A Completelly Local and Realistic Simulation

This question is a means of preventing automated form submissions by spambots.

BBCode is ON
[img] is ON
[flash] is OFF
[url] is ON
Smilies are OFF
Topic review

Re: A Completelly Local and Realistic Simulation

FrediFizzx wrote:
Guest wrote:This is an R version of Fred's simulation.

Looking at the code, you'll see that the original detectors angles are set to zero depending on the value of the hidden variables s and z. This is equivalent to data rejection, although it's a subtle way to do it. Just look at how the correlations are computed and the net effect of the change of those original random detectors angles to zero.

Please, don't take me wrong. I don't want to start a war. Don't shoot the messenger.

No problem. We already know about that interpretation. Thanks for the R code.
.

Forgot to mention that "s" is not a hidden variable here. QM knows about "s" but does not know about lambda thus "z". And can't be equivalent to data rejection since all particles are detected.

But I'm working on a different configuration that won't have this problem. It's not easy though but must exist since Nature can do the negative cosine curve from +/- 1 outcomes. Well, must exist in a local fashion since I firmly believe that all action of this type must be local. The current simulation is just a clue to the final one perhaps.
.

Re: A Completelly Local and Realistic Simulation

Guest wrote:This is an R version of Fred's simulation.

Looking at the code, you'll see that the original detectors angles are set to zero depending on the value of the hidden variables s and z. This is equivalent to data rejection, although it's a subtle way to do it. Just look at how the correlations are computed and the net effect of the change of those original random detectors angles to zero.

Please, don't take me wrong. I don't want to start a war. Don't shoot the messenger.

No problem. We already know about that interpretation. Thanks for the R code.
.

Re: A Completelly Local and Realistic Simulation

This is an R version of Fred's simulation.

Code: Select all
set.seed(1234)n <- 10^6s <- runif(n, min = 0, max = 360)z <- (2 / sqrt(1 + 3*runif(n, min = 0, max = pi)/pi)) - 1a <- sample(0:360, size = n, replace = TRUE)a[abs(cos((a - s)*pi/180)) < z] <- 0spin_A <- -sign(cos((a - s)*pi/180))b <- sample(0:360, size = n, replace = TRUE)b[abs(cos((b - s)*pi/180)) < z] <- 0spin_B <- sign(cos((b - s)*pi/180))rho <- numeric(720)for (th in 1:720) {   idx <- (a - b + 360 == th)   rho[th] <- mean(spin_A[idx] * spin_B[idx])}plot(1:720, rho, col = "blue", pch = 19, cex = 0.5, ylim = c(-1, 1))lines(1:720, -cos((1:720)*pi/180), col = "red", lwd = 2)

Looking at the code, you'll see that the original detectors angles are set to zero depending on the value of the hidden variables s and z. This is equivalent to data rejection, although it's a subtle way to do it. Just look at how the correlations are computed and the net effect of the change of those original random detectors angles to zero.

Please, don't take me wrong. I don't want to start a war. Don't shoot the messenger.

Re: A Completelly Local and Realistic Simulation

FrediFizzx wrote:
gill1109 wrote:So you want
$f(\lambda)=\,-1+\frac{2}{\sqrt{1+3(\frac{\lambda}{\pi})}}\,\, \text{with}\,\,\lambda \in [0, \pi].$
$A({\bf a},\,{\bf s},\,\lambda) = \,-\, \text{sgn}({\bf a}\cdot{\bf s}),\,\text{if}\,(|({\bf a}\cdot{\bf s})|>f(\lambda)),\,\text{else}\,\text{sgn}({\bf s}\cdot{\bf n}),$
$B({\bf b},\,{\bf s},\,\lambda) = \,+\, \text{sgn}({\bf b}\cdot{\bf s}),\,\text{if}\,(|({\bf b}\cdot{\bf s})|>f(\lambda)),\,\text{else}\,\text{sgn}({\bf s}\cdot{\bf n})$
where "n" is the "null vector?

Thanks. Almost good.
$A({\bf a},\,{\bf s},\,\lambda) = \,-\, \text{sgn}({\bf a}\cdot{\bf s}),\,\text{if}\,(|({\bf a}\cdot{\bf s})|>f(\lambda)),\,\text{else}\,\text{sgn}({\bf s}\cdot{\bf n_a}),$
$B({\bf b},\,{\bf s},\,\lambda) = \,+\, \text{sgn}({\bf b}\cdot{\bf s}),\,\text{if}\,(|({\bf b}\cdot{\bf s})|>f(\lambda)),\,\text{else}\,\text{sgn}({\bf s}\cdot{\bf n_b})$

This is still not quite right. A null vector is a vector without directon or magnitude, so the subsripts a and b on it seems wrong, or at least redundant. More seriously, ${\bf s}\cdot{\bf n_a}$ is identically equal to zero, so $\text{sgn}({\bf s}\cdot{\bf n_a})$ is ambiguous.

***

Re: A Completelly Local and Realistic Simulation

gill1109 wrote:So you want
$f(\lambda)=\,-1+\frac{2}{\sqrt{1+3(\frac{\lambda}{\pi})}}\,\, \text{with}\,\,\lambda \in [0, \pi].$
$A({\bf a},\,{\bf s},\,\lambda) = \,-\, \text{sgn}({\bf a}\cdot{\bf s}),\,\text{if}\,(|({\bf a}\cdot{\bf s})|>f(\lambda)),\,\text{else}\,\text{sgn}({\bf s}\cdot{\bf n}),$
$B({\bf b},\,{\bf s},\,\lambda) = \,+\, \text{sgn}({\bf b}\cdot{\bf s}),\,\text{if}\,(|({\bf b}\cdot{\bf s})|>f(\lambda)),\,\text{else}\,\text{sgn}({\bf s}\cdot{\bf n})$
where "n" is the "null vector?

Thanks. Almost good.
$A({\bf a},\,{\bf s},\,\lambda) = \,-\, \text{sgn}({\bf a}\cdot{\bf s}),\,\text{if}\,(|({\bf a}\cdot{\bf s})|>f(\lambda)),\,\text{else}\,\text{sgn}({\bf s}\cdot{\bf n_a}),$
$B({\bf b},\,{\bf s},\,\lambda) = \,+\, \text{sgn}({\bf b}\cdot{\bf s}),\,\text{if}\,(|({\bf b}\cdot{\bf s})|>f(\lambda)),\,\text{else}\,\text{sgn}({\bf s}\cdot{\bf n_b})$
.

Re: A Completelly Local and Realistic Simulation

So you want
$f(\lambda)=\,-1+\frac{2}{\sqrt{1+3(\frac{\lambda}{\pi})}}\,\, \text{with}\,\,\lambda \in [0, \pi].$
$A({\bf a},\,{\bf s},\,\lambda) = \,-\, \text{sgn}({\bf a}\cdot{\bf s}),\,\text{if}\,(|({\bf a}\cdot{\bf s})|>f(\lambda)),\,\text{else}\,\text{sgn}({\bf s}\cdot{\bf n}),$
$B({\bf b},\,{\bf s},\,\lambda) = \,+\, \text{sgn}({\bf b}\cdot{\bf s}),\,\text{if}\,(|({\bf b}\cdot{\bf s})|>f(\lambda)),\,\text{else}\,\text{sgn}({\bf s}\cdot{\bf n})$
where "n" is the "null vector?

Re: A Completelly Local and Realistic Simulation

gill1109 wrote:As far as I know, you can't take the cosine of a vector. But you can take the cosine of the angle between two vectors ...

Sure. "...relative to the lab frame". What I don't have in there is the null vector. Didn't know how to do that in what Joy was requesting.
.

Re: A Completelly Local and Realistic Simulation

FrediFizzx wrote:
Guest wrote:
FrediFizzx wrote:OK, not so messy after all. Here are the basic functions.
$f(\lambda)=\,-1+\frac{2}{\sqrt{1+3(\frac{\lambda}{\pi})}}\,\, \text{with}\,\,\lambda \in [0, \pi].$
$A({\bf a},\,{\bf s},\,\lambda) = \,-\, \text{sgn}({\bf a}\cdot{\bf s}),\,\text{if}\,(|({\bf a}\cdot{\bf s})|>f(\lambda)),\,\text{else,}\,=\,-\, \text{sgn}(\cos{({\bf s})}),$
$B({\bf b},\,{\bf s},\,\lambda) = \,+\, \text{sgn}({\bf b}\cdot{\bf s}),\,\text{if}\,(|({\bf b}\cdot{\bf s})|>f(\lambda)),\,\text{else,}\,=\,+\, \text{sgn}(\cos{({\bf s})}).$
Of course that is not the complete story. Have to figure out how to get the rest in.

Hi Fred. If I understand it correctly, s is a unit vector. So, what does cos(s) mean in the above? Thanks.

It is the cosine of the particle spin vector relative to the lab frame.

As far as I know, you can't take the cosine of a vector. But you can take the cosine of the angle between two vectors ...

Re: A Completelly Local and Realistic Simulation

Guest wrote:
FrediFizzx wrote:OK, not so messy after all. Here are the basic functions.

$f(\lambda)=\,-1+\frac{2}{\sqrt{1+3(\frac{\lambda}{\pi})}}\,\, \text{with}\,\,\lambda \in [0, \pi].$

$A({\bf a},\,{\bf s},\,\lambda) = \,-\, \text{sgn}({\bf a}\cdot{\bf s}),\,\text{If}\,(|({\bf a}\cdot{\bf s})|>f(\lambda)),\,\text{else,}\,=\,-\, \text{sgn}(\cos{({\bf s})}),$
$B({\bf b},\,{\bf s},\,\lambda) = \,+\, \text{sgn}({\bf b}\cdot{\bf s}),\,\text{If}\,(|({\bf b}\cdot{\bf s})|>f(\lambda)),\,\text{else,}\,=\,+\, \text{sgn}(\cos{({\bf s})}).$

Of course that is not the complete story. Have to figure out how to get the rest in.
.

Hi Fred. If I understand it correctly, s is a unit vector. So, what does cos(s) mean in the above? Thanks.

It is the cosine of the particle spin vector relative to the lab frame.
.

Re: A Completelly Local and Realistic Simulation

FrediFizzx wrote:OK, not so messy after all. Here are the basic functions.

$f(\lambda)=\,-1+\frac{2}{\sqrt{1+3(\frac{\lambda}{\pi})}}\,\, \text{with}\,\,\lambda \in [0, \pi].$

$A({\bf a},\,{\bf s},\,\lambda) = \,-\, \text{sgn}({\bf a}\cdot{\bf s}),\,\text{If}\,(|({\bf a}\cdot{\bf s})|>f(\lambda)),\,\text{else,}\,=\,-\, \text{sgn}(\cos{({\bf s})}),$
$B({\bf b},\,{\bf s},\,\lambda) = \,+\, \text{sgn}({\bf b}\cdot{\bf s}),\,\text{If}\,(|({\bf b}\cdot{\bf s})|>f(\lambda)),\,\text{else,}\,=\,+\, \text{sgn}(\cos{({\bf s})}).$

Of course that is not the complete story. Have to figure out how to get the rest in.
.

Hi Fred. If I understand it correctly, s is a unit vector. So, what does cos(s) mean in the above? Thanks.

Re: A Completelly Local and Realistic Simulation

OK, not so messy after all. Here are the basic functions.

$f(\lambda)=\,-1+\frac{2}{\sqrt{1+3(\frac{\lambda}{\pi})}}\,\, \text{with}\,\,\lambda \in [0, \pi].$

$A({\bf a},\,{\bf s},\,\lambda) = \,-\, \text{sgn}({\bf a}\cdot{\bf s}),\,\text{If}\,(|({\bf a}\cdot{\bf s})|>f(\lambda)),\,\text{else,}\,=\,-\, \text{sgn}(\cos{({\bf s})}),$
$B({\bf b},\,{\bf s},\,\lambda) = \,+\, \text{sgn}({\bf b}\cdot{\bf s}),\,\text{If}\,(|({\bf b}\cdot{\bf s})|>f(\lambda)),\,\text{else,}\,=\,+\, \text{sgn}(\cos{({\bf s})}).$

Of course that is not the complete story. Have to figure out how to get the rest in.
.

Re: A Completelly Local and Realistic Simulation

Joy Christian wrote:
FrediFizzx wrote:
Joy Christian wrote:***
Hi Fred, Can you write down the functions A(a, h) and B(b, h) analytically so that I can understand what is going on? Thanks.
***

That is going to be pretty messy. I'll try later. Just tell me what you don't understand in the 3 Do loops. Might be quicker.

As far as I can see from the 3 Do loops, Alice gets an instruction from the hidden variable whether to choose a = o or a = a, and likewise for Bob. But that kind of "conspiracy" is not allowed.
***

??? How the heck could Alice and Bob get any instructions from the HV? They still choose whatever they want to choose as evidenced by the RandomInteger functions. It is the S^3 topology that makes a and b null vectors during the constraints. Granted that I am still working on figuring out the math for it.
.

Re: A Completelly Local and Realistic Simulation

FrediFizzx wrote:
Joy Christian wrote:***
Hi Fred, Can you write down the functions A(a, h) and B(b, h) analytically so that I can understand what is going on? Thanks.
***

That is going to be pretty messy. I'll try later. Just tell me what you don't understand in the 3 Do loops. Might be quicker.

As far as I can see from the 3 Do loops, Alice gets an instruction from the hidden variable whether to choose a = o or a = a, and likewise for Bob. But that kind of "conspiracy" is not allowed.

***

Re: A Completelly Local and Realistic Simulation

Joy Christian wrote:***
Hi Fred, Can you write down the functions A(a, h) and B(b, h) analytically so that I can understand what is going on? Thanks.
***

That is going to be pretty messy. I'll try later. Just tell me what you don't understand in the 3 Do loops. Might be quicker.
.

Re: A Completelly Local and Realistic Simulation

***
Hi Fred, Can you write down the functions A(a, h) and B(b, h) analytically so that I can understand what is going on? Thanks.

***

Re: A Completelly Local and Realistic Simulation

I've simplified the code in the A and B station Do loops. Took out one of the if statements as it was un-necessary.

EPRsims/newCS-5.pdf

After trying several other simulation scenarios, I am becoming more convinced that this is the way Nature works or very close to it. The a and b vectors become null vectors during the constraints. What is going on here that you don't see is that the hidden variable lambda is actually varying the radius of the e vector in a non-linear way from 0 to 1. IOW, "z" is the e vector radius. Then that is being compared to the absolute value of n.s to produce the constraints. Most likely all due to the S^3 topology of the singlet.

.

Re: A Completelly Local and Realistic Simulation

FrediFizzx wrote:You saw how silly the non-local simulation was.

Which non-local simulation? One of yours or one of mine?

The simulations which I showed are *local simulations* of the coloured spinning disk model. Curves like those I posted are representative of what LR can do subject to the constraints of symmetry under switch of Alice/Bob, switch of outcomes +/-1, switch of clockwise/anti-clockwise, and perfect correlation and anti-correlation with equal and opposite angles respectively.

Those who believe Bell's logic is correct know that you can't create the negative cosine in that way. Folklore has it that Bell says you must get the saw-tooth, or that you can't get correlations stronger than the saw-tooth. My simulations show you that things are more subtle than that.

Re: A Completelly Local and Realistic Simulation

minkwe wrote:
Heinera wrote:It seems that the others have given up on this (Joy, local and minkwe) and you are the last man standing.

I know you are obsessed with me but you have no idea what I have given up on or not so why do you make such stupid claims? Leave me out of your trolling, please.

Come on guys, let's stay on topic here. Please take comments like that to a private message. Or hit the "report a post" button and complain about it.
.

Re: A Completelly Local and Realistic Simulation

Heinera wrote:It seems that the others have given up on this (Joy, local and minkwe) and you are the last man standing.

I know you are obsessed with me but you have no idea what I have given up on or not so why do you make such stupid claims? Leave me out of your trolling, please.

Re: A Completelly Local and Realistic Simulation

gill1109 wrote:My last picture in my previous post shows that *classical correlations can be stronger than the strongest quantum correlations*. It was hard to find!

This is also stronger than the quantum correlations,

Unfortunately when averaged in with the negative cosine curve data, it gives straight lines. But I'm getting closer I think.
.

Top