Gill's theorem refuted (GTR)

[gill1109]

Where does CFD come in? Well forget CFD for just a moment, suppose that we have a LHV model. That means that Nature chooses lambda, Alice chooses a and Bob chooses b. Alice and Bob then get to see A(a, lambda) and B(b, lambda). But since A and B are just a couple of functions I can also think of A(a', lambda) for all possible values of a' and B(b', lambda) for all possible values of b', at the same time. Within my mathematical model they are defined, too, even though they don't correspond to anything in the experiment ... well, what they correspond to, is what the outcome would have been, had Alice chosen a' instead of a, while Nature had still made the same choice lambda.

Good, you have just clearly and concisely explained how CFD arises in the STRONGLY objective interpretation. This is not what I asked you. You said you were using the WEAKLY objective interpretation please provide a clear and concise explanation of how it arises in the WEAKLY objective interpretation please, without rambling about simulations. My question again in case you still did not understand it is :
How is CFD important for your derivation, if you are using the weakly objective interpretation?

I disagree. I think I am using what you call "weakly objective". Perhaps you can repeat what it is supposed to mean.

[minkwe]

I disagree. I think I am using what you call "weakly objective". Perhaps you can repeat what it is supposed to mean.

Here is the discussion from the other thread where this started for your reminder.

There is one and only one interpretation of the QM E(a, b): it stands for the probability two measured spins are equal minus the probability they are unequal.

You say that because you do not yet understand the issue. Every probability can be interpreted as either strongly objective or weakly objective. If I tell you that the probability of heads P(H) is 0.75, you have to decide, unless I tell you which interpretation to use or more information, "strongly objective" or "weakly objective". The strongly objective view is that P(H) is the probability of repeatedly tossing the same coin many times, while the "weakly objective" view is that P(H) is the probability of tossing many different "similar" coins each just one time. Once you pick an interpretation, you must consistently use that interpretation, otherwise you shoot yourself in the foot and drown in paradoxes. The recent discussion involving degrees of freedom, clearly highlight what the issues are when you mix the interpretations willy-nilly.

The set of values E(a,b), E(a,c) and E(b,c) does not tell you which interpretation to use. The "weakly objective" interpretation says the three expectation values represent separate measurements on three different sets of particles, The "strongly objective" view says they represent joint properties of a single set (aka population means). Once you pick one interpretation, you must stick with it. What Bell and later on Gill does is to mix the two interpretations and as a result with end up with the garbage that is Bell's theorem.

Adenier was, ten years ago, in my opinion, badly confused.

Adenier was not confused, then. You are confused now. The truth is timeless. Whether or not the truth is published does not change the fact that it is true. To demonstrate that you are confused, I'll ask you a couple of question, your answers will clearly reveal that it is you who is confused:

The short version of the two questions are: What interpretation does Gill use for the terms in Bell's inequality strongly objective or weakly objective? What interpretation does Gill use for the terms from QM strongly objective or weakly objective?

So we shall see if you are being logically consistent as you answer these questions.

I take the weakly objective interpretation of E(a, b), both with respect to QM and with respect to a possible LHV theory "behind" QM.

There were two questions. Do you answer "weakly objective" for both? Are you sure that is your choice, because you just opened Pandoras box.

Yes.

[gill1109]

Thanks! This is too much to read on an iPhone in a wobbling train without my best reading glasses. Please be patient. Remind me in a day or two if I forget to follow this up.

[gill1109]

Gordon, where are you? You claim you have refuted my theorem. Yet it has been revealed you are unable to read it, and have difficulties understanding logic. The theorem says that whatever value of N you pick, however you fill in that Nx4 table, and whatever value of eta you choose, then a certain probability (referring to 2N independent fair coin tosses) is at least as large as a certain number.

Try picking a large value of N, e.g. 10^6, and a small but not terribly small value of eta, e.g. 0.01. What is the number on the right hand side? What is the probability on the left hand side (I mean: the probability of what event?)?

Is this result trivial? Is it surprising?

After answering these questions it could make sense to talk about the relevance, if any to Bell's theorem. But if you can't even read my formula (3) then this is not a good starting point for a discussion. We would need to back up, even further, and first talk about even more simple things, even (apparently) further from Bell's theorem.

Like: do you know the Chernoff bound? Do you understand what it says? Do you believe it is true?
http://en.wikipedia.org/wiki/Chernoff_bound

[harry]

Where does CFD come in? Well forget CFD for just a moment, suppose that we have a LHV model. That means that Nature chooses lambda, Alice chooses a and Bob chooses b. Alice and Bob then get to see A(a, lambda) and B(b, lambda). But since A and B are just a couple of functions I can also think of A(a', lambda) for all possible values of a' and B(b', lambda) for all possible values of b', at the same time. Within my mathematical model they are defined, too, even though they don't correspond to anything in the experiment ... well, what they correspond to, is what the outcome would have been, had Alice chosen a' instead of a, while Nature had still made the same choice lambda.

Good, you have just clearly and concisely explained how CFD arises in the STRONGLY objective interpretation. This is not what I asked you. You said you were using the WEAKLY objective interpretation please provide a clear and concise explanation of how it arises in the WEAKLY objective interpretation please, without rambling about simulations. My question again in case you still did not understand it is :
How is CFD important for your derivation, if you are using the weakly objective interpretation?

I just read the very interesting discussion here above, and perhaps I have a solution to the mutual misunderstanding here. For it appears to me that technically speaking, for simulations and derivations Gill (and probably everyone else!) uses not exactly CFD but what I will call UFD: unfactual determinism. This may be the source of the misunderstanding that also came up in other threads, appearing in a different form.

In a simulation one can calculate based on theoretical considerations what will happen to an entity if angle a is chosen OR what will happen if instead angle a' is chosen. And according to theory, it makes no difference for the end result of measuring on a large number of entities if first angle a and then angle a' is chosen, or if first a' and then a is chosen. On each entity only one measurement is performed in a real experiment, and also that can be simulated. Thus, a method that looks like your "strong interpretation" ("what if") can be used to predict with imaginary experiments the outcome of real experiments - and with real experiments your "weak interpretation" applies (each entity measured only once).

[gill1109]

Where does CFD come in? Well forget CFD for just a moment, suppose that we have a LHV model. That means that Nature chooses lambda, Alice chooses a and Bob chooses b. Alice and Bob then get to see A(a, lambda) and B(b, lambda). But since A and B are just a couple of functions I can also think of A(a', lambda) for all possible values of a' and B(b', lambda) for all possible values of b', at the same time. Within my mathematical model they are defined, too, even though they don't correspond to anything in the experiment ... well, what they correspond to, is what the outcome would have been, had Alice chosen a' instead of a, while Nature had still made the same choice lambda.

Good, you have just clearly and concisely explained how CFD arises in the STRONGLY objective interpretation. This is not what I asked you. You said you were using the WEAKLY objective interpretation please provide a clear and concise explanation of how it arises in the WEAKLY objective interpretation please, without rambling about simulations. My question again in case you still did not understand it is :
How is CFD important for your derivation, if you are using the weakly objective interpretation?

I just read the very interesting discussion here above, and perhaps I have a solution to the mutual misunderstanding here. For it appears to me that technically speaking, for simulations and derivations Gill (and probably everyone else!) uses not exactly CFD but what I will call UFD: unfactual determinism. This may be the source of the misunderstanding that also came up in other threads, appearing in a different form.

In a simulation one can calculate based on theoretical considerations what will happen to an entity if angle a is chosen OR what will happen if instead angle a' is chosen. And according to theory, it makes no difference for the end result of measuring on a large number of entities if first angle a and then angle a' is chosen, or if first a' and then a is chosen. On each entity only one measurement is performed in a real experiment, and also that can be simulated. Thus, a method that looks like your "strong interpretation" ("what if") can be used to predict with imaginary experiments the outcome of real experiments - and with real experiments your "weak interpretation" applies (each entity measured only once).

Exactly, Harry!
This is how Evidence Based Medicine works. Double Blind Randomized Clinical Trials. You cannot give the same patient two different treatments. You assign patients at random to one or the other treatment. The cure rate in each of the two subsamples tells us what the cure rate is for new patients picked from the same population and always given just one of the two treatments.

One of the ingredients of a loophole free experiment is the random choice of measurement settings, time and time again, while the particles are on their way from the source to the detector. Alice's measurement has to be finished before Bob's setting could even be known at Alice's place (supposing that no information goes faster than the speed of light).

[harry]

I just read the very interesting discussion here above, and perhaps I have a solution to the mutual misunderstanding here. For it appears to me that technically speaking, for simulations and derivations Gill (and probably everyone else!) uses not exactly CFD but what I will call UFD: unfactual determinism. This may be the source of the misunderstanding that also came up in other threads, appearing in a different form.

In a simulation one can calculate based on theoretical considerations what will happen to an entity if angle a is chosen OR what will happen if instead angle a' is chosen. And according to theory, it makes no difference for the end result of measuring on a large number of entities if first angle a and then angle a' is chosen, or if first a' and then a is chosen. On each entity only one measurement is performed in a real experiment, and also that can be simulated. Thus, a method that looks like your "strong interpretation" ("what if") can be used to predict with imaginary experiments the outcome of real experiments - and with real experiments your "weak interpretation" applies (each entity measured only once).

Exactly, Harry!
This is how Evidence Based Medicine works. Double Blind Randomized Clinical Trials. You cannot give the same patient two different treatments. You assign patients at random to one or the other treatment. The cure rate in each of the two subsamples tells us what the cure rate is for new patients picked from the same population and always given just one of the two treatments.

One of the ingredients of a loophole free experiment is the random choice of measurement settings, time and time again, while the particles are on their way from the source to the detector. Alice's measurement has to be finished before Bob's setting could even be known at Alice's place (supposing that no information goes faster than the speed of light).

Yes... BUT: I'm afraid that if minkwe reads my reply in the light of your comment, he may miss the point that I tried to make. I suspect that the things you tell here already were clear to him - he might even say that it's also his point that each particle can only be measured once! However, perhaps you already made the same point as me, although less elaborated, when you stressed "imagine".

CFD, as minkwe highlighted, corresponds to actually performed experiments, in which we hypothise the effect of choosing a setting that was not chosen compared to one that in fact was chosen. Strictly speaking, your simulations do not use CFD although what you do is similar: they do not emulate such a hypothetical effect of (impossible and never performed) multiple settings on a single entity; instead they predict the possible outcomes for series of different entities as function of chosen detection angles.

Perhaps miknwe's example of flipping coins should be elaborated. Then what you are doing, I guess, corresponds to considering a population of coins, some old and damaged, other new; and you predict by calculation or simulation how likely a random coin will be accepted by coffee machine A or B (which looks a bit like CFD but it is not) - and from that, what fraction of coins will be accepted by each machine.

That does of course not imply that you are making a prediction for a coin that is accepted by machine A, how much chance there would have been to have been accepted by machine B (CFD).

In summary, maybe with "realism" you mean what I call "determinism"; and determinism leads to CFD when considering really performed experiments. Does that work for you?

[gill1109]

I just read the very interesting discussion here above, and perhaps I have a solution to the mutual misunderstanding here. For it appears to me that technically speaking, for simulations and derivations Gill (and probably everyone else!) uses not exactly CFD but what I will call UFD: unfactual determinism. This may be the source of the misunderstanding that also came up in other threads, appearing in a different form.

In a simulation one can calculate based on theoretical considerations what will happen to an entity if angle a is chosen OR what will happen if instead angle a' is chosen. And according to theory, it makes no difference for the end result of measuring on a large number of entities if first angle a and then angle a' is chosen, or if first a' and then a is chosen. On each entity only one measurement is performed in a real experiment, and also that can be simulated. Thus, a method that looks like your "strong interpretation" ("what if") can be used to predict with imaginary experiments the outcome of real experiments - and with real experiments your "weak interpretation" applies (each entity measured only once).

Exactly, Harry!
This is how Evidence Based Medicine works. Double Blind Randomized Clinical Trials. You cannot give the same patient two different treatments. You assign patients at random to one or the other treatment. The cure rate in each of the two subsamples tells us what the cure rate is for new patients picked from the same population and always given just one of the two treatments.

One of the ingredients of a loophole free experiment is the random choice of measurement settings, time and time again, while the particles are on their way from the source to the detector. Alice's measurement has to be finished before Bob's setting could even be known at Alice's place (supposing that no information goes faster than the speed of light).

Yes... BUT: I'm afraid that if minkwe reads my reply in the light of your comment, he may miss the point that I tried to make. I suspect that the things you tell here already were clear to him - he might even say that it's also his point that each particle can only be measured once! However, perhaps you already made the same point as me, although less elaborated, when you stressed "imagine".

CFD, as minkwe highlighted, corresponds to actually performed experiments, in which we hypothise the effect of choosing a setting that was not chosen compared to one that in fact was chosen. Strictly speaking, your simulations do not use CFD although what you do is similar: they do not emulate such a hypothetical effect of (impossible and never performed) multiple settings on a single entity; instead they predict the possible outcomes for series of different entities as function of chosen detection angles.

Perhaps miknwe's example of flipping coins should be elaborated. Then what you are doing, I guess, corresponds to considering a population of coins, some old and damaged, other new; and you predict by calculation or simulation how likely a random coin will be accepted by coffee machine A or B (which looks a bit like CFD but it is not) - and from that, what fraction of coins will be accepted by each machine.

That does of course not imply that you are making a prediction for a coin that is accepted by machine A, how much chance there would have been to have been accepted by machine B (CFD).

In summary, maybe with "realism" you mean what I call "determinism"; and determinism leads to CFD when considering really performed experiments. Does that work for you?

That can work for me. Realism says that apparent randomness is classical physical randomness or "merely" pseudo-randomness.

[minkwe]

In a simulation one can calculate based on theoretical considerations what will happen to an entity if angle a is chosen OR what will happen if instead angle a' is chosen. And according to theory, it makes no difference for the end result of measuring on a large number of entities if first angle a and then angle a' is chosen, or if first a' and then a is chosen. On each entity only one measurement is performed in a real experiment, and also that can be simulated. Thus, a method that looks like your "strong interpretation" ("what if") can be used to predict with imaginary experiments the outcome of real experiments - and with real experiments your "weak interpretation" applies (each entity measured only once).

I just discovered this long-unanswered question by harry. Very good question indeed.

In a simulation one can calculate based on theoretical considerations what will happen to an entity if angle a is chosen OR what will happen if instead angle a' is chosen.

True. A theory can predict a value for measuring at a or a'. Even if only one of them is measured.

And according to theory, it makes no difference for the end result of measuring on a large number of entities if first angle a and then angle a' is chosen, or if first a' and then a is chosen.

True, also, the actual value of the prediction should not be different whichever one is measured first, they can both be measured on separate systems and produce reproducible results.

But all of that is not relevant to the problem, which is the question of whether the prediction for a single system, is exactly the same prediction for different systems. There is a hidden assumption that the two correlations predicted for a single system (strongly objective) by the theory, only one of which can actually be measured, is the same as the two correlations predicted for two separate systems (weakly objective), each of which can be measured. The inequality is derived using the strongly objective interpretation ONLY, ie both correlations pertain to the same system, and then wrongly applied to correlations from separate systems by making the hidden assumption that the two correlations are the same. The apparent violations arise simply because the hidden assumption is false.

The weakly objective interpretation is the assumption that the correlations pertain to separate independent sets of particle pairs. If that is the case, then there is no concept of counterfactual definiteness and any conclusion that CFD should be rejected based on such logic is simply baseless.

We've shown in viewtopic.php?f=6&t=181, that the three strongly objective correlations (or 4) in Bell's inequalities (or the CHSH) can not all be simultaneously equal to 4 weakly objective correlations such as those from QM, or those measure experimentally on 4 independent sets of particle pairs.

[FrediFizzx]

We've shown in viewtopic.php?f=6&t=181, that the three strongly objective correlations (or 4) in Bell's inequalities (or the CHSH) can not all be simultaneously equal to 4 weakly objective correlations such as those from QM, or those measure experimentally on 4 independent sets of particle pairs.

Presumably people have been "shifting the goal posts" unknowingly. Or................. we are missing something really really subtle. NOT!

[minkwe]

Presumably people have been "shifting the goal posts" unknowingly. Or................. we are missing something really really subtle. NOT!

I think the goal-post shifting has been deliberate . One other thing, Gordon made a prophesy to start this thread:

IF Richard Gill's theorem supports Bell's theorem (BT) in some way, please provide a link and commentary to the latest version of that theorem here.

It will then be refuted, as time permits.

Until then, just regard this as prophecy.

And what do you know, his prophesy has been fulfilled https://pubpeer.com/publications/D985B4 ... 3E3A314522
Fascinating display of goal-post shifting. Life must be hard in Bell land. All the experiments previously claimed to support quantum mysticism now have local realistic explanations, with simulations to boot. All the inequalities have been shown to be flawed. The ultimate Bell-test experiment they've been promising for 15 years has still not been done, or probably has been done, but the results are not what mysterians want. My prediction is that new inequalities will show up in a little while, or they might ditch inequalities altogether and weave another web which would take a long time to untangle (eg. PBR theorem)

[FrediFizzx]

The ultimate Bell-test experiment they've been promising for 15 years has still not been done, or probably has been done, but the results are not what mysterians want. My prediction is that new inequalities will show up in a little while, or they might ditch inequalities altogether and weave another web which would take a long time to untangle (eg. PBR theorem)

The so-called "loophole-free" experiment will only confirm that the results of an EPRB type experiment is -a.b. Since the inequalities have been shown to be mathematically impossible to violate, the term "loophole" is ridiculous now. However, it will be good to finally know without a doubt that the result is -a.b.

I was asking in another thread that now that Bell's "theorem" has been completely demolished, what is next? Perhaps a thread about the PBR theorem should be started?

[Joy Christian]

I was asking in another thread that now that Bell's "theorem" has been completely demolished, what is next? Perhaps a thread about the PBR theorem should be started?

We can start a new thread about such new fads for entertainment, but logically there is no need. A local-realistic derivation of E(a,b) = -a.b was all that was needed.

Here is why: Back in 1935 EPR proved, once and for all -- by employing a logically impeccable argument -- that quantum mechanics is an incomplete theory of nature.

This should have been the end of quantum mysticism, but for the misdirection by Bell in 1964, which has been enforced by his followers ever since by outright denial, intimidation, harassment, and dirty academic politics. But not any more. As Michel pointed out, we have now not only exposed the flaws in Bell's so-called "theorem", but explicitly produced the strong correlation E(a,b) = -a.b in a manifestly local-realistic setting. In fact, as you know, I have been able to reproduce ALL conceivable quantum correlations, no matter how complicated, in a purely local-realistic setting, as correlations among the points of a parallelized 7-sphere. This should have put THE END to Bell-inspired quantum mysticism, but for the outright denial, intimidation, harassment, and dirty academic politics. More importantly, our refutations of Bell's theorem reinforces the logical impact of the EPR argument with vengeance, mitigating any need for entertaining the new fads like the so-called "PBR theorem."

[FrediFizzx]

We can start a new thread about such new fads for entertainment, but logically there is no need. A local-realistic derivation of E(a,b) = -a.b was all that was needed.

Granted, but besides entertainment perhaps the readers on the forum would like to see more specifically what the flaw is in their argument. IOW, entertainment and education.