Various QRC simulations in one Mathematica file

[Joy Christian]

Here's what all the noise is about. When zero events are removed, the CHSH inequality must be modified.

I am afraid the noise is completely misguided. Show me exactly where in this theoretical analysis the "zero events" are removed: http://arxiv.org/abs/1405.2355.

Show me exactly where in Eq. (B10) of this paper the "zero events" are removed.

Now you may say "I am only concerned about the simulations (i.e., only about the numerical implementations of the analytical model, not about the model itself)."

Fine.

Then show me exactly where in this numerical simulation (which is essentially the same as the one you have recast in Mathematica) the "zero events" are removed, from the observed events A(a, e) and B(b, e). Note that there is exact, one-to-one matching between the initial states "e" and the observed pair of events A and B.

As I have stressed before, one cannot remove that which doesn't exist in the first place. You are stuck on "detection loophole" which has no relevance in my model.

[minkwe]

Here's what all the noise is about. When zero events are removed, the CHSH inequality must be modified.

Hi John,
You are of course free to do what you like in your simulation. But I think it would be disingenuous if you do not also realize the fact that whenever the terms are independent, the inequality must be modified, and end up not also making the appropriate changes to account for that fact in the simulation. (see http://arxiv.org/abs/quant-ph/0006014)

You will find that nothing violates the CHSH, not even QM.

[jreed]

Here's what all the noise is about. When zero events are removed, the CHSH inequality must be modified.

Then show me exactly where in this numerical simulation (which is essentially the same as the one you have recast in Mathematica) the "zero events" are removed, from the observed events A(a, e) and B(b, e). Note that there is exact, one-to-one matching between the initial states "e" and the observed pair of events A and B.

As I have stressed before, one cannot remove that which doesn't exist in the first place. You are stuck on "detection loophole" which has no relevance in my model.

In your R program there are the following lines of code:

# Event-ready preparation of the initial states e

C = sign(g(a,w,s))
D = sign(g(b,w,s))

o = x[C & D]
p = y[C & D]
q = z[C & D]


I ran your R program using only 10 samples so I could see what was happening. C and D have 10 samples each with +1, -1 AND 0. When o, p, and q are computed these outputs have seven lines of code with the points having 0 in either C or D being removed. This is where the elimination of the zero points takes place. You should do this test yourself so you can get a better understanding of R. I don't know much about this language, but I do like to see what a program is doing. Apparently statements like o = x[C & D] means take the values only where C and D are both non-zero.

[Joy Christian]

In your R program there are the following lines of code:

# Event-ready preparation of the initial states e

C = sign(g(a,w,s))
D = sign(g(b,w,s))

o = x[C & D]
p = y[C & D]
q = z[C & D]


I ran your R program using only 10 samples so I could see what was happening. C and D have 10 samples each with +1, -1 AND 0. When o, p, and q are computed these outputs have seven lines of code with the points having 0 in either C or D being removed. This is where the elimination of the zero points takes place. You should do this test yourself so you can get a better understanding of R. I don't know much about this language, but I do like to see what a program is doing. Apparently statements like o = x[C & D] means take the values only where C and D are both non-zero.

You analysis above is completely correct. And I have done many such tests. What I have published is but a fraction of what I have tested and derived mathematically.

So, again, your analysis above is completely correct. But it has nothing whatsoever to do with the detection loophole. Why? Because as I noted before,

"Detection loophole" can be invoked when there is a real or perceived mismatch between the initial states "e" and the measurement events A and B. But when there is exact match between the initial states "e" and the measurement events A and B (as in this simulation) then "detection loophole" type explanation is not even possible.

And I asked:

... show me exactly where in this numerical simulation ... the "zero events" are removed, from the observed events A(a, e) and B(b, e). Note that there is exact, one-to-one matching between the initial states "e" and the observed pair of events A and B.

The important point here is that nothing is removed from the observed events A and B. So there is no exploitation of the "detection loophole" in my simulation.

[Heinera]

Well, in your code, a zero event at Alice also implies removal of the corresponding observed event at Bob. So your claim that nothing is removed from the observed events is plainly wrong, and indicates that someone else has written the code for you.

[Joy Christian]

Well, in your code, a zero event at Alice also implies removal of the corresponding observed event at Bob. So your claim that nothing is removed from the observed events is plainly wrong, and indicates that someone else has written the code for you.

This is utter garbage. There are no "zero events", either at Alice or Bob. Nothing is removed from the observed events A and B. Wake up from your delusions, please.

For the record, the current code is written and tested entirely by me: http://rpubs.com/jjc/105450.

PS: The reason Heinera keeps making such idiotic claims about my simulations is because he has absolutely no understanding of the underlying analytical model.

[jreed]

In your R program there are the following lines of code:

# Event-ready preparation of the initial states e

C = sign(g(a,w,s))
D = sign(g(b,w,s))

o = x[C & D]
p = y[C & D]
q = z[C & D]


I ran your R program using only 10 samples so I could see what was happening. C and D have 10 samples each with +1, -1 AND 0. When o, p, and q are computed these outputs have seven lines of code with the points having 0 in either C or D being removed. This is where the elimination of the zero points takes place. You should do this test yourself so you can get a better understanding of R. I don't know much about this language, but I do like to see what a program is doing. Apparently statements like o = x[C & D] means take the values only where C and D are both non-zero.

You analysis above is completely correct. And I have done many such tests. What I have published is but a fraction of what I have tested and derived mathematically.

So, again, your analysis above is completely correct. But it has nothing whatsoever to do with the detection loophole. Why? Because as I noted before,

"Detection loophole" can be invoked when there is a real or perceived mismatch between the initial states "e" and the measurement events A and B. But when there is exact match between the initial states "e" and the measurement events A and B (as in this simulation) then "detection loophole" type explanation is not even possible.

And I asked:

... show me exactly where in this numerical simulation ... the "zero events" are removed, from the observed events A(a, e) and B(b, e). Note that there is exact, one-to-one matching between the initial states "e" and the observed pair of events A and B.

The important point here is that nothing is removed from the observed events A and B. So there is no exploitation of the "detection loophole" in my simulation.

Ok, let's try this again. I reran the model again with M = 10 samples and this is what I got:
The initial states of the event-ready model e, you call them C and D and they have 10 samples as called for by M = 10:

C = {1, 1, 0, 0, 1, 1, 1, -1, -1, 0}
D = {1, 0, 0, 0, 1, -1, 1, 1, -1, 0}

Note that there are 6 entries in the two arrays above where both are non-zero.
Now you compute o, p, and q which are the initial x, y and z vectors where C and D are non-zero:

o = x[C & D]
p = y[C & D]
q = z[C & D]

o = {.844, .269, .228, .370, -.348, -.778}
p = {.416, .296, -.801, -.023, .950, -.583}
q = {-.335, .916, .553, .928, .039, .232}

These vectors are the result of getting rid of the zero values, those combinations where one or both the observations were below the hidden variable threshold.

These three vectors are converted into a matrix you call e, the initial states of spin, and are multiplied by a and b, the directions of Alice and Bob's detectors. The detector outputs are found by taking the sign function of this product:

A = +sign[a.e]
B = -sign[b.e] giving

A = {1, 1, 1, 1, -1, -1}
B = {-1, -1, 1, -1, -1, 1}

The result is that the original set of 10 measurements has been reduced to a set of 6. This is the detection loophole. That seems clear to me. How else do you explain this?

[Joy Christian]

Ok, let's try this again. I reran the model again with M = 10 samples and this is what I got:
The initial states of the event-ready model e, you call them C and D and they have 10 samples as called for by M = 10:

C = {1, 1, 0, 0, 1, 1, 1, -1, -1, 0}
D = {1, 0, 0, 0, 1, -1, 1, 1, -1, 0}

Note that there are 6 entries in the two arrays above where both are non-zero.
Now you compute o, p, and q which are the initial x, y and z vectors where C and D are non-zero:

o = x[C & D]
p = y[C & D]
q = z[C & D]

o = {.844, .269, .228, .370, -.348, -.778}
p = {.416, .296, -.801, -.023, .950, -.583}
q = {-.335, .916, .553, .928, .039, .232}

These vectors are the result of getting rid of the zero values, those combinations where one or both the observations were below the hidden variable threshold.

So far so good. The unphysical "zeros" are removed from o, p, and q. "Zeros" don't belong to the model. They have nothing to do with either the physics or the model.

These three vectors are converted into a matrix you call e, the initial states of spin...

Yes. e represents the initial state of the spins. The state of the spins is now prepared. No experiment has taken place as yet. Alice and Bob are not even in their labs as yet, let alone having chosen their measurement directions. All we have done so far is prepare the initial state of the spins for them, as done in a real experiment.

Next these initial states e are sent to Alice and Bob by the source. While the spins are in midflights between the source and the labs of Alice and Bob, Alice and Bob freely choose their respective measurement directions a and b. Theoretically the detector outputs of Alice and Bob are calculated as sign functions as you have done:

A = +sign[a.e]
B = -sign[b.e]

giving

A = {1, 1, 1, 1, -1, -1}
B = {-1, -1, 1, -1, -1, 1}

This should be the end of the story, but you continue:

The result is that the original set of 10 measurements has been reduced to a set of 6.

What 10 measurements? What original set? No one has made any measurements on the "original set", because it does not even exist in the model. It is not physical.

The number of "original" spinning particles is 6, not 10. If 6 is, say, a painting by Picasso, then 10 is just the wooden frame on which the painting has been mounted. The frame is not the painting. It can be set arbitrarily -- in an ad hoc manner -- to any number whatsoever. It has nothing to do with anything physical in the model.

You seem to have no understanding of what is meant by "detection loophole." There are only 6 initial spins,

{ e } = 6.

And all 6 of them are detected,

{ A } = 6 and { B } = 6.

Six spins, and all six of them are detected by both Alice and Bob. Where is the "detection loophole" ?

In the code I have the following line which is not used in the calculation of the main correlation:

Code: Select all

# corrs[i,j] = length(A*B)/N   # Verifies (# of A*B) = (# of e)


Run the code with this line and see what you get for the correlation. You should now be able to understand what that means. It mean what it says in the comments.

[jreed]

And all 6 of them are detected,

{ A } = 6 and { B } = 6.

Six spins, and all six of them are detected by both Alice and Bob. Where is the "detection loophole" ?

.

It's clear you don't understand what the program is doing. To help you here is a short review of what is happening:

M is the number of experiments analyzed, in my example this is 10.
10 random unit 3D vectors are set up and put in the matrix w. These are the spins of one electron in each experiment.
Set up the hidden variable f, and a function g to apply it.

A do loop is now run over each angle in Alice's detector (alpha) and each angle in Bob's detector (beta).
The vectors C and D are found which apply the hidden variable. In this step the projection of the detector angles onto the electron spin is found. If this value is greater than the hidden variable, the output is +1 or -1 depending on the sign of the projection. If less than the hidden variable, 0 is output. The arrays C and D therefore contain +1, -1 and 0 values and are of length 10.

Now the detector loophole is introduced. The vectors o, p and q contain x, y, and z values only where C and D have nonzero values. A new matrix e is generated containing these new x, y and z values. You call these initial states, but they are really the old states obtained by hidden variable selection. There are less of these than the original 10 we started with. This e matrix is used along with the alpha and beta angles to find the measurement vectors A and B.

This should be easy to understand and is a clear example of the detection loophole.

[FrediFizzx]

And all 6 of them are detected,

{ A } = 6 and { B } = 6.

Six spins, and all six of them are detected by both Alice and Bob. Where is the "detection loophole" ?

.

It's clear you don't understand what the program is doing. To help you here is a short review of what is happening:

M is the number of experiments analyzed, in my example this is 10.

No. It is 6. The other 4 don't exist in the first place so how can they be analyzed? Joy knows exactly what the program is doing. That is not the issue here. The issue is looking at the whole scenario from an S^3 perspective. Granted, that doesn't seem to be very easy to do for some people.

[Joy Christian]

M is the number of experiments analyzed, in my example this is 10.

False! As Fred says above, the number of experiments analyzed is 6, not 10. 6 spins emerge from the source, and 6 spins are detected by Alice and Bob.

10 random unit 3D vectors are set up and put in the matrix w. These are the spins of one electron in each experiment.

False again. w are not the spins. The spins are represented by the e-vectors, not w-vectors.

Now the detector loophole is introduced. The vectors o, p and q contain x, y, and z values only where C and D have nonzero values. A new matrix e is generated containing these new x, y and z values. You call these initial states, but they are really the old states obtained by hidden variable selection. There are less of these than the original 10 we started with.

False again. No "detector loophole" is introduced. One cannot introduce a "detector loophole" at the source. As yet no detectors exist anywhere. How can one introduce a "detector loophole" -- at the source -- without any detectors set up for Alice and Bob -- at their stations. No detectors, no detector loophole. Simple!!!

This e matrix is used along with the alpha and beta angles to find the measurement vectors A and B.

Correct. More importantly, there is one-to-one match between the e matrices and the measurement results A and B. So there cannot be any "detection loophole."

[jreed]

M is the number of experiments analyzed, in my example this is 10.

False! As Fred says above, the number of experiments analyzed is 6, not 10. 6 spins emerge from the source, and 6 spins are detected by Alice and Bob.

10 random unit 3D vectors are set up and put in the matrix w. These are the spins of one electron in each experiment.

False again. w are not the spins. The spins are represented by the e-vectors, not w-vectors.

Now the detector loophole is introduced. The vectors o, p and q contain x, y, and z values only where C and D have nonzero values. A new matrix e is generated containing these new x, y and z values. You call these initial states, but they are really the old states obtained by hidden variable selection. There are less of these than the original 10 we started with.

False again. No "detector loophole" is introduced. One cannot introduce a "detector loophole" at the source. As yet no detectors exist anywhere. How can one introduce a "detector loophole" -- at the source -- without any detectors set up for Alice and Bob -- at their stations. No detectors, no detector loophole. Simple!!!

This e matrix is used along with the alpha and beta angles to find the measurement vectors A and B.

Correct. More importantly, there is one-to-one match between the e matrices and the measurement results A and B. So there cannot be any "detection loophole."

I'm sorry that neither of you can seem to see what to me is completely obvious and simple to understand. 10 experiments were done, that's what M is. 4 were eliminated because one or both the electrons were not detected by the observers. These 4 were eliminated. Isn't that easy to see? What's so difficult in understanding this? I guess I'm dealing with people who use a different kind of logic than I learned. I don't think I can communicate with you and will have to stop now. I hope you will have a nice discussion with each other.

[Ben6993]

Fred wrote:
No. It is 6. The other 4 don't exist in the first place so how can they be analyzed? Joy knows exactly what the program is doing. That is not the issue here. The issue is looking at the whole scenario from an S^3 perspective. Granted, that doesn't seem to be very easy to do for some people.

I think a problem is that although you say, and believers agree, that you have to look from an S^3 perspective rather than from an R^3 perspective, it does look fishy from the point of view of flatlanders. It looks fishy because of the way in which the randomness in S^3 is generated. Is it possible to generate random data in S^3 direct rather than starting with randomness in R^3 and then deleting the zero data? Deleting the zero data does not look like a random process. It would look so much better if the randomness in S^3 was a direct and wholly random step.

I long ago said that I did not think this issue was resolvable because what looks like a loophole to flatlanders was not a loophole to 3spherers. The two points of view being confounded together. Still, a purely random production of data in S^3 would help appearances. Another possibility is to investigate the nature of the generated data in S^3 to see if it chimes with Thompson's chaotic ball.

[Joy Christian]

I'm sorry that neither of you can seem to see what to me is completely obvious and simple to understand.

We are sorry that you fail to see what to us is completely obvious and simple to understand. Please read this analytical model first: http://arxiv.org/abs/1405.2355.

10 experiments were done, that's what M is.

No. Only 6 experiments were done. M has nothing to do with physics. The number of initial states e is N, not M. M is like a pre-reduced phase space in the language of gauge theory, and N is like the reduced or physical phase space. Please read the preamble of this original simulation to understand this: http://rpubs.com/jjc/84238.

4 were eliminated because one or both the electrons were not detected by the observers. These 4 were eliminated.

Nothing was eliminated from the set { e } = 6 of initial states e of the spins. Every single of the 6 initial states e where detected by Alice and Bob, as explained above.

I hope you will have a nice discussion with each other.

We sure will. Thank you for your contribution. It has made possible to eliminate some of the persistent confusions about my analytical model among the Bell believers.

[Heinera]

What jreed realizes, based on the code, is that the exact manner of how the 10 experiments are reduced to 6 depends on the detector settings. With different settings, the reduction could be to for instance 5 or 7. So if this reduction takes place in the theory before the settings are even decided by the experimenters, clearly a miracle is involved.

[Joy Christian]

What jreed realizes, based on the code, is that the exact manner of how the 10 experiments are reduced to 6 depends on the detector settings.

There are no 10 experiments. There are only 6 experiments in John Reed's example. Once again, you are seeing things. You have no clue what you are talking about.

[Heinera]

What jreed realizes, based on the code, is that the exact manner of how the 10 experiments are reduced to 6 depends on the detector settings.

There are no 10 experiments. There are only 6 experiments in John Reed's example. Once again, you are seeing things. You have no clue what you are talking about.

Ok, let me rephrase:

What jreed realizes, based on the code, is that the exact manner of how the 10 pairs are reduced to 6 experiments depends on the detector settings.

[Joy Christian]

What jreed realizes, based on the code, is that the exact manner of how the 10 experiments are reduced to 6 depends on the detector settings.

There are no 10 experiments. There are only 6 experiments in John Reed's example. Once again, you are seeing things. You have no clue what you are talking about.

Ok, let me rephrase:

What jreed realizes, based on the code, is that the exact manner of how the 10 pairs are reduced to 6 experiments depends on the detector settings.

No, it does not:

In the code I have the following line which is not used in the calculation of the main correlation:

Code: Select all

# corrs[i,j] = length(A*B)/N   # Verifies (# of A*B) = (# of e)


Run the code with this line and see what you get for the correlation. You should now be able to understand what that means. It mean what it says in the comments.

[Mikko]

M is the number of experiments analyzed, in my example this is 10.

False! As Fred says above, the number of experiments analyzed is 6, not 10. 6 spins emerge from the source, and 6 spins are detected by Alice and Bob.

10 random unit 3D vectors are set up and put in the matrix w. These are the spins of one electron in each experiment.

False again. w are not the spins. The spins are represented by the e-vectors, not w-vectors.

Now the detector loophole is introduced. The vectors o, p and q contain x, y, and z values only where C and D have nonzero values. A new matrix e is generated containing these new x, y and z values. You call these initial states, but they are really the old states obtained by hidden variable selection. There are less of these than the original 10 we started with.

False again. No "detector loophole" is introduced. One cannot introduce a "detector loophole" at the source. As yet no detectors exist anywhere. How can one introduce a "detector loophole" -- at the source -- without any detectors set up for Alice and Bob -- at their stations. No detectors, no detector loophole. Simple!!!

This e matrix is used along with the alpha and beta angles to find the measurement vectors A and B.

Correct. More importantly, there is one-to-one match between the e matrices and the measurement results A and B. So there cannot be any "detection loophole."

I'm sorry that neither of you can seem to see what to me is completely obvious and simple to understand. 10 experiments were done, that's what M is. 4 were eliminated because one or both the electrons were not detected by the observers. These 4 were eliminated. Isn't that easy to see? What's so difficult in understanding this? I guess I'm dealing with people who use a different kind of logic than I learned. I don't think I can communicate with you and will have to stop now. I hope you will have a nice discussion with each other.

The problem is that two different systems can be simulated with the same algorithms. The end result is the same, but the simulated processes are not. One system is a detection loophole model where (in a particular case) 10 pairs are created but only 6 of them is measured at both detectors. Another model is a non-local model where only 6 pairs are generated and the other four are just an artifact of the algorithm. The nature of the non-locality is not modelled in detail but can represent time-reversed causation or superdeterminism or some other weird process.

[Joy Christian]

Another model is a non-local model where only 6 pairs are generated and the other four are just an artifact of the algorithm. The nature of the non-locality is not modelled in detail but can represent time-reversed causation or superdeterminism or some other weird process.

Baseless speculation, driven by wishful thinking. Both the analytical model as well as its various simulations are manifestly local and realistic:

Abstract: A local, deterministic, and realistic model within a Friedmann-Robertson-Walker spacetime with constant spatial curvature is presented which describes simultaneous measurements of the spins of two fermions emerging in a singlet state from the decay of a spinless boson. Exact agreement with the probabilistic predictions of quantum theory is achieved in the model without data rejection, remote contextuality, superdeterminism, or backward causation. An event-by-event numerical simulation of the model is presented, which confirms our analytical results with the accuracy of 4 in 10^4 parts: http://arxiv.org/abs/1405.2355.