The real puzzle

[Heinera]

And in your opinion QM says (-1, 0, 1) is not allowed? On what basis do you reject my (-1, 0, 1) attempt. (hidden assumption alert)

It is not allowed by the definitions of the theorem. Furthermore, an experiment has been performed on trapped ions where the outcomes where only (-1, 1), i.e., 100% detection.

First of all, the claims of 100% detection are false, read the paper. Secondly, QM does not say every particle must be observed. In fact QM does not say anything about a single particle.

Of course QM does not say that every particle must be detected. But is is a premise of Bell's theorem that the outcomes are only (-1, 1), so a program that uses non-detection, (-1, 0, 1), is not a counter-example to Bell's theorem, as Joy claims, no matter what the program achieves.

(I prefer to concentrate on the "theorem"-part of Bell's theorem, and leave any physical or metaphysical inferences to each and every one.)

[Joy Christian]

"...a program that uses non-detection, (-1, 0, 1), is not a counter-example to Bell's theorem, as Joy claims..."

I do not claim that at all. In my model there are no non-detections. There is a strict 1-to-1 correspondence between initial states (e, theta) and measurement outcomes A and B. Every initial state (e, theta) is detected, and every measurement outcome A or B corresponds to an initial state.

[minkwe]

Bell did not prove a theorem. He was a physicist, not a mathematician.

The attack by many so-called Bell-deniers on the so-called Bell theorem (e.g. the "theorem" quoted by Michel Fodje) is a straw-man attack.

I didn't know mathematics could only be practiced by mathematicians. I suggest anyone who might be deceived to believe this statement should check the Wikipedia Article on Bell's theorem: http://en.wikipedia.org/wiki/Bell's_theorem and do not stop at the front page where Bell's theorem is clearly stated. Also check out the Talk pages where the "editors" of the article discuss it. Notice that our beloved Richard is one of the authors of the "so-called" straw-man article he now disowns.

To date, computer simulations by de Raedt, Fodje, Christian and others have always been of the wrong experiment. Not of the experiment desired, specified, described, by Bell.

Bell's experiment is impossible, it is the wrong experiment. Bell is the odd man out. QM, Weihs' & Aspect's type experiments, de Raedt's simulation, Fodje's Simulation, Christian's model, all EPR experiments ever performed all agree with each other and are testing/simulating the same thing. Bell is the odd man out, yet Gill continues to believe all those experiments and simulations are the wrong thing, and Bell's super-duper experiment which involves measuring incompatible counterfactual outcomes on a single set of particles. The loophole is in Bell not any experiment or simulation.

[minkwe]

We are making progress! We already agreed that mathematical inequalities cannot be violated, now we see that Bell's theorem is not Bell's theorem. And finally we see that all so-called Bell experiments to date, and all simulations of these past experiments, are irrelevant, too.

I think you meant that Bell's inequalities are irrelevant to physics, though you appear to be saying physics is irrelevant for Bell's inequalities. QM, all EPR-experiments to date, and all simulations of the experiments all agree with each other. Bell is the only odd man out. Bell's theorem is false, the loophole business is misguided. Bell's inequalities are irrelevant to physics. I'm happy you are now seeing it Richard.

[minkwe]

Of course QM does not say that every particle must be detected. But is is a premise of Bell's theorem that the outcomes are only (-1, 1), so a program that uses non-detection, (-1, 0, 1), is not a counter-example to Bell's theorem, as Joy claims, no matter what the program achieves.

(I prefer to concentrate on the "theorem"-part of Bell's theorem, and leave any physical or metaphysical inferences to each and every one.)

But you are here defending Bell's theorem and claiming it's claims are true. Yet you can not provide a single justification for why Bell's theorem assumes that non-detection is impossible. On what Basis does Bell's theorem assume that non-detection is impossible if QM does not say that?

BTW, if Heinera is standing at a station and recording results as his detectors are firing (+1 for one and -1) for the other, will he ever write down a 0, if he is using only local information at his station? So I wonder why you are so fixated on the 0. They do not exist as outcomes. Besides, I have another simulation in which all particles are detected, 100%. But I'm sure you will invoke "time-delays" as a reason to disbelieve it, even though you won't be able to answer on what justification do you assume that time-delays are not permitted.

So like I tell Richard, the odd man out is Bell theorem and it's unreasonable, unphysical assumptions. Every loophole is a physically plausible situation which Bell was ignorant of in forming his theorem. The loopholes are in Bell's theorem not experiments or simulations. So we have now deduced that Bell's theorem really is the claim that:

No physical theory of local hidden variables, in which every particle is detected (cf detection loophole), and time-delays between particles are forbidden (cf coincidence time loophole), and momentum transfers are forbidden (cf memory loophole), and counter-factual outcomes are measured on the same set of particles as actual ones, can ever reproduce all of the predictions of quantum mechanics.

Obviously, such a theory meeting those constraints will not be a physical theory.

[gill1109]

Bell's experiment is impossible, it is the wrong experiment.

This interesting remark proves you haven't read Bell's famous "Bertlmann's socks" paper. I am not talking about some mathematical derivation of some silly inequality. I am talking about a description of a possible real world experiment.

In the early preprint version:
http://cds.cern.ch/record/142461/files/198009299.pdf
pages 11 and 12, the discussion referring to Figure 7.

Here is a link to the 1981 version

http://hal.archives-ouvertes.fr/docs/00/22/06/88/PDF/ajp-jphyscol198142C202.pdf

See pages C2-53 and C2-54 (again, figure 7 is crucial).

There is another paper by Bell with even a more extensive and detailed story of the experiment. It's in chapter 13 of "Speakable and Unspeakable" and is entitled "Atomic-cascade photons and quantum-mechanical nonlocality". See Figure 1.

The description of what is nowadays called "event-ready detectors" is crucial.

So: Bell is not responsible for the so-called Bell's theorem.

Bell is not responsible for past so-called Bell-EPR experiments.

The experts are waiting for a good experiment. Till then, the whole question is completely open. Simulations of fatally flawed experiments are irrelevant. Sure - the predictions of QM are confirmed, again and again. But the predictions of QM in the critical context still have not been confirmed. Maybe it will never happen.

[gill1109]

QM, all EPR-experiments to date, and all simulations of the experiments all agree with each other.

Yes, and this agreement is irrelevant, as Caroline Thompson so cogently argued. And why we are still waiting for a definitive experiment and why the experimenters are getting excited because it is getting close.

[minkwe]

QM, all EPR-experiments to date, and all simulations of the experiments all agree with each other.

Yes, and this agreement is irrelevant

The agreement is irrelevant!? The fact that the experiments confirm QM predictions is irrelevant, the fact that simulations of the experiments agree with QM and the experimental results is irrelevant? Astounding!

Sounds to me like Bell inequalities/theorem worship -- the suggestion that it must be everything else that is irrelevant to Bell's inequalities and not Bell's inequalities/theorem that is irrelevant to everything else, Bell's theorem/inequalities are so special that in 50 years nobody has been able to test it experimentally, yet it must be true and we must abandon realism because of it. Sounds very reasonable to me. NOT.

[gill1109]

QM, all EPR-experiments to date, and all simulations of the experiments all agree with each other.

Yes, and this agreement is irrelevant

The agreement is irrelevant!? The fact that the experiments confirm QM predictions is irrelevant, the fact that simulations of the experiments agree with QM and the experimental results is irrelevant? Astounding!

Astounding but true. Caroline Thompson said so. I say so. We carefully gave the reasons. Michel apparently did not quite grasp them yet. No problem.

The experimenters know it too, though they won't admit it explicitly.

All that past stuff was of course not *totally* irrelevant. The experiments have been getting better and better slowly approaching "the right experiment". When we cross the magic barrier, five years from now, something interesting will happen. Either theory (QM) will diverge from experiment, ie the experiment will fail. It will still be local-realistic simulatable but obviously it won't statistically significantly violate any 2x2x3 case generalized Bell inequality. Or QM and experiment will stick together but leave the simulations behind. The theorems by Larsson, Gill and others show precisely what can be simulated and what can't be simulated.

[gill1109]

The real puzzle is why no-one has carefully read the best chapters in John Bell's book "Speakable and unspeakable in quantum mechanics". Chapter 16 even has a careful discussion of the statistical issues involved (randomized settings, sample averages, standard errors). Most important of all, Bell describes the experiment which needs to be done, which still has not been done.

Excerpts from "Speakable and unspeakable"

Chapter 13
Atomic-cascade photons and quantum-mechanical nonlocality

Avoiding internal details for the moment, consider just a long black box with three inputs and three outputs. The inputs are three on–off switches – a master switch in the middle and a switch at each end. The outputs are three corresponding printers. The one in the middle prints ‘yes’ or ‘no’ soon after the start of a run, and the others each print ‘yes’ or ‘no’ when it ends. While the switches are ‘off’ the box restores itself as far as possible to some given initial condition in preparation for a run. The master switch is then operated and left ‘on’ for a predetermined time T. At time (T – δ each of the other switches may or may not – depending, for example, on random signals from independent radioactive sources external to the black box – be thrown to ‘on’ for a time δ. The length L of the box is such that L/c >> δ, where c is the velocity of light. So the operation of a switch at one end would not, according to Einstein, be relevant to the output at the other end.
We will consider only runs certified by a ‘yes’ from the middle printer, and not mention it any more. It just guarantees, as will be seen, that the internal process gets off to a good start. Let A (with values ± 1) denote the yes/no response of the left printer, and B( ± 1) likewise for the right printer. Let a ( = 1,2) denote whether or not the left switch is operated during the run, and b( = 1,2) likewise for the right switch. With sufficient statistics we can test hypotheses about the joint probability of A and B given a and b: ρ(A, B | a, b).

Going into the black box, we could find what is sketched (at the ‘Gedanken’ level) in Fig. 1. Only the centre and one end are drawn. The other end is the mirror image of the first. An oven provides a beam of suitable atoms in their (j, P) = (0, +) ground states. A pulse of laser photons γ00 is activated (after a predetermined delay during which remote equipment is alerted) by the master switch. This excites some atoms to a certain (1, –) level (Fig. 2). Most of these decay straight back to the ground state, but some cascade back with emission of photons γ0, γ1, γ2. Some such cases are identified by a γ0 counter C0 with a suitable filter. And, for some of these, photons γ1 and γ2 go towards detecting equipment at the two ends of the box. Filters F1 and F2 pass only the correct photons γ1 and γ2, and signal when they absorb wrong ones (i.e., they are a little more articulate than filters commercially available). Veto counters V identify events in which photons go off in other unwanted directions. Only the operation of counter C0 and the nonoperation of the vetos V and F1,2 authorize the middle printer to issue a ‘yes’ certificate for the event. Photons γx and γ2 then go towards distant detectors, Cx and C2, preceded by linear polarizers. These latter are set to pass polarizations at angles to the vertical controlled by the corresponding switches.
The firing or nonfiring of counters C1 and C2 authorizes the corresponding printers to print ‘yes’ or ‘no’.
The heart of the matter is a strong correlation of polarization between photons γ1 and γ2, dictated by the spins and parities of levels A and C in Fig. 2. Because the atom has initially and finally no angular momentum, the photons can carry none away. For back-to-back the photons can carry none away. For back-to-back photons this means a perfect circular polarization correlation – left-handed polarization for γ1 implies left-handed γ2, and right-handed γ1 implies right-handed γ2. Allowing also for parity conservation this translates into an equally strong linear polarization correlation: a given linear polarization on one side implies the same polarization on the other. In detail, in the ideal case of small opening angles and fully efficient counters, the probabilities of the various responses of C1 and C2 according to quantum mechanics are ... [including an image of the atomic decay sequence envisaged by Bell] ... 2 sqrt 2.

Fig. 1. Centre and left-hand-side of Gedanken set-up.



Fig. 2. Suitable atomic-level sequence.



Chapter 16
Bertlmann’s socks and the nature of reality

Consider the general experimental set-up of Fig. 7. To avoid inessential details it is represented just as a long box of unspecified equipment, with three inputs and three outputs. The outputs, above in the figure, can be three pieces of paper, each with either ‘yes’ or ‘no’ printed on it. The central input is just a ‘go’ signal which sets the experiment off at time tx. Shortly after that the central output says ‘yes’ or ‘no’. We are only interested in the ‘yes’s, which confirm that everything has got off to a good start (e.g., there are no ‘particles’ going in the wrong directions, and so on). At time t1 + T the other outputs appear, each with ‘yes’ or ‘no’ (depending for example on whether or not a signal has appeared on the ‘up’ side of a detecting screen behind a local Stern–Gerlach magnet). The apparatus then rests and recovers internally in preparation for a subsequent repetition of the experiment. But just before time t1 + T, say at time t1 + T – δ, signals a and b are injected at the two ends. (They might for example dictate that Stern–Gerlach magnets be rotated by angles a and b away from some standard position). We can arrange that cδ << L, where c is the velocity of light and L the length of the box; we would not then expect the signal at one end to have any influence on the output at the other, for lack of time, whatever hidden connections there might be between the two ends.

Fig. 7. General EPR set-up, with three inputs below and three outputs above.

[gill1109]

Here's some more material from "Bertlmann's socks" which shows that people who criticise Bell ought to find out what he actually said, especially in his more definitive later works.

But trivialities like this, you will exclaim, are of no interest in consumer research! You are right; we are straining here a little the analogy between consumer research and quantum philosophy. Moreover, you will insist, the statement has no empirical content. There is no way of deciding that a given sock could survive at one temperature and not at another. If it did not survive the first test it would not be available for the second, and even if it did survive the first test it would no longer be new, and subsequent tests would not have the original significance.
Suppose, however, that the socks come in pairs. And suppose that we know by experience that there is little variation between the members of a pair, in that if one member passes a given test then the other also passes that same test if it is performed. Then from d’ Espagnat’s inequality we can infer the following:
...
This is not yet empirically testable, for although the two tests in each bracket are now on different socks, the different brackets involve different tests on the same sock. But we now add the random sampling hypothesis: if the sample of pairs is sufficiently large and if we choose at random a big enough subsample to suffer a given pair of tests, then the pass/fail fractions of the subsample can be extended to the whole sample with high probability. Identifying such fractions with probabilities in a thoroughly conventional way, we now have
...
Moreover this is empirically meaningful is so far as probabilities can be determined by random sampling.
We formulated these considerations first for pairs of socks, moving with considerable confidence in those familiar objects. But why not reason similarly for the pairs of particles of the EPRB experiment?

[gill1109]

So Bell wrote: "if the sample of pairs is sufficiently large and if we choose at random a big enough subsample to suffer a given pair of tests, then the pass/fail fractions of the subsample can be extended to the whole sample with high probability. Identifying such fractions with probabilities in a thoroughly conventional way, we now have ..."

I must say, I have to criticise him a little, but of the course the guy was a theoretical physicist, not an experimentalist, so he can be excused.

When we extrapolate from a large sample to the population from which it is taken, we can't say that fractions equal probabilities. Only that with high probability they are close. We estimate the probabilities with fractions. Experimentalists report the standard error so as to indicate the typical amount by which the two are likely to differ. Experimentalists say that things are experimentally "proven" when the "signal" is five standard errors above base-line. cf. Higgs Boson, now "proven" to exist.

[minkwe]

This is really Bell's theorem:

No physical theory of local hidden variables, in which every particle is detected (cf detection loophole), and time-delays between particles are forbidden (cf coincidence time loophole), and momentum transfers are forbidden (cf memory loophole), and counter-factual outcomes are measured on the same set of particles as actual ones, can ever reproduce all of the predictions of quantum mechanics.

I rest my case.

[gill1109]

Fodje's theorem:

No physical theory of local hidden variables, in which every particle is detected (cf detection loophole), and time-delays between particles are forbidden (cf coincidence time loophole), and momentum transfers are forbidden (cf memory loophole), and counter-factual outcomes are measured on the same set of particles as actual ones, can ever reproduce all of the predictions of quantum mechanics.

Remark. This is rather original: I never saw it anywhere before.

Proof. Trivially, nothing satisfies the assumptions of the theorem. It is therefore trivially true.

Fact. Bell neither stated nor proved any theorem, and certainly not anything resembling the so-called theorem invented by Clauser, Horne, Shimony and Holt, and embarassingly attributed by them to Bell. Poor John Stuart Bell. Read him. Especially the two papers from which I quoted. Find out what the rest of the world has been talking about all these fifty years.

[minkwe]

Fact. Bell neither stated nor proved any theorem, and certainly not anything resembling the so-called theorem invented by Clauser, Horne, Shimony and Holt, and embarassingly attributed by them to Bell. Poor John Stuart Bell. Read him. Especially the two papers from which I quoted. Find out what the rest of the world has been talking about all these fifty years.

Are you going to edit your wikipedia page to correct your misrepresentation of Bell then? While doing that, remember to correct your misrepresentation of Jaynes too.

[gill1109]

Are you going to edit your wikipedia page to correct your misrepresentation of Bell then? While doing that, remember to correct your misrepresentation of Jaynes too.

(a) No-one "owns" a wikipedia page.

(b) I did not write on that page the usual statement of what is usually called Bell's theorem, which is displayed there, slavishly following the literature (so-called "reliable sources"). You can change it if you like but as long as 99.99% of all physicists out there think that the so-called theorem written there is (a) true and (b) Bell's theorem, then Wikipedia will say so too. Don't blame me. Blame Wikipedia policies if you like. If you don't like Wikipedia policies write a paper yourself, wait five or ten years to become famous, and then Wikipedia will be able to write things your way.

(c) I did not misrepresent Jaynes. You misinterpret both Jaynes and myself (and frankly, I am not sure that you know enough about probability theory in order to say anything about the matter at all). Caroline Thompson and Steve Gull (one of the founders of "geometric algebra") agree with me. My own "interpretation" has appeared in a peer-reviewed publication and no-one has since contradicted it in a peer-reviewed publication.

Have you got yourself a copy of "Speakable and unspeakable..." yet? I really recommend you study chapters 13 and 16, carefully. There is so much in there.

[minkwe]

(a) No-one "owns" a wikipedia page.

But the page has authors, and you are one of them, and you are now claiming disowning the article you helped write.

(b) I did not write on that page the usual statement of what is usually called Bell's theorem, which is displayed there, slavishly following the literature (so-called "reliable sources"). You can change it if you like but as long as 99.99% of all physicists out there think that the so-called theorem written there is (a) true and (b) Bell's theorem, then Wikipedia will say so too.

Funny thing is, all your posts on these forums and elsewhere are repeating the same claim you are now disowning. The claim that it is impossible for a local realistic theory to reproduce the predictions of quantum mechanics. In fact you have a few active bets based on this claim, aka Bell's theorem.

(c) I did not misrepresent Jaynes.

You did. You have claimed in many places that Jaynes admitted he was wrong, which is untrue. You never met Jaynes, and you cannot point to any of his statements published or unpublished where he even implies such a thing.

and frankly, I am not sure that you know enough about probability theory in order to say anything about the matter at all

I'm not sure you know enough about anything related to Bell, despite appearances. For example, you still haven't told us what the upper bound is for the expression (from your LG paper), when the coincidence probability is γ=0.5:

δ > 0
δ ≥ 4 − 3/γ
| E(AC′|ΛAC′) + E(AD′|ΛAD′)| + |E(BC′|ΛBC′) − E(BD′|ΛBD′)|≤ 6/γ − 4

it is a simple calculation, just replace gamma in those expressions by 0.5 and see the ceiling collapse, and it immediately reveals how fatally flawed the paper is. I suggest you withdraw your current paper, get yourself a copy of Jayne's book on Probability theory, and study it carefully before you publish anything in the future. And BTW, since you like Bell's papers so much, I suggest you read his 1966 paper http://fy.chalmers.se/~delsing/QI/Bell-RMP-66.pdf very carefully.

[FrediFizzx]

Funny thing is, all your posts on these forums and elsewhere are repeating the same claim you are now disowning. The claim that it is impossible for a local realistic theory to reproduce the predictions of quantum mechanics. In fact you have a few active bets based on this claim, aka Bell's theorem.

[removed personal comment] He never disowned "the claim that it is impossible for a local realistic theory to reproduce the predictions of quantum mechanics." Because that is just a fact of mathematics. He merely says that to date, there has been no experiment performed that can distinguish between the predictions of quantum mechanics and predictions of a local realistic theory.

[gill1109]

I suggest you ... get yourself a copy of Jayne's book on Probability theory, and study it carefully before you publish anything in the future. And BTW, since you like Bell's papers so much, I suggest you read his 1966 paper http://fy.chalmers.se/~delsing/QI/Bell-RMP-66.pdf very carefully.

I know Jayne's book very well. Highly recommended. As also is, of course, Bell's most famous paper. Chapter 2 of "Speakable and Unspeakable", if I remember correctly.

The two chapters which I recommend so much were obviously written much later, after a lot of discussion had already taken place, some of it very useful, but a lot of it "pure noise". Bell does his best in Chapters 13 and 16 to dispel some common misconceptions by dwelling more deeply and carefully on several points where he had often been misunderstood. It's a pity these misunderstandings persist so widely, to this day, especially among amateurs and newcomers.

[gill1109]

You still haven't told us what the upper bound is for the expression (from your LG paper), when the coincidence probability is γ=0.5:

δ > 0
δ ≥ 4 − 3/γ
| E(AC′|ΛAC′) + E(AD′|ΛAD′)| + |E(BC′|ΛBC′) − E(BD′|ΛBD′)|≤ 6/γ − 4

it is a simple calculation, just replace gamma in those expressions by 0.5 and see the ceiling collapse, and it immediately reveals how fatally flawed the paper is

If we take gamma equal to 0.5 then the bound in the third inequality is 8, which is trivially satisfied. The bound on delta in the second inequality is empty, too. The result is trivially true. It is true, for all gamma, whether interesting or not.

Now take gamma equal, say, to 10/11. The bound in the third inequality is now 2.6. Quantum mechanics predicts that we might observe 2.828....

If an experiment is performed with gamma at least 10/11 and does a good job at recovering the quantum correlations, the experimenters will get the Nobel prize. You will be unable to simulate it. (Assuming the usual other loopholes are excluded by decent experimental design).

The Gisin ... consortium did do this experiment last year only the distance between the measurement stations was not yet large enough for this to qualify as a "loophole free" experiment. But they are getting bloody close!