Gull and Gill's theory

[minkwe]

So . This has nothing to do with signaling.

Does have anything to do with signalling?

Yes. Because it means that Bob can learn something about Alice's setting by seeing whether or not B happens (while, of course, knowing b). The probability of what he sees varies, depending on Alice's setting a. So he can rightly make different bets on what b is, depending on whether or not B happens (while knowing, of course, b).

The same thing for A in the previous expression, yet you guys consider one as signaling and not the other.

[Heinera]

[...]
But first, what do you understand by "signaling"?

I snipped the previous part of your post because I think this last sentence covers the essence of it.

"Signaling" means that there is a procedure whereby someone with a hypothetical free will has some means to somehow change the physical configuration at another place in time and space (also known as "transferring information"). This should be interpreted in a way that also includes change in entropy; i.e. any transfer of information entropy counts as signaling. Thus any statistical procedure for transferring information will also count as signaling.

This is not a mathematical definition, because there is no unique mathematical definition. Since signaling is in its essence a physical process, any mathematical definition will necessarily be domain dependent. (The one that got closest to an all-encompassing definition was Claude Shannon.)

However, the definition above has the advantage of clearly placing the burden of proof: If someone claims that signaling is possible for a particular physical configuration, it is up to that person to provide a specific mechanism (or in the case of statistical data, an algorithm) whereby information can be transferred.

In the EPR experiment we are discussing here it is obvious that outcomes at the stations cannot be used to transfer information, since they are beyond the observer's control.

[minkwe]

In the EPR experiment we are discussing here it is obvious that outcomes at the stations cannot be used to transfer information, since they are beyond the observer's control.

So why does Alice bother to change settings if the outcomes cannot be influenced?

[Heinera]

In the EPR experiment we are discussing here it is obvious that outcomes at the stations cannot be used to transfer information, since they are beyond the observer's control.

So why does Alice bother to change settings if the outcomes cannot be influenced?

But they can't be influenced. No matter her settings they will be 50/50. And the same goes for Bob.

The correlation can be influenced, but that doesn't help any of them, since they have to come together to compute the correlation.

[minkwe]

But they can't be influenced. No matter her settings they will be 50/50. And the same goes for Bob.

So what is the point of the setting if the outcome cannot be influenced by it? Are you not understanding my question?

[Heinera]

But they can't be influenced. No matter her settings they will be 50/50. And the same goes for Bob.

So what is the point of the setting if the outcome cannot be influenced by it? Are you not understanding my question?

The correlation can be influenced, but that doesn't help any of them, since they have to come together to compute the correlation.

[minkwe]

The correlation can be influenced, but that doesn't help any of them, since they have to come together to compute the correlation.

I'm actually not interested in helping anyone. I just want to understand why anyone bothers changing settings if they don't influence the outcomes and how the correlation can be influenced by the settings unless the outcomes themselves used to calculate the correlations have first been influenced by the settings.

Alice: Setting -> outcome -> correlation <- outcome <- setting <- : Bob

Do you see the problem? The correlation is calculated using outcomes and you are claiming the correlation can be influenced by the settings but not the outcomes. How does this influence propagate? What is the mechanism of it?

It looks like we don't even need proof of inequalities to arrive at the spooky business. We have it right here at the start of the discussion.

[Heinera]

Why do you call it "spooky"? There is no way to transfer information from Alice to Bob or vice versa, so everything is perfectly consistent with special relativity. Correlation is not causation.

But obviously, Bell's theorem tells us that we can't think about this the same way as we think about classical physics. The pioneers of QM knew this way before Bell. What you are doing is simply rehashing the arguments Einstein had with Bohr.

[minkwe]

Why do you call it "spooky"? There is no way to transfer information from Alice to Bob or vice versa, so everything is perfectly consistent with special relativity. Correlation is not causation.

But obviously, Bell's theorem tells us that we can't think about this the same way as we think about classical physics. The pioneers of QM knew this way before Bell. What you are doing is simply rehashing the arguments Einstein had with Bohr.

I note that you can't tell me how the settings influence the correlation without influencing the outcomes used to calculate the correlations. What is spooky is the idea that Alice and Bob change their settings but those settings don't influence the outcomes actually measured. Then months later when some dude decides to do correlation calculations, the influence pops into existence and influences the correlations. This is the Cadillac of spooky business. Where was this influence lurking in the interim?

[gill1109]

Why do you call it "spooky"? There is no way to transfer information from Alice to Bob or vice versa, so everything is perfectly consistent with special relativity. Correlation is not causation.

But obviously, Bell's theorem tells us that we can't think about this the same way as we think about classical physics. The pioneers of QM knew this way before Bell. What you are doing is simply rehashing the arguments Einstein had with Bohr.

I note that you can't tell me how the settings influence the correlation without influencing the outcomes used to calculate the correlations. What is spooky is the idea that Alice and Bob change their settings but those settings don't influence the outcomes actually measured. Then months later when some dude decides to do correlation calculations, the influence pops into existence and influences the correlations. This is the Cadillac of spooky business. Where was this influence lurking in the interim?

Michel: I will explain why the “no-signalling” assumption is named in that way; and how to signal when it is not true:

Suppose P(A|a b1) is not equal P(A|a b2) for some settings a, b1 and b2
Suppose these probabilities are known - Alice and Bob have already experimented and communicated for a long time. They can now communicate in the following way. Bob wants to send one bit to Alice. They choose a sufficiently large N and then Bob either inputs b1 or b2, N times, while Alice inputs a N times. Alice can now decide correctly with very large probability by seeing if the rate at which A happened was close to P(A|a b1) or to P(A|a b2).

Alice can see what Bob was doing *without any communication* in the second run of N trials. There was ordinary, classical, communication in advance, to set up the communication channel.

[minkwe]

Suppose P(A|a b1) is not equal P(A|a b2) for some settings a, b1, and b2

Have you thought about what P(A|a) = 1/2 while P(A|a b1) =/= 1/2 means?
Also, can you answer the question I was asking Heinera, do the settings influence the outcome or not?

[gill1109]

Suppose P(A|a b1) is not equal P(A|a b2) for some settings a, b1, and b2

Have you thought about what P(A|a) = 1/2 while P(A|a b1) =/= 1/2 means?

Yes I have thought about it.
If there are only two settings for Bob, then P(A|a) = P(b1|a)P(A|a b1) + P(b2|a)P(A|a b2), where P(b1|a)+Pb2|a) = 1.
So the inequality P(A|a b1) =/= 1/2 implies P(A|a b2) =/= 1/2 too; one is larger than 1/2, the other is smaller than 1/2, provided P(b1|a) and P(b2|a) are both positive.
What do you think?

Also, can you answer the question I was asking Heinera, do the settings influence the outcome or not?

The settings influence the outcomes. Each setting influences its own outcome.
What do you think?

[gill1109]

Alice: Setting -> outcome -> correlation <- outcome <- setting <- Bob
The correlation is calculated using outcomes and you are claiming the correlation can be influenced by the settings but not the outcomes. How does this influence propagate? What is the mechanism of it?
It looks like we don't even need proof of inequalities to arrive at the spooky business. We have it right here at the start of the discussion.

Michel, you are missing an important component of the experiment: the source. There is another line:

Code: Select all


     Setting A – > Detector A < – Source – > Detector B < – Setting B

                        |                                      |
                        v                                      v

                   Outcome A                               Outcome B



This set-up is now repeated N times. At the end of the day we collect N quadruples of Setting A, Setting B, Outcome A, Outcome B
We then compute conditional correlations between outcomes (conditional on observed setting pairs)

[minkwe]

Alice: Setting -> outcome -> correlation <- outcome <- setting <- Bob
The correlation is calculated using outcomes and you are claiming the correlation can be influenced by the settings but not the outcomes. How does this influence propagate? What is the mechanism of it?
It looks like we don't even need proof of inequalities to arrive at the spooky business. We have it right here at the start of the discussion.

Michel, you are missing an important component of the experiment: the source. There is another line:

Code: Select all


     Setting A – > Detector A < – Source – > Detector B < – Setting B

                        |                                      |
                        v                                      v

                   Outcome A                               Outcome B



This set-up is now repeated N times. At the end of the day we collect N quadruples of Setting A, Setting B, Outcome A, Outcome B
We then compute conditional correlations between outcomes (conditional on observed setting pairs)

I'm not missing anything. I'm asking a very simple question: Do the settings influence the outcomes or not? I assume it is obvious to everyone that the source influences the outcomes.

[gill1109]

Alice: Setting -> outcome -> correlation <- outcome <- setting <- Bob
The correlation is calculated using outcomes and you are claiming the correlation can be influenced by the settings but not the outcomes. How does this influence propagate? What is the mechanism of it?
It looks like we don't even need proof of inequalities to arrive at the spooky business. We have it right here at the start of the discussion.

Michel, you are missing an important component of the experiment: the source. There is another line:

Code: Select all


     Setting A – > Detector A <~~ Source ~~> Detector B < - Setting B

                        |                          |
                        v                          v

                   Outcome A                   Outcome B



This set-up is now repeated N times. At the end of the day we collect N quadruples of Setting A, Setting B, Outcome A, Outcome B
We then compute conditional correlations between outcomes (conditional on observed setting pairs)

I'm not missing anything. I'm asking a very simple question: Do the settings influence the outcomes or not? I assume it is obvious to everyone that the source influences the outcomes.

Yes, the settings can influence the outcomes. The source can influence the outcomes.
Something *was* wrong in the picture: the rightmost down-arrow, and “Outcome B”, should have been moved to the left. I have fixed it now. I also indicated that the arrows from source to detectors may be a bit special. The other arrows are classical: classical information is *copied* from one place to another. The big question is: can we reproduce the quantum predicted correlations when we replace the wavy quantum arrows with classical arrows?

[minkwe]

Yes, the settings can influence the outcomes.

Thank you for admitting that. Therefore knowledge of the outcomes can tell us something about the settings and the distinction between


and


in which one represents signalling and the other does not, is on even more shaky ground.

According to QM, and .

[gill1109]

Yes, the settings can influence the outcomes.

Thank you for admitting that. Therefore knowledge of the outcomes can tell us something about the settings and the distinction between


and


in which one represents signalling and the other does not, is on even more shaky ground.

According to QM, and .

I explained to you how to use (1) for signalling, without physical contact between Alice and Bob, after a set-up phase.

[gill1109]

Yes, the settings can influence the outcomes.

Thank you for admitting that. Therefore knowledge of the outcomes can tell us something about the settings and the distinction between


and


in which one represents signalling and the other does not, is on even more shaky ground.

According to QM, and .

I explained to you how to use (1) for signalling, without physical contact between Alice and Bob, after a set-up phase.

It's a nice comparison, Michel!

Formula (1) can be used by Bob to learn about "a" from observation of B and his own choice of "b". In fact, by repetition many times, he can learn certainly what "a" was, having chosen "b" and observed B a large number of times. Thus nearly certain knowledge about "a", freely chosen by Alice, is transmitted to Bob, without transmission of anything between them. They just have to agree in advance on a suitable protocol, and set up many shared pairs of particles in the singlet state, also in advance.

Formula (2) can be used for Bob to learn something about A from observation of B and "b". But what's the point? Alice can't force A to take one value of the other. So this fact can't be used to transmit information from Alice to Bob.

[gill1109]

I’m giving a talk soon on Gull’s theorem. Here are the slides
https://www.math.leidenuniv.nl/~gill/gull-talk.pdf

Steve Gull’s challenge
An impossible Monte Carlo simulation project in distributed computing

At the 8th MaxEnt conference in 1998, held in Cambridge UK, Ed Jaynes was the star of the show. His opening lecture has the following abstract: “We show how the character of a scientific theory depends on one’s attitude toward probability. Many circumstances seem mysterious or paradoxical to one who thinks that probabilities are real physical properties existing in Nature. But when we adopt the “Bayesian Inference” viewpoint of Harold Jeffreys, paradoxes often become simple platitudes and we have a more powerful tool for useful calculations. This is illustrated by three examples from widely different fields: diffusion in kinetic theory, the Einstein–Podolsky–Rosen (EPR) paradox in quantum theory [he refers here to Bell’s theorem and Bell’s inequalities], and the second law of thermodynamics in biology.”

Unfortunately Jaynes was completely wrong in believing that John Bell had merely muddled up his conditional probabilities in proving the famous Bell inequalities and deriving the famous Bell theorem. At the conference, astrophysicist Steve Gull presented a three line proof of Bell’s theorem using some well known facts from Fourier analysis. The proof sketch can be found in a scan of four smudged overhead transparencies on Gull’s personal webpages at Cambridge University.

Together with Dilara Karakozak I believe I have managed to decode Gull’s proof, https://arxiv.org/abs/2012.00719, though this did require quite some inventiveness. I will present our solution and point out further open problems. I have the feeling progress could be made on interesting generalisations using newer probability inequalities for functions of Hadamard variables.

[gill1109]

I gave the talk on Gull's theorem again, using some different tools. In particular YouTube. (3x approx 15 mins)
https://gill1109.com/2021/01/14/steve-g ... computing/
https://www.youtube.com/watch?v=W6uuaM4 ... 9RGdejBwAY