49 posts
• Page **3** of **3** • 1, 2, **3**

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

- gill1109
- Mathematical Statistician
**Posts:**2219**Joined:**Tue Feb 04, 2014 10:39 pm**Location:**Leiden

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")

- gill1109
- Mathematical Statistician
**Posts:**2219**Joined:**Tue Feb 04, 2014 10:39 pm**Location:**Leiden

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")

Perfect! Thanks for that explanation.

- jreed
**Posts:**94**Joined:**Mon Feb 17, 2014 5:10 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...

- gill1109
- Mathematical Statistician
**Posts:**2219**Joined:**Tue Feb 04, 2014 10:39 pm**Location:**Leiden

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];

.

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];

.

- FrediFizzx
- Independent Physics Researcher
**Posts:**2180**Joined:**Tue Mar 19, 2013 7:12 pm**Location:**N. California, USA

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

- jreed
**Posts:**94**Joined:**Mon Feb 17, 2014 5:10 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,

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

0 to 60 we get

0 to 90

0 to 120

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

.

- FrediFizzx
- Independent Physics Researcher
**Posts:**2180**Joined:**Tue Mar 19, 2013 7:12 pm**Location:**N. California, USA

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).

- gill1109
- Mathematical Statistician
**Posts:**2219**Joined:**Tue Feb 04, 2014 10:39 pm**Location:**Leiden

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.

.

- FrediFizzx
- Independent Physics Researcher
**Posts:**2180**Joined:**Tue Mar 19, 2013 7:12 pm**Location:**N. California, USA

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