregate(x = ABvec, by = list(dvec), FUN = mean)
dvals <- out[ , 1]
corrs <- out[ , 2]
plot(dvals, corrs, type = "l")
lines(dvals, -cos(pi * dvals/180), col = "magenta")


Image

You can see the plot in higher resolution here
https://gill1109.com/2021/01/09/r-stuff/

Notice, I did not sample settings of Alice and Bob at random. No need to do that, since the measurement functions are two deterministic functions of the relevant setting. It is a local, deterministic model, and hence it is a local realistic model. There is no violation of any Bell inequality... nothing weird. No connection at all between the two measurement stations!

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