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I'm going to go ahead and post the code for this new simulation even though I am not entirely satisfied with it..., yet. Perhaps someone else might be interested in tinkering with it to improve it? Or to collaborate with it?

720 degrees worth of data at one degree resolution. No events dropped. Here is a PDF of the code and the Mathematica notebook file.

EPRsims/newCS-1.pdf

EPRsims/newCS-1.nb

It utilizes the complete states function. You can see from the code that during the constraints, the a and b vector angles subtract from themselves. I have yet to figure out a good physical justification for that. Perhaps some S^3 action at work? But the simulation is completely local and completely predictable for the A and B outcomes if you know a, b, e and lambda so it is 100 percent realistic.

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720 degrees worth of data at one degree resolution. No events dropped. Here is a PDF of the code and the Mathematica notebook file.

EPRsims/newCS-1.pdf

EPRsims/newCS-1.nb

It utilizes the complete states function. You can see from the code that during the constraints, the a and b vector angles subtract from themselves. I have yet to figure out a good physical justification for that. Perhaps some S^3 action at work? But the simulation is completely local and completely predictable for the A and B outcomes if you know a, b, e and lambda so it is 100 percent realistic.

.

- FrediFizzx
- Independent Physics Researcher
**Posts:**1732**Joined:**Tue Mar 19, 2013 7:12 pm**Location:**N. California, USA

Ah..., perhaps during the constraints a and b become null vectors due to S^3 action?

.

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- FrediFizzx
- Independent Physics Researcher
**Posts:**1732**Joined:**Tue Mar 19, 2013 7:12 pm**Location:**N. California, USA

FrediFizzx wrote:Ah..., perhaps during the constraints a and b become null vectors due to S^3 action?

I don't read Mathematica codes very well, but so far you have not managed to attract the bulls to your red cloth. That is surprising.

***

- Joy Christian
- Research Physicist
**Posts:**2187**Joined:**Wed Feb 05, 2014 4:49 am**Location:**Oxford, United Kingdom

Joy Christian wrote:FrediFizzx wrote:Ah..., perhaps during the constraints a and b become null vectors due to S^3 action?

I don't read Mathematica codes very well, but so far you have not managed to attract the bulls to your red cloth. That is surprising.

***

What can they say about it other than what I already mentioned?

The Mathematica code is fairly straight forward to understand. You just need to understand the first three Do loops. The rest is analysis. I think the first Do loop is perfectly understandable. The only thing in the second and third loops is the if-then-else statements. After the first comma is the "then" and after the second comma is the "else". So..., anything else you don't understand?

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- FrediFizzx
- Independent Physics Researcher
**Posts:**1732**Joined:**Tue Mar 19, 2013 7:12 pm**Location:**N. California, USA

FrediFizzx wrote:Joy Christian wrote:FrediFizzx wrote:Ah..., perhaps during the constraints a and b become null vectors due to S^3 action?

I don't read Mathematica codes very well, but so far you have not managed to attract the bulls to your red cloth. That is surprising.

***

What can they say about it other than what I already mentioned?

The Mathematica code is fairly straight forward to understand. You just need to understand the first three Do loops. The rest is analysis. I think the first Do loop is perfectly understandable. The only thing in the second and third loops is the if-then-else statements. After the first comma is the "then" and after the second comma is the "else". So..., anything else you don't understand?

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I'm interested in simulation programs which can be tested without studying the code. I need to be able to supply settings myself, and to have the program output raw (binary) measurement outcomes, for any number of trials. I also want the option to be able to save and to reset the pseudo random number generator, so that all experiments are completely reproducible.

- gill1109
- Mathematical Statistician
**Posts:**1682**Joined:**Tue Feb 04, 2014 10:39 pm**Location:**Leiden

gill1109 wrote:I'm interested in simulation programs which can be tested without studying the code. I need to be able to supply settings myself, and to have the program output raw (binary) measurement outcomes, for any number of trials. I also want the option to be able to save and to reset the pseudo random number generator, so that all experiments are completely reproducible.

Oh, for heaven's sake. There is nothing complicated about the Mathematica code. You should be able to program this up in R quite easily with your random seed so you can have reproducible runs. And play around with the settings. It is only the first three Do loops. You can do your own analysis programming which you probably already have.

This could be how Nature does it.

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- FrediFizzx
- Independent Physics Researcher
**Posts:**1732**Joined:**Tue Mar 19, 2013 7:12 pm**Location:**N. California, USA

FrediFizzx wrote:gill1109 wrote:I'm interested in simulation programs which can be tested without studying the code. I need to be able to supply settings myself, and to have the program output raw (binary) measurement outcomes, for any number of trials. I also want the option to be able to save and to reset the pseudo random number generator, so that all experiments are completely reproducible.

Oh, for heaven's sake. There is nothing complicated about the Mathematica code. You should be able to program this up in R quite easily with your random seed so you can have reproducible runs. And play around with the settings. It is only the first three Do loops. You can do your own analysis programming which you probably already have.

This could be how Nature does it.

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Sure, I will take a look. Still: my point is that your program is not a simulation of real experiments in which settings are repeatedly chosen at random by outside physical mechanisms. So it may be how Nature generates what we nowadays call "quantum correlations" in some circumstances, but not necessarily in all circumstances.

When we run your program on a laptop (on battery power, with wireless and BlueTooth switched off) we have a physical example of the natural generation of quantum correlations in a more or less isolated physical system - namely a bunch of metal and plastic on your lap. Bell experiments explore what happens when we have several physical systems working, as far as possible independently of one another, and with inputs and outputs under strong causal limitations. David Bohm thought that this was pretty meaningless and wrote a book, together with David Hiley, called "The Undivided Universe" https://www.amazon.com/Undivided-Universe-Ontological-Interpretation-Quantum/dp/041512185X

- gill1109
- Mathematical Statistician
**Posts:**1682**Joined:**Tue Feb 04, 2014 10:39 pm**Location:**Leiden

Here are some new completely local and realistic simulations by myself: https://rpubs.com/gill1109/singlet.

- gill1109
- Mathematical Statistician
**Posts:**1682**Joined:**Tue Feb 04, 2014 10:39 pm**Location:**Leiden

gill1109 wrote:Here are some new completely local and realistic simulations by myself: https://rpubs.com/gill1109/singlet.

Not even close. What are your A and B functions per Bell?

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- FrediFizzx
- Independent Physics Researcher
**Posts:**1732**Joined:**Tue Mar 19, 2013 7:12 pm**Location:**N. California, USA

FrediFizzx wrote:gill1109 wrote:Here are some new completely local and realistic simulations by myself: https://rpubs.com/gill1109/singlet.

Not even close.

What are your A and B functions per Bell?

They can't be close - that's Bell's theorem for you!

Thanks for your comments. I'm revising the accompanying paper at the moment, and you are giving me good ideas for more things which I should add to it.

The point is that some of the curves do exceed the negative cosine in some places where both are positive. They don't lie "inside" the area enclosed by the zig-zag / saw-tooth / triangle-wave, though many people seem to think that that is what Bell's theorem says. The hidden variable is an angle.

The A and B functions: the little disks in the pictures tell you in each case what A and B are, it's the famous coloured spinning disk model, with just two colours. The A and B curves are piecewise constant. In order to make sure that there is perfect (anti) correlation at various setting differences, one is the negative of the other. Remember that Caroline Thompson had a spinning ball model with three colours, one of the colours being for "no detection". With three colours, one of the colours being "no detection", one can recover the negative cosine perfectly, as Pearle essentially showed long ago. And as Michel Fodje discovered for himself, independently. No doubt there have been others, too. Hans de Raedt (University of Groningen, Netherlands) has been publishing simulations of that nature for a long time.

Could you post your Mathematica code as a plain text file? Copy-pasting from the pdf doesn't work well. The notebook file is a text document but it contains much, much more than the Mathematica code itself. Which is hard to extract from the notebook. I'll then do a quick translation into R. It will certainly help me understand what you're doing

- gill1109
- Mathematical Statistician
**Posts:**1682**Joined:**Tue Feb 04, 2014 10:39 pm**Location:**Leiden

FrediFizzx wrote:I'm going to go ahead and post the code for this new simulation even though I am not entirely satisfied with it..., yet. Perhaps someone else might be interested in tinkering with it to improve it? Or to collaborate with it?

...

...

http://www.sciphysicsforums.com/spfbb1/EPRsims/newCS-1.pdf

http://www.sciphysicsforums.com/spfbb1/EPRsims/newCS-1.nb

It utilizes the complete states function. You can see from the code that during the constraints, the a and b vector angles subtract from themselves. I have yet to figure out a good physical justification for that. Perhaps some S^3 action at work? But the simulation is completely local and completely predictable for the A and B outcomes if you know a, b, e and lambda so it is 100 percent realistic.

The subtractions aa = (a - a) and bb = (b - b) mean that CA and CB contain values -1, 0 and +1, and these values go into AliceD and BobD too. This means that when you count joint outcomes pPP, pPN, pNP, pNN you only count the +/-1's. The claim "No Events are Dropped" is not quite true. They are not explicitly dropped. But they are not counted.

Some would say that that is correct, since physically they never happened anyway.

Michel Fodje did not have (2/Sqrt[1 + (3 \[Lambda])/\[Pi]] - 1), he had something a little bit different. But he did come amazingly close!

From a purely mathematical point of view, this is actually *exactly* Philip Pearle's (1970) model, though it is quite hard to recognise it if you would try to find it in that paper. Philip did not have that actual formula, but after you correct several misprints and some real errors (a wrong normalisation constant) in Pearle's paper, you can determine that his formula (22) (corrected) is equivalent to your (2/Sqrt[1 + (3 \[Lambda])/\[Pi]] - 1).

https://journals.aps.org/prd/abstract/10.1103/PhysRevD.2.1418 (Pearle's paper)

https://www.researchgate.net/profile/Philip_Pearle/publication/235524553_Hidden-Variable_Example_Based_upon_Data_Rejection/links/5e33616a458515072d70faeb/Hidden-Variable-Example-Based-upon-Data-Rejection.pdf

https://www.mdpi.com/1099-4300/22/1/1 (my analysis of Pearle's paper)

https://www.preprints.org/manuscript/202001.0045/v1 (my analysis of Michel Fodje's models)

I am of course proud to say here that this is the simulation model used in "Bell’s Theorem Versus Local Realism in a Quaternionic Model of Physical Space" by J. Christian https://ieeexplore.ieee.org/document/8836453

- gill1109
- Mathematical Statistician
**Posts:**1682**Joined:**Tue Feb 04, 2014 10:39 pm**Location:**Leiden

gill1109 wrote:The subtractions aa = (a - a) and bb = (b - b) mean that CA and CB contain values -1, 0 and +1, and these values go into AliceD and BobD too. This means that when you count joint outcomes pPP, pPN, pNP, pNN you only count the +/-1's. The claim "No Events are Dropped" is not quite true. They are not explicitly dropped. But they are not counted.

While these subtractions are indeed the culprits, the mechanism in Fred's latest attempt is not quite like you describe. The variables a and b are not detection results, but detector angles. So, if the hidden variable satisfy a certain condition the detector angle is simply set to zero. This is of course absurd, since the setting of the detectors should not depend on the value of the hidden variable.

- Heinera
**Posts:**699**Joined:**Thu Feb 06, 2014 1:50 am

Heinera wrote:gill1109 wrote:The subtractions aa = (a - a) and bb = (b - b) mean that CA and CB contain values -1, 0 and +1, and these values go into AliceD and BobD too. This means that when you count joint outcomes pPP, pPN, pNP, pNN you only count the +/-1's. The claim "No Events are Dropped" is not quite true. They are not explicitly dropped. But they are not counted.

While these subtractions are indeed the culprits, the mechanism in Fred's latest attempt is not quite like you describe. The variables a and b are not detection results, but detector angles. So, if the hidden variable satisfy a certain condition the detector angle is simply set to zero. This is of course absurd, since the setting of the detectors should not depend on the value of the hidden variable.

Thanks! You are better at reading Mathematica than I am. (I am pretty lousy at checking other people's code. Bad enough at checking my own).

- gill1109
- Mathematical Statistician
**Posts:**1682**Joined:**Tue Feb 04, 2014 10:39 pm**Location:**Leiden

Heinera wrote:gill1109 wrote:The subtractions aa = (a - a) and bb = (b - b) mean that CA and CB contain values -1, 0 and +1, and these values go into AliceD and BobD too. This means that when you count joint outcomes pPP, pPN, pNP, pNN you only count the +/-1's. The claim "No Events are Dropped" is not quite true. They are not explicitly dropped. But they are not counted.

While these subtractions are indeed the culprits, the mechanism in Fred's latest attempt is not quite like you describe. The variables a and b are not detection results, but detector angles. So, if the hidden variable satisfy a certain condition the detector angle is simply set to zero. This is of course absurd, since the setting of the detectors should not depend on the value of the hidden variable.

Yes, that is what it looks like at first glance. And no events are dropped. What happens is all the events during the constraints are at 0 lab frame angle and average to -1. Well, at 360 degrees in the plot since I shifted everything by 2pi since theta is used as an index.

However, this might be subject to some interpretation. It is not the hidden variable that necessarily "causes" the a and b vectors to become null vectors during the constraints. It could be S^3 topological action. Of course I will need to show the math of how that works then. That is the part that I am stuck on right now. Another option to consider is that the topological action needs to be in the "then" function part and then a and b don't become null vectors.

.

- FrediFizzx
- Independent Physics Researcher
**Posts:**1732**Joined:**Tue Mar 19, 2013 7:12 pm**Location:**N. California, USA

FrediFizzx wrote:Heinera wrote:

While these subtractions are indeed the culprits, the mechanism in Fred's latest attempt is not quite like you describe. The variables a and b are not detection results, but detector angles. So, if the hidden variable satisfy a certain condition the detector angle is simply set to zero. This is of course absurd, since the setting of the detectors should not depend on the value of the hidden variable.

Yes, that is what it looks like at first glance. And no events are dropped. What happens is all the events during the constraints are at 0 lab frame angle and average to -1. Well, at 360 degrees in the plot since I shifted everything by 2pi since theta is used as an index.

However, this might be subject to some interpretation. It is not the hidden variable that necessarily "causes" the a and b vectors to become null vectors during the constraints. It could be S^3 topological action. Of course I will need to show the math of how that works then. That is the part that I am stuck on right now. Another option to consider is that the topological action needs to be in the "then" function part and then a and b don't become null vectors.

.

OK, so in a sense no events are dropped. They are all represented somewhere in your graph. But the events which go to make up the value of the curve at any setting difference theta not equal to zero, are only those events where the difference in the settings was theta *and* both particles were detected. Not *all* the events where the difference in settings was theta.

You performed a non local operation: if either particle is not detected then the settings of both those particles are altered and the outcomes are altered too.

- gill1109
- Mathematical Statistician
**Posts:**1682**Joined:**Tue Feb 04, 2014 10:39 pm**Location:**Leiden

gill1109 wrote:FrediFizzx wrote:Yes, that is what it looks like at first glance. And no events are dropped. What happens is all the events during the constraints are at 0 lab frame angle and average to -1. Well, at 360 degrees in the plot since I shifted everything by 2pi since theta is used as an index.

However, this might be subject to some interpretation. It is not the hidden variable that necessarily "causes" the a and b vectors to become null vectors during the constraints. It could be S^3 topological action. Of course I will need to show the math of how that works then. That is the part that I am stuck on right now. Another option to consider is that the topological action needs to be in the "then" function part and then a and b don't become null vectors.

.

OK, so in a sense no events are dropped. They are all represented somewhere in your graph. But the events which go to make up the value of the curve at any setting difference theta not equal to zero, are only those events where the difference in the settings was theta *and* both particles were detected. Not *all* the events where the difference in settings was theta.

You performed a non local operation: if either particle is not detected then the settings of both those particles are altered and the outcomes are altered too.

All particles are detected so not sure what you mean here. Theta ends up being 0 only if both a and b are null vectors during the constraints. But theta can also be 0 not during the constraints if a and b are equal.

.

- FrediFizzx
- Independent Physics Researcher
**Posts:**1732**Joined:**Tue Mar 19, 2013 7:12 pm**Location:**N. California, USA

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