Some people do not understand Counterfactual Definiteness

[gill1109]

In reality you can only choose one setting and get to observe one outcome. Now, suppose you dream up a local hidden variables model and program a computer simulation of the experiment. At some point the computer generates a realisation of a hidden variable lambda and asks the user to input a setting. The user could input a, or he could input a’. You can imagine making an exact clone of the computer at that precise moment. You clone not just the hardware but also the contents of memory and the contents of the hard disk. Now you have two identical deterministic machines both waiting for an input. You give one the input a, and the other the input a’. Now you get both outputs.

[minkwe]

Michel, suppose Alice actually chooses to insert setting a, and Bob b. They do this by the tosses of two coins. They could have chosen a’ and b’. Then A(a, lambda) and B(b, lambda) are the outcomes they actually observe. A(a’, lambda) and B(b’, lambda) are the outcomes they would have observed, had their coin tosses fallen differently.

What is the problem here?

The problem is you won't answer a simple question. But I'm not holding my breath.


The answer is that in Bell's formulation, only one of P(a,b), P(b,c) or P(a,c) is actual and the other two must be based on counterfactual outcomes. Thus if Alice measured P(a,b), then both P(b,c) and P(a,c) are based on counterfactual outcomes as is obvious from equation 14a



In fact, there is no other justification for the integral, which would be wrong in the context of an EPRB experiment unless Bell was integrating counterfactual outcomes alongside actual ones.

And that is why you wrote in your paper that

its formulation refers to outcomes of measurements which are not actually performed, so we have to assume their existence, alongside the outcomes of those actually performed: the principle of realism, or more precisely, counterfactual definiteness.
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Under realism we can imagine, for each run, alongside of the outcomes of the actually measured pair of variables, also the outcomes of the not measured pair. Under locality, the outcomes in Alice’s wing cannot depend on the choice of which variable is measured in Bob’s wing. Thus, for each run there is a suite of potential outcomes A, A', B and B', but only one of A and A', and only one of B and B' actually gets to be observed. By freedom, the choices are statistically independent of the actual values of the four. I will assume furthermore that the suite of counterfactual outcomes in the j-th run does not actually depend on which particular variables were observed in previous runs.
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We must first agree that though, say, only A and B are actually measured in one particular run, still, in a mathematical sense, A' and B' also exist (or at least may be constructed) alongside of the other two; and moreover, they may be thought to be located in space and time just where one would imagine.

You are assuming that it is fine to have all those terms in the same mathematical expression because you've assumed that they mathematically exist along side each other.

[Joy Christian]

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I can't believe the statistical swindle is not being invoked by the statistician for this long. We are on page 3 already. How long is it going to take before he brings in statistics?
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[FrediFizzx]

Fred also wrote

That is what we have been saying all along. It is impossible for there to be conterfactual outcomes of the other two setting pairs because they can't happen at the same time. The Bell fans only response is that they don't have to happen at the same time.

If you have a local hidden variables model, and Alice chooses setting a, but not a’, then according to that model she observes A(a, lambda). She doesn’t observe A(a’, lambda). But both functions of lambda do exist. Both of those two numbers exist. “A” is a function. “lambda” is an element of some set. “a” and “a’” are elements of another set. “A(a, lambda)” and “A(a’, lambda)” are elements of the set {-1, +1}.

In an experimental context, it is impossible for both to physically exist at the same. However, to demonstrate that QM exceeds the bounds of the inequality, they pretend that they do physically exist at the same time. It's nonsense.
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[gill1109]

You are assuming that it is fine to have all those terms in the same mathematical expression because you've assumed that they mathematically exist along side each other.

Yes, exactly.

More precisely: I deduced the consequences of assuming that those terms mathematically existed alongside each other. Just as Bell did. I did not say that I believed those assumptions, and neither did Bell.

Bell tried to motivate the physical assumptions which led him to his inequality. He motivated them, very carefully. He knew they are controversial. In 1900 everyone would have agreed with them. But not anymore by 1920. Please read his most careful and extensive justifications in the Bertlmann’s socks paper. You can find it in “Speakable and unspeakable” but also (free) on the internet: https://hal.archives-ouvertes.fr/jpa-00220688/document

The fact that the inequality is violated in experiments tells us that the physical assumptions which Bell made are untenable. Bell agreed that the assumptions must be invalid. I suggest we discuss them. What are those functions A and B and what is lambda? Why might we imagine that these things exist? This is the assumption of determinism, I think. Or realism. Aristotle told us that everything happens for a reason. This idea is the foundation of Western thinking and the foundation of modern science, it’s also part of our brains’ hard wired thinking, as researchers in neurolinguistics have deduced.

You referred us to a paper by Hess, de Raedt, and Michielsen. https://arxiv.org/pdf/1605.04889.pdf They accept determinism. Lots of people create event-by-event simulations of Bell experiments. They believe in determinism. Let’s discuss the Hess et al. model.

Read it carefully and try to explain it to us. I think it is muddled, wrong, mistaken. But there are things in it worth thinking about. It might even lead us into probability theory (in particular, martingale theory) and even into statistics.

We can also discuss the relevance of Bell’s arguments to computer simulations. A program running on an ordinary PC is a very deterministic thing. Every careful programmer thinks about what would happen given any possible input. The computer has a state “lambda”.

In an experimental context, it is impossible for both to physically exist at the same. However, to demonstrate that QM exceeds the bounds of the inequality, they pretend that they do physically exist at the same time. It's nonsense.
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Those who are contented with quantum mechanics must indeed believe it is nonsense. For them, there is no “lambda”. Nature is irreducible stochastic. All we can do is calculate probabilities. However, they should still take note of the logic, of the maths. The logic and maths is not nonsense. For instance, one can use Bell’s reasoning to deduce the impossibility of event-by-event simulations with strictly imposed locality to reproduce QM correlations (up to statistical variation).

[FrediFizzx]

... For instance, one can use Bell’s reasoning to deduce the impossibility of event-by-event simulations with strictly imposed locality to reproduce QM correlations (up to statistical variation).

More freakin' nonsense. You actually have no rigorous mathematical proof of that. Bell's theory has been shot down so you can't use Bell as proof. Gull's theory is shot down so you have no proof.
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[gill1109]

... For instance, one can use Bell’s reasoning to deduce the impossibility of event-by-event simulations with strictly imposed locality to reproduce QM correlations (up to statistical variation).

More freakin' nonsense. You actually have no rigorous mathematical proof of that. Bell's theory has been shot down so you can't use Bell as proof. Gull's theory is shot down so you have no proof.

Dear Fred, with all respect, if anyone is talking freakin' nonsense here, it's you! I do have rigorous mathematical proof; in fact two very different proofs of the same theorem. My paper with my student Dilara Karakozak is currently being reviewed by a journal, and so far, nobody has found anything wrong with it. https://arxiv.org/abs/2012.00719 (NB: currently at version 5).
Title: Gull's theorem revisited
Authors: Richard D. Gill, Dilara Karakozak
Abstract: Steve Gull, in unpublished work available on his Cambridge University homepage, has outlined a proof of Bell's theorem using Fourier theory. Gull's philosophy is that Bell's theorem can be seen as a no-go theorem for a project in distributed computing (with classical, not quantum, computers!). We present his argument, correcting misprints and filling gaps. In his argument, there were two completely separated computers in the network. We need three in order to fill all the gaps in his proof: a third computer supplies a stream of random numbers to the two computers, which represent the two measurement stations in Bell's work. At the end of the day, one can imagine that computer replaced by a cloned, virtual computer, generating the same pseudo-random numbers within each of Alice and Bob's computers. Gull's proof then just needs a third step: writing an expectation as the expectation of a conditional expectation, given the hidden variables.

We thank you in the acknowledgements section. Your criticism was really important. We also thank Joy Christian since our work was started in answer to a challenge of his.

Notice that there are two quite different proofs of the same theorem. Both Bell, and Gull, essentially give us proofs, or outlines of proofs, that distributed computers limited by locality constraints cannot reproduce the singlet correlations (not even approximately). Bell's proof as refined by myself in 2003 (introduction of martingale methods) uses the CHSH inequality. Gull's proof as fixed by Dilara and me just a few weeks ago uses Fourier theory. The mapping from a function to its sequence of Fourier series coefficients is an isomorphism between L^2_C((-pi, pi], uniform probability distribution) and ell^2_C(Z, counting measure).

You can show that these proofs are wrong by building an app or setting up an interactive website which does the simulation while adhering to the rules stipulated here: http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=460 "The 64 thousand Euro challenge". Notice typo corrected by http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=460#p12316. Feel free to implement one of Joy Christian's models, if you can.

If you disagree with the rules, please explain why, on the thread I just mentioned.

[FrediFizzx]

Egads! Another boring book. Hess, et al, shot down your "martingales" proof here. Gull's theory has already been shown to be complete nonsense. There is no fixing it. And..., there is plenty of nonsense published in journals. Your paper is rejected via peer review right on this forum. You've got no proof.
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[Joy Christian]

Egads! Another boring book. Hess, et al, shot down your "martingales" proof here. Gull's theory has already been shown to be complete nonsense. There is no fixing it. And..., there is plenty of nonsense published in journals. Your paper is rejected via peer review right on this forum. You've got no proof.
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Gill's "theorem" was also shredded to pieces four years ago on PubPeer: https://pubpeer.com/publications/D985B4 ... 3E3A314522. It is just poetry, not unlike Gull's "theorem."
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[Gordon Watson]

2. Let the three mathematical relations between Bell's equations (14) and (15) be, respectively: (14a), (14b), (14c).

3. Then Bell's error is his move from (14a) to (14b).

The contradiction is present even on the left-hand side of 14a.

P(a,b) - P(a,c) = "The correlation obtained if Alice and Bob measure at settings (a,b)" - "The correlation obtained if Alice and Bob measure at settings (a,c)"

The two terms contain contradictory premises. If Alice and Bob measured at (a,b) then they did not measure at (a,c). P(a,c) is counterfactual to P(a,b). The antecedents are contradictory therefore the combination of terms does not make physical sense since there is no universe in which True is False.

Michel and Gordon:just read Bell’s own answer to this criticism. It’s as old the hills, often been repeated, and it’s wrong. Chapter 8 of “Speakable and Unspeakable” is a two page paper, and I wrote it out for you here: http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=441&start=20#p12423

Richard,

1: I've pointed out that minkwe's claim re contradictions in LHS (14a) is mistaken; see above.

2: Then, re your point, my principal objection to Chapter 8 of “Speakable and Unspeakable” relates to this:

"With these local forms, it is not possible to find functions and and a probability distribution which give the correlation (1). This is the theorem. The proof will not be repeated here." [GW emphasis.]

For Bell's proof relies on a false inequality: derived under EPRB, which is a quantum experiment. That is: Bell (1964) derives an inequality THAT CANNOT HANDLE quantum mechanical expectation values.

So, under EPRB, Bell made a mistake. And that mistake is in his move from (14a) to (14b): ie, the EPRB quantum observables are pairwise-bound and Bell breaches that bond.

This breach — Bell's erroneous move from Bell 1964:(14a) to Bell 1964:(14b) — is defined via this next (or similar, for there are other false routes to Bell's inequality):



(Similar errors produce the equally false CHSH-Bell inequality.)

Yet, via nothing more than high-school math: I derive irrefutable inequalities that refute those by Bell and CHSH-Bell. And I test them with quantum mechanical expectation values. I find that my inequalities survive all possible combinations of such expectations: the Bell and CHSH-Bell inequalities do not.

So, Richard, please explain the "realism" or the CFD that allows Bell and CHSH-Bell to proceed so incorrectly; ie, please explain the "false" realism that Bell CHSH-Bell employ but you reject.

Further. While I spot Bell's errors, and can explain and correct them: your 2014 reads to me like an attempt to save Bell via a vaguely-diluted Bohrian realism.

FOR Gill (2014) includes: "So “realism” actually refers to models of reality, not to reality itself (p.2). In view of the experimental support for violation of Bell’s inequality, the present writer prefers to imagine a world in which “realism” is not a fundamental principle of physics but only an emergent property in the familiar realm of daily life. In this way, we can keep quantum mechanics, locality and freedom (p.3). It seems to me that we are pretty much forced into rejecting realism, which, please remember, is actually an idealistic concept: outcomes “exist” of measurements which were not performed (p.8)." [GW emphasis.]

YET, in Bell's important and extensive 1990 recapitulation of his dilemma and difficulties, I find that Bell makes NO use of these words: REAL, REALITY, REALISM.

Finally, from Bell (1964): "Let this more complete specification*** be effected by means of parameters ."

*** NB: NOT a wholly complete specification!

Thus my use of provides a more complete specification. That is: I match "elements of physical reality" to equivalence classes and thereby deliver quantum mechanical expectation values.

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[gill1109]

Gordon, Bell summarises the physical and metaphysical assumptions and reasoning which would ensure that functions A, B and rho exist *with certain properties* and which would reproduce the singlet correlations. According to that point of view, A(a, lambda) = +/-1 is the outcome which Alice would observe if she chose setting a, while the state of detectors, source and transmissions lines between them was described by lambda. Bell does not say that he agrees with those assumptions. It is however clear, I think, that Einstein, and all physicists of his generation and before, would have agreed with them. Many later physicists do too. Many people active on this forum seem to believe in “local realism”, and they cite approvingly others (e.g. Hess, de Raedt, Michielsen), who do too.

I’m not a physicist nor a philosopher, I try to stick to maths, though of course I do have opinions and a (Buddhist) world view.

Bell’s purely mathematical proof that A, B and rho (*with the desired properties*) do not exist is waterproof, in my opinion, though e.g. Joy Christian thinks it is flawed.

It seems you agree with Bell, on essentials: there are no A, B and rho *with the usual properties* which reproduce the singlet correlations. You just don’t understand his maths and his logic.

I have no idea what you mean by true local realism. I suspect you are an adherent of the Copenhagen school. You have some mystical belief in the reality of noncommuting Hilbert space operators. I think that that is a religious belief, not a scientific viewpoint. I have looked for, but failed to discover, any convincing stand-alone original mathematics in your works, sorry. Seems you are happy with QM as it is; you follow Bohr. I don’t know what you take as hidden variable “lambda”, I haven’t seen any “complete description” of an EPR-B experiment in your works.

You keep mentioning that Bell nowhere talks about realism. He was a physicist, not a philosopher. He had no need to use the word. I do often use the phrase “local realism” because it has become very common. When I use it, I say what I mean by it.

[FrediFizzx]

...
Bell’s purely mathematical proof that A, B and rho (*with the desired properties*) do not exist is waterproof, in my opinion, though e.g. Joy Christian thinks it is flawed. ...

Sorry, Bell's theory sunk and drowned. We don't think it is flawed; we know it is flawed by some really simple counter examples to start with.
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[gill1109]

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Bell’s purely mathematical proof that A, B and rho (*with the desired properties*) do not exist is waterproof, in my opinion, though e.g. Joy Christian thinks it is flawed. ...

Sorry, Bell's theory sunk and drowned. We don't think it is flawed; we know it is flawed by some really simple counter examples to start with.

I agree they are really simple. The main one seems to be this:
A(a, lambda) = -B(b, lambda) = +/-1 for all settings a and b.
This model *is* the model of Bertlmann’s socks.
So far, Joy Christian’s paper in Royal Society Open Science has not gathered many citations. However, Karl Hess has referenced it favourably in https://m.scirp.org/papers/94973.

Happy New Year, everybody!

[Joy Christian]

I agree they are really simple. The main one seems to be this:
A(a, lambda) = -B(b, lambda) = +/-1 for all settings a and b.
This model *is* the model of Bertlmann’s socks.

Making extremely elementary mathematical and conceptual mistakes is your specialty, not mine!

If what you are claiming is true, then how come your tabloid papers are not accepted by RSOS and IEEE Access at once? After all, it has been over two months since you submitted your junk.
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[Gordon Watson]

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NOTE: I am copying my most recent post, and Richard Gill's reply, to "Bell's theorem refuted via elementary probability theory."

Reason: My reply to Richard will have more to do with mathematics, and less to do with Counterfactual Definiteness.
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[gill1109]

I agree they are really simple. The main one seems to be this:
A(a, lambda) = -B(b, lambda) = +/-1 for all settings a and b.
This model *is* the model of Bertlmann’s socks.

Making extremely elementary mathematical and conceptual mistakes is your specialty, not mine!
If what you are claiming is true, then how come your tabloid papers are not accepted by RSOS and IEEE Access at once? After all, it has been over two months since you submitted your junk.

Yes, that's an interesting question! Well, they each have to get reports from more than a dozen referees. I don't think it's been two months since submission, more like one month. Indeed I already received one set of reports, and was asked to submit a revision. I've done that, and am waiting again. I imagine that things will get moving again now that the New Year has come. I will keep you informed.

If my papers are accepted then you will have a chance to have the last word, don't worry.

[FrediFizzx]

Ok guys, off topic here. Let's try to stay on topic.

Here is hoping we will all have a Happy New Year. 2020 can kiss my behind!
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[gill1109]

Ok guys, off topic here. Let's try to stay on topic.

Here is hoping we will all have a Happy New Year. 2020 can kiss my behind!

Hear, hear!

[Gordon Watson]

Ok guys, off topic here. Let's try to stay on topic.

Thanks Fred.

To help return this important thread to a positive direction, I suggest that we each submit our definition of Counterfactual Definiteness in the context of Bell's Theorem: with an example.

It's my understanding that "counterfactual" was first used in 1946: meaning contrary to fact. So let's see how this flies:

(1) Definition: In the context of Bell's theorem, Counterfactual Definiteness (CD) is a definiteness that is contrary to fact.

(2) Example: In deriving his inequality — and contrary to fact — Bell (1964) assumes that quantum observables commute: eg, see his move from (14a) to (14b).
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[gill1109]

Ok guys, off topic here. Let's try to stay on topic.

Thanks Fred.

To help return this important thread to a positive direction, I suggest that we each submit our definition of Counterfactual Definiteness in the context of Bell's Theorem: with an example.

It's my understanding that "counterfactual" was first used in 1946: meaning contrary to fact. So let's see how this flies:

(1) Definition: In the context of Bell's theorem, Counterfactual Definiteness (CD) is a definiteness that is contrary to fact.

(2) Example: In deriving his inequality — and contrary to fact — Bell (1964) assumes that quantum observables commute: eg, see his move from (14a) to (14b).
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Logicians and philosophers have talked about counterfactual reasoning for a long time. Would Napoleon have taken his army to Moscow if he had been a woman? The business of courts of law, and of writers of history, and those who are interested in ethics (e.g., those who bring up children) is making Counterfactual assertions.

In the field of quantum foundations it has a specific technical meaning. Read the Wikipedia article https://en.wikipedia.org/wiki/Counterfactual_definiteness.

Gordon is wrong twice.

1. In the EPR experiment, we argue that particle A has a definite position even if we don’t measure it. We just realise that we *could* measure the position of particle B without disturbing particle A, and then we would know what we would find if we measured particle A. In EPR-B we imagine deterministic theories such that A(a, lambda) is the result which we would observe if we measured particle 1 in direction a when both particles’ joint state prior to measurement of either particle, in whatever way, is lambda.

2. Bell assumes that *classical* variables commute. He assumes that a classical reality “behind the scenes” explains the observable correlations predicted by quantum theory. He shows that such a theory cannot reproduce quantum predictions. Gordon is not surprised. Bohr is not surprised. Einstein however is upset. Bell concludes that one of four things might be the case: QM might be wrong; nature might be non-local; the future might effect the past; there may be no deeper explanation of things - it just is so [Shut up and calculate]. He also agreed that it might be the case that we could never ever find out, because the quantum laws of nature themselves might prevent a successful loophole free experiment from ever being realised.

Nowadays it seems that options are narrowing.