Coming Soon!

[Justo]

@Justo There is nothing illogical about A_2 having no value if A_1 has a value. But perhaps we can make that more specific in an additional explanation. So, thanks for that.

Yes. A1 and A2 are mutually exclusive. If A1 is nonzero, then A2 is zero. And if A2 is nonzero, then A1 is zero.
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It is important to notice that A_2 cannot be left undefined in equation (1). As I said before it is only for completeness and logical consistency. I suggest you review definitions (1) through (7) before sending to peer-review.
Notice that a similar problem may be happening with the other terms in equation (1). For instance, if condition k_A \neq K_B applies, the A_4 is left undefined.

[FrediFizzx]

@Justo There is nothing illogical about A_2 having no value if A_1 has a value. But perhaps we can make that more specific in an additional explanation. So, thanks for that.

Yes. A1 and A2 are mutually exclusive. If A1 is nonzero, then A2 is zero. And if A2 is nonzero, then A1 is zero.
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Yes, I guess you can say that having no value is equivalent to 0. But the code actually gives no value, not even zero.
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[FrediFizzx]

@Justo There is nothing illogical about A_2 having no value if A_1 has a value. But perhaps we can make that more specific in an additional explanation. So, thanks for that.

Yes. A1 and A2 are mutually exclusive. If A1 is nonzero, then A2 is zero. And if A2 is nonzero, then A1 is zero.
.

It is important to notice that A_2 cannot be left undefined in equation (1). As I said before it is only for completeness and logical consistency. I suggest you review definitions (1) through (7) before sending to peer-review.
Notice that a similar problem may be happening with the other terms in equation (1). For instance, if condition k_A \neq K_B applies, the A_4 is left undefined.

A_2 is not undefined in eq. (1). It is defined to have no value or zero if you wish.
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[Justo]

@Justo There is nothing illogical about A_2 having no value if A_1 has a value. But perhaps we can make that more specific in an additional explanation. So, thanks for that.

Yes. A1 and A2 are mutually exclusive. If A1 is nonzero, then A2 is zero. And if A2 is nonzero, then A1 is zero.
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Yes, I guess you can say that having no value is equivalent to 0. But the code actually gives no value, not even zero.
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I guess so, you don't need to use equation (1) in your code to define the value of A(a,\theta_k).
A malicious reviewer may reject the paper just based on what I have noticed. But, of course, I will not tell you guys about malicious reviewers.

[FrediFizzx]

@Justo There is nothing illogical about A_2 having no value if A_1 has a value. But perhaps we can make that more specific in an additional explanation. So, thanks for that.

Yes. A1 and A2 are mutually exclusive. If A1 is nonzero, then A2 is zero. And if A2 is nonzero, then A1 is zero.
.

Yes, I guess you can say that having no value is equivalent to 0. But the code actually gives no value, not even zero.
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I guess so, you don't need to use equation (1) in your code to define the value of A(a,\theta_k).
A malicious reviewer may reject the paper just based on what I have noticed. But, of course, I will not tell you guys about malicious reviewers.

Eq. (1) is in the code. It is this line,

outA = Sort[Catenate[{listA4, outA2, listA6}], #1[[3]] < #2[[3]] &];
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[Joy Christian]

@Justo There is nothing illogical about A_2 having no value if A_1 has a value. But perhaps we can make that more specific in an additional explanation. So, thanks for that.

Yes. A1 and A2 are mutually exclusive. If A1 is nonzero, then A2 is zero. And if A2 is nonzero, then A1 is zero.
.

It is important to notice that A_2 cannot be left undefined in equation (1). As I said before it is only for completeness and logical consistency. I suggest you review definitions (1) through (7) before sending to peer-review.
Notice that a similar problem may be happening with the other terms in equation (1). For instance, if condition k_A \neq K_B applies, the A_4 is left undefined.

I am not sure what the issue is here. Just as A1 and A2 are mutually exclusive, A3 and A4 are mutually exclusive. If A3 occurs (or exists), then A4 does not, and vice versa.
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[Justo]

@Justo There is nothing illogical about A_2 having no value if A_1 has a value. But perhaps we can make that more specific in an additional explanation. So, thanks for that.

Yes. A1 and A2 are mutually exclusive. If A1 is nonzero, then A2 is zero. And if A2 is nonzero, then A1 is zero.
.

It is important to notice that A_2 cannot be left undefined in equation (1). As I said before it is only for completeness and logical consistency. I suggest you review definitions (1) through (7) before sending to peer-review.
Notice that a similar problem may be happening with the other terms in equation (1). For instance, if condition k_A \neq K_B applies, the A_4 is left undefined.

I am not sure what the issue is here. Just as A1 and A2 are mutually exclusive, A3 and A4 are mutually exclusive. If A3 occurs (or exists), then A4 does not, and vice versa.
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Notice that A4 is in (1) so all cases should cover it. Also, A3 is used to define A6 that is in (1).

[FrediFizzx]

It is important to notice that A_2 cannot be left undefined in equation (1). As I said before it is only for completeness and logical consistency. I suggest you review definitions (1) through (7) before sending to peer-review.
Notice that a similar problem may be happening with the other terms in equation (1). For instance, if condition k_A \neq K_B applies, the A_4 is left undefined.

I am not sure what the issue is here. Just as A1 and A2 are mutually exclusive, A3 and A4 are mutually exclusive. If A3 occurs (or exists), then A4 does not, and vice versa.
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Notice that A4 is in (1) so all cases should cover it. Also, A3 is used to define A6 that is in (1).

Not sure what your point is here.
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[Justo]

It is important to notice that A_2 cannot be left undefined in equation (1). As I said before it is only for completeness and logical consistency. I suggest you review definitions (1) through (7) before sending to peer-review.
Notice that a similar problem may be happening with the other terms in equation (1). For instance, if condition k_A \neq K_B applies, the A_4 is left undefined.

I am not sure what the issue is here. Just as A1 and A2 are mutually exclusive, A3 and A4 are mutually exclusive. If A3 occurs (or exists), then A4 does not, and vice versa.
.

Notice that A4 is in (1) so all cases should cover it. Also, A3 is used to define A6 that is in (1).

Not sure what your point is here.
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In fact, it is a triviality. If you assume that not defined=0 there is no problem. I only gave the opinion that from a purely mathematical and logical standpoint, since expression (1) must be defined for all cases, in your mathematical definition some terms in (1) are left undefined depending on the different cases.
You already told me that it does not affect your code.

I do have another worry that is not trivial.

[FrediFizzx]

@Justo Not sure what your definition of "definition" is but everything is perfectly defined. Why can't "no result" be a definition? What is your other worry?
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[Justo]

@Justo Not sure what your definition of "definition" is but everything is perfectly defined. Why can't "no result" be a definition? What is your other worry?
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I am assuming that your simulation of Bell test experiments is purely theoretical in the sense that you are not considering the simulations of experimental loopholes. If that is true, then I don't understand why you are considering different values for k_A and k_B.
I seems to we that by considering cases when k_A is different from k_B you are including the coincidence loophole.

[FrediFizzx]

@Justo Not sure what your definition of "definition" is but everything is perfectly defined. Why can't "no result" be a definition? What is your other worry?
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I am assuming that your simulation of Bell test experiments is purely theoretical in the sense that you are not considering the simulations of experimental loopholes. If that is true, then I don't understand why you are considering different values for k_A and k_B.
I seems to we that by considering cases when k_A is different from k_B you are including the coincidence loophole.

No, I don't think so. It is a thought experiment. Actual experiments don't have k_A and k_B. In this model, k_A and k_B are part of the hidden variables since they are actually shared numbers between Alice and Bob.
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[Justo]

@Justo Not sure what your definition of "definition" is but everything is perfectly defined. Why can't "no result" be a definition? What is your other worry?
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I am assuming that your simulation of Bell test experiments is purely theoretical in the sense that you are not considering the simulations of experimental loopholes. If that is true, then I don't understand why you are considering different values for k_A and k_B.
I seems to we that by considering cases when k_A is different from k_B you are including the coincidence loophole.

No, I don't think so. It is a thought experiment. Actual experiments don't have k_A and k_B. In this model, k_A and k_B are part of the hidden variables since they are actually shared numbers between Alice and Bob.
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I agree that k is part of the hidden variables, however, if you are multiplying values of A and B evaluated for different experimental trials then you are simulating the coincidence loophole. Theoretically that should not happen.

[Joy Christian]

@Justo Not sure what your definition of "definition" is but everything is perfectly defined. Why can't "no result" be a definition? What is your other worry?
.

I am assuming that your simulation of Bell test experiments is purely theoretical in the sense that you are not considering the simulations of experimental loopholes. If that is true, then I don't understand why you are considering different values for k_A and k_B.
I seems to we that by considering cases when k_A is different from k_B you are including the coincidence loophole.

No, I don't think so. It is a thought experiment. Actual experiments don't have k_A and k_B. In this model, k_A and k_B are part of the hidden variables since they are actually shared numbers between Alice and Bob.

Yes. k_A is exactly equal to k_B in eq. (1). But in (4) they are not. That is the defect of the crude functions A1, A2, B1, and B2. It is a theoretical defect. This defect is corrected by the process described in (4) to (7). In the resulting equation, eq. (1), k_A = k_B = k, as it must be, because, as Fred says, it is part of the common cause or initial state that is shared between Alice and Bob for each run of the experiment.

Note also that no such theoretical defect occurs in my Geometric Algebra model because it uses more sophisticated mathematics compared to the crude functions in A1, A2, B1, and B2.

The coincidence loophole is something else. It is about the experimental impossibility of detections happening simultaneously at A and B. There is always a window of experimental error.
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[Justo]

@Justo Not sure what your definition of "definition" is but everything is perfectly defined. Why can't "no result" be a definition? What is your other worry?
.

I am assuming that your simulation of Bell test experiments is purely theoretical in the sense that you are not considering the simulations of experimental loopholes. If that is true, then I don't understand why you are considering different values for k_A and k_B.
I seems to we that by considering cases when k_A is different from k_B you are including the coincidence loophole.

No, I don't think so. It is a thought experiment. Actual experiments don't have k_A and k_B. In this model, k_A and k_B are part of the hidden variables since they are actually shared numbers between Alice and Bob.

Yes. k_A is exactly equal to k_B in eq. (1). But in (4) they are not. That is the defect of the crude functions A1, A2, B1, and B2. It is a theoretical defect. This defect is corrected by the process described in (4) to (7). In the resulting equation, eq. (1), k_A = k_B = k, as it must be, because, as Fred says, it is part of the common cause or initial state that is shared between Alice and Bob for each run of the experiment.

Note also that no such theoretical defect occurs in my Geometric Algebra model because it uses more sophisticated mathematics compared to the crude functions in A1, A2, B1, and B2.

The coincidence loophole is something else. It is about the experimental impossibility of detections happening simultaneously at A and B. There is always a window of experimental error.
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If you end up calculating with kA=kB after correction then I agree there is no coincidence loophole.

[FrediFizzx]

Yes, the defect is quite simple. When you separate the events into A_1 and A_2, etc., you find events in A_1 that don't have a matching event in B_1. Likewise you find events in B_1 that don't have a matching event in A_1. Because those matching events are in A_2 and B_2.
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[gill1109]

Maybe I just don't understand it. But in equation (1) you define a function A that depends on A_2. Let us assume the argument \theta_k is in the range given by equation (2). What is the value for A_2 that you put in equation (1)?

Well, A actually depends on only one of the three functions per event depending on the definitions below eq. (1). Yes, it is a little bit confusing but you should have read the explanation at the end of the paragraph that eq. (1) is in.

After the formulas (1) to (7) the text of Fred and Joy’s ResearchGate paper http://dx.doi.org/10.13140/RG.2.2.28311.91047 says “where k_A is … and k_B is ...” and “k_A and k_B must be the same”. But k_A and k_B do not appear in those equations. In fact, they are nowhere defined in the paper. They do not appear anywhere else in the paper. The paper says that the matching parts were suggested by Bill Nelson but no reference is given to his proposal. Please give us a version of the code in R or Python. I think you will need to make your simulation easily reproducible on freely available software in order to get this published. Perhaps the Mathematica code defines k_A and k_B? Then the Mathematica code needs to be clearly annotated. The mismatch between text and formulas on the one hand, and Mathematica code on the other, is much too big for non Mathematica experts to be able to read the paper.

You have become too old for this stuff. Perhaps you should find some less demanding hobby for your retirement.

We can see k_A and k_B in equations (4) and (5) of the paper.

And just below equation (7) we can read "where k_A is the trial number recorded by Alice, k_B is the trial number recorded by Bob, ..."

Sorry, indeed, there is mention of k_A and k_B in equations (1) to (7) and in the sentence immediately following. But they are not defined there, nor elsewhere in the paper. The words in the equations and just below the equations do not make any sense. Do k_A and k_B actually depend on k?

I repeat my question: what is the definition of k_A and k_B? Does each of the trials k = 1, 2, ... have an associated pair of trial numbers k_A(k) and k_B(k)?

The paper has the typical problems of a collaboration of two authors with different expertise. One can write LaTeX formulas but not read Mathematica code, the other can write Mathematica code but not read LaTeX formulas.

I looked at the code again. First data is generated. Variables f1 and g1 are not defined. Nor are f2 and g2. But if they have been defined, then we see that the variable C1 depends on Alice's angle and the variable C2 depends on Bob's angle, and both depend on the hidden variable. I suppose that the matching business uses C1 and C2.

Nobody can repeat these experiments using a modern programming language of choice. I am too poor to buy Mathematica and too old to learn it, especially without being able to play with it myself. Anyway: it is not my problem that this paper is not going to have any impact in the world, in its present state. It's the authors' task to make it accessible to non Mathematica experts. Good luck!

By the way, you try to justify the matching stuff by reference to ancient papers [2] (Clauser and Shimony, 1978) and [3] (Aspect et al., 1982. You also mention Aspect [4] (2015) but that paper would tell you, if you read it, that things have changed now. In modern experiments, e.g. Vienna and NIST om 2015, there is no post-experiment matching. There is no detection loophole, no coincidence loophole. The experimental unit is "time slot". There are time slots in each wing of the experiment numbered in advance 1, 2, ..., N and per time slot Alice and Bob each insert one randomly chosen binary setting and each register one binary measurement outcome. [In Delft and Munich, 2015, there are three players: Alice, Bob, and Caspar. One studies the correlations between Alice and Bob's outcomes given Alice and Bob's setting and Caspar's outcome]

[FrediFizzx]

Sorry, indeed, there is mention of k_A and k_B in equations (1) to (7) and in the sentence immediately following. But they are not defined there, nor elsewhere in the paper. The words in the equations and just below the equations do not make any sense. Do k_A and k_B actually depend on k?

I repeat my question: what is the definition of k_A and k_B? Does each of the trials k = 1, 2, ... have an associated pair of trial numbers k_A(k) and k_B(k)?

The paper has the typical problems of a collaboration of two authors with different expertise. One can write LaTeX formulas but not read Mathematica code, the other can write Mathematica code but not read LaTeX formulas.

I looked at the code again. First data is generated. Variables f1 and g1 are not defined. Nor are f2 and g2. But if they have been defined, then we see that the variable C1 depends on Alice's angle and the variable C2 depends on Bob's angle, and both depend on the hidden variable. I suppose that the matching business uses C1 and C2.

Nobody can repeat these experiments using a modern programming language of choice. I am too poor to buy Mathematica and too old to learn it, especially without being able to play with it myself. Anyway: it is not my problem that this paper is not going to have any impact in the world, in its present state. It's the authors' task to make it accessible to non Mathematica experts. Good luck!

By the way, you try to justify the matching stuff by reference to ancient papers [2] (Clauser and Shimony, 1978) and [3] (Aspect et al., 1982. You also mention Aspect [4] (2015) but that paper would tell you, if you read it, that things have changed now. In modern experiments, e.g. Vienna and NIST om 2015, there is no post-experiment matching. There is no detection loophole, no coincidence loophole. The experimental unit is "time slot". There are time slots in each wing of the experiment numbered in advance 1, 2, ..., N and per time slot Alice and Bob each insert one randomly chosen binary setting and each register one binary measurement outcome. [In Delft and Munich, 2015, there are three players: Alice, Bob, and Caspar. One studies the correlations between Alice and Bob's outcomes given Alice and Bob's setting and Caspar's outcome]

CHSH = 2.78608 You are spewing a bunch of freakin' nonsense again. Please stop doing that.
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[jreed]

Good news! I am able to duplicate the results of all that Mathematica code that does the analysis of the observations (outA and outB) to arrive at outA5 and outB5 with two statements and two simple do loops:

outA5 = outA;
outB5 = outB;

Do[If[outB[[i]][[4]] == f2 && outA[[i]][[2]] != outA[[i]][[5]],
outA5[[i]][[2]] = outA[[i]][[2]]*-1], {i, m}]

Do[If[outA[[i]][[4]] == f1 && outB[[i]][[2]] != outB[[i]][[5]],
outB5[[i]][[2]] = outB[[i]][[2]]*-1], {i, m}]

I am able to duplicate the results of finding CHSH and also the plot of the cosine function.

I was able to do this by taking Fred's code and seeing what it is actually doing. This took me some time, but the final result really quite simple. Now the program is much faster, and by looking at the do loop you can clearly see that the calculation is non-local. The program modifies A depending on values in B and vice versa.

[FrediFizzx]

Good news! I am able to duplicate the results of all that Mathematica code that does the analysis of the observations (outA and outB) to arrive at outA5 and outB5 with two statements and two simple do loops:

outA5 = outA;
outB5 = outB;

Do[If[outB[[i]][[4]] == f2 && outA[[i]][[2]] != outA[[i]][[5]],
outA5[[i]][[2]] = outA[[i]][[2]]*-1], {i, m}]

Do[If[outA[[i]][[4]] == f1 && outB[[i]][[2]] != outB[[i]][[5]],
outB5[[i]][[2]] = outB[[i]][[2]]*-1], {i, m}]

I am able to duplicate the results of finding CHSH and also the plot of the cosine function.

I was able to do this by taking Fred's code and seeing what it is actually doing. This took me some time, but the final result really quite simple. Now the program is much faster, and by looking at the do loop you can clearly see that the calculation is non-local. The program modifies A depending on values in B and vice versa.

Except that is not my model. It's your model which is not the same as mine. You are not using the trial numbers which are part of the hidden variables since shared by Alice and Bob.
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