Gull and Gill's theory

[local]

Perhaps this paper will interest you guys. Shan Gao claims to refute superdeterminism (Section 5.2) and retrocausality (Section 5.3). Shan Gao is a well-known and respected quantum nonlocalist. He co-edited 'Quantum Nonlocality and Reality' with Mary Bell (should be good enough street cred). He also has an interesting paper in that book. It's a great book, by the way. Belongs in every foundationalist's library.

http://philsci-archive.pitt.edu/16155/1 ... %20v99.pdf

I post this here because Austin is discussing retrocausality as a mechanism and Richard has mentioned superdeterminism.

[Austin Fearnley]

BeyondBell2019 v99.pdf, page 12
"Thus, a retrocausal theory will need to ensure that the spin of the
particles have definite values along all directions. But this contradicts Bell’s theorem"

I am not exactly clear why this is said, but I think my classical model of a polarised particle will cope with this criticism.

First a Stern-Gerlach measurement along angle a will polarise a particle along a or -a. A second apparatus measuring at angle b will polarise the same particles along angle b. The second apparatus will find some particles filtered out (according to Malus's Law). The second apparatus does not filter out all particles just because they had been pre-polarised along angle a. This, though, may not correspond exactly with the idea of a superobserver wiping out the first measurement.

The argument in the paper does not note that it is only the antiparticles which are going backwards in time. Maybe my model is unusual in restricting the retro aspect to antiparticles.

My particles do have definite values in all directions. The antiparticles are catered for more simply as they arrive unpolarised and depart the first measurement polarised. It hardly seems a difficulty if the measurement were to be undone and redone. As the antiparticle measurement happens earlier [earlier in the time track of the positron although 'at the same time' in the time track of the electron] than the second measurement [of the electron], there is time for the second measurement to cope with the revised first measurement.

The spin directions of the electrons, always measured second in my retrocausal model, only need to cover all directions appropriate to a polarised particle. That is not all directions. My paper points out that the polarised particles point in all directions in a hemisphere. But there is a statistical distribution covering the directions most favoured.

I mentioned a concavo-convex distribution somewhere on this site. That is because I started with (Chantal Roth's) random-on-a-sphere distribution and showed that was no good. That gives the all-directions are equally likely which are rightly said in this paper to contradict Bell. Then I built up more likelyhood of directions near the pole and fewer near the equator of the hemisphere. Which is a concavo-concex distribution. But if you start with a straight line you can form something like a normal distribution of spin directions on the hemisphere. That would be a 3D distribution which is too complex for me to even think about. But it would be symmetric about the polar axis and have a 2D normal distribution in cross section.

Such a distribution would have spin vectors in all directions in the hemisphere but would not have a random distribution in all directions. Malus's Law gives you the exact classical distribution of spin vectors [you need to differentiate the Malus formula].

The exact spin distribution is 0.5*cos (theta) where you set theta as a deviation from the incoming polarisation angle for the measurement of the electrons. Most spin vectors of the polarised electrons point at theta=0 before measurement.

As this is a statistical distribution the measurement outcomes are variables.

So when the author says "Thus, when Alice measures again the spin of particle 1 at angle b, her second result may be different from her first result and thus will be not anti-correlated with Bob’s result. This contradicts the predictions of quantum mechanics" [page 12] it does not really apply to my method as my method does not use deterministic or fixed outcomes per measurement.

Further, if one could know [like nature knows] which particles were electrons and which were positrons when measuring them, one would not need to use exact pairings [and nature does not need to use exact pairings as it can keep track of which ones are the electrons]. That is because the statistical element takes care of the -a.b result and the entanglement, although it plays its part, is not the driver of the QM correlation. Polarisation is the driver. And Malus's Law shows us that the QM correlation is driven by polarisation alone.

[I also have a VB program on line that simulates S-G measurement results using the above statistical distribution of spin vectors in a polarised beam.]

[gill1109]

Perhaps this paper will interest you guys. Shan Gao claims to refute superdeterminism (Section 5.2) and retrocausality (Section 5.3). Shan Gao is a well-known and respected quantum nonlocalist. He co-edited 'Quantum Nonlocality and Reality' with Mary Bell (should be good enough street cred). He also has an interesting paper in that book. It's a great book, by the way. Belongs in every foundationalist's library.

http://philsci-archive.pitt.edu/16155/1 ... %20v99.pdf

I post this here because Austin is discussing retrocausality as a mechanism and Richard has mentioned superdeterminism.

Wow, fantastic!

Gao has indeed published a book with Cambridge University Press. And the whole book is on arXiv... https://arxiv.org/pdf/1611.02738.pdf

[Heinera]

My intent is not to refute Joy's work, nor do I think I have done so. In fact, I am only familiar with it in a passing way.

Ok. And that seems to be reciprocal:

I have not read Graft's paper.

[local]

Great minds think alike.

[FrediFizzx]

But you don’t say whether you are working within quantum mechanics, or within local realism, or both.

No system can obtain -a.b for space-like separated EPRB, and my posts specifically say so. The Graft papers I have cited make that obvious as well.

Of course that is not true. The GA models easily obtain -a.b.

It looks like Gill's theory is up against another problem. He can't prove within QM that -a.b is even the correct prediction.
.

[gill1109]

But you don’t say whether you are working within quantum mechanics, or within local realism, or both.

No system can obtain -a.b for space-like separated EPRB, and my posts specifically say so. The Graft papers I have cited make that obvious as well.

Of course that is not true. The GA models easily obtain -a.b.

It looks like Gill's theory is up against another problem. He can't prove within QM that -a.b is even the correct prediction.
.

My dear Fred, with all respect, *you* are getting mixed up with the discussion in another thread. I can prove that -a.b is mathematically correct given conventional assumptions. What is physically correct depends on physical assumptions and they obviously should depend on relevant physical circumstances.

The standard QM calculation is:

Expectation of product of spins of Alice and Bob’s particles in a and b directions: <psi| (a.sigma) (x) (b.sigma) |psi>,
where (x) stands for tensor product, and the state vector |psi> = ( |+z> (x) |-z> - |-z> (x) |+z> ) / sqrt 2.

The observables a.sigma, b.sigma could be thought to be “at” the locations where the measurements are done. The state can justly be called a non-local state: it is an equal weight quantum superposition (not a probabilistic mixture) of two orthogonal product states, namely |up, down> and |down, up>.

Particle physics tells us that this is the state of the two particles as they are created, at the source. See Bohm and Aharonovich. Wave particle duality! Quantum superposition of two possible “classical two particle states” is a wave-like phenomenon. The system of two particles has wave-like or particle-like properties, depending on how you interact with it.

Depending on the physical situation, the state of the particles at the detectors could be the same, could be different.

When they arrive at the detectors each particle will likely have experienced a separate unitary transformation, ie, a rotation in the Bloch sphere, depending on the medium through which they travel. Vacuum is one thing, glass fibre at room temperature is another.

In the case of two separate unitary transformations, the “up” and “down” directions (z-axis) at the source, of Alice’s particle, will correspond to two different, opposite, directions at Alice’s detector. In real experiments a period of “tuning” is done, before the definitive experiment starts, to find the correspondence between directions at the two measurement locations. The amounts of rotation in the Bloch sphere depend on the time durations of travel, and maybe on more things too (temperature, electro-magnetic fields encountered en route, ...). The times of travel will not be exactly the same in the two arms of the experiment.

It is also physically possible that some decoherence has occurred. In that case the separate particles can have undergone just about any state transformation allowed by quantum mechanics, due to interaction with other systems “en route”. We know exactly what QM allows and can describe it succinctly in mathematical terms. The density matrix can undergo any transformation described by a completely positive, normalised, positive map. There are elegant mathematical representations of the class of all such maps.

So it is easy to describe *all possible* correlation functions allowed in this experiment by QM. Which one will hold in a given experiment depends on the physical circumstances in that case.

[FrediFizzx]

But you don’t say whether you are working within quantum mechanics, or within local realism, or both.

No system can obtain -a.b for space-like separated EPRB, and my posts specifically say so. The Graft papers I have cited make that obvious as well.

Of course that is not true. The GA models easily obtain -a.b.

It looks like Gill's theory is up against another problem. He can't prove within QM that -a.b is even the correct prediction.
.

My dear Fred, with all respect, *you* are getting mixed up with the discussion in another thread. I can prove that -a.b is mathematically correct given conventional assumptions. What is physically correct depends on physical assumptions and they obviously should depend on relevant physical circumstances.

The standard QM calculation is:

Expectation of product of spins of Alice and Bob’s particles in a and b directions: <psi| (a.sigma) (x) (b.sigma) |psi>,
where (x) stands for tensor product, and the state vector |psi> = ( |+z> (x) |-z> - |-z> (x) |+z> ) / sqrt 2. ...

Sorry, once you have the observables, psi no longer exists. That calculation is a farce. Bottom line is that you can't use the singlet wavefunction in separated measurements. So, try again without using psi.
.

[gill1109]

The standard QM calculation is:
Expectation of product of spins of Alice and Bob’s particles in a and b directions: <psi| (a.sigma) (x) (b.sigma) |psi>,
where (x) stands for tensor product, and the state vector |psi> = ( |+z> (x) |-z> - |-z> (x) |+z> ) / sqrt 2.

Sorry, once you have the observables, psi no longer exists. That calculation is a farce. Bottom line is that you can't use the singlet wavefunction in separated measurements. So, try again without using psi.

That is the calculation which Jay Yablon wrote out, and which you programmed in Mathematica.

The singlet state-vector is shown by particle physics calculations to be the (pure) state of the particles’ spin state at the moment they are created. Read Aharonov and Bohm, 1957. Physicists (working within QM) tell me that depending on the time and means of transmission, their state as they reach the detectors might be the same, might be different.

Please tell me how you think the state evolves. Or are you saying that QM is a farce, we should use something completely quite different? Anyway, do you think that the right answer is -a.b, or do you think it is something else?

[FrediFizzx]

The standard QM calculation is:
Expectation of product of spins of Alice and Bob’s particles in a and b directions: <psi| (a.sigma) (x) (b.sigma) |psi>,
where (x) stands for tensor product, and the state vector |psi> = ( |+z> (x) |-z> - |-z> (x) |+z> ) / sqrt 2.

Sorry, once you have the observables, psi no longer exists. That calculation is a farce. Bottom line is that you can't use the singlet wavefunction in separated measurements. So, try again without using psi.

That is the calculation which Jay Yablon wrote out, and which you programmed in Mathematica.

The singlet state-vector is shown by particle physics calculations to be the (pure) state of the particles’ spin state at the moment they are created. Read Aharonov and Bohm, 1957. Physicists (working within QM) tell me that depending on the time and means of transmission, their state as they reach the detectors might be the same, might be different.

Please tell me how you think the state evolves. Or are you saying that QM is a farce, we should use something completely quite different? Anyway, do you think that the right answer is -a.b, or do you think it is something else?

I don't care how the state evolves. Once those two singlet particles hit the polarizers, the state is gone. You can't use the state to calculate what happens. The only thing we know that remains is that if one of the particles spin vector is "s" then the other one has to be "-s" at the time right before they hit the polarizers.

With the calculation Jay did, the observables would have to happen at the same time the singlet particles were created. It's probably wrong. At this point I don't know what the QM prediction should be. Or even if QM can actually do the prediction. My local QM calculation says it can be and it is -a.b but had to resort to a funky limit process to circumvent a flaw in the math of QM.
.

[gill1109]

The standard QM calculation is:
Expectation of product of spins of Alice and Bob’s particles in a and b directions: <psi| (a.sigma) (x) (b.sigma) |psi>,
where (x) stands for tensor product, and the state vector |psi> = ( |+z> (x) |-z> - |-z> (x) |+z> ) / sqrt 2.

Sorry, once you have the observables, psi no longer exists. That calculation is a farce. Bottom line is that you can't use the singlet wavefunction in separated measurements. So, try again without using psi.

That is the calculation which Jay Yablon wrote out, and which you programmed in Mathematica.

The singlet state-vector is shown by particle physics calculations to be the (pure) state of the particles’ spin state at the moment they are created. Read Aharonov and Bohm, 1957. Physicists (working within QM) tell me that depending on the time and means of transmission, their state as they reach the detectors might be the same, might be different.

Please tell me how you think the state evolves. Or are you saying that QM is a farce, we should use something completely quite different? Anyway, do you think that the right answer is -a.b, or do you think it is something else?

I don't care how the state evolves. Once those two singlet particles hit the polarizers, the state is gone. You can't use the state to calculate what happens. The only thing we know that remains is that if one of the particles spin vector is "s" then the other one has to be "-s" at the time right before they hit the polarizers.

With the calculation Jay did, the observables would have to happen at the same time the singlet particles were created. It's probably wrong. At this point I don't know what the QM prediction should be. Or even if QM can actually do the prediction. My local QM calculation says it can be and it is -a.b but had to resort to a funky limit process to circumvent a flaw in the math of QM.
.

Ah, I think I get you. When you say “the observables happen” you mean “when the measurements [of the “observables”] get done”.

Well, when particle A meets detector A something happens, and I think people would tend to think that it must depend on the state of particle A and the state of detector A. I am using the word “state” in a non-technical sense. I don’t mean the state as it is represented in QM. I think of the state as it would be in classical physics. The physical state of the stuff that is actually there, positions, momenta etc, also in internal (“hidden”) degrees of freedom.

That’s certainly what Einstein thought. Bohr thought differently and later, Bohm thought differently. They thought that what happened at A and B depended on the state of everything at A and B, and *couldn’t* be separated into separate considerations concerning separate parts of space time. David Bohm wrote a book called “the undivided universe”. Bohemian mechanics reproduces quantum mechanics perfectly (but is non-local).

Historical side remarks: Bohm was the favourite student of the father of the A-bomb, Robert Oppenheimer. Bohm was agreed by everyone to be utterly brilliant. Then everyone agreed he went nuts. But nobody could find any mistakes in his work. But he had briefly been a communist. That was the end of his career in the US. The US had no problem in employing former nazi nuclear physicists and rocket scientists. When the Sputnik was launched some said “their Germans must be better than ours”. The US and USSR rushed to collect the best. The UK was not interested.

[FrediFizzx]

So, say we don't do the limit substitution for the product calculation of the local QM scenario. What do we get? We will also switch to angles between the vectors otherwise will we drown in a sea of mixed vector components. We will also label the particle spin vectors separately. The result is,



There are 4 occurrences to consider,

up - up = -1
down - down = -Cos[2 a] Cos[2 b]
up - down = -Cos[2 b]
down - up = -Cos[2 a]

Add them together and simplify you get,



So, that should be the prediction from local separate measurements.
.

[FrediFizzx]

So, say we don't do the limit substitution for the product calculation of the local QM scenario. What do we get? We will also switch to angles between the vectors otherwise will we drown in a sea of mixed vector components. We will also label the particle spin vectors separately. The result is,



There are 4 occurrences to consider,

up - up = -1
down - down = -Cos[2 a] Cos[2 b]
up - down = -Cos[2 b]
down - up = -Cos[2 a]

Add them together and simplify you get,



So, that should be the prediction from local separate measurements.
.

Of course that result doesn't make sense. Probably have to just go with the 4 occurrences.
.

[gill1109]

So, say we don't do the limit substitution for the product calculation of the local QM scenario. What do we get? We will also switch to angles between the vectors otherwise will we drown in a sea of mixed vector components. We will also label the particle spin vectors separately. The result is,

There are 4 occurrences to consider,
up - up = -1
down - down = -Cos[2 a] Cos[2 b]
up - down = -Cos[2 b]
down - up = -Cos[2 a]
Add them together and simplify you get,

So, that should be the prediction from local separate measurements.
.

Of course that result doesn't make sense. Probably have to just go with the 4 occurrences.

It’s puzzling, Fred, I agree. Meanwhile My paper with my student Dilara on Gull’s proof is on arXiv. https://arxiv.org/abs/2012.00719 We fixed Gull’s proof up to the last line. Don’t know how to do that yet, but this morning I have a new idea.

I must also add to the paper, the fact that this project was a response to a challenge proposed by Joy Christian http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=275#p6681

[gill1109]

Yeah! Gull's proof is saved. https://www.math.leidenuniv.nl/~gill/gull.pdf

[FrediFizzx]

Yeah! Gull's proof is saved. https://www.math.leidenuniv.nl/~gill/gull.pdf

Well, I doubt that but it doesn't matter now anyways. You can't prove that -a.b is the correct prediction. You would think after all these years someone should have seen that the prediction only works if everything happens all at once.
.

[gill1109]

Yeah! Gull's proof is saved. https://www.math.leidenuniv.nl/~gill/gull.pdf

Well, I doubt that but it doesn't matter now anyways. You can't prove that -a.b is the correct prediction. You would think after all these years someone should have seen that the prediction only works if everything happens all at once.
.

Gull’s proof, and Gill’s proof, are proofs of a theorem about Local Realism, not proofs of a theorem about Quantum Mechanics. The theorem says that -a.b is the wrong prediction in local realism, too. In fact, the theorem is Bell’s theorem. The proofs are alternative proofs. Gull’s proof uses Fourier theory.

Gull’s proof can be fixed but it needs one extra step, and it needs a lot of expansion. I’m really grateful to y’all here for pushing me to get it sorted out. I thank Fred and Joy in the acknowledgments. I was thinking of inviting you to be co-authors but I decided you would not be interested. Let me know if I was wrong.

There are other people who think -a.b can’t be derived in QM when the measurements are done separately, and far from the source. I am not qualified to say much about that. Aspect did his experiments at a time when many people in quantum physics expected he would not find -a.b. But that’s what he found. Then people like Caroline Thompson argued that his data analysis was wrong. So the experiment got improved, re-done, .... That’s science.

[FrediFizzx]

Yeah! Gull's proof is saved. https://www.math.leidenuniv.nl/~gill/gull.pdf

Well, I doubt that but it doesn't matter now anyways. You can't prove that -a.b is the correct prediction. You would think after all these years someone should have seen that the prediction only works if everything happens all at once.
.

Gull’s proof, and Gill’s proof, are proofs of a theorem about Local Realism, not proofs of a theorem about Quantum Mechanics. The theorem says that -a.b is the wrong prediction in local realism, too. In fact, the theorem is Bell’s theorem. The proofs are alternative proofs. Gull’s proof uses Fourier theory.

Gull’s proof can be fixed but it needs one extra step, and it needs a lot of expansion. I’m really grateful to y’all here for pushing me to get it sorted out. I thank Fred and Joy in the acknowledgments. I was thinking of inviting you to be co-authors but I decided you would not be interested. Let me know if I was wrong.

There are other people who think -a.b can’t be derived in QM when the measurements are done separately, and far from the source. I am not qualified to say much about that. Aspect did his experiments at a time when many people in quantum physics expected he would not find -a.b. But that’s what he found. Then people like Caroline Thompson argued that his data analysis was wrong. So the experiment got improved, re-done, .... That’s science.

You don't get it do you? Those so-called "proofs" use the so-called prediction of QM. If you can't prove the QM prediction then they don't go through.

Is there a plot of Aspect's finding of -a.b? Or did he just agree with CHSH?
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[gill1109]

You don't get it do you? Those so-called "proofs" use the so-called prediction of QM. If you can't prove the QM prediction then they don't go through.

Is there a plot of Aspect's finding of -a.b? Or did he just agree with CHSH?
.

Dear Fred, You don’t get it, I think! Read the paper. You are mentioned in it.

It mentions (does not even use) the QM prediction -a.b when the measurements are not “separate”.

When Joy Christian plots the negative cosine and derives it with GA, he does not “use” the QM “prediction”.

Aspect’s famous papers contain plots, I believe. He neither agrees nor disagrees with the CHSH inequality. They are experimental papers.

[FrediFizzx]

You don't get it do you? Those so-called "proofs" use the so-called prediction of QM. If you can't prove the QM prediction then they don't go through.

Is there a plot of Aspect's finding of -a.b? Or did he just agree with CHSH?
.

Dear Fred, You don’t get it, I think! Read the paper. You are mentioned in it.

It mentions (does not even use) the QM prediction -a.b when the measurements are not “separate”.

When Joy Christian plots the negative cosine and derives it with GA, he does not “use” the QM “prediction”.

Aspect’s famous papers contain plots, I believe. He neither agrees nor disagrees with the CHSH inequality. They are experimental papers.

What is this? Some kind of clown show act? You are claiming that a local theory can't do the -a.b prediction with event by event outcomes!

I meant "exceeds CHSH" instead of "agree with CHSH". I believe he only exceeded CHSH which doesn't necessarily validate -a.b as you well know. Could be something else.
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