GAViewer Simulation No Hidden Variable

[FrediFizzx]

If what you say is true, then why does it have to be pre-programmed? We can just send both stations the singlet spin vector for every event.

Yes, that would be unproblematic.

And..., it looks like Heine gave up on Gull's number (3).
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Not at all, but since you are still discussing number (2) no one has yet asked about (3).

I did ask about number (3) back a few posts. That is why I thought maybe you had given up deciphering this nonsense.

"Well Heine, I can't tell if Gill agrees with this or not. It looks like he doesn't but not sure. If it is the two measurement functions, then what is "p" in Gull's number (3). And for that matter, what is what looks like "mp2"?"

Anyways, yes unproblematic. What Gill doesn't understand I guess is that the A and B programs load and run for each and every event. So, A generates c, the singlet spin vector, and sends to B. Then the programs load, run and give their outcomes. Next event just repeat, etc. There is no communication when the two programs are running.
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[gill1109]

If what you say is true, then why does it have to be pre-programmed? We can just send both stations the singlet spin vector for every event.

Yes, that would be unproblematic.

And..., it looks like Heine gave up on Gull's number (3).
.

Not at all, but since you are still discussing number (2) no one has yet asked about (3).

I did ask about number (3) back a few posts. That is why I thought maybe you had given up deciphering this nonsense.

"Well Heine, I can't tell if Gill agrees with this or not. It looks like he doesn't but not sure. If it is the two measurement functions, then what is "p" in Gull's number (3). And for that matter, what is what looks like "mp2"?"

Anyways, yes unproblematic. What Gill doesn't understand I guess is that the A and B programs load and run for each and every event. So, A generates c, the singlet spin vector, and sends to B. Then the programs load, run and give their outcomes. Next event just repeat, etc. There is no communication when the two programs are running.
.

You had better more carefully read what Gull writes. After the two computers have been set up and after the two programs are running, there is no communication between them allowed. Each program once set up and running, is in a loop. The following is repeated till we have enough data: print “n” and request next angle; user enters an angle; print an outcome +/-1 which is a function of n and the angle *only*; increment “n” by 1 and go to the beginning of the loop. If you like, you can do a million trials on Alice’s computer and then a million on Bob’s. All hidden variables of source and both detectors, for all million trials, are functions of what is already in the two computers before the loop starts. They are “in” Alice’s function p, and in Bob’s function q = -p.

If you like we can let the two computers and their initial content be identical clones of one another. They each run the same program. Bob can flip the signs of his program’s outputs himself.

Steve Gull is English, he’s at Cambridge, he must be about 80 (I’m about 70). He wrote those slides 15 years ago, and used to give that exam question in the 80s to students in the theoretical physics master programme. Our way of writing might be difficult for West-coast Americans to understand. In Hollywood movies, people like us are always type-cast as villains.

[FrediFizzx]

...
I did ask about number (3) back a few posts. That is why I thought maybe you had given up deciphering this nonsense.

"Well Heine, I can't tell if Gill agrees with this or not. It looks like he doesn't but not sure. If it is the two measurement functions, then what is "p" in Gull's number (3). And for that matter, what is what looks like "mp2"?"

Anyways, yes unproblematic. What Gill doesn't understand I guess is that the A and B programs load and run for each and every event. So, A generates c, the singlet spin vector, and sends to B. Then the programs load, run and give their outcomes. Next event just repeat, etc. There is no communication when the two programs are running.
.

You had better more carefully read what Gull writes. After the two computers have been set up and after the two programs are running, there is no communication between them allowed. Each program once set up and running, is in a loop. The following is repeated till we have enough data: print “n” and request next angle; user enters an angle; print an outcome +/-1 which is a function of n and the angle *only*; increment “n” by 1 and go to the beginning of the loop. If you like, you can do a million trials on Alice’s computer and then a million on Bob’s. All hidden variables of source and both detectors, for all million trials, are functions of what is already in the two computers before the loop starts. They are “in” Alice’s function p, and in Bob’s function q = -p.

If you like we can let the two computers and their initial content be identical clones of one another. They each run the same program. Bob can flip the signs of his program’s outputs himself.
...

Will you please stop waffling and writing nonsense? "... print an outcome +/-1 which is a function of n and the angle *only*;" Complete nonsense! The outcomes are functions of the angle and lambda *only*. And also carry an index "n" to keep track of what is correlated to what. The outcomes are NEVER a function of "n". Some how you are all mixed up.

And..., that is NOT exactly what Gull wrote, "There must be no communication between the computers after the time of program load." The two programs load and run for each and every event! There is no communication while the two programs are running. When the outcomes happen, the programs are no longer running. I can't believe you don't understand that simple fact.
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[gill1109]

...
I did ask about number (3) back a few posts. That is why I thought maybe you had given up deciphering this nonsense.

"Well Heine, I can't tell if Gill agrees with this or not. It looks like he doesn't but not sure. If it is the two measurement functions, then what is "p" in Gull's number (3). And for that matter, what is what looks like "mp2"?"

Anyways, yes unproblematic. What Gill doesn't understand I guess is that the A and B programs load and run for each and every event. So, A generates c, the singlet spin vector, and sends to B. Then the programs load, run and give their outcomes. Next event just repeat, etc. There is no communication when the two programs are running.
.

You had better more carefully read what Gull writes. After the two computers have been set up and after the two programs are running, there is no communication between them allowed. Each program once set up and running, is in a loop. The following is repeated till we have enough data: print “n” and request next angle; user enters an angle; print an outcome +/-1 which is a function of n and the angle *only*; increment “n” by 1 and go to the beginning of the loop. If you like, you can do a million trials on Alice’s computer and then a million on Bob’s. All hidden variables of source and both detectors, for all million trials, are functions of what is already in the two computers before the loop starts. They are “in” Alice’s function p, and in Bob’s function q = -p.

If you like we can let the two computers and their initial content be identical clones of one another. They each run the same program. Bob can flip the signs of his program’s outputs himself.
...

Will you please stop waffling and writing nonsense? "... print an outcome +/-1 which is a function of n and the angle *only*;" Complete nonsense! The outcomes are functions of the angle and lambda *only*. And also carry an index "n" to keep track of what is correlated to what. The outcomes are NEVER a function of "n". Some how you are all mixed up.

And..., that is NOT exactly what Gull wrote, "There must be no communication between the computers after the time of program load." The two programs load and run for each and every event! There is no communication while the two programs are running. When the outcomes happen, the programs are no longer running. I can't believe you don't understand that simple fact.
.

Why does Gull write p(theta, n)? Why does he never talk about a lambda? Answer: because the two programs load and run just once, and thereafter keep running continuously. The programs set up a dialogue and repeatedly print something, wait for a response, and print something out. It's a loop. The results are collected and analysed later.

We are talking about Gull's outline proof of Gull's theorem. Not about Gull's failed proof of Fred's theorem, whatever that might be.

I get the impression, Fred, that you are totally bored and have no interest in Gull's work, or Gill's work, or Bell's work. You are interested only in your own GAViewer simulation program, which Joy thinks has got something to do with his mission to promote his own refutation of Bell's theorem.

I'm very interested in your joint Sokal-like hoax, except that it is not actually a hoax, since you both believe in it. But you are revealing the rottenness of present-day science publishing, and that is a good thing. I applaud you, both. Please keep up the good work.

Now: wouldn't it be interesting now to move on to formula (3)? The bit where we at last do some Fourier theory? If you are interested, I am happy to explain what Gull is doing there.

[Heinera]

The outcomes are functions of the angle and lambda *only*. And also carry an index "n" to keep track of what is correlated to what. The outcomes are NEVER a function of "n".
.

You can just copy your code snippet that generates your hidden variables (the spin-vector) to both computers. Then you have the setup described by Gull. Use n to keep things in sync, e.g. as a seed to an RNG.

[gill1109]

The outcomes are functions of the angle and lambda *only*. And also carry an index "n" to keep track of what is correlated to what. The outcomes are NEVER a function of "n".
.

You can just copy your code snippet that generates your hidden variables (the spin-vector) to both computers. Then you have the setup described by Gull. Use n to keep things in sync, e.g. as a seed to an RNG.

You could say that “n” stands for time. It seems physically reasonable to allow that there is time variation in the dynamics. The two computers represent the two overlapping parts of the whole experiment. The overlap equals the source. The idea is that the state of *all* the hidden variables in the entire physical system of detectors plus source *at time zero* are represented by the state, duplicated, of both computers, at the time the programs are started. If nature is really deterministic (God does not throw dice) then after this, the state at later times is a function of the state at earlier times.

Gull does need to assume that the states of the two computers at time “n” does not depend on the settings introduced at earlier times. Gill’s (2003) theorem was designed in order to take account of that possibility.

https://arxiv.org/abs/quant-ph/0110137,

Accardi contra Bell (cum mundi): The Impossible Coupling

Richard D. Gill

An experimentally observed violation of Bell's inequality is supposed to show the failure of local realism to deal with quantum reality. However, finite statistics and the time sequential nature of real experiments still allow a loophole for local realism, known as the memory loophole. We show that the randomized design of the Aspect experiment closes this loophole. Our main tool is van de Geer's (2000) supermartingale version of the classical Bernstein (1924) inequality guaranteeing, at the root n scale, a not-heavier-than-Gaussian tail of the distribution of a sum of bounded supermartingale differences. The results are used to specify a protocol for a public bet between the author and L. Accardi, who in recent papers (Accardi and Regoli, 2000a,b, 2001; Accardi, Imafuku and Regoli, 2002) has claimed to have produced a suite of computer programmes, to be run on a network of computers, which will simulate a violation of Bell's inequalites. At a sample size of thirty thousand, both error probabilities are guaranteed smaller than one in a million, provided we adhere to the sequential randomized design. The results also show that Hess and Philipp's (2001a,b) recent claims are mistaken that Bell's theorem fails because of time phenomena supposedly neglected by Bell.

Journal reference: pp. 133-154 in: Mathematical Statistics and Applications: Festschrift for Constance van Eeden. Eds: M. Moore, S. Froda and C. Léger. IMS Lecture Notes -- Monograph Series, Volume 42 (2003). Institute of Mathematical Statistics. Beachwood, Ohio

[FrediFizzx]

The outcomes are functions of the angle and lambda *only*. And also carry an index "n" to keep track of what is correlated to what. The outcomes are NEVER a function of "n".
.

You can just copy your code snippet that generates your hidden variables (the spin-vector) to both computers. Then you have the setup described by Gull. Use n to keep things in sync, e.g. as a seed to an RNG.

That doesn't work. The singlet spin vector is the same for both stations per event. That would generate two different spin vectors per event.
.

[gill1109]

The outcomes are functions of the angle and lambda *only*. And also carry an index "n" to keep track of what is correlated to what. The outcomes are NEVER a function of "n".
.

You can just copy your code snippet that generates your hidden variables (the spin-vector) to both computers. Then you have the setup described by Gull. Use n to keep things in sync, e.g. as a seed to an RNG.

That doesn't work. The singlet spin vector is the same for both stations per event. That would generate two different spin vectors per event.
.

But we are not trying to simulate standard QM. We are trying to simulate an experiment in a world running according to the rules of Local Realism. We want to see if in a LR world, the same statistical results could be produced as we would expect in a QM world. We are also interested in what can be seen in our actual world.

Joy Christian doesn’t just claim that he can reproduce the statistics predicted by QM. He also claims that his model satisfies “local realism”. He claims that Bell’s theorem is false. He claims to have a counterexample to purely mathematical assertions made by Bell.

[Heinera]

The outcomes are functions of the angle and lambda *only*. And also carry an index "n" to keep track of what is correlated to what. The outcomes are NEVER a function of "n".
.

You can just copy your code snippet that generates your hidden variables (the spin-vector) to both computers. Then you have the setup described by Gull. Use n to keep things in sync, e.g. as a seed to an RNG.

That doesn't work. The singlet spin vector is the same for both stations per event. That would generate two different spin vectors per event.
.

You use the exact same code on both computers. They will generate the same spin vector per event. Random number generators must be initialized with the same seed on both computers

[FrediFizzx]

The outcomes are functions of the angle and lambda *only*. And also carry an index "n" to keep track of what is correlated to what. The outcomes are NEVER a function of "n".
.

You can just copy your code snippet that generates your hidden variables (the spin-vector) to both computers. Then you have the setup described by Gull. Use n to keep things in sync, e.g. as a seed to an RNG.

That doesn't work. The singlet spin vector is the same for both stations per event. That would generate two different spin vectors per event.
.

You use the exact same code on both computers. They will generate the same spin vector per event. Random number generators must be initialized with the same seed on both computers

Hmm... not sure GAViewer will do a seed. I'll have to look through the manual. But you know that there is nothing wrong with doing it the other way. A sends B the singlet spin vector the programs run for event 1 then terminate, repeat for additional events.

Still more rambling waffling from Gill. He thinks we are doing an experiment. Gull only said, "... which mimics the QM predictions for the EPR setup." I'm ONLY doing QM predictions.
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[gill1109]

Still more rambling waffling from Gill. He thinks we are doing an experiment. Gull only said, "... which mimics the QM predictions for the EPR setup." I'm ONLY doing QM predictions.
.

Don't be so dimm, Fred (and don't be so rude. And: you may call me Richard).

Yes, you're only doing QM predictions, and you are doing them with a program which (according to Gull) can't be separated into two programs on two computers which run according to Gull's strict protocol.

Gull has sketched the proof of a theorem. You think that your own GAViewer program provides a counter-example. But you can't follow Gull's argument, anyway.

Gull's theorem is about mathematical models of an experiment where Alice and Bob each repeatedly provide settings (angles) to a detector and their detectors repeatedly respond with outcomes +/-1.

You are confused by Gull's set-up and object to his preliminary assumptions because you are brainwashed by what you have been taught about quantum mechanics. But we are now studying the question, whether the statistics predicted by quantum mechanics could also be generated by a local and deterministic mechanism of the kind that Einstein spent his whole life searching for.

So do I understand that you don't want to talk about Gull's proof, after all? Fine by me ...

Alternatively, I propose that once we have jointly clarified that argument (if that ever happens), and if we have found out that it is OK, then we together write up the proof in more detail and with more supporting motivation, and submit a paper to a decent journal. We can write a discussion about whether or not the theorem is physically interesting. We can agree to differ on that issue, but we can lay out the arguments, for the benefit of new people coming to work in this field.

[FrediFizzx]

You can just copy your code snippet that generates your hidden variables (the spin-vector) to both computers. Then you have the setup described by Gull. Use n to keep things in sync, e.g. as a seed to an RNG.

That doesn't work. The singlet spin vector is the same for both stations per event. That would generate two different spin vectors per event.
.

You use the exact same code on both computers. They will generate the same spin vector per event. Random number generators must be initialized with the same seed on both computers

Hmm... not sure GAViewer will do a seed. I'll have to look through the manual. But you know that there is nothing wrong with doing it the other way. A sends B the singlet spin vector the programs run for event 1 then terminate, repeat for additional events.

Still more rambling waffling from Gill. He thinks we are doing an experiment. Gull only said, "... which mimics the QM predictions for the EPR setup." I'm ONLY doing QM predictions.
.

Nope. It doesn't look like there is a way to set a seed in GAViewer. So, has to be done the other way.
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[gill1109]

Nope. It doesn't look like there is a way to set a seed in GAViewer. So, has to be done the other way.
.

rand(): returns random number (uniform distribution between 0.0 and 1.0)
randSeed(arg1): sets the random seed to arg1
time(): returns current time, millisecond resolution. May be used for randSeed()
randGauss(arg1, arg2): returns random number (gaussion distribution with specified mean; arg1 = mean, arg2 = variance)
randGaussStd(): returns random number (gaussion distribution with mean = 0.0; variance = 1.0)

[FrediFizzx]

...
That doesn't work. The singlet spin vector is the same for both stations per event. That would generate two different spin vectors per event.
.

You use the exact same code on both computers. They will generate the same spin vector per event. Random number generators must be initialized with the same seed on both computers

Hmm... not sure GAViewer will do a seed. I'll have to look through the manual. But you know that there is nothing wrong with doing it the other way. A sends B the singlet spin vector the programs run for event 1 then terminate, repeat for additional events.

Still more rambling waffling from Gill. He thinks we are doing an experiment. Gull only said, "... which mimics the QM predictions for the EPR setup." I'm ONLY doing QM predictions.
.

Nope. It doesn't look like there is a way to set a seed in GAViewer. So, has to be done the other way.
.

Ok, tried it out. randSeed(1234) seems to work so we can do it that way. Maybe.

You guys are stalling out on Gull's number (3). Come on! Bring forth the nonsense. Let's see it.
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[Heinera]

Ok, tried it out. randSeed(1234) seems to work so we can do it that way. Maybe.

You guys are stalling out on Gull's number (3). Come on! Bring forth the nonsense. Let's see it.
.

I was under the impression that you should now write code that can be run on two computers.

[FrediFizzx]

Ok, tried it out. randSeed(1234) seems to work so we can do it that way. Maybe.

You guys are stalling out on Gull's number (3). Come on! Bring forth the nonsense. Let's see it.
.

I was under the impression that you should now write code that can be run on two computers.

That is already done.
.

[FrediFizzx]

Ok, randSeed(1234) doesn't work. It sets a and b and c to the same angle for each event. It is going to have to be done the other way.
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[FrediFizzx]

Ok, randSeed(1234) doesn't work. It sets a and b and c to the same angle for each event. It is going to have to be done the other way.
.

Correction; it just sets a and b to the same angle. Which is no good of course.
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[gill1109]

You guys are stalling out on Gull's number (3). Come on! Bring forth the nonsense. Let's see it.
.

OK. See (3) in http://www.mrao.cam.ac.uk/~steve/maxent2009/images/bell.pdf. To make things simpler, assume there is no dependence on "n". So we just have one function "p" of one argument theta in [0, 2 pi]. Alice's measurement device responds p(theta) = +/-1 when she supplies setting theta, Bob's responds -p(phi) = +/-1 when he supplies setting phi. Suppose Alice picks the setting U and Bob picks the setting V = U + theta where U is Uniform(0, 2 pi). Suppose this happens repeatedly. What is the correlation? It is
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Define q(v) = p(-v) for all v. Then I can rewrite the previous displayed equation like this:
.
On the right hand side we see minus the convolution of the function p with the function q, evaluated at the argument -theta.
The Fourier transform of a convolution is the product of the Fourier transforms of the functions.
The Fourier transform of q is the complex conjugate of the Fourier transform of p.
So we find (where I use a tilde to denote Fourier transform, and see e.g. https://en.wikipedia.org/wiki/Convolution_theorem to refresh your memory):
.
Now please continue with (4), (5) and (6) yourselves. This was the clever part.

Exercise 1: do this also with p depending on n. Exercise 2: do this also with p_n depending on the past history of the process at both measurement stations including past settings. Hint: use some martingale ideas from Gill (2003), already on arXiv in 2001 https://arxiv.org/abs/quant-ph/0110137. Write up and submit as a paper to IEEE Access. Don't forget to acknowledge Gull and myself and the stackexchange article https://physics.stackexchange.com/questions/547039/help-understanding-prof-steve-gulls-explanation-of-bells-theorem which we looked at earlier.

[FrediFizzx]

You guys are stalling out on Gull's number (3). Come on! Bring forth the nonsense. Let's see it.
.

OK. See (3) in http://www.mrao.cam.ac.uk/~steve/maxent2009/images/bell.pdf. To make things simpler, assume there is no dependence on "n". So we just have one function "p" of one argument theta in [0, 2 pi]. Alice's measurement device responds p(theta) = +/-1 when she supplies setting theta, Bob's responds -p(phi) = +/-1 when he supplies setting phi. Suppose Alice picks the setting U and Bob picks the setting V = U + theta where U is Uniform(0, 2 pi). Suppose this happens repeatedly. What is the correlation? It is
.
Define q(v) = p(-v) for all v. Then I can rewrite the previous displayed equation like this:
.
On the right hand side we see minus the convolution of the function p with the function q, evaluated at the argument -theta.
The Fourier transform of a convolution is the product of the Fourier transforms of the functions.
The Fourier transform of q is the complex conjugate of the Fourier transform of p.
So we find (where I use a tilde to denote Fourier transform, and see e.g. https://en.wikipedia.org/wiki/Convolution_theorem to refresh your memory):
. ... .

Sorry, but that doesn't look at all like what Gull wrote in number (3). Doesn't seem to relate very much to the EPR setup either. And..., what is "u" in your first equation? Please define everything.
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