Coming Soon!

[jreed]

It looks like both Alice and Bob each make and record observations using two detectors at each location (A, AA, B, BB). These detectors are sometimes oriented at a 90 degree angle to each other, and other times not, depending on lambda. What actual experiment is being simulated here? I'm not familiar with any experiment like that.

[FrediFizzx]

It looks like both Alice and Bob each make and record observations using two detectors at each location (A, AA, B, BB). These detectors are sometimes oriented at a 90 degree angle to each other, and other times not, depending on lambda. What actual experiment is being simulated here? I'm not familiar with any experiment like that.

AA and BB are not detections and are not dependent on lambda. They are only dependent on the angle and the singlet spin vector and are just a recording as if every event was a constrained event. No particular experiment, it's an EPR thought experiment. Plus it is a realistic model not a quantum model. AA and BB can be predicted. In fact, you could just say that the program is predicting the raw unmatched A and B outputs as well as AA and BB.
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[FrediFizzx]

I've tweaked the CHSH version a little bit.

CHSH = 2.78024!

It is now closer to the theoretical limit.

EPRsims/newCS-10-CHSH-forum3.pdf
EPRsims/newCS-10-CHSH-forum3.nb
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[gill1109]

Indeed, it should work if the collected terms are averaged properly.
Every time you start up Mathematica and take a new random sample, the seed is different from what it was the time before. Unless you deliberately set it to be the same, which is useful for testing purposes. Are you saying that Mathematica is stupid?

No, I'm saying you are stupid for saying to change the seed each time. Just don't have a seed.

You do have a seed. Mathematica makes it for you. And changes it every time. Unless you ask Mathematica to behave otherwise.

[FrediFizzx]

Indeed, it should work if the collected terms are averaged properly.
Every time you start up Mathematica and take a new random sample, the seed is different from what it was the time before. Unless you deliberately set it to be the same, which is useful for testing purposes. Are you saying that Mathematica is stupid?

No, I'm saying you are stupid for saying to change the seed each time. Just don't have a seed.

You do have a seed. Mathematica makes it for you. And changes it every time. Unless you ask Mathematica to behave otherwise.

CHSH = 2.78024!
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[jreed]

Fred's latest version does set the seed:
SeedRandom[5476];
The result will be the same unless this is changed.

[FrediFizzx]

Fred's latest version does set the seed:
SeedRandom[5476];
The result will be the same unless this is changed.

Thanks John for paying attention. Having a seed seems silly to me because what you really want is to get nearly the same result with different initial conditions.
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[Heinera]

Fred's latest version does set the seed:
SeedRandom[5476];
The result will be the same unless this is changed.

Thanks John for paying attention. Having a seed seems silly to me because what you really want is to get nearly the same result with different initial conditions.
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The discussion about seeds is a distraction. It has nothing to do with your results. Your silly trick has a completely different explanation.

[FrediFizzx]

@Heinera What is this trick you are claiming?
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[Austin Fearnley]

Hi Fred

Not heard back from you, so:

I have calculated and re-calculated the results using Joy's exact formulae on a spreadsheet with 360 pairs of simulated particles.
The correlation is positive instead of negative so I guess the inequalities are back to front in some or all places in Joy's formulae?
Anyone else find this?

Also the correlation is less than 0.5 so I guess that Joy's formula are not equivalent to your method since Joy's formulae give unremarkable results.
Not sure what your method is so I cannot help there.

Best wishes
Austin

[FrediFizzx]

Hi Fred

Not heard back from you, so:

I have calculated and re-calculated the results using Joy's exact formulae on a spreadsheet with 360 pairs of simulated particles.
The correlation is positive instead of negative so I guess the inequalities are back to front in some or all places in Joy's formulae?
Anyone else find this?

Also the correlation is less than 0.5 so I guess that Joy's formula are not equivalent to your method since Joy's formulae give unremarkable results.
Not sure what your method is so I cannot help there.

Best wishes
Austin

Sorry Austin, got real busy on a different project. Joy's formula is not complete yet. You get straight lines with that. I believe Joy was waiting to see if John Reed is going to do the pseudo-code so he could understand it better.
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[jreed]

Hi Fred

Not heard back from you, so:

I have calculated and re-calculated the results using Joy's exact formulae on a spreadsheet with 360 pairs of simulated particles.
The correlation is positive instead of negative so I guess the inequalities are back to front in some or all places in Joy's formulae?
Anyone else find this?

Also the correlation is less than 0.5 so I guess that Joy's formula are not equivalent to your method since Joy's formulae give unremarkable results.
Not sure what your method is so I cannot help there.

Best wishes
Austin

Sorry Austin, got real busy on a different project. Joy's formula is not complete yet. You get straight lines with that. I believe Joy was waiting to see if John Reed is going to do the pseudo-code so he could understand it better.
.

I am working on an explanation, but I'm having some difficulty with this. I decided to rewrite the code so I can better understand what is being done in the program. So far, my rewrite results don't match the original code results. More later...

[gill1109]

Hi Fred

Not heard back from you, so:

I have calculated and re-calculated the results using Joy's exact formulae on a spreadsheet with 360 pairs of simulated particles.
The correlation is positive instead of negative so I guess the inequalities are back to front in some or all places in Joy's formulae?
Anyone else find this?

Also the correlation is less than 0.5 so I guess that Joy's formula are not equivalent to your method since Joy's formulae give unremarkable results.
Not sure what your method is so I cannot help there.

Best wishes
Austin

Sorry Austin, got real busy on a different project. Joy's formula is not complete yet. You get straight lines with that. I believe Joy was waiting to see if John Reed is going to do the pseudo-code so he could understand it better.
.

I am working on an explanation, but I'm having some difficulty with this. I decided to rewrite the code so I can better understand what is being done in the program. So far, my rewrite results don't match the original code results. More later...

I'm looking forward to your findings, John.

[jreed]

Here's what I have found with Fred's final version of his Mathematica program:
The number of experiments will referred to as m in what follows.
The particle's spin axis is set up as an random angle over the range 0-360 degrees with m values. This is the same for both observers.
A random variable is set up called lambda, the same one used by Fodje in epr-simple with m values, the same for both observers.

The data is generated in two separate loops over m, one for Alice and one for Bob. In each of these loops, a random variable is generated over 0-360 degrees. This is the detector angle. The difference between the spin axis angle and detector angle is found, and its absolute value is compared to lambda. If this value is less than lambda, this observation is labelled with f (failure), if greater, it is labelled with g (good). A detector value is found: If the observation is good (g), the Sign of the Cos of the difference angle is used. If the observation is a fail, the Sign of the Sin is used. Each observation is recorded as a record: {detector angle, detector value (+ or - 1), experiment number, f or g, and a second detector value, the Sign of the Sin of the difference angle}. These records are similar to Fodje's program, except for the Sin and Cos usage.

These observation records are then manipulated. I won't attempt to describe this complex process, although in looking at the difference between the input records and output records, it appears that if Alice has a failed experiment, the corresponding experiment in Bob's record has the detector value multiplied by -1, and visa versa for Bob and Alice. After this is completed, the usual analysis is done to find mean values for plotting and computation of CHSH values.

If anyone has questions about this I will be happy to try to answer them.

[FrediFizzx]

Everything in the matching section is a black box. The important part is that the same a setting comes out as was put in. Same for the b setting.
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[jreed]

Everything in the matching section is a black box. The important part is that the same a setting comes out as was put in. Same for the b setting.
.

Take your final, stable version and run a short test with m = 30 or 40. Now compare the input lists outA and outB to the output list outA5 and outB5. You will find that nearly each time f1 appears in one of the outA measurements, the same outB5 measurement will have the detector value with a changed sign. The same thing happens with the outB and outA5 lists. I said nearly because sometimes this doesn't happen, but it almost always does.

This could be done with much simpler programming. It would be interesting to see how this sign flip affects the CHSH values and final plot.

[FrediFizzx]

Everything in the matching section is a black box. The important part is that the same a setting comes out as was put in. Same for the b setting.
.

Take your final, stable version and run a short test with m = 30 or 40. Now compare the input lists outA and outB to the output list outA5 and outB5. You will find that nearly each time f1 appears in one of the outA measurements, the same outB5 measurement will have the detector value with a changed sign. The same thing happens with the outB and outA5 lists. I said nearly because sometimes this doesn't happen, but it almost always does.

This could be done with much simpler programming. It would be interesting to see how this sign flip affects the CHSH values and final plot.

You have do that for proper matching of constrained events vs. non-constrained. If the signs are the same it doesn't change. This was the most simple local programming I could figure out. If you don't do it I believe the final plot will be straight lines.
.

[gill1109]

Everything in the matching section is a black box. The important part is that the same a setting comes out as was put in. Same for the b setting.

Take your final, stable version and run a short test with m = 30 or 40. Now compare the input lists outA and outB to the output list outA5 and outB5. You will find that nearly each time f1 appears in one of the outA measurements, the same outB5 measurement will have the detector value with a changed sign. The same thing happens with the outB and outA5 lists. I said nearly because sometimes this doesn't happen, but it almost always does.

This could be done with much simpler programming. It would be interesting to see how this sign flip affects the CHSH values and final plot.

You have do that for proper matching of constrained events vs. non-constrained. If the signs are the same it doesn't change. This was the most simple local programming I could figure out. If you don't do it I believe the final plot will be straight lines.

So do you, Fred, recommend experimenters to use your matching method in future? I suppose they couldn't, because the hidden variables are ... hidden to them.

[FrediFizzx]

Everything in the matching section is a black box. The important part is that the same a setting comes out as was put in. Same for the b setting.

Take your final, stable version and run a short test with m = 30 or 40. Now compare the input lists outA and outB to the output list outA5 and outB5. You will find that nearly each time f1 appears in one of the outA measurements, the same outB5 measurement will have the detector value with a changed sign. The same thing happens with the outB and outA5 lists. I said nearly because sometimes this doesn't happen, but it almost always does.

This could be done with much simpler programming. It would be interesting to see how this sign flip affects the CHSH values and final plot.

You have do that for proper matching of constrained events vs. non-constrained. If the signs are the same it doesn't change. This was the most simple local programming I could figure out. If you don't do it I believe the final plot will be straight lines.

So do you, Fred, recommend experimenters to use your matching method in future? I suppose they couldn't, because the hidden variables are ... hidden to them.

CHSH = 2.78024!
.

[jreed]

Everything in the matching section is a black box. The important part is that the same a setting comes out as was put in. Same for the b setting.
.

Take your final, stable version and run a short test with m = 30 or 40. Now compare the input lists outA and outB to the output list outA5 and outB5. You will find that nearly each time f1 appears in one of the outA measurements, the same outB5 measurement will have the detector value with a changed sign. The same thing happens with the outB and outA5 lists. I said nearly because sometimes this doesn't happen, but it almost always does.

This could be done with much simpler programming. It would be interesting to see how this sign flip affects the CHSH values and final plot.

You have do that for proper matching of constrained events vs. non-constrained. If the signs are the same it doesn't change. This was the most simple local programming I could figure out. If you don't do it I believe the final plot will be straight lines.
.

Your program is doing the sign flips. This is a non-local calculation since Alice has to have information from Bob about his experiments in order to change the signs. The non-locality is clear in the way your program uses the routine Intersection. You should read up on what it is doing. The arguments for Intersection are outA1 (Alice's experiments) and listbd (Bob's experiment numbers). This uses information from Bob's experiments to change Alice's experiments. That's non-local.