Coming Soon!

[FrediFizzx]

Here is the link to the revised paper,

http://dx.doi.org/10.13140/RG.2.2.28311.91047/1

Enjoy!
.

[FrediFizzx]

Here is the link to the revised paper,

http://dx.doi.org/10.13140/RG.2.2.28311.91047/1

Enjoy!
.

Yep, Gill is finished and doesn't even realize it yet.
.

[gill1109]

Here is the link to the revised paper,
http://dx.doi.org/10.13140/RG.2.2.28311.91047/1
Enjoy!

Very enjoyable indeed! Good luck with getting it published in a nice journal. I would be delighted to be asked to referee it, and otherwise to submit a "Comment".

I feel you should also have thanked John Reed and myself for our careful reading of the paper and especially of the code since this certainly led to improvements.

[FrediFizzx]

Which improvements?
.

[gill1109]

Which improvements?

The description of the matching process and the meaning of k_A and k_B is a whole lot better.

[FrediFizzx]

Which improvements?

The description of the matching process and the meaning of k_A and k_B is a whole lot better.

Well good. Thank you. Justo got us started off, and I think I thanked him. We put in "otherwise no result" in A1, A2, B1 and B2 to better define those.
.

[FrediFizzx]

Slightly revised version of the paper,

EPRsims/Event_by_Event_Numerical_Simulation_of_the_Strong_Singlet_Correlations_rev1.pdf

Also at,

DOI: http://dx.doi.org/10.13140/RG.2.2.28311.91047/2

Enjoy!
.

[gill1109]

Slightly revised version of the paper,

EPRsims/Event_by_Event_Numerical_Simulation_of_the_Strong_Singlet_Correlations_rev1.pdf

Also at,

DOI: http://dx.doi.org/10.13140/RG.2.2.28311.91047/2

Enjoy!

I enjoyed this. You write, explaining displayed formula (9): "For this purpose we will use the following discrete version of the expectation function (6) assuming uniform probability distribution p(λ) = 1".

This is not a discrete version of the expectation function. This is (for each n) the empirical distribution which puts probability mass 1/n on each of n independent and identically distributed realised values lambda_1, lambda_2, ... lambda_n coming from the probability distribution rho(lambda). You are using the strong law of large numbers: empirical averages converge to theoretical expectation values. According to that theorem, the expression (9) is with probability one identically equal to the usual expression: the integral of A(a, lambda) B(b, lambda) rho(lambda) d lambda, i.e. the displayed formula (6).

At least, (6) and (9) are identical if the lambda_k are indeed independent and identically distributed realisations of values of lambda taken from a fixed probability distribution rho (which does not depend on a and b).

I don't see the point of using an explicit limit of empirical averages instead of its known value, unless you plan to let the hidden variable lambda depend on the settings a and b.

[Joy Christian]

Slightly revised version of the paper,

EPRsims/Event_by_Event_Numerical_Simulation_of_the_Strong_Singlet_Correlations_rev1.pdf

Also at,

DOI: http://dx.doi.org/10.13140/RG.2.2.28311.91047/2

Enjoy!

I enjoyed this. You write, explaining displayed formula (9): "For this purpose we will use the following discrete version of the expectation function (6) assuming uniform probability distribution p(λ) = 1".

This is not a discrete version of the expectation function. This is (for each n) the empirical distribution which puts probability mass 1/n on each of n independent and identically distributed realised values lambda_1, lambda_2, ... lambda_n coming from the probability distribution rho(lambda). You are using the strong law of large numbers: empirical averages converge to theoretical expectation values. According to that theorem, the expression (9) is with probability one identically equal to the usual expression: the integral of A(a, lambda) B(b, lambda) rho(lambda) d lambda, i.e. the displayed formula (6).

At least, (6) and (9) are identical if the lambda_k are indeed independent and identically distributed realisations of values of lambda taken from a fixed probability distribution rho (which does not depend on a and b).

I don't see the point of using an explicit limit of empirical averages instead of its known value, unless you plan to let the hidden variable lambda depend on the settings a and b.

Whatever. You are toast in any case.
.

[FrediFizzx]

Whatever. You are toast in any case.
.

Is Gill posting nonsense again? I warned him about doing that.
.

[Joy Christian]

.
These are the key figures from the paper:



Incorporating the spinorial sign changes is all that is needed for the dull sawtooth-shaped lines to blossom into -cosine correlations.
.

[gill1109]

Whatever. You are toast in any case.

Is Gill posting nonsense again? I warned him about doing that.

I was suggesting an opportunity for improvement of your joint paper: just a small question of terminology. An empirical average uses equal weights of size 1/n. It does not use a probability mass function with p(.) = 1. Probabilities have to be nonnegative and sum to one. Probability densities have to integrate to one.

According to the law of large numbers, https://en.wikipedia.org/wiki/Law_of_large_numbers, sample averages converge to theoretical mean values, under certain conditions.

[Joy Christian]

Whatever. You are toast in any case.

Is Gill posting nonsense again? I warned him about doing that.

I was suggesting an opportunity for improvement of your joint paper: just a small question of terminology. An empirical average uses equal weights of size 1/n. It does not use a probability mass function with p(.) = 1. Probabilities have to be nonnegative and sum to one. Probability densities have to integrate to one.

According to the law of large numbers, https://en.wikipedia.org/wiki/Law_of_large_numbers, sample averages converge to theoretical mean values, under certain conditions.

We have set p(\lambda) = 1 in our eq. (6) following Bell in his book (chapter 1, section 2, last equation), who calls it "uniform averaging over \lambda."
.

[gill1109]

Whatever. You are toast in any case.

Is Gill posting nonsense again? I warned him about doing that.

I was suggesting an opportunity for improvement of your joint paper: just a small question of terminology. An empirical average uses equal weights of size 1/n. It does not use a probability mass function with p(.) = 1. Probabilities have to be nonnegative and sum to one. Probability densities have to integrate to one.

According to the law of large numbers, https://en.wikipedia.org/wiki/Law_of_large_numbers, sample averages converge to theoretical mean values, under certain conditions.

We have set p(\lambda) = 1 in our eq. (6) following Bell in his book (chapter 1, section 2, last equation), who calls it "uniform averaging over \lambda."
.

Thank you, Joy! I have checked in Bell's book. At that location in the book he is doing "uniform averaging over lambda" when lambda has the uniform distribution on [-1/2, +1/2]. It is a theoretical mean. The probability density is p(lambda) = 1, for lambda in [-1/2, +1/2]; p(lambda) = 0 outside that interval. It *integrates* to 1.

[FrediFizzx]

Here is a version of the simulation that more explicitly shows the conservation of angular momentum. The minus signs are gone on the A side and we send theta[e] +180 degrees to the B side. This is like Michel has it in epr-simple only he was in radians so e + pi.

https://www.wolframcloud.com/obj/fredif ... -AMtest.nb

Enjoy!
.

[FrediFizzx]

Another slightly revised version. Just doing some fine tuning.

EPRsims/Event_by_Event_Numerical_Simulation_of_the_Strong_Singlet_Correlations_rev1.pdf

Enjoy!
.

[gill1109]

Another slightly revised version. Just doing some fine tuning.

EPRsims/Event_by_Event_Numerical_Simulation_of_the_Strong_Singlet_Correlations_rev1.pdf

Enjoy!

Great! Good to see you put p(lambda_k) = 1/n in equation (9).

[gill1109]

I would also suggest that you add to the paper internet links to two Mathematica notebooks of the two simulations (Appendix A, Appendix B). Copying and pasting from a pdf file introduces all kinds of annoying errors and costs a lot of time.

To begin with, please give us two links here on the forum so we can reproduce the appendices with ease. It’s really great you have now separated a classical cosine curve experiment simulation from a classical CHSH experiment simulation.

A lot of people nowadays use SageMath for symbolic computing and more. Open source, free. Steve Wolfram has used dubious legal copyright tricks to prevent the development of an open source implementation of the Mathematica language.

https://www.sagemath.org/

[FrediFizzx]

I would also suggest that you add to the paper internet links to two Mathematica notebooks of the two simulations (Appendix A, Appendix B). Copying and pasting from a pdf file introduces all kinds of annoying errors and costs a lot of time.

To begin with, please give us two links here on the forum so we can reproduce the appendices with ease. It’s really great you have now separated a classical cosine curve experiment simulation from a classical CHSH experiment simulation.

A lot of people nowadays use SageMath for symbolic computing and more. Open source, free. Steve Wolfram has used dubious legal copyright tricks to prevent the development of an open source implementation of the Mathematica language.
https://www.sagemath.org/

Ya mean like here,

viewtopic.php?f=6&t=484#p13694

I'll put up the CHSH version as soon as I clean it up to match the paper. Tried Sage when I was playing around with, Niles Johnson's stuff. It is a bit geeky compared to Mathematica. Plus with Mathematica, you get two when you buy one. You can evaluate notebook files on the Wolfram Cloud but they have to run within 1 minute. But good for short testing if local Mathematica is tied up with long evaluations.

PS. CHSH version is up at the above link.
.

[gill1109]

I would also suggest that you add to the paper internet links to two Mathematica notebooks of the two simulations (Appendix A, Appendix B). Copying and pasting from a pdf file introduces all kinds of annoying errors and costs a lot of time.

To begin with, please give us two links here on the forum so we can reproduce the appendices with ease. It’s really great you have now separated a classical cosine curve experiment simulation from a classical CHSH experiment simulation.

A lot of people nowadays use SageMath for symbolic computing and more. Open source, free. Steve Wolfram has used dubious legal copyright tricks to prevent the development of an open source implementation of the Mathematica language.
https://www.sagemath.org/

Ya mean like here,

viewtopic.php?f=6&t=484#p13694

I'll put up the CHSH version as soon as I clean it up to match the paper. Tried Sage when I was playing around with, Niles Johnson's stuff. It is a bit geeky compared to Mathematica. Plus with Mathematica, you get two when you buy one. You can evaluate notebook files on the Wolfram Cloud but they have to run within 1 minute. But good for short testing if local Mathematica is tied up with long evaluations.

PS. CHSH version is up at the above link.
.

Great! That worked. Here’s my copy for further testing https://www.wolframcloud.com/obj/gill1109/Published/newCS-11-CHSH-paper-RDG.nb