Gull and Gill's theory

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

Gull and Gill's theory

Postby gill1109 » Mon Nov 02, 2020 10:39 pm

FrediFizzx wrote:
gill1109 wrote:
FrediFizzx wrote:
FrediFizzx wrote:Gull's number (4) is correct but he neglected to mention that those 3 non-zero FT components are Dirac Delta infinite spikes.
.

According to what he had to use for number (3) to make it correct, one of the two is wrong. If you integrate a cyclical function from -infinity to +infinity of course you will get infinity. It is silly to do that transform for a cyclical function. We are typically only interested in what happens over one cycle.
.

Exactly. You need the Fourier series, not the Fourier transform. ...

Nonsense.

Image

The Fourier Series of that function is just the same as converting the function to exponentials.
.

Yes, exactly!!!!

The "Fourier series" is, strictly speaking, a *sequence* of complex numbers indexed by n in Z, found by applying the discrete Fourier transform. Your sequence has just three non-zero coefficients.

The reverse discrete Fourier transform takes the sequence, multiplies those numbers by exp(i n theta), and sums over n. That infinite summation is what Mathematica is showing you. In your case, it is a finite summation of just three terms.

When you ask Mathematica for the Fourier series of a function, it simply rewrites your function as sum c_n exp(i n theta).

The terminology is a bit tricky, and not everyone uses the same.

Can you ask Mathematica for the sequence of Fourier coefficients?
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Re: Gull and Gill's theory

Postby FrediFizzx » Tue Nov 03, 2020 1:14 pm

I'll say it again. Looks like more nonsense piled on top of nonsense. Write your paper then we will discuss your nonsense here. :mrgreen:
.
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Re: Gull and Gill's theory

Postby Joy Christian » Tue Nov 03, 2020 2:17 pm

FrediFizzx wrote:
I'll say it again. Looks like more nonsense piled on top of nonsense. Write your paper then we will discuss your nonsense here. :mrgreen:

You have wasted too much time on this junk. But I hope you had some fun along the way. These guys are on the wrong side of history, incapable of accepting that their horse is long dead.

***
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Re: Gull and Gill's theory

Postby gill1109 » Tue Nov 03, 2020 8:24 pm

Joy Christian wrote:
FrediFizzx wrote:
I'll say it again. Looks like more nonsense piled on top of nonsense. Write your paper then we will discuss your nonsense here. :mrgreen:

You have wasted too much time on this junk. But I hope you had some fun along the way. These guys are on the wrong side of history, incapable of accepting that their horse is long dead.

I had a lot of fun! All issues are now resolved. Got some writing to do. I’ll be back. 8-)
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Re: Gull and Gill's theory

Postby FrediFizzx » Wed Nov 04, 2020 6:15 am

Joy Christian wrote:
FrediFizzx wrote:
I'll say it again. Looks like more nonsense piled on top of nonsense. Write your paper then we will discuss your nonsense here. :mrgreen:

You have wasted too much time on this junk. But I hope you had some fun along the way. These guys are on the wrong side of history, incapable of accepting that their horse is long dead.

***

It is fun banging around with Mathematica and watching someone make a fool of themselves. Typical case; the Fourier Series of the function just returns the function itself in a different form. Sure there are 3 components but there are no zero components either like in the case with the transform. So, why would you call the 3 components "non-zero"? Sure they are non-zero because that is the only components there are.

This Fourier Transform business is truly a bunch of nonsense. Gull's "proof" is shot down. If Nature does it, it can be modelled both analytically and with computers. Simple as that.
.
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Re: Gull and Gill's theory

Postby gill1109 » Wed Nov 04, 2020 10:02 am

FrediFizzx wrote:
Joy Christian wrote:
FrediFizzx wrote:I'll say it again. Looks like more nonsense piled on top of nonsense. Write your paper then we will discuss your nonsense here. :mrgreen:

You have wasted too much time on this junk. But I hope you had some fun along the way. These guys are on the wrong side of history, incapable of accepting that their horse is long dead.

It is fun banging around with Mathematica and watching someone make a fool of themselves. Typical case; the Fourier Series of the function just returns the function itself in a different form. Sure there are 3 components but there are no zero components either like in the case with the transform. So, why would you call the 3 components "non-zero"? Sure they are non-zero because that is the only components there are.
This Fourier Transform business is truly a bunch of nonsense. Gull's "proof" is shot down. If Nature does it, it can be modelled both analytically and with computers. Simple as that.

Of course, it can be done with a computer. But not with distributed computing.

You really helped me, Fred, understand Gull's proof better. So you did great work. But, you are so blind. You just don't want to see. You twigged Gull's (4). But you forgot about his (3). So you never got to the punchline.

The Fourier series representation of a function does just that: it reproduces the function, representing it as a sum of sines and cosines. It's called a series because it's usually an infinite summation. The point is that we can learn something about the Fourier series of the measurement functions, from looking at the Fourier series of the correlation function.

Here is a first incomplete draft. https://www.math.leidenuniv.nl/~gill/gull.pdf. There is an interesting math problem to solve. If you (or someone else) can help us with the last line of the proof, you can join us as co-author. I agree now that Gull's theorem ends with a heuristic (intuitive) argument. I think it can be made rigorous but nobody did that yet. The stackexchange guy also left that bit informal.

Fortunately, Gill's (2003) theorem was already much stronger. And doesn't ask for perfect anti-correlation at equal settings. But maybe Gull's argument can be generalised in that direction too.
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Re: Gull and Gill's theory

Postby gill1109 » Thu Nov 05, 2020 3:57 am

I found a good book on the Fourier stuff: https://calhoun.nps.edu/handle/10945/39313

An Introduction to Fourier Analysis.
Fourier Series, Partial Differential Equations and Fourier Transforms.
Notes prepared for MA3139, by Arthur L. Schoenstadt
(Department of Applied Mathematics Naval Postgraduate School Code MA/Zh, Monterey, California 93943)
August 18, 2005

You just need:

Section 2.6. The Complex Form of the Fourier Series.
Section 6.2. Convolution and Fourier Transforms.
Section 6.9. Correlation.
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Re: Gull and Gill's theory

Postby gill1109 » Thu Nov 05, 2020 10:05 am

gill1109 wrote:I found a good book on the Fourier stuff: https://calhoun.nps.edu/handle/10945/39313

An Introduction to Fourier Analysis.
Fourier Series, Partial Differential Equations and Fourier Transforms.
Notes prepared for MA3139, by Arthur L. Schoenstadt
(Department of Applied Mathematics Naval Postgraduate School Code MA/Zh, Monterey, California 93943)
August 18, 2005

You just need:

Section 2.6. The Complex Form of the Fourier Series.
Section 6.2. Convolution and Fourier Transforms.
Section 6.9. Correlation.

Meantime, I'm beginning to think that Gull's proof can't be finished. The theorem is true, but I'm beginning to fear that Gull's argument can't be completed. Stuck on the last line. Anyone who comes up with a resolution - we have a paper together!

Fortunately, we still have Bell's argument, and Gill's strengthening thereof.
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Re: Gull and Gill's theory

Postby Heinera » Fri Nov 06, 2020 4:23 am

gill1109 wrote:Meantime, I'm beginning to think that Gull's proof can't be finished.

I agree with you. We have sequence of discontinuous functions that all have an infinity of fourier coefficients, but there is a priori no reason why that sequence could not converge to a function with only a finite number of coefficients.

And we already have much simpler proofs of Bell's theorem, so I don't see how Gull's proof (if indeed it can be turned into a proper proof) can add any kind of intuition to what is after all a rather trivial theorem.
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Re: Gull and Gill's theory

Postby gill1109 » Fri Nov 06, 2020 5:31 am

Heinera wrote:
gill1109 wrote:Meantime, I'm beginning to think that Gull's proof can't be finished.

I agree with you. We have sequence of discontinuous functions that all have an infinity of fourier coefficients, but there is a priori no reason why that sequence could not converge to a function with only a finite number of coefficients.

And we already have much simpler proofs of Bell's theorem, so I don't see how Gull's proof (if indeed it can be turned into a proper proof) can add any kind of intuition to what is after all a rather trivial theorem.

I agree. But I do see a challenging, and interesting, mathematical puzzle. Gull has a nice idea. Can it be turned into a proof which might appeal to more people, than the existing (incontrovertible) existing proofs do? Obviously, those whose minds are already made up, won’t be impressed. But it could make an impression on those whose minds do still allow a possibility that their instincts are wrong. This, kind of, separates the “believers” from the “scientists”. At least, it further reduces the set of “Joy Christian believers” to a tiny cargo cult. Of course, maybe they are right! I can always be wrong. Joy Christian has stated that he cannot be wrong. Interesting!
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Re: Gull and Gill's theory

Postby Austin Fearnley » Fri Nov 06, 2020 6:22 am

What a shame! There ought to be a mathematical law against it (against Heinera's point). Gull presumably thought so?

Functions A and B, if they were to exist, need to be step functions as the measurement outputs are 1 or 0 {or 1 and -1}. For example, "measurement A = 1 if particle vector > alpha degrees else A = 0". So you have an average of products of two step functions in the p++ cell of the 2x2 results table of a Bell experiment. It seems easy to sympathise with Gull in assuming (if that is what he did) that you cannot model such an angular 'curve' (composed of step-function products) using only two terms of a fourier series.

Is there no way of showing that the products of step functions are straight lines? The classical correlation is the sawtooth curve, 2*θ/π -1, which is a straight line in (0, pi/2). The value in the first cell of the 2x2 Bell results table is also proportional to θ.

The Fourier series in Wolfram for θ (that is for a straight line) gives
iexp(-iθ) - iexp(iθ) - (1/2)iexp(-2iθ) + (1/2)iexp(2iθ)
+ (1/3)iexp(-3iθ) - (1/3)iexp(3iθ) etc ... with many terms...

It seems very anti the spirit of Fourier (but what do know as I learned it in the 1960s and haven't used it since) to take one 'straight curve' and fit an infinite number of Fourier component curves to it to get a good match asymptotically ... but then to worry that we could have found a match with just two Fourier curves if only we knew those two curves.

It seems essential to show that an average of products of step functions is a straight line? And afterwards, is it only intuition that you need a lot of Fourier terms (>>2) to model a straight line?
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Re: Gull and Gill's theory

Postby FrediFizzx » Fri Nov 06, 2020 8:50 am

Heinera wrote:
gill1109 wrote:Meantime, I'm beginning to think that Gull's proof can't be finished.

...
And we already have much simpler proofs of Bell's theorem, so I don't see how Gull's proof (if indeed it can be turned into a proper proof) can add any kind of intuition to what is after all a rather trivial theorem.

All the other "proofs" are shot down two ways. The simple fact that NOTHING can exceed the Bell inequalities and we have GA models that match the predictions of quantum mechanics. All that was left is Gull's junk "proof" and it is shot down now also. So, Gill's "theorem" is now just a theory.
.
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Re: Gull and Gill's theory

Postby gill1109 » Fri Nov 06, 2020 9:15 am

Austin Fearnley wrote:What a shame! There ought to be a mathematical law against it (against Heinera's point). Gull presumably thought so?

Functions A and B, if they were to exist, need to be step functions as the measurement outputs are 1 or 0 {or 1 and -1}. For example, "measurement A = 1 if particle vector > alpha degrees else A = 0". So you have an average of products of two step functions in the p++ cell of the 2x2 results table of a Bell experiment. It seems easy to sympathise with Gull in assuming (if that is what he did) that you cannot model such an angular 'curve' (composed of step-function products) using only two terms of a fourier series.

Is there no way of showing that the products of step functions are straight lines? The classical correlation is the sawtooth curve, 2*θ/π -1, which is a straight line in (0, pi/2). The value in the first cell of the 2x2 Bell results table is also proportional to θ.

The Fourier series in Wolfram for θ (that is for a straight line) gives
iexp(-iθ) - iexp(iθ) - (1/2)iexp(-2iθ) + (1/2)iexp(2iθ)
+ (1/3)iexp(-3iθ) - (1/3)iexp(3iθ) etc ... with many terms...

It seems very anti the spirit of Fourier (but what do know as I learned it in the 1960s and haven't used it since) to take one 'straight curve' and fit an infinite number of Fourier component curves to it to get a good match asymptotically ... but then to worry that we could have found a match with just two Fourier curves if only we knew those two curves.

It seems essential to show that an average of products of step functions is a straight line? And afterwards, is it only intuition that you need a lot of Fourier terms (>>2) to model a straight line?

The average of products of step functions is *not* a straight line. There are lots of things it can be. See my paper https://arxiv.org/abs/1312.6403. Lots of nice pictures!
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Re: Gull and Gill's theory

Postby gill1109 » Fri Nov 06, 2020 9:24 am

FrediFizzx wrote:
Heinera wrote:
gill1109 wrote:Meantime, I'm beginning to think that Gull's proof can't be finished.

...
And we already have much simpler proofs of Bell's theorem, so I don't see how Gull's proof (if indeed it can be turned into a proper proof) can add any kind of intuition to what is after all a rather trivial theorem.

All the other "proofs" are shot down two ways. The simple fact that NOTHING can exceed the Bell inequalities and we have GA models that match the predictions of quantum mechanics. All that was left is Gull's junk "proof" and it is shot down now also. So, Gill's "theorem" is now just a theory.

Gill’s theorem has never been shot down. It has stood unchallenged since 2001. https://arxiv.org/abs/quant-ph/0110137. Gill says that it is not possible to reproduce the singlet correlations on two networked PC’s, which each have to repeatedly deliver a measurement outcome on being given a measurement setting, without knowledge of the other computer’s setting. Of course, there is a chance they might do this, to some approximation, in a finite length run of N trials just by luck, but the chance is exponentially small. Gill’s theorem tells you how big you should take N, in order to get the chance below any level you like.

Gull’s conjectured theorem is also true. It’s a weaker claim. He only talks about the limiting case when N has converged to infinity. Gill deals with finite N. The limiting case is a corollary.

But whether or not Gull’s heuristic proof can be completed is open. It’s an amusing and challenging problem. All hands on deck! We can publish a nice paper on this, when we have found a solution (filled in the gap in his proof).

We have no GA model that runs on two separated computers.

True theorems are tautologies. Bell’s theorem is a true theorem. You can only avoid the conclusion by not satisfying the assumptions. Fred Diether’s GAViewer program is no exception. It cannot be converted into two networked programs, each receiving only one stream (Alice’s or Bob’s) of angles, and still reproduce the singlet correlations.

The only way to do it would be to use quantum computers and quantum internet connections between them! That is how nature does it.
Last edited by gill1109 on Fri Nov 06, 2020 9:41 am, edited 2 times in total.
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Re: Gull and Gill's theory

Postby FrediFizzx » Fri Nov 06, 2020 9:40 am

gill1109 wrote:
FrediFizzx wrote:
Heinera wrote:
gill1109 wrote:Meantime, I'm beginning to think that Gull's proof can't be finished.

...
And we already have much simpler proofs of Bell's theorem, so I don't see how Gull's proof (if indeed it can be turned into a proper proof) can add any kind of intuition to what is after all a rather trivial theorem.

All the other "proofs" are shot down two ways. The simple fact that NOTHING can exceed the Bell inequalities and we have GA models that match the predictions of quantum mechanics. All that was left is Gull's junk "proof" and it is shot down now also. So, Gill's "theorem" is now just a theory.

Gill’s theorem has never been shot down. (nonsense snipped out) ...

You have NO proof so it can't be a theorem. It is now just a theory. But if Nature does in fact do it, then your theory is most likely shot down.
.
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Re: Gull and Gill's theory

Postby gill1109 » Fri Nov 06, 2020 9:47 am

FrediFizzx wrote:You have NO proof so it can't be a theorem. It is now just a theory. But if Nature does in fact do it, then your theory is most likely shot down.

Please read my paper. It’s been on arXiv for 19 years, it’s been peer reviewed and published for 17. The main result has been improved, sharpened, both by myself and by others. It was used in all four 2015 loophole free experiments. The experimentalists cited my work and acknowledged my contribution.

Nature does it, using quantum entanglement.
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Re: Gull and Gill's theory

Postby FrediFizzx » Fri Nov 06, 2020 9:58 am

gill1109 wrote:
FrediFizzx wrote:You have NO proof so it can't be a theorem. It is now just a theory. But if Nature does in fact do it, then your theory is most likely shot down.

Please read my paper. It’s been on arXiv for 19 years, it’s been peer reviewed and published for 17. The main result has been improved, sharpened, both by myself and by others. It was used in all four 2015 loophole free experiments. The experimentalists cited my work and acknowledged my contribution.

Nature does it, using quantum entanglement.

Sorry, Jay Yablon shot down quantum entanglement with his successful demonstration that QM is local for the EPR-Bohm scenario. So, you really should get off that nonsense. All the experiments do is validate QM. Nothing more since ALL the "proofs" of Bell's junk physics theory are shot down.
.
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Re: Gull and Gill's theory

Postby local » Fri Nov 06, 2020 10:07 am

gill1109 wrote: At least, it further reduces the set of “Joy Christian believers” to a tiny cargo cult.


Of course, maybe they are right!

This stuff is why you have zero credibility. You acknowledge that “Joy Christian believers” (already a slur) may be right, but you have no problem dismissing it as a "tiny cargo cult". Shame on you!
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Re: Gull and Gill's theory

Postby FrediFizzx » Fri Nov 06, 2020 5:46 pm

Austin Fearnley wrote:What a shame! There ought to be a mathematical law against it (against Heinera's point). Gull presumably thought so?

Functions A and B, if they were to exist, need to be step functions as the measurement outputs are 1 or 0 {or 1 and -1}. For example, "measurement A = 1 if particle vector > alpha degrees else A = 0". So you have an average of products of two step functions in the p++ cell of the 2x2 results table of a Bell experiment. It seems easy to sympathise with Gull in assuming (if that is what he did) that you cannot model such an angular 'curve' (composed of step-function products) using only two terms of a fourier series.

Is there no way of showing that the products of step functions are straight lines? The classical correlation is the sawtooth curve, 2*θ/π -1, which is a straight line in (0, pi/2). The value in the first cell of the 2x2 Bell results table is also proportional to θ.

The Fourier series in Wolfram for θ (that is for a straight line) gives
iexp(-iθ) - iexp(iθ) - (1/2)iexp(-2iθ) + (1/2)iexp(2iθ)
+ (1/3)iexp(-3iθ) - (1/3)iexp(3iθ) etc ... with many terms...

It seems very anti the spirit of Fourier (but what do know as I learned it in the 1960s and haven't used it since) to take one 'straight curve' and fit an infinite number of Fourier component curves to it to get a good match asymptotically ... but then to worry that we could have found a match with just two Fourier curves if only we knew those two curves.

It seems essential to show that an average of products of step functions is a straight line? And afterwards, is it only intuition that you need a lot of Fourier terms (>>2) to model a straight line?

Well, the problem I'm seeing with doing simulations is the sign function. Which is basically a step function. The sign function is essentially a linear function. So, I have been trying to think of a novel way of generating the +/-1 outcomes using a function that is not so linear.
.
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Re: Gull and Gill's theory

Postby gill1109 » Fri Nov 06, 2020 6:41 pm

FrediFizzx wrote:
gill1109 wrote:
FrediFizzx wrote:You have NO proof so it can't be a theorem. It is now just a theory. But if Nature does in fact do it, then your theory is most likely shot down.

Please read my paper. It’s been on arXiv for 19 years, it’s been peer reviewed and published for 17. The main result has been improved, sharpened, both by myself and by others. It was used in all four 2015 loophole free experiments. The experimentalists cited my work and acknowledged my contribution.

Nature does it, using quantum entanglement.

Sorry, Jay Yablon shot down quantum entanglement with his successful demonstration that QM is local for the EPR-Bohm scenario. So, you really should get off that nonsense. All the experiments do is validate QM. Nothing more since ALL the "proofs" of Bell's junk physics theory are shot down.
.

Jay redefined “local”. He is not the first to resolve the problem in this way.

David Bohm came to the conclusion that nature is one undivided whole, and in effect argued that the word “local” is meaningless.

Experiments validate QM.

Nobody has been able to simulate quantum correlations on ordinary networked PCs without violating local causality or using conspiratorial means.

Nobody has found errors in the mathematical proofs that the networked computer simulation is impossible.

A handful of people dream that Bell was wrong. I support their efforts, even though I am sure their dream cannot become reality. But they can be on to something. The mainstream becomes complacent, arrogant. We need original outsider thinkers who challenge orthodoxy. Amateurs can and do deliver breakthroughs from time to time. Just occasionally, foundations are shaken. People discover that they were asking the wrong question. “Yes” and “no” can both be a right answer, if the question is ill-posed.

I hope Fred keeps on trying and I hope that this forum continues to be a place of spirited argument.
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