Commonsense local realism refutes Bell's theorem

[Heinera]

[..] I mentioned this paper because Gill's derivation might help you to better understand Bell's derivation, especially since you think Bell mixed up Alice's outcomes with Bob's outcomes from different pairs of particles.

I apprecaite that. However, I don't just think so, in my elaboration of Bell's derivation in Watson's manner I found indeed a mix-up between different pairs of particles. If I understood it correctly, Gill suggested that the mix-up is innocent because it averages out, but you suggest that the mix-up doesn't occur in Bell's derivation.

No, then you misunderstood him. There is no mix-up (and if it were, it would not be innocent That would certainly be a flaw in the proof). Where do you think he suggested that the mix-up is innocent because it averages out (just curious)?

b) no such mix-up occurs in Bell's derivation, but then the question is where is the mistake in Watson's critique of Bell's derivation as I elaborated. Also X-ray didn't find the error in Watson's paper, maybe you want to point it out to him? I have reconstructed the whole derivation in full detail, making it easy to point out mistakes.

So, which is it? We can't have both.

The error in Watson's critique is that he just assumes that there is a mix-up, and goes on from there. Obviously, when he then mixes Alices's outcomes with Bob's outcomes from different pairs as he does, he will be able to derive different things than what Bell did, and thereby claim that Bell was wrong.

The point being, there is no mix-up in the first place. But, Bell can (and does) discuss different outcomes associated with different detector settings for one and the same value of the hidden variable. And he can do that because he is essentially discussing what we today would call computer simulations. That is something very different from mixing up pairs of particles.

[harry]

[..] There is no mix-up (and if it were, it would not be innocent That would certainly be a flaw in the proof). [..]
The point being, there is no mix-up in the first place. But, Bell can (and does) discuss different outcomes associated with different detector settings for one and the same value of the hidden variable. [..]. That is something very different from mixing up pairs of particles.

Ah that's much clearer, thanks! That makes a lot of sense to me (I hope that it's the same for others).

Then I presume, the essential point is that Bell assumes that in real experiments effectively the same lambda(i) or equivalent must be acting on the same fraction of experiments for each detector setting; and thus he groups the results to be averaged as lambda(j) = lambda(i) by design. Correct? Indeed, then the issue at hand needs to be formulated quite differently from (and somewhat contrary to) the way Watson formulated it. Now I have a strange "deja-vu" feeling, probably I knew this some time ago but simply forgot it...

Surely that is also what Gill meant when he wrote:

[..] Now we can think of an experiment where 100 times we measure A and B. In roughly 1/10 of the runs lambda will equal l0 and this will give a contribution roughly equal to 1/10 times A(l0)B(l0) to the average value of A times B. Now do another 200 runs, measuring A and C. In roughly 1/10 of the runs lambda will equal l0 and this will give a contribution roughly equal to 1/10 times A(l0)C(l0) to the average value of A times C.

I misunderstood him to mean that the mix-up is innocent, because according to him we can regroup the terms like that; but of course, it is what Bell did from the start.

And with that correction we are led back, regretfully, to the same old discussion that has been going on for years, by De Raedt and others... But for me this was not totally lost time, for now I will be able to understand better what they are talking about.

[minkwe]

Harry,
Unfortunately you have been misled, your original understanding was spot on:

I do not have the time/interest at this moment to go into very detail but consider the following:

Bell's inequality is 1 + E(b,c) >= E(a,b) + E(a,c). Now ponder the meaning of those terms: E(a,b) is an expectation value of paired-outcomes of an imagined experiment.

Then Bell's theorem is: "No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics.", where "predictions of QM" is referring to those same E(a,b) expectation values. Knowing fully well that QM only talks about outcomes of performable experiments, it then is interesting to ask what the key difference is between those outcomes as imagined and used by Bell in his derivation, and as implied in QM.

Now, you've been told by some that Bell is not dealing with experiments at all. Obviously untrue as anyone can tell by pondering what the meanings of the terms are, and the fact that statements are being made about QM expectation values. (a point you eloquently stated earlier).

Then you've been told not to focus on Bell's early work but to read other works by Bell and his followers. That however is distraction from the main issue. First we must all honestly look at Bell's original work and identify all the errors (not just poor presentation).

The point which deRaedt and Watson and many others have made is quite simple: Since ultimately, we will rely on experiments to decide, we must start from performable experiments, and prove that we still can derive the inequality. That is the only basis any reasonable scientist could have for comparing inequalities to QM expectation values. In performable experiments, no particles are or can be measured more than once. Simply enforcing this requirement, prevents a successful derivation of the inequalities. This is what Watson has done.

In fact, Bell's "imagination" makes use of measuring the same particles more than once as I've explained many times on these forums. This is an uncontested fact clearly laid out in his algebra for all to see. Unfortunately for Bell and his followers, that crucial assumption introduces the schism between the inequalities and performable experiments, as well as QM. That schism has nothing to do with LHV theories or models. It has only to do with the fact that Bell's imagination is an unperformable experiment that should never have been compared with QM and actual experimental results to begin with.

[Xray]

Nice work minkwe. One of the best valid Refutations that I have seen. (As you now, many 'refutations' miss the mark.) Certainly, with its clarity, this is one of your best efforts.

PS: Small correction, in no way reducing the strength of your case:

Bell's experimentally erroneous inequality is 1 + E(b,c) >= | E(a,b) - E(a,c) |.

Xray

[gill1109]

Then I presume, the essential point is that Bell assumes that in real experiments effectively the same lambda(i) or equivalent must be acting on the same fraction of experiments for each detector setting; and thus he groups the results to be averaged as lambda(j) = lambda(i) by design. Correct? Indeed, then the issue at hand needs to be formulated quite differently from (and somewhat contrary to) the way Watson formulated it. Now I have a strange "deja-vu" feeling, probably I knew this some time ago but simply forgot it...

Surely that is also what Gill meant when he wrote:

[..] Now we can think of an experiment where 100 times we measure A and B. In roughly 1/10 of the runs lambda will equal l0 and this will give a contribution roughly equal to 1/10 times A(l0)B(l0) to the average value of A times B. Now do another 200 runs, measuring A and C. In roughly 1/10 of the runs lambda will equal l0 and this will give a contribution roughly equal to 1/10 times A(l0)C(l0) to the average value of A times C.

I misunderstood him to mean that the mix-up is innocent, because according to him we can regroup the terms like that; but of course, it is what Bell did from the start.

And with that correction we are led back, regretfully, to the same old discussion that has been going on for years, by De Raedt and others... But for me this was not totally lost time, for now I will be able to understand better what they are talking about.

In a computer simulation of a delayed choice event-ready detectors Bell type experument, lambda is chosen by some random mechanism at the source, ignorant of what measurement settings are going to be in force at the two measurement stations. The particles fly to their destinations; independently of this, the experimenters pick settings a or a', b or b'.

So suppose one particular value of lambda, say l0, occurs 10% of the time. 10% of the time when the setting pairs are a and b, lambda = l0. 10% of the time when the setting pairs are a and b', lambda = l0. 10% of the time when the setting pairs are a' and b, lambda = l0. 10% of the time when the setting pairs are a' and b', lambda = l0.

This is the grouping which Bell does. He groups the results for the four subexperiments according to the different possible values of lambda, and he assumes that the relative frequencies of any particular value, say l0, ate the same across the four subexperiments. rho(lambda) does not depend on a or b.

If the settings aren't repeatedly chosen anew at random, thinks can go wrong. rho can "drift" along with changing settings.

If some particles fail to arrive, things can go wrong. The relative frequency of different lambda can be made to change as detector settings change, by selectively rejecting "bad" lambda. This is called the detection loophole.

[gill1109]

In fact, Bell's "imagination" makes use of measuring the same particles more than once as I've explained many times on these forums. This is an uncontested fact clearly laid out in his algebra for all to see. Unfortunately for Bell and his followers, that crucial assumption introduces the schism between the inequalities and performable experiments, as well as QM. That schism has nothing to do with LHV theories or models. It has only to do with the fact that Bell's imagination is an unperformable experiment that should never have been compared with QM and actual experimental results to begin with.

Bell's imagination was no different from Einstein's in the EPR paper.

Followers of Bohr will say (and do say) that imagination is not allowed by the Copenhagen Dogma.

Fact is, a local hidden variables model, by definition, allows us the luxury of imagining what values would be realised, if a particle were measured in different ways. An event-based computer simulation allows us the same luxury. Of course, if you are not interested in LHV models anyway, then you are not interested in Bell's so-called theorem.

De Raedt simulates real past experiments which did not have repeated local random choice of detector settings, or *did* have undetected or even deliberately rejected particles. The successful event-based simulations to date have all been of past experiments which did not have the rigorous design insisted on by Bell in chapters 13 and 16 of "Speakable and Unspeakable".

[gill1109]

Here are some words from "Bertlmann's socks":

Sufficiently many repetitions of the experiment will allow tests of hypotheses about the joint conditional probability distribution

P(A,B|a, b)

for results A and B at the two ends for given signals a and b.
Now of course it would be no surprise to find that the two results A and B are correlated, i.e., that P does not split into a product of independent factors:

P(A,B|a,b) ≠ P1(A|a)P2(B|b)

But we will argue that certain particular correlations, realizable according to quantum mechanics, are locally inexplicable. They cannot be explained, that is to say, without action at a distance.

Notice the distinction between experiment, which gives us empirical (and statistical) information about the joint probability distributions of outcomes given settings P(A,B|a, b); and theory ... namely that assuming LHV allows us to deduce some necessary further properties of P(A,B|a, b).

Yet again: if you have no interest in local hidden variables theories anyway, and are quite happy with QM as it stands, then you have no interest whatsoever in Bell's so-called theorem! On the other hand, if your life's work is building event-based computer simulations of past QM experiments, then you do have interest in LHV theories, since your computer simulations *are* local hidden variable theories.

This is why, for instance, de Raedt and Hess are so interested in the Larsson-Gill work on the coincidence loophole, since that work tells them exactly to what limits they can go in their coincidence loophole simulation models. Walter Hess even claims that Larsson and Gill "stole" the idea of the coincidence loophole from the Hess-Phillip disaster.

[Heinera]

Then Bell's theorem is: "No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics.", where "predictions of QM" is referring to those same E(a,b) expectation values. Knowing fully well that QM only talks about outcomes of performable experiments, it then is interesting to ask what the key difference is between those outcomes as imagined and used by Bell in his derivation, and as implied in QM.

Bell's theorem: The Quantum Randi Challenge cannot be won.

Not only is there no mention of any actual experiment in that challenge; it can just as well be regarded a a challenge in Computer Science instead of Physics.

Now, instead of discussing alleged errors in Bell's proof that the challenge can't be won, just go for the kill and win the challenge. That would be convincing.

[harry]

Harry,
Unfortunately you have been misled, your original understanding was spot on:
[...]
E(a,b) is an expectation value of paired-outcomes of an imagined experiment.

[..] The point which deRaedt and Watson and many others have made is quite simple: Since ultimately, we will rely on experiments to decide, we must start from performable experiments, and prove that we still can derive the inequality. [..] This is what Watson has done. [..]

There is no doubt that the expectation values concern paired outcomes; surely we all agree on that. However, clearly Watson thinks (or thought, if he read the above) that Bell grouped his derivation corresponding to experimental sequence N. But as others pointed out, that is wrong. Indeed, Bell's integral is not over N or t, but over λ. Bell keeps λ constant over each integration step: on purpose one whole line corresponds to a single λ - and not, as Watson had it, a λi and a different λn+i which have different outcomes.

Here's an illustration. A carpenter determines the average length of two similar beams as follows: He places them on top of each other, puts a mark halfway between the ends of the two beams as follows:

-------------- . . . . x
---------------------------------

Next he measures the length upto the mark of the top beam. I see him do that, and happen to know the lengths of the two beams.
So I calculate (230+240) / 2 = 235 cm and shout out that number to him. He shouts back: "Right - how did you know?"

My calculation should in theory give the same result as the measurement, despite the fact that there is not a 1-to-1 correspondence between the two. Bell did similarly not stick to the experimental procedure for his derivation of what may be predicted as experimental outcomes. That doesn't mean that Bell didn't make a mistake, but it does mean that Bell did not make the striking mistake that Watson ascribes (or ascribed) to Bell.

[minkwe]

Indeed, Bell's integral is not over N or t, but over λ. Bell keeps λ constant over each integration step

So let me ask you then:

1) How many distinct lambdas are there in Bell's integral? (call that number N)
2) Now if each particle pair measured has a distinct lambda, do you still think Bell's derivation follows?
3) Do you now understand Watson's point?

Bell assumed that for each expectation value, the same set of lambda values applies. The only way that works is if all expectation values are calculated from the same set of particles (cf actual & counterfactual).

[Ben6993]

Why should anyone try to disprove the QRC or find a 4xN table with CHSH correlation > 0.5? Can QM be used to make such a table? The Table would contain observable outcomes of a simulated experiment. So why cannot QM be used to populate such a table with observables, even where those QM calculations would be permitted to use formulae which relied on action at a distance? So why is it OK for QM to fail to make such a table of observables, but not OK for a hidden variable model to fail to make such a table?

[FrediFizzx]

Bell's theorem: The Quantum Randi Challenge cannot be won.

Not only is there no mention of any actual experiment in that challenge; it can just as well be regarded a a challenge in Computer Science instead of Physics.

Of course the QRC can't be won since Bell's theorem is rigged against actual physical scenarios, it too is rigged.
viewtopic.php?f=6&t=17
While it might be OK for computer science, it is useless for physics.

[minkwe]

Why should anyone try to disprove the QRC or find a 4xN table with CHSH correlation > 0.5? Can QM be used to make such a table? The Table would contain observable outcomes of a simulated experiment. So why cannot QM be used to populate such a table with observables, even where those QM calculations would be permitted to use formulae which relied on action at a distance? So why is it OK for QM to fail to make such a table of observables, but not OK for a hidden variable model to fail to make such a table?

Great Question Ben. The funny thing is the same people making the demands about the QRC, claim that experiments agree with QM and that QM violates the CHSH. When it comes to making claims about QM, and experiments, they don't mention 4xN, yet when it comes to making demands about the QRC, they bring up 4xN. It is now clear that in their minds, local realism = 4xN -- a very naive view, given that even the most basic local realistic model of the EPRB experiment does not have 4xN outcomes but 2xN1, 2xN2, 2xN3, 2xN4 where N1, N2, N3, N4 are disjoint.

It then becomes clear why they prefer to talk about abstract computer simulations, because any garbage can be simulated and they can examine and manipulate numbers in any unphysical way they like, such as simultaneously measure the same particle at more than one angle, or by resetting random number seeds, they can recover pristine particles and re-measure them -- all very possible to do on the computer, but absolutely garbage when it comes to physical relevance.

They did not learn anything from viewtopic.php?f=6&t=39

[pk0]

This is in reply to a post by minkwe on Thu May 29, 2014 9:02 pm, which starts as follows:
"Harry,
Unfortunately you have been misled, your original understanding was spot on:..."

I was so impressed by minkwe's reasoning that I am writing this to say solely and exactly that, here, now. Maybe I will come up with something that actually contributes to the argument, and at that point, I will say more. For now, it is good to see minkwe is "on the (right?; yes, that's it) team."

[gill1109]

Indeed, Bell's integral is not over N or t, but over λ. Bell keeps λ constant over each integration step

So let me ask you then:

1) How many distinct lambdas are there in Bell's integral? (call that number N)
2) Now if each particle pair measured has a distinct lambda, do you still think Bell's derivation follows?
3) Do you now understand Watson's point?

Bell assumed that for each expectation value, the same set of lambda values applies. The only way that works is if all expectation values are calculated from the same set of particles (cf actual & counterfactual).

No. That works as long as the same set of possible values of lambda, with the same relative frequencies rho(lambda) d lambda, apply whatever pair of settings is in force.

Nature chooses a particle, a value of lambda, different values occurring with different rekative frequencies.

Alice chooses a setting a, and Bob chooses a setting b. Their choices have no effect, statistical or otherwise, on Nature's choice of the value lambda carried by the pair of particles.

Unless of course the distribution of lambda changes in time, and. Alice and Bob's setting choices are statistcally correlated with time. Or if Alice and Bob's apparatus's reject some particles (some values of lambda more often than others) depending on the measurement settings: detection loophole. Or Alice and Bob reject some particles because their arrival times are too early or too late, in a way which depends on the measurement settings (coincendence loophole). Or if Nature knows in advance what Alice and Bob's settings are going to be (conspiracy loophole).

[Heinera]

Bell's theorem: The Quantum Randi Challenge cannot be won.

Not only is there no mention of any actual experiment in that challenge; it can just as well be regarded a a challenge in Computer Science instead of Physics.

Of course the QRC can't be won since Bell's theorem is rigged against actual physical scenarios, it too is rigged.

The challenge is only "rigged" if you believe Bell's theorem is true, because then it is unwinnable. If Bell was wrong, then a winning solution to the challenge exists.
If you believe both that the challenge is unwinnable and Bell was wrong, then you read something more into Bell's theorem than what is actually there.

While it might be OK for computer science, it is useless for physics.

Bell's theorem is certainly useful for anyone spending their spare time trying to create no-loophole LHV computer simulations that generate the cosine correlations. It tells them something about how likely they are to succeed.

[gill1109]

It then becomes clear why they prefer to talk about abstract computer simulations, because any garbage can be simulated and they can examine and manipulate numbers in any unphysical way they like, such as simultaneously measure the same particle at more than one angle

So Einstein wrote a heap of garbage in the EPR paper? He talks of measurement both of position and of momentum on the same particle. In fact, on a pair of particles; Alice can choose between measuring position and momentum on hers, and so can Bob. The EPR paradox was converted by David Bohm into the EPR-B paradox... and that was where John Bell came in.

So Einstein (+ Podolsky and Rosen) was a nutter? David Bohm was a fool?

By the way, not any garbage can be simulated. Even Michel Fodje can't simulate a delayed-choice event-ready-detectors Bell-CHSH experiment reproducing the singlet correlations (up to statistical fluctuationns) in a local-realist event-based manner.

Actually Einstein, Bohm, Bell and everyone else don't talk about simultaneous measurement of incompatible observables. They only talk about what each of the outcomes would have been, if each of the different measurements had been done. Which is certainly possible to do if we are talking of one of Fodje's simulations. Not only is it possible, it's also useful. One can deduce certain limits to the operating characteristics of the computer program. What can it do? What can it not do?

[gill1109]

Bell's theorem: The Quantum Randi Challenge cannot be won.

Not only is there no mention of any actual experiment in that challenge; it can just as well be regarded a a challenge in Computer Science instead of Physics.

Of course the QRC can't be won since Bell's theorem is rigged against actual physical scenarios, it too is rigged.
viewtopic.php?f=6&t=17
While it might be OK for computer science, it is useless for physics.

Is computer science useless for physics? Interesting point of view. Throw away that expensive Mathematica.

Fred: your friend Joy Christian hopes to win a computer challenge. Maybe computer science would be useful for him. In fact, computer science proves he can't win. Computer science also proves that his physics experiment will certainly fail. If you want him to succeed, you need to help him rewrite page 4 of his experimental paper. Write the Mathematica computer program which implements the geometric algebraic product sign(a.u) sign(b.v) on a computer.

[gill1109]

It is now clear that in their minds, local realism = 4xN -- a very naive view, given that even the most basic local realistic model of the EPRB experiment does not have 4xN outcomes but 2xN1, 2xN2, 2xN3, 2xN4 where N1, N2, N3, N4 are disjoint.

Local realism implies that behind the N = N1 + N2 + N3 + N4, there can be imagined a 4xN table.

Local realism implies that one can imagine alongside of the actual outcomes of the actually performed measurements, also the outcomes of the not-performed measurements.

In the EPR paper, Einstein uses the perfect anti-correlation of the singlet correlations, and locality, in order to *deduce* realism. Ie for Einstein, QM + locality => locality + realism => simultaneous existence of values of both measured and unmeasured observables.

For instance, Alice chooses setting a, Bob chooses setting b, Nature chooses hidden variable lambda ... we get to see A(a, lambda) and B(b, lambda); but A(a', lambda) and B(b', lambda) are mathematically defined, and exist mathematically, whether you like it or not.

Of course if you prefer not to use your imagination, you'll not see so much.

[gill1109]

Why should anyone try to disprove the QRC or find a 4xN table with CHSH correlation > 0.5? Can QM be used to make such a table? The Table would contain observable outcomes of a simulated experiment. So why cannot QM be used to populate such a table with observables, even where those QM calculations would be permitted to use formulae which relied on action at a distance? So why is it OK for QM to fail to make such a table of observables, but not OK for a hidden variable model to fail to make such a table?

Ben: QM cannot populate the 4xN table, because QM cannot be simulated in a local realist way.

If you don't care about local realism, then you don't have to care a damn. Niels Bohr would have said: told you so.

Read chapter 16 (Bertlnann's socks) of Bell's book "Speakable and unspeakable", where Bell lists four possible points of view to take concerning his findings. One of those points of view is "so what?". Bell ascribes it to Bohr. The Copenhagen interpretation. There is nothing going on behind the scenes. It's counterproductive to go looking for it.

If you think QM is just fine, and are not bothered that it makes predictions which can't be simulated in an event-based, local realist way, then you have no problems.

QRC is interesting as a test of quantum c****pot claims. Eg dr J J Christian (Oxford) claims he has a local realist model reproducing the singlet correlations. If he was right, he could easily win QRC. But ut is impossible to win QRC. Hence his claims are false.

One can also dive into the fantasy math and exhibit the errors but then (a) JJC will say you are an idiot (b) write a new version of his theory even more inpenetrable than the preceding one. Florin Moldoveanu has already carefully tracked 8 (eight!) such transitions. We call it the "bump in the carpet". You can't get it to go away. The best you can do is try to hide it under the sofa.