GAViewer Simulation No Hidden Variable

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

Re: GAViewer Simulation No Hidden Variable

Postby FrediFizzx » Wed Oct 28, 2020 8:47 am

gill1109 wrote:
FrediFizzx wrote:Ok, so back to running the GAVIewer program on two computers. I'm 100 percent convinced there will be no difference in the results whether it is run on one or two computers. So, it is indeed a perfect counter-example to Gull's nonsense.
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The point is not whether or not your GAViewer program gives the same results on several computers. The point is whether or not you can write two new programs, each running a separate dialogue on a separate computer; each getting their own stream of angles, supplied externally. You don’t control the inputs. We, scientists and amateur scientists of the world, do.

Please try! Write the two programs, so that anyone can test them, themselves, run completely separately; one taking Alice’s angles, one taking Bob’s angles. Each program must run that loop-with-dialogue.

Once again, I'm only doing Bell's theory not Gill's theory with this GAViewer simulation. Bell and Gull are shot down 100 percent!
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Re: GAViewer Simulation No Hidden Variable

Postby gill1109 » Wed Oct 28, 2020 9:06 am

FrediFizzx wrote:
gill1109 wrote:
FrediFizzx wrote:Ok, so back to running the GAVIewer program on two computers. I'm 100 percent convinced there will be no difference in the results whether it is run on one or two computers. So, it is indeed a perfect counter-example to Gull's nonsense.
.

The point is not whether or not your GAViewer program gives the same results on several computers. The point is whether or not you can write two new programs, each running a separate dialogue on a separate computer; each getting their own stream of angles, supplied externally. You don’t control the inputs. We, scientists and amateur scientists of the world, do.

Please try! Write the two programs, so that anyone can test them, themselves, run completely separately; one taking Alice’s angles, one taking Bob’s angles. Each program must run that loop-with-dialogue.

Once again, I'm only doing Bell's theory not Gill's theory with this GAViewer simulation. Bell and Gull are shot down 100 percent!
.

You haven’t shot down Gull or Bell till you can write programmes for two separate computers which successfully perform Gull’s two dialogues problem.

If Bell were wrong, there would exist functions A and B and a probability density rho such that etc etc etc. If such existed, then you could generate a lot of independent realisations of lambda, and store them on two computers, in fact store them as constants inside the two programs. On each computer, you program A and B; lambda_1, lambda_2, ... are constants inside the programs. At the n’th trial, an angle theta_n is given to Alice’s computer and the program outputs A(theta_n, lambda_n). An angle phi_n is given to Bob’s computer, and it outputs B(phi_n, lambda_n).

Bell and Gull are equivalent. Bell’s theorem says that the Gull programming task is impossible (I’ve just given you the argument for this claim). Gull’s theorem says that the Bell maths task (find functions ... such that ...) is impossible (exercise: give the argument).

Your GAViewer simulation is an utter waste of time. It draws the negative cosine function by a rather inefficient Monte Carlo simulation.

It cannot be separated into two modules, each running on a separate computer, one of which receives angles theta_1, theta_2, ... and the other phi_1, phi_2, ... supplied by an outside user.

If I’m wrong, then show everyone that I’m wrong. Give us two programs which fulfil Gull’s specifications.
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Re: GAViewer Simulation No Hidden Variable

Postby FrediFizzx » Wed Oct 28, 2020 9:49 am

Blah, Blah, Blah. You are still mixing up your theory with Bell's theory.
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Re: GAViewer Simulation No Hidden Variable

Postby jreed » Wed Oct 28, 2020 11:05 am

Here's a question about Gull's little paper: In note (2) he shows what I assume is a time series of values that are obtained when an observation of a detectors is observed during an experiment with hidden variables. I think he must mean +1 and -1 rather than +1 and 0. Anyway, he says if you take the FT of this series, it will have many Fourier components. That is true. Then he says for a quantum experiment the result (1-Cos(delta*theta)/4 only has 3 components. That is also true. The conclusion he comes to is that you can't get the quantum result from the hidden variable result.

The problem I have with this is that the quantum result is a probability function obtained from many trials, but the hidden variable result is only one trial. The two things aren't the same and don't seem to be comparable. What am I missing here?
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Re: GAViewer Simulation No Hidden Variable

Postby FrediFizzx » Wed Oct 28, 2020 12:28 pm

jreed wrote:Here's a question about Gull's little paper: In note (2) he shows what I assume is a time series of values that are obtained when an observation of a detectors is observed during an experiment with hidden variables. I think he must mean +1 and -1 rather than +1 and 0. Anyway, he says if you take the FT of this series, it will have many Fourier components. That is true. Then he says for a quantum experiment the result (1-Cos(delta*theta)/4 only has 3 components. That is also true. The conclusion he comes to is that you can't get the quantum result from the hidden variable result.

The problem I have with this is that the quantum result is a probability function obtained from many trials, but the hidden variable result is only one trial. The two things aren't the same and don't seem to be comparable. What am I missing here?

There is only one FT result per correlation event. It is either 0 or 1. There is really no difference between 0 and 1 and +/-1 for outcomes. What do you mean by "3 components"? I get that the FT of (1-Cos(delta*theta)/4 = 1/4. How do we know Gull is doing a hidden variable result? He never specified the exact function for . It is really a bunch of nonsense.
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Re: GAViewer Simulation No Hidden Variable

Postby FrediFizzx » Wed Oct 28, 2020 7:31 pm

There is one component for the FT of this function,



If you set the transform variable to zero like Gull did in number (3) you get,


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Re: GAViewer Simulation No Hidden Variable

Postby jreed » Thu Oct 29, 2020 7:09 am

FrediFizzx wrote:
jreed wrote:Here's a question about Gull's little paper: In note (2) he shows what I assume is a time series of values that are obtained when an observation of a detectors is observed during an experiment with hidden variables. I think he must mean +1 and -1 rather than +1 and 0. Anyway, he says if you take the FT of this series, it will have many Fourier components. That is true. Then he says for a quantum experiment the result (1-Cos(delta*theta)/4 only has 3 components. That is also true. The conclusion he comes to is that you can't get the quantum result from the hidden variable result.

The problem I have with this is that the quantum result is a probability function obtained from many trials, but the hidden variable result is only one trial. The two things aren't the same and don't seem to be comparable. What am I missing here?

There is only one FT result per correlation event. It is either 0 or 1. There is really no difference between 0 and 1 and +/-1 for outcomes. What do you mean by "3 components"? I get that the FT of (1-Cos(delta*theta)/4 = 1/4. How do we know Gull is doing a hidden variable result? He never specified the exact function for . It is really a bunch of nonsense.
.


If you write the expression for the averaged quantum result, 1/4-Cos[theta]/4 in terms of complex exponentials, you will find a zero frequency term, 1/4 and a -theta and +theta term. That makes 3 Fourier components for the quantum result.

Now for the experiment discussed in Gull's paper. This is a hidden variable calculation. If you read the first part of the description you will see there are two particles with opposite spins traveling to the two detectors. The unknown spin is the hidden variable. The rest is all local, realistic calculations. The quantum result was obtained by averaging many experiments and results in the cosine function. The local, realistic hidden variable result should be done the same way, by averaging many experiments. If that is done you get the well known triangle result. There is a difference in the Fourier spectra of this function and the quantum function, but this has been known for a long time.
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Re: GAViewer Simulation No Hidden Variable

Postby FrediFizzx » Thu Oct 29, 2020 7:27 am

jreed wrote:
FrediFizzx wrote:
jreed wrote:Here's a question about Gull's little paper: In note (2) he shows what I assume is a time series of values that are obtained when an observation of a detectors is observed during an experiment with hidden variables. I think he must mean +1 and -1 rather than +1 and 0. Anyway, he says if you take the FT of this series, it will have many Fourier components. That is true. Then he says for a quantum experiment the result (1-Cos(delta*theta)/4 only has 3 components. That is also true. The conclusion he comes to is that you can't get the quantum result from the hidden variable result.

The problem I have with this is that the quantum result is a probability function obtained from many trials, but the hidden variable result is only one trial. The two things aren't the same and don't seem to be comparable. What am I missing here?

There is only one FT result per correlation event. It is either 0 or 1. There is really no difference between 0 and 1 and +/-1 for outcomes. What do you mean by "3 components"? I get that the FT of (1-Cos(delta*theta)/4 = 1/4. How do we know Gull is doing a hidden variable result? He never specified the exact function for . It is really a bunch of nonsense.
.


If you write the expression for the averaged quantum result, 1/4-Cos[theta]/4 in terms of complex exponentials, you will find a zero frequency term, 1/4 and a -theta and +theta term. That makes 3 Fourier components for the quantum result.

Now for the experiment discussed in Gull's paper. This is a hidden variable calculation. If you read the first part of the description you will see there are two particles with opposite spins traveling to the two detectors. The unknown spin is the hidden variable. The rest is all local, realistic calculations. The quantum result was obtained by averaging many experiments and results in the cosine function. The local, realistic hidden variable result should be done the same way, by averaging many experiments. If that is done you get the well known triangle result. There is a difference in the Fourier spectra of this function and the quantum function, but this has been known for a long time.

Well, write out your expression. Let's see the math. Why make us guess at it? You can do it in Mathematica and then copy it as LaTeX to paste into the tex function here.

No where does Gull mention a hidden variable until the last page. What is more, he makes us guess at what the function might be for . Your task would be to tell us what the correlation would be given theta and "n". IOW, what is the function that could possibly do that?
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Re: GAViewer Simulation No Hidden Variable

Postby FrediFizzx » Thu Oct 29, 2020 11:54 am

The generic expression for the Fourier Transform is,

,

where omega is the transform variable. However, particle physics uses just 1/2pi instead of the square root of 1/2pi,

.

Gull must be using this,

,

since an angle theta is involved and in number (3) he must be setting the transform variable to zero.
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Re: GAViewer Simulation No Hidden Variable

Postby gill1109 » Thu Oct 29, 2020 10:52 pm

FrediFizzx wrote:The generic expression for the Fourier Transform is,

,

where omega is the transform variable. However, particle physics uses just 1/2pi instead of the square root of 1/2pi,

.

Gull must be using this,

,

since an angle theta is involved and in number (3) he must be setting the transform variable to zero.
.

No. In formula (3) he is setting one function equal to another. rho and p are two functions on [0, 2 pi]. “FT” converts a function to another function. If we denote the correlation (as function of the difference between the two setting angles) by rho, then he is saying (I correct the sign) rho = - FT(|FT(p)|^2). His definition of Fourier Transform of functions defined on [0, 2 pi] is arranged so as to make it its own inverse. I think that the normalisation factor then has to be 1/sqrt(2 pi). You can check yourself, easily. We want the integral of the square of the absolute value of the FT to equal the integral of the square of the absolute value of the function itself.

The slides have a lot of minor errors. He mixes up polarisers (photons) and Stern Gerlach devices (electrons). rho must be the negative cosine, varies between -1 and +1, period 2 pi. The wording is kind of 80s Cambridge physicist, very short (insider language).

See also https://math.stackexchange.com/questions/329576/fourier-transform-on-the-circle
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Re: GAViewer Simulation No Hidden Variable

Postby FrediFizzx » Fri Oct 30, 2020 1:35 am

:mrgreen: That is so wrong I'm going back to sleep. You are making stuff up that isn't there. As usual.
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Re: GAViewer Simulation No Hidden Variablet

Postby gill1109 » Fri Oct 30, 2020 3:21 am

FrediFizzx wrote::mrgreen: That is so wrong I'm going back to sleep. You are making stuff up that isn't there. As usual.
.

Ah, I think I got it now. We need https://en.wikipedia.org/wiki/Convolution_theorem#Convolution_theorem_for_Fourier_series_coefficients. See also the second answer to this question https://math.stackexchange.com/questions/329576/fourier-transform-on-the-circle.
In the generalised sense, the Fourier transform of a function on the unit circle is a doubly infinite series. The Fourier transform of a doubly infinite series is a function on the unit circle. They are one another’s inverse. The Fourier transform of a convolution of two functions on a circle is the series whose terms are the term-wise products of the terms of the series of the two functions. Our correlation is minus the convolution of p and the function q defined by q(phi) = p(-phi). The Fourier series of q is the term-wise complex conjugate of the series of p. So the series of the correlation rho has terms which are the negative if the absolute value, squared, of those of p. But this contradicts what you can easily find out about the Fourier series of the function “negative cosine”.

Sorry, I confused things by mixing up functions on the circle and sequences with terms indexed by the integers Z (both positive and negative).

Also, Gull is mixing up “correlation” (mean of product of +/-1 answers) and “probability of ++” (mean of product of 0/1 answers).

Let’s take the outcomes to be +/-1 valued. Then we already agreed that denoting q by Bob’s outcome, we must have q(phi, n) = -p(phi, n) for all n and phi. If Alice and Bob repeatedly are given a random pair of angles differing by Delta theta, say: u_n and u_n - Delta theta, then the expectation value of the average of the products of their outcomes in N trials is
- 1/N int_0^{2 pi} p(u, n) p(-u - Delta theta) d u / 2 pi. (u_n is the realisation of a uniformly distributed random angle U_n).
We recognise the convolution of p and q. The Fourier series of q is the term-by-term complex conjugate of that of p. QED.
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Re: GAViewer Simulation No Hidden Variable

Postby FrediFizzx » Fri Oct 30, 2020 9:06 am

Write your paper. As said, looks like more nonsense piled on top of nonsense.
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Re: GAViewer Simulation No Hidden Variable

Postby FrediFizzx » Fri Oct 30, 2020 5:07 pm

jreed wrote: ...
If you write the expression for the averaged quantum result, 1/4-Cos[theta]/4 in terms of complex exponentials, you will find a zero frequency term, 1/4 and a -theta and +theta term. That makes 3 Fourier components for the quantum result. ...

I guess jreed is talking nonsense here since he didn't post the expression he is talking about. Figures. I tried to guess at it with no luck. And not sure why he is talking "-theta and +theta" terms since theta disappears in the transform result. ???
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Re: GAViewer Simulation No Hidden Variable

Postby jreed » Sat Oct 31, 2020 7:29 am

FrediFizzx wrote:
jreed wrote: ...
If you write the expression for the averaged quantum result, 1/4-Cos[theta]/4 in terms of complex exponentials, you will find a zero frequency term, 1/4 and a -theta and +theta term. That makes 3 Fourier components for the quantum result. ...

I guess jreed is talking nonsense here since he didn't post the expression he is talking about. Figures. I tried to guess at it with no luck. And not sure why he is talking "-theta and +theta" terms since theta disappears in the transform result. ???
.


Please refer to page 1 of Gull's paper. You will see a graph of 1/4(1-Cos[delta theta]). This function has 3 Fourier components. That's what I'm talking about.

On page 3 he shows a graph of values (0,1) vs. theta for the hidden variable calculation. This function has many Fourier components. The conclusion he comes to is that the two functions are totally different, and the hidden variable result can never be made to match the quantum result.

I don't think he should be comparing these two things since one (the quantum result) was obtained by averaging many runs of the experiment, whereas the hidden variable result is a single instance of the experiment. He should be comparing averaging of these values also. In that case you will get the triangle result. These two results do have different Fourier spectra.
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Re: GAViewer Simulation No Hidden Variable

Postby FrediFizzx » Sat Oct 31, 2020 8:57 am

jreed wrote:
FrediFizzx wrote:
jreed wrote: ...
If you write the expression for the averaged quantum result, 1/4-Cos[theta]/4 in terms of complex exponentials, you will find a zero frequency term, 1/4 and a -theta and +theta term. That makes 3 Fourier components for the quantum result. ...

I guess jreed is talking nonsense here since he didn't post the expression he is talking about. Figures. I tried to guess at it with no luck. And not sure why he is talking "-theta and +theta" terms since theta disappears in the transform result. ???
.

Please refer to page 1 of Gull's paper. You will see a graph of 1/4(1-Cos[delta theta]). This function has 3 Fourier components. That's what I'm talking about.

On page 3 he shows a graph of values (0,1) vs. theta for the hidden variable calculation. This function has many Fourier components. The conclusion he comes to is that the two functions are totally different, and the hidden variable result can never be made to match the quantum result.

I don't think he should be comparing these two things since one (the quantum result) was obtained by averaging many runs of the experiment, whereas the hidden variable result is a single instance of the experiment. He should be comparing averaging of these values also. In that case you will get the triangle result. These two results do have different Fourier spectra.

You keep claiming that probability function has 3 Fourier components but don't show the math for it. So, until you do show us some math it is nonsense. Here is what I get for that function.



Here is the plot for that result remembering that omega is a continuous transform variable,

Image

The dashed curve is the imaginary part and the solid the real part. So I would say for that FT expression we have two components. Now, say we take the integration from -pi to +pi which is still just one cycle,



Here is the plot for that result noting that the imaginary component has dropped out,

Image

So, I would say for that expression we have only one component. The real part.

How do we know the graph on page 3 is a hidden variable result? He never defines the function. I don't see lambda anywhere in sight. That function and plot could be for some experiment. Plus in number (3) he is just doing the FT for one single event. But you are correct that his comparison is a bunch of nonsense. :)
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Re: GAViewer Simulation No Hidden Variable

Postby gill1109 » Sat Oct 31, 2020 9:38 am

Gull is talking about Fourier series, not Fourier transform. I think I know how to fix his proof. There are a number of small mistakes and big unexplained jumps. I am writing a paper with a student, however, she has a day job as well as her studies, you guys will have to be patient. We plan to be finished in two weeks.

Of course Gull does not “define the function”. He is arguing that it does not exist. And I already told you where lambda is. The code of the two programs includes, perhaps as initial constants, lambda_1, lambda_2, ... , lambda_N. Alternatively it includes the seed and the parameters of a pseudo random number generator and the code of the generator. The randomness in his model is that he uses pairs of settings U_n, U_n - Delta theta, where U_1, U_2 are independent uniform [0, 2 pi]. He computes the expected number of ++ outcomes in N trials. And then the Fourier series of that number, as function of Delta theta. He compares that with the Fourier series of the singlet state expected number. You have to realise that from an abstract point of view, the operation of computing a Fourier series, and of inverting a Fourier series, are both Fourier transforms from a Lie group to its dual. It’s a fancy abstract way of saying things. But fortunately, not a nonsensical way of saying things. But you need a lot of maths background. https://en.wikipedia.org/wiki/Pontryagin_duality

Don’t worry, my student and I will write it up using simple language.
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Re: GAViewer Simulation No Hidden Variable

Postby jreed » Sat Oct 31, 2020 9:57 am

FrediFizzx wrote:
jreed wrote:
FrediFizzx wrote:
jreed wrote: ...
If you write the expression for the averaged quantum result, 1/4-Cos[theta]/4 in terms of complex exponentials, you will find a zero frequency term, 1/4 and a -theta and +theta term. That makes 3 Fourier components for the quantum result. ...

I guess jreed is talking nonsense here since he didn't post the expression he is talking about. Figures. I tried to guess at it with no luck. And not sure why he is talking "-theta and +theta" terms since theta disappears in the transform result. ???
.

Please refer to page 1 of Gull's paper. You will see a graph of 1/4(1-Cos[delta theta]). This function has 3 Fourier components. That's what I'm talking about.

On page 3 he shows a graph of values (0,1) vs. theta for the hidden variable calculation. This function has many Fourier components. The conclusion he comes to is that the two functions are totally different, and the hidden variable result can never be made to match the quantum result.

I don't think he should be comparing these two things since one (the quantum result) was obtained by averaging many runs of the experiment, whereas the hidden variable result is a single instance of the experiment. He should be comparing averaging of these values also. In that case you will get the triangle result. These two results do have different Fourier spectra.

You keep claiming that probability function has 3 Fourier components but don't show the math for it. So, until you do show us some math it is nonsense. Here is what I get for that function.


How do we know the graph on page 3 is a hidden variable result? He never defines the function. I don't see lambda anywhere in sight. That function and plot could be for some experiment. Plus in number (3) he is just doing the FT for one single event. But you are correct that his comparison is a bunch of nonsense. :)
.


Just go into Mathematica, define the function f=(1+Cos[theta[)/4 then enter FourierSeries[f,theta,omega]. You'll see the three components expressed as dirac delta functions in omega. If you had some experience with Fourier series, you would see that just looking at the expression for f.
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Re: GAViewer Simulation No Hidden Variable

Postby FrediFizzx » Sat Oct 31, 2020 1:03 pm

jreed wrote: ...
Just go into Mathematica, define the function f=(1+Cos[theta[)/4 then enter FourierSeries[f,theta,omega]. You'll see the three components expressed as dirac delta functions in omega. If you had some experience with Fourier series, you would see that just looking at the expression for f.

Whoa! Gull never said anything about Fourier Series. Plus Mathematica gives for what you said,

Image

Looks like nonsense to me. If you are getting Dirac Deltas, you are not doing something right. Show your math or you are just talking more nonsense.
.
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Re: GAViewer Simulation No Hidden Variable

Postby jreed » Sat Oct 31, 2020 4:07 pm

FrediFizzx wrote:
jreed wrote: ...
Just go into Mathematica, define the function f=(1+Cos[theta[)/4 then enter FourierSeries[f,theta,omega]. You'll see the three components expressed as dirac delta functions in omega. If you had some experience with Fourier series, you would see that just looking at the expression for f.

Whoa! Gull never said anything about Fourier Series. Plus Mathematica gives for what you said,

Image

Looks like nonsense to me. If you are getting Dirac Deltas, you are not doing something right. Show your math or you are just talking more nonsense.
.

Sorry, my mistake. That should have FourierTransform.
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