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Ok folks, are you ready for yet another simulation that shoots down Bell's theory? Of course you are. I've modified and enhanced John Reed's original Mathematica quaternion simulation to use full 3D vectors and no hidden variable that follows the GAViewer simulation here. The quaternions actually work better for the production calculation. Here is a PDF file of the Mathematica simulation,

EPRsims/prod_calc_quat2.pdf

Here is the notebook file,

EPRsims/prod_calc_quat2.nb

Of course the product calculation is exactly -a.b,



The blue is the product calculation data points and the red is the negative cosine curve. So, we have yet another completely local model that is a counter example to Bell's junk physics theory! Bam!
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Great work!

Chantal Roth also produced a quaternion simulation last year (in collaboration with me): http://rpubs.com/chenopodium/516072.

Her situation is cited as Reference [48] in my first IEEE Access paper: https://ieeexplore.ieee.org/stamp/stamp ... er=8836453.
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Joy Christian wrote:.
Great work!

Chantal Roth also produced a quaternion simulation last year (in collaboration with me): http://rpubs.com/chenopodium/516072.

Her situation is cited as Reference [48] in my first IEEE Access paper: https://ieeexplore.ieee.org/stamp/stamp ... er=8836453.
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Great! Of course. The quaternion algebra is the algebra of the Pauli spin matrices. This is a pretty way to do the standard QM calculations in the EPR-B model. No hidden variables. No event-by-event local outcomes.

The 2x2 complex matrices form an 8 real-dimensional associative, non-commutative, and unitary (there is a multiplicative unit element) algebra. It's called Cl(3, 0)(R). https://arxiv.org/pdf/1203.1504.pdf. "Does Geometric Algebra provide a loophole to Bell’s Theorem?" (with correction note).

Joy Christian wrote:.
Great work!

Chantal Roth also produced a quaternion simulation last year (in collaboration with me): http://rpubs.com/chenopodium/516072.

Her situation is cited as Reference [48] in my first IEEE Access paper: https://ieeexplore.ieee.org/stamp/stamp ... er=8836453.
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Thanks. Somehow I missed that one by Roth. Similar to what Reed did but hard to follow. Mine is different in that it works with no lambda +/-1 toggle. And the product calculation Da Ls Ls Db works right using quaternions.
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gill1109 wrote:
The 2x2 complex matrices form an 8 real-dimensional associative, non-commutative, and unitary (there is a multiplicative unit element) algebra. It's called Cl(3, 0)(R). https://arxiv.org/pdf/1203.1504.pdf. "Does Geometric Algebra provide a loophole to Bell’s Theorem?" (with correction note).

It should be noted that the arXiv preprint Gill has linked contains numerous elementary mathematical and conceptual mistakes. I have exposed all of his mistakes in the following papers:

(1) Refutation of Richard Gill's Argument Against my Disproof of Bell's Theorem, https://arxiv.org/abs/1203.2529,

(2) Macroscopic Observability of Fermionic Sign Changes: A Reply to Gill, https://arxiv.org/abs/1501.03393,

(3) Refutation of Scott Aaronson's Critique of my Disproof of Bells Theorem, https://www.academia.edu/38423874/Refut ... ls_Theorem.

You may wonder why do I care or bother responding to Gill's fallacious claims month after month, year after year. Well, because Gill has made so much negative noise about my work during the past ten years that all those who matter in the physics community --- namely, the peer-reviewers selected by physics journals --- think that my work has long been "canceled by Richard D. Gill", as Howard Wiseman (who was one of the peer-reviewers of my RSOS paper according to a blog post by Florin Moldoveanu) put it in his official referee report for RSOS. But Richard D. Gill has by no means "canceled" anything. All Gill has done during the past ten years is exposed his own extremely elementary mathematical and conceptual mistakes regarding my work.
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FrediFizzx wrote:

Joy Christian wrote:.
Great work!

Chantal Roth also produced a quaternion simulation last year (in collaboration with me): http://rpubs.com/chenopodium/516072.

Her situation is cited as Reference [48] in my first IEEE Access paper: https://ieeexplore.ieee.org/stamp/stamp ... er=8836453.
.

Thanks. Somehow I missed that one by Roth. Similar to what Reed did but hard to follow. Mine is different in that it works with no lambda +/-1 toggle. And the product calculation Da Ls Ls Db works right using quaternions.
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Well, I take back the part about the product calculation working right. It works correctly in GAViewer also. I had never tried the method that I used on this simulation in GAViewer. Just tried it and it works.

BTW, both simulations do work with the lambda +/-1 toggle also. It is not excluded. But without it you can switch to the singlet vector being the HV.
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FrediFizzx wrote:
BTW, both simulations do work with the lambda +/-1 toggle also. It is not excluded. But without it you can switch to the singlet vector being the HV.

I suspect you don't need lambda = +/- toggle because you are making the settings a and b random variables. In that case, a x b term would vanish automatically.

If you keep the settings a and b fixed, as Alice and Bob are allowed to do, then you may need lambda = +/- toggle to make the a x b term vanish.
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Joy Christian wrote:

FrediFizzx wrote:
BTW, both simulations do work with the lambda +/-1 toggle also. It is not excluded. But without it you can switch to the singlet vector being the HV.

I suspect you don't need lambda = +/- toggle because you are making the settings a and b random variables. In that case, a x b term would vanish automatically.

If you keep the settings a and b fixed, as Alice and Bob are allowed to do, then you may need lambda = +/- toggle to make the a x b term vanish.
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Well, that is another difference. Perhaps true if you go to a S^3 model. This simulation is a R^3 model so the a x b term can be set to zero as unphysical since a and b are physically separated.
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FrediFizzx wrote:

FrediFizzx wrote:

Joy Christian wrote:.
Great work!

Chantal Roth also produced a quaternion simulation last year (in collaboration with me): http://rpubs.com/chenopodium/516072.

Her situation is cited as Reference [48] in my first IEEE Access paper: https://ieeexplore.ieee.org/stamp/stamp ... er=8836453.
.

Thanks. Somehow I missed that one by Roth. Similar to what Reed did but hard to follow. Mine is different in that it works with no lambda +/-1 toggle. And the product calculation Da Ls Ls Db works right using quaternions.
.

Well, I take back the part about the product calculation working right. It works correctly in GAViewer also. I had never tried the method that I used on this simulation in GAViewer. Just tried it and it works.

BTW, both simulations do work with the lambda +/-1 toggle also. It is not excluded. But without it you can switch to the singlet vector being the HV.
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Exactly. The state vector of the two particles is the original hidden variable, as Bell and many others pointed out, long, long, ago. But it is not a *local* hidden variable.

Blah! Blah! Blah!

I've made a simplification improvement to the Mathematica simulation. I temporally forgot that the polarizer action could be simplified to the Sign function. So now the A and B functions and product calculation are more consistent.

EPRsims/prod_calc_quat4.pdf
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FrediFizzx wrote:Blah! Blah! Blah!

I've made a simplification improvement to the Mathematica simulation. I temporally forgot that the polarizer action could be simplified to the Sign function. So now the A and B functions and product calculation are more consistent.

EPRsims/prod_calc_quat4.pdf
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The pdf doesn’t download, Fred. Can you check if it really there?

gill1109 wrote:

FrediFizzx wrote:Blah! Blah! Blah!

I've made a simplification improvement to the Mathematica simulation. I temporally forgot that the polarizer action could be simplified to the Sign function. So now the A and B functions and product calculation are more consistent.

EPRsims/prod_calc_quat4.pdf
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The pdf doesn’t download, Fred. Can you check if it really there?

I just downloaded it. It works for me. Anyone else having problems downloading the PDF?
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FrediFizzx wrote:

gill1109 wrote:

FrediFizzx wrote:Blah! Blah! Blah!

I've made a simplification improvement to the Mathematica simulation. I temporally forgot that the polarizer action could be simplified to the Sign function. So now the A and B functions and product calculation are more consistent.

EPRsims/prod_calc_quat4.pdf
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The pdf doesn’t download, Fred. Can you check if it really there?

I just downloaded it. It works for me. Anyone else having problems downloading the PDF?
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Ah, it was my internet connection! Hotel WiFi blocked it. On 4G it comes in a flash.

The forum uses http, not https. I suspect that is the cause.

Here is the result of a simulation using the A and B outcomes that is quite simple. It only uses

A = -Sign[Cos[a Degree]];
B = Sign[Cos[b Degree]];

With the -1 factor from the singlet on the A function. Of course that is also necessary for anti-correlation when a=b.



Keep in mind that the plot has been shifted by 2pi for indexing purposes so that 0 degrees is actually at 360. Everything to the left of that is actually negative. Not much of it is very linear. We see a break at about 90 degrees to 180 where is goes very nonlinear. Then nonlinear all the was to 270. Then all -1's to 360. And of course the negative side is the mirror image.
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FrediFizzx wrote:Here is the result of a simulation using the A and B outcomes that is quite simple. It only uses

A = -Sign[Cos[a Degree]];
B = Sign[Cos[b Degree]];

With the -1 factor from the singlet on the A function. Of course that is also necessary for anti-correlation when a=b.

... strange plot ...

Keep in mind that the plot has been shifted by 2pi for indexing purposes so that 0 degrees is actually at 360. Everything to the left of that is actually negative. Not much of it is very linear. We see a break at about 90 degrees to 180 where is goes very nonlinear. Then nonlinear all the was to 270. Then all -1's to 360. And of course he negative side is the mirror image.
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Very strange. Will you also post your Mathematica code?

gill1109 wrote:

FrediFizzx wrote:Here is the result of a simulation using the A and B outcomes that is quite simple. It only uses

A = -Sign[Cos[a Degree]];
B = Sign[Cos[b Degree]];

With the -1 factor from the singlet on the A function. Of course that is also necessary for anti-correlation when a=b.

... strange plot ...

Keep in mind that the plot has been shifted by 2pi for indexing purposes so that 0 degrees is actually at 360. Everything to the left of that is actually negative. Not much of it is very linear. We see a break at about 90 degrees to 180 where is goes very nonlinear. Then nonlinear all the was to 270. Then all -1's to 360. And of course he negative side is the mirror image.
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Very strange. Will you also post your Mathematica code?

Strange indeed. I was expecting the straight line triangle correlation and got this instead. The idea comes from the fact that in the quaternion sim, the singlet vector only provides a -1 and all the action is actually in the a and b settings toggling plus or minus 1. There is not much more to the code other than those settings,

a = RandomInteger[{1, 360}];
b = RandomInteger[{1, 360}];

Just one degree increments in degrees from 1 to 360 randomly chosen. Makes it easier to do the theta = (b - a) calculation.
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I think we need to see the entire code.

gill1109 wrote:I think we need to see the entire code.

It's too messy and I don't feel like cleaning it up for something so simple. You can easily program this up in R to check it.
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FrediFizzx wrote:

gill1109 wrote:I think we need to see the entire code.

It's too messy and I don't feel like cleaning it up for something so simple. You can easily program this up in R to check it

I know a theorem from machine learning and AI (a distributed computing no-go theorem) which tells me not to try...

gill1109 wrote:

FrediFizzx wrote:

gill1109 wrote:I think we need to see the entire code.

It's too messy and I don't feel like cleaning it up for something so simple. You can easily program this up in R to check it

I know a theorem from machine learning and AI (a distributed computing no-go theorem) which tells me not to try...

Suit yourself. I have given all the info necessary for anyone to do a sim on a different program.

a = RandomInteger[{1, 360}]; Random angle in one degree increments
b = RandomInteger[{1, 360}];
A = -Sign[Cos[a Degree]];
B = Sign[Cos[b Degree]];

If QM could do event by event outcome prediction is this perhaps the prediction it would give?
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