Metric Topology and the Origins of Quantum Correlations

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Expand view Topic review: Metric Topology and the Origins of Quantum Correlations

Re: Metric Topology and the Origins of Quantum Correlations

Post by Joy Christian » Wed Aug 26, 2015 7:32 am

FrediFizzx wrote:
Joy Christian wrote:A rigorous experiment confirming the predictions of my local-realistic 3-sphere model has been finally performed. :D

http://arxiv.org/abs/1508.05949.

And here is one of the simulations of my 3-sphere model discussed above (see also http://rpubs.com/jjc/105450).

The theoretical analysis can be found here: http://arxiv.org/abs/1405.2355.

That is great that we have further experimental validation that the predictions of your model and quantum theory are correct. Very clever experimenters but too bad they are suffering under the mainstream delusions about local realistic models via Bell. And of course, they don't really violate Bell-CHSH since their expectation terms are independent. They are not going to release the raw data until after publication but it probably won't take long to get published.

This experiment finally proves that we do indeed live in a quaternionic 3-sphere!

Re: Metric Topology and the Origins of Quantum Correlations

Post by FrediFizzx » Wed Aug 26, 2015 12:01 am

Joy Christian wrote:A rigorous experiment confirming the predictions of my local-realistic 3-sphere model has been finally performed. :D

http://arxiv.org/abs/1508.05949.

And here is one of the simulations of my 3-sphere model discussed above (see also http://rpubs.com/jjc/105450).

The theoretical analysis can be found here: http://arxiv.org/abs/1405.2355.

That is great that we have further experimental validation that the predictions of your model and quantum theory are correct. Very clever experimenters but too bad they are suffering under the mainstream delusions about local realistic models via Bell. And of course, they don't really violate Bell-CHSH since their expectation terms are independent. They are not going to release the raw data until after publication but it probably won't take long to get published.

Re: Metric Topology and the Origins of Quantum Correlations

Post by Joy Christian » Tue Aug 25, 2015 10:33 pm

A rigorous experiment confirming the predictions of my local-realistic 3-sphere model has been finally performed. :D

http://arxiv.org/abs/1508.05949.

And here is one of the simulations of my 3-sphere model discussed above (see also http://rpubs.com/jjc/105450).

The theoretical analysis can be found here: http://arxiv.org/abs/1405.2355.

Re: Metric Topology and the Origins of Quantum Correlations

Post by Joy Christian » Mon Aug 24, 2015 6:03 am

There have been a lot of noise and suspicion about the so-called "zero outcomes" in the simulations like mine discussed above and Michel's "EPR simple", so I have written up another simple version of my simulation to make it plain that there are simply no "zero outcomes" in these simulations: http://rpubs.com/jjc/105450.

The crucial point is that one can separate out the "event-ready preparation" of the initial states of the spin from the computation of the correlation, as I have done.

Re: Metric Topology and the Origins of Quantum Correlations

Post by FrediFizzx » Sat Aug 22, 2015 10:19 am

FrediFizzx wrote:Here is a link to a PDF file of the Mathematica notebook file after running it on my Mathematica. Probably easier to read.

download/Reed_Bell_EPR2.pdf

Thanks John for emailing me the notebook file. Let me know if anything is wrong in the PDF at the link. For those that have Mathematica, here is a link to the notebook file.

download/Reed_Bell_EPR.nb

Here is a link to the notePad.txt data file for those that might be interested in running the Physics Today section of John's Mathematica code.

download/notePad.txt

A new topic was created for this simulation program.

viewtopic.php?f=6&t=192#p5245

Re: Metric Topology and the Origins of Quantum Correlations

Post by Joy Christian » Sat Aug 22, 2015 7:34 am

jreed wrote:The option EPRsimple which is Michel's version can also be made to resemble the quantum results by specifying removeZeros=True in the program.

That makes sense, because phenomenologically the only significant difference between EPR simple and my simulation is the distribution function f(s), which is slightly "non-exact" in the EPR simple case. Conceptually, however, there is a considerable difference between the two. For example, in my case I do not like your choice of the words "removeZeros" in the program, because that gives a wrong impression about "zeros" in the corresponding analytical model: http://arxiv.org/abs/1405.2355.

In any event, it would be interesting to study all the cases you have studied with "removeZeros = True", especially in the case of the experimental data you have used.

Re: Metric Topology and the Origins of Quantum Correlations

Post by jreed » Sat Aug 22, 2015 5:48 am

The code is in PDF format. I copied it and will paste it here:[/quote]
Here is a link to a PDF file of the Mathematica notebook file after running it on my Mathematica. Probably easier to read.

download/Reed_Bell_EPR2.pdf

Thanks John for emailing me the notebook file. Let me know if anything is wrong in the PDF at the link. For those that have Mathematica, here is a link to the notebook file.

download/Reed_Bell_EPR.nb[/quote]

Here are a couple more things:

If you generate a copy of my program using the CDF option in Mathematica and make it available, anyone can read and execute it by downloading the program CDF Player from Wolfram Research. It's free and will execute a CDF file.

The option EPRsimple which is Michel's version can also be made to resemble the quantum results by specifying removeZeros=True in the program.

Re: Metric Topology and the Origins of Quantum Correlations

Post by Joy Christian » Sat Aug 22, 2015 2:02 am

I think this little illustration I made elsewhere on this forum is a very good pedagogical device to illustrate the basic relationship between the R^3 and S^3 models:

viewtopic.php?f=6&t=55&p=4911#p4908

And here is the official website of the Flat Earth Society, which Michel has kindly linked elsewhere on this forum:

http://www.theflatearthsociety.org/cms/

Needless to say, in my view the Bell believers are the modern day flat-earthers. As long as they cannot liberate themselves from R^3, they are unlikely to get S^3.

PS: Albert Jan Wonnink has also made a similar point about my S^3 model on his website: http://challengingbell.blogspot.co.uk/2 ... tians.html

Re: Metric Topology and the Origins of Quantum Correlations

Post by FrediFizzx » Fri Aug 21, 2015 9:39 pm

Joy Christian wrote:But to us these results are not surprising.

Well, I spent some time trying to figure out the procedure to make it work right. Thanks to John Reed for figuring it out.

Re: Metric Topology and the Origins of Quantum Correlations

Post by Joy Christian » Fri Aug 21, 2015 8:58 pm

FrediFizzx wrote:
jreed wrote:Joy's simulation, being discussed here:
Cross correlation is zero
Bell violated
CHSH = 2.395

Comments:
Joy's simulation and quantum mechanical simulation appear very close.
EPR simple looks very much like the 85% loophole simulation.

John Reed

OK, Vongehr specified that n = 800 for his QRC. I have set Joy's 3D S^3 section to n = 800 and the results are consistently like this,

During evaluation of In[141]:= 3D simulation

Out[142]= "correlation at equal angles is correct and equals zero"

Out[143]= {"Bell's inequality is violated, NU1 > NU3+NE2! ", "NU1, \NU3 + NE2 = ", 90, 54}

Out[145]= {2.44081, "CHSH inequality (can not be >2) is violated!"}

Joy's 3-sphere model simulation does beat the QRC!

Of course the Bell fans will claim "loopholes" because they simply can't get out of their R^3 thinking to see what is actually going on in Nature.

But to us these results are not surprising. I also cannot see how anyone can claim "loopholes" when every single particle [ or the initial state (e, s)] is being counted in the following manifestly local-realistic prescription. I have explicitly shown in the corresponding analytical model that there is one-to-one correspondence between the initial states (e, s) and the measurement events A = +/-1 and B = +/-1 within the 3-sphere model. For every single pair (e, s) there is a pair (A, B), and vice versa:

Code: Select all
A = +sign(g(a,e,s))  # Alice's measurement results A(a, e, s) = +/-1
         
B = -sign(g(b,e,s))  # Bob's measurement results B(b, e, s) = -/+1
       
N = length((A*B)[A & B]) # Number of all possible events observed in S^3
       
corrs[i,j] = sum(A*B)/N  # Product moment correlation coefficient E(a, b)

Clearly, a measurement event cannot occur if there does not exist a state which can bring about that event. One cannot detect that which is not there to begin with.

Re: Metric Topology and the Origins of Quantum Correlations

Post by FrediFizzx » Fri Aug 21, 2015 5:56 pm

jreed wrote:Joy's simulation, being discussed here:
Cross correlation is zero
Bell violated
CHSH = 2.395

Comments:
Joy's simulation and quantum mechanical simulation appear very close.
EPR simple looks very much like the 85% loophole simulation.

John Reed

OK, Vongehr specified that n = 800 for his QRC. I have set Joy's 3D S^3 section to n = 800 and the results are consistently like this,

During evaluation of In[141]:= 3D simulation

Out[142]= "correlation at equal angles is correct and equals zero"

Out[143]= {"Bell's inequality is violated, NU1 > NU3+NE2! ", "NU1, \NU3 + NE2 = ", 90, 54}

Out[145]= {2.44081, "CHSH inequality (can not be >2) is violated!"}

Joy's 3-sphere model simulation does beat the QRC!

Of course the Bell fans will claim "loopholes" because they simply can't get out of their R^3 thinking to see what is actually going on in Nature.

Re: Metric Topology and the Origins of Quantum Correlations

Post by FrediFizzx » Fri Aug 21, 2015 4:43 pm

jreed wrote:
FrediFizzx wrote:
Joy Christian wrote:Thanks, John.

Can you please provide a link to your code? Or you can post it here in some form if you wish. I don't know Mathematica, but at least Fred does.

Yes, you can just copy and paste the code here by using the Code function in the posting interface.
Code: Select all
Put your code here

Thanks.


The code is in PDF format. I copied it and will paste it here:

Here is a link to a PDF file of the Mathematica notebook file after running it on my Mathematica. Probably easier to read.

download/Reed_Bell_EPR2.pdf

Thanks John for emailing me the notebook file. Let me know if anything is wrong in the PDF at the link. For those that have Mathematica, here is a link to the notebook file.

download/Reed_Bell_EPR.nb

Re: Metric Topology and the Origins of Quantum Correlations

Post by jreed » Fri Aug 21, 2015 4:22 pm

FrediFizzx wrote:
Joy Christian wrote:
jreed wrote:Joy's simulation and quantum mechanical simulation appear very close.
EPR simple looks very much like the 85% loophole simulation.

John Reed

Thanks, John.

Can you please provide a link to your code? Or you can post it here in some form if you wish. I don't know Mathematica, but at least Fred does.

Yes, you can just copy and paste the code here by using the Code function in the posting interface.
Code: Select all
Put your code here

Thanks.


The code is in PDF format. I copied it and will paste it here:

Code: Select all
In[1]:= (* Latest version, Aug 21, 2015 *)
In[2]:= spin = 1 / 2;
If[spin ⩵ 1 / 2, δ = π / 4];
If[spin ⩵ 1, δ = π / 8];
(* Angle setting for detectors. All will be set at a multiple of δ *)
a1 = 0; a2 = 3 δ;
b1 = 0;
b2 = 2 δ;
In[7]:= (* Remove zero events function
This function does the same thing as the R function length((A*B}[A & B])
which only computes the product if both elements are non zero *)
removeZero[α1_, β1_, A1_, B1_] := Module[{key, k},
{ key = Abs[A1 B1];
k = 1;
Do[{If[key[[i]] ≠ 0, {A[[k]] = A1[[i]],
B[[k]] = B1[[i]], α[[k]] = α1[[i]], β[[k]] = β1[[i]], k++}]}, {i, n}];
nn = k - 1;
A = Take[A, nn];
B = Take[B, nn];
α = Take[α, nn];
β = Take[β, nn];
n = nn};]
In[8]:= (* Hidden variables section, like Sascha's program *)
hiddenVar := {
n = 10 000;
α = RandomChoice[{a1, a2}, n]; (* Alice's angles *)
β = RandomChoice[{b1, b2}, n]; (* Bob's angles *)
λ = RandomChoice[{0, 1}, {n, 3}]; (* a hidden variable *)
A = Table[If[α[[j]] ⩵ 0, 1 - λ[[j, 2]], λ[[j, 1]]], {j, n}] ;
(* Alice's measurements *)
B = Table[λ[[j, If[β[[j]] == 0, 2, 3]]], {j, n}]; (* Bob's measurements *)
remove = False;
id = "Hidden variables particles selected";}
In[9]:= (* quantum section following Sascha's version *)
quantum := {
n = 10 000;
α = RandomChoice[{a1, a2}, n]; (* Alice's angles *)
β = RandomChoice[{b1, b2}, n]; (* Bob's angles *)
A = RandomChoice[{0, 1}, n];
B = Table[If[RandomReal[] < Sin[spin (β[[j]] - α[[j]])]^2, A[[j]], 1 - A[[j]]], {j, n}];
remove = False;
id = "Quantum particles selected";}
In[10]:= (* Loophole50 section Expect 50% violations of Bell and CSHS*)
loophole50 := {
n = 10 000;
α = RandomChoice[{a1, a2}, n]; (* Alice's angles *)
β = RandomChoice[{b1, b2}, n]; (* Bob's angles *)
λ = RandomChoice[{0, 1}, {n, 3}];
(* Hidden variable *)
i = Table[4 λ[[j, 1]] + 2 λ[[j, 2]] + λ[[j, 3]], {j, n}];
Do[{
If[i[[j]] ⩵ 2 || i[[j]] ⩵ 5, λ[[j, 1]] = 1 - λ[[j, 1]]]}, {j, n}];
A = Table[If[α[[j]] ⩵ 0, 1 - λ[[j, 2]], λ[[j, 1]]], {j, n}];
B = Table[λ[[j, If[β[[j]] ⩵ 0, 2, 3]]], {j, n}];
remove = False;
id = "Loophole50 selected: 50% Bell and CHSH violations";}
In[11]:= (* Loophole85 section Expect 85% violations of Bell and CSHS*)
loophole85 := {
n = 10 000;
α = RandomChoice[{a1, a2}, n]; (* Alice's angles *)
β = RandomChoice[{b1, b2}, n]; (* Bob's angles *)
λ = RandomChoice[{0, 1}, {n, 3}];
(* Hidden variable *)
i = Table[4 λ[[j, 1]] + 2 λ[[j, 2]] + λ[[j, 3]], {j, n}];
Do[{
If[i[[j]] ⩵ 2 || i[[j]] ⩵ 5, λ[[j, 1]] = 1 - λ[[j, 1]]]}, {j, n}];
A = Table[If[α[[j]] ⩵ 0, If[i[[j]] ⩵ 1, λ[[j, 2]], 1 - λ[[j, 2]]], λ[[j, 1]]], {j, n}];
B = Table[λ[[j, If[β[[j]] ⩵ 0, 2, 3]]], {j, n}];
remove = False;
id = "Loophole85 selected: Expect 85% Bell and CHSH violations";}
In[12]:= (* EPRsimple section *)
EPRsimple := {
n = 10 000;
ϕa = RandomReal[{0, 2 π}, n]; (* E vector *)
α = RandomChoice[{a1, a2}, n]; (* Alice's angles *)
β = RandomChoice[{b1, b2}, n]; (* Bob's angles *)
If[spin ⩵ 1 / 2, ϕb = ϕa + π , ϕb = ϕa + π / 2];
λ = Sin[RandomReal[{0, π / 2}, n]]^2 / 2;
A = Table[
If[Abs[Cos[(α[[j]] - ϕa[[j]])]] > λ[[j]], Sign[Cos[(α[[j]] - ϕa[[j]])]], 0], {j, n}];
B = Table[If[Abs[Cos[(β[[j]] - ϕb[[j]])]] > λ[[j]],
Sign[Cos[(β[[j]] - ϕb[[j]])]], 0], {j, n}];
remove = True;
id = "EPRsimple selected";}
2 Bell EPR.nb
In[13]:= (* Joy's 3D simulation *)
EPR3D := {
n = 10 000;
r = RandomReal[{0, 2 π}, n];
z = RandomReal[{-1, 1}, n];
h = Sqrt[1 - z^2];
e = Table[{h[[i]] Cos[r[[i]]], h[[i]] Sin[r[[i]]], z[[i]]}, {i, n}];
s = RandomReal[{0, π}, n];
λ = -1 + 2 / Sqrt[1 + 3 s / π];
α = RandomChoice[{a1, a2}, n]; (* Alice's angles *)
β = RandomChoice[{b1, b2}, n]; (* Bob's angles *)
αVect = Table[{Cos[α[[i]]], Sin[α[[i]]], 0}, {i, n}];
βVect = Table[{Cos[β[[i]]], Sin[β[[i]]], 0}, {i, n}];
A = ConstantArray[0, n];
B = ConstantArray[0, n];
Do[{
If[Abs[αVect[[i]].e[[i]]] > λ[[i]], A[[i]] = Sign[αVect[[i]].e[[i]]]];
If[Abs[βVect[[i]].e[[i]]] > λ[[i]], B[[i]] = -Sign[βVect[[i]].e[[i]]]];};,
{i, n}];
remove = True;
id = "3D simulation ";}
Bell EPR.nb 3
In[14]:= (* experimental data section from Physics Today, April 1985
You won't be able to execute this version since you won't have the file
of experimental data which I pulled from this article.
The experimental data has 563 observations and gives a cross correlation of 0,
does not violate Bell and has a CHSH of 2.29 *)
experiment := {
NotebookDirectory[];
SetDirectory["C:\\Users\\John\\Desktop\\Bell's Theorem\\EPR\\"];
file = Import["notePad.txt", "List"];
n = Length[file];
α = ConstantArray[0, n];
β = ConstantArray[0, n];
A = ConstantArray[0, n];
B = ConstantArray[0, n];
δ = π / 8;
Do[{
entry = Characters[file[[j]]];
a1 = ToExpression[Part[entry, 1]];
If[a1 != 1 && a1 != 2 && a1 ≠ 3, Break];
Switch[a1, 1, α[[j]] = 0, 2, α[[j]] = 2 δ, 3, α[[j]] = 3 δ];
b1 = ToExpression[Part[entry, 2]];
If[b1 != 1 && b1 != 2 && b1 != 3, Break];
Switch[b1, 1, β[[j]] = 0, 2, β[[j]] = 2 δ, 3, β[[j]] = 3 δ];
idA = Part[entry, 3];
If[idA ≠ "G" && idA ≠ "R", {Print["error in A ", j]; Break}];
If[idA ⩵ "G", A[[j]] = 1, A[[j]] = 0];
idB = Part[entry, 4];
If[idB ≠ "G" && idB ≠ "R", {Print["error in B ", j]; Break}];
If[idB ⩵ "G", B[[j]] = 0, B[[j]] = 1];
}, {j, 1, n}];
remove = False;
id = "experimental data selected";
}
4 Bell EPR.nb
In[15]:= analysis := 
N0 = 
j=1
Length[α]
If[Abs[β[[j]] - α[[j]]] ⩵ 0, 1, 0];
N1 = 
j=1
Length[α]
If[Abs[β[[j]] - α[[j]]] ⩵ δ, 1, 0];
N2 = 
j=1
Length[α]
If[Abs[β[[j]] - α[[j]]] ⩵ 2 δ, 1, 0];
N3 = 
j=1
Length[α]
If[Abs[β[[j]] - α[[j]]] ⩵ 3 δ, 1, 0] ;
NE0 = 
j=1
Length[A]
If[Abs[β[[j]] - α[[j]]] ⩵ 0 && A[[j]] ⩵ B[[j]], 1, 0];
NE1 = 
j=1
Length[A]
If[Abs[β[[j]] - α[[j]]] ⩵ δ && A[[j]] ⩵ B[[j]], 1, 0];
NE2 = 
j=1
Length[A]
If[Abs[β[[j]] - α[[j]]] ⩵ 2 δ && A[[j]] ⩵ B[[j]], 1, 0];
NE3 = 
j=1
Length[A]
If[Abs[β[[j]] - α[[j]]] ⩵ 3 δ && A[[j]] ⩵ B[[j]], 1, 0];
NU0 = 
j=1
Length[A]
If[Abs[β[[j]] - α[[j]]] ⩵ 0 && A[[j]] ≠ B[[j]], 1, 0];
NU1 = 
j=1
Length[A]
If[Abs[β[[j]] - α[[j]]] ⩵ δ && A[[j]] ≠ B[[j]], 1, 0];
NU2 = 
j=1
Length[A]
If[Abs[β[[j]] - α[[j]]] ⩵ 2 δ && A[[j]] ≠ B[[j]], 1, 0];
NU3 = 
j=1
Length[A]
If[Abs[β[[j]] - α[[j]]] ⩵ 3 δ && A[[j]] ≠ B[[j]], 1, 0];
In[16]:= (* methods for the particle generation:
quantum - quantum mechanical calculation
hiddenVar - hidden variables
loophole50 - detection loophole giving 50% violations
loophole85 - detection loophole giving 85% violations
EPRsimple - EPR simple algorithm
EPR3D - Joy's 3D siimulation
experiment - Data from "Is the Moon There..."
*)
Bell EPR.nb 5
In[17]:= (* set up run time parameters:*)
Clear[A, B, α, β, λ, n];
EPR3D; (* method to use, see above *)
removeZeros = True; (* the removal of zero data is optional for some methods *)
If[removeZeros && remove, removeZero[α, β, A, B]];
analysis;
In[21]:= Print["Number of arrivals in each group: ",
"N0=" , N0, " N1=", N1, " N2=", N2, " N3=", N3]
Number of arrivals in each group: N0=1752 N1=1268 N2=1232 N3=1310
In[22]:= Print["Equal correlations: " , "NE0=" ,
NE0, " NE1=", NE1, " NE2=", NE2, " NE3=", NE3]
Equal correlations: NE0=0 NE1=165 NE2=619 NE3=1120
In[23]:= Print["Unequal correlations: ", "NU0=" ,
NU0, " NU1=", NU1, " NU2=", NU2, " NU3=", NU3]
Unequal correlations: NU0=1752 NU1=1103 NU2=613 NU3=190
In[24]:= (* Analysis Section *)
Print[id];
If[NE0 > 0, N[100 - 100 * NE0 / N0]
"% of correct correlation. Model fails to describe correlation
correctly when Alice and Bob happen to measure with the same angle.",
"correlation at equal angles is correct and equals zero"]
If[NU3 + NE2 < NU1,
{"Bell's inequality is violated, NU1 > NU3+NE2! ", "NU1, NU3 + NE2 = ", NU1, NU3 + NE2},
{"Bell is not violated, NU1 < NU3+NE2. ", " NU1, NU3 + NE2 = ", NU1, NU3 + NE2}]
CHSH := {
E0 := (NE0 - NU0) / N0;
E1 := (NE1 - NU1) / N1;
E2 := (NE2 - NU2) / N2;
E3 := (NE3 - NU3) / N3;
CHV = N[Max[Abs[E0 + E1 + E2 - E3],
Abs[E0 + E1 - E2 + E3], Abs[E0 - E1 + E2 + E3], Abs[E1 + E2 + E3 - E0]]],
If[CHV > 2, "CHSH inequality (can not be >2) is violated!",
"CHSH inequality (is not >2) is not violated."]};
CHSH (* this prints out the important results of the run *)
3D simulation
Out[25]= correlation at equal angles is correct and equals zero
Out[26]= {Bell's inequality is violated, NU1 > NU3+NE2! , NU1, NU3 + NE2 = , 1103, 809}
Out[28]= {2.4448, CHSH inequality (can not be >2) is violated!}
6 Bell EPR.nb

Re: Metric Topology and the Origins of Quantum Correlations

Post by FrediFizzx » Fri Aug 21, 2015 10:33 am

Joy Christian wrote:
jreed wrote:Joy's simulation and quantum mechanical simulation appear very close.
EPR simple looks very much like the 85% loophole simulation.

John Reed

Thanks, John.

Can you please provide a link to your code? Or you can post it here in some form if you wish. I don't know Mathematica, but at least Fred does.

Yes, you can just copy and paste the code here by using the Code function in the posting interface.
Code: Select all
Put your code here

Thanks.

Re: Metric Topology and the Origins of Quantum Correlations

Post by minkwe » Fri Aug 21, 2015 8:26 am

jreed wrote:You might find the following of interest in regards to this simulation. I've just finished a Mathematica program that can simulate quantum experiments, hidden variable experiments, several hidden variable with loopholes, Michel's EPR simple, and Joy's simulation being discussed here. Some of the Mathematica program comes from Sascha Vongehr's Randi challenge. I've corrected several things in that program and added a lot.

The simulations all use the same two sets of angles: {0, 135} and {0,90}. The simulations involve random choices of the detector angles, and random values of the spin vectors. I use 10,000 trials. Here are some results:

quantum mechanical calculation:
Cross correlation at zero lag is 0
Bell violated
CHSH violated at 2.43 (can't be greater than 2)

Hidden variables:
Cross correlation is 0
Bell not violated
CHSH = 1.07, not violated

Hidden variables with 50% loophole:
Cross correlation is 0
Bell violated (after several runs)
CHSH = 2.016, violated

Hidden variables with 85% loophole:
Cross correlation is 87% correct
Bell violated
CHSH = 1.98, not violated

EPR simple:
Cross correlation is 83% correct
Bell violated
CHSH = 1.96

Joy's simulation, being discussed here:
Cross correlation is zero
Bell violated
CHSH = 2.395

Comments:
Joy's simulation and quantum mechanical simulation appear very close.
EPR simple looks very much like the 85% loophole simulation.

John Reed

You will have to provide more details about what you are doing. As it stands your description is as clear as mud to me.

Re: Metric Topology and the Origins of Quantum Correlations

Post by Joy Christian » Fri Aug 21, 2015 7:27 am

jreed wrote:Joy's simulation and quantum mechanical simulation appear very close.
EPR simple looks very much like the 85% loophole simulation.

John Reed

Thanks, John.

Can you please provide a link to your code? Or you can post it here in some form if you wish. I don't know Mathematica, but at least Fred does.

Re: Metric Topology and the Origins of Quantum Correlations

Post by jreed » Fri Aug 21, 2015 6:55 am

Joy Christian wrote:Since 2007 I have argued that the strong (or "quantum") correlations we observe in Nature are entirely topological effects, originating from the very topology of the physical space we live in [ cf. discussions in my book ; see also "Topology", by James R. Munkres (2000) ]. In other words, the so-called "quantum" correlations have nothing to do with the bizarre notions like "quantum entanglement", or "non-locality", or "non-reality", or "irreducible randomness", as some would have us believe.

Joy Christian


You might find the following of interest in regards to this simulation. I've just finished a Mathematica program that can simulate quantum experiments, hidden variable experiments, several hidden variable with loopholes, Michel's EPR simple, and Joy's simulation being discussed here. Some of the Mathematica program comes from Sascha Vongehr's Randi challenge. I've corrected several things in that program and added a lot.

The simulations all use the same two sets of angles: {0, 135} and {0,90}. The simulations involve random choices of the detector angles, and random values of the spin vectors. I use 10,000 trials. Here are some results:

quantum mechanical calculation:
Cross correlation at zero lag is 0
Bell violated
CHSH violated at 2.43 (can't be greater than 2)

Hidden variables:
Cross correlation is 0
Bell not violated
CHSH = 1.07, not violated

Hidden variables with 50% loophole:
Cross correlation is 0
Bell violated (after several runs)
CHSH = 2.016, violated

Hidden variables with 85% loophole:
Cross correlation is 87% correct
Bell violated
CHSH = 1.98, not violated

EPR simple:
Cross correlation is 83% correct
Bell violated
CHSH = 1.96

Joy's simulation, being discussed here:
Cross correlation is zero
Bell violated
CHSH = 2.395

Comments:
Joy's simulation and quantum mechanical simulation appear very close.
EPR simple looks very much like the 85% loophole simulation.

John Reed

Re: Metric Topology and the Origins of Quantum Correlations

Post by Joy Christian » Sun Aug 16, 2015 6:15 am

Ben6993 wrote:Won't the torsion effects be even more exotic in S^7 than in S^3, even for non-singlet electrons?
In my scenario, the "-obs" observer who has written L on his left hand might need to also write TOP on his forehead. When the observer changes to a different torsional space in S^7 he may notice that L ain't what it used to be (it now seems to be R) and TOP ain't what it used to be, too? Which would explain his new headache.

The intrinsic torsion within S^7 is indeed "more exotic" in S^7 than it is in S^3. Torsion is constant throughout S^3, whereas it varies from point to point within S^7, at least in the manner I have set things up. The non-associativity of octonions is replaced with variable torsion in my set up. But I think Fred's point is that we should not rely too much on intuitive arguments. While the general point you are making is valid, the details of your intuition may not be supported by the mathematics of S^7.

Re: Metric Topology and the Origins of Quantum Correlations

Post by Ben6993 » Sun Aug 16, 2015 2:12 am

Won't the torsion effects be even more exotic in S^7 than in S^3, even for non-singlet electrons?
In my scenario, the "-obs" observer who has written L on his left hand might need to also write TOP on his forehead. When the observer changes to a different torsional space in S^7 he may notice that L ain't what it used to be (it now seems to be R) and TOP ain't what it used to be, too? Which would explain his new headache.

Re: Metric Topology and the Origins of Quantum Correlations

Post by FrediFizzx » Sun Aug 16, 2015 12:27 am

Joy Christian wrote:
Ben6993 wrote:
Fred wrote:
You are taking Joy's model further than it is meant to be valid. I believe it only works with singlet states. IOW, it is about a system of pairs of particles that had a common creation.
So non-singlet state electrons could live in flatland? And not in S^3?

No. For states more general than the singlet state we have to go to S^7, which is a much richer space than S^3 (cf. this paper: http://arxiv.org/abs/1101.1958).

Yeah, that is better. "Valid" was not the correct term to use.

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