Bell’s Theorem Refuted: Bell’s 1964:(15) is False

[gill1109]

Gordon, if Bell is wrong, you should be able to win the quantum Randi challenge http://www.science20.com/alpha_meme/official_quantum_randi_challenge-80168. Or mine http://arxiv.org/pdf/quant-ph/0110137v4.pdf. That will make you famous, and destroy Bell for ever.

Why has no-one been able to do so? Who will be first?

[Gordon Watson]

Gordon, if Bell is wrong, you should be able to win the quantum Randi challenge http://www.science20.com/alpha_meme/official_quantum_randi_challenge-80168. Or mine http://arxiv.org/pdf/quant-ph/0110137v4.pdf. That will make you famous, and destroy Bell for ever.

Why has no-one been able to do so? Who will be first?

Richard,

IF Bell is wrong??

1. He analysed EPRB and got the wrong answer. That is:

2. He says his (14a) = his (15). Wrong!

3. He says his 1964:(2) ≠ his 1964:(3). Wrong, once you sort out his sloppy notation (see next)!

4. Please answer: Is A(λ, a) = ±1 in his (1) the same as A(λ, a) in his (2)? Please give an example of such a function as you propose!

5. He, needing both (but not able to admit to AAD), repeatedly spoke in double-think re action-at-a-distance and NO action-at-a-distance.

Which brings us nicely to the double-speak in the QRC challenge:

"The Quantum Randi Challenge, hence forth QRC, challenges any pseudo-scientist who claims that quantum physics is not true and that quantum entanglement experiments can be explained by a classically realistic and locally causal model."

I'm an engineer who claims that quantum physics is true (in its calculations) and that quantum entanglement experiments can be explained by a classically realistic and locally causal model.

Am I allowed to enter? I'm guessing you have some escape-clauses re the direct-quotation above?

Further: Re your challenge: Since Bell IS wrong, what stops you winning QRC?

This is a serious question. So maybe you'll be more comfortable telling me why Bell is right and what, exactly, he is right about?

PS: Truly, I have no clue as to where you think my essay is flawed.

How about referring to specific paragraphs and equations, please? They are numbered for that very purpose.
.

[Ben6993]

Hi Gordon.

Some posts back, you mentioned Pisa and Paris to me. Coincidentally, last month I was in Pisa for a break and I flew over Paris to get there. Very nice, too! And when I was over Paris I was not in Pisa and when I was in Pisa I was not over Paris.

I cannot see why you deny the use of A(λ)squared = 1 in the formula, as A(λParis)squared = 1 and A(λPisa)squared = 1. The fact that maybe A(λparis) x A(λPisa) = -1 is wholly irrelevant to the integration.

I agree with Michel's point in his latest post. I think that he stated that there was no error in the formula so long as one realises that the range of λs is over all possible values. This would match Michel's "strong" condition. And if you take that over an infinity of all possible λ values you have Richard's population case.

As Michel often notes, no experiment can sample over an infinity of λ values, nor get anywhere near a matching of the λ values in the run for Alice and the run for Bob. So experiments necessarily only use a "weak" condition. A weak condition is not matching the conditions of the Bell formula and so can break the Bell limits. And that can also be described as experiments use samples rather than a population, also allowing a breaking of Bell limits.

But all that is in flatland where rotations have periodicity 2pi. Joy is making use of a rotational periodicity of 4pi, which Richard wrote that is something with which most experimenters would disagree. That is strange as I have heard Leonard Susskind in an online lecture say that he has done the experiment himself (as long ago as 1967) showing 4pi rotational periodicity.

This is a just an analogy, but may correspond to your Paris/Pisa explanation. If A(λPisa) = -1 or +1 because space is 'double covered' ie 4pi periodicity rather than 2pi periodicity. Then it may be possible for A(λPisa)squared to be -1*1 = -1. That would ruin the integration. However, if one believes in a double cover of space then one would not be using flatland algebra in the first place but start again from scratch using geometric algebra.

[Q-reeus]

...I have heard Leonard Susskind in an online lecture say that he has done the experiment himself (as long ago as 1967) showing 4pi rotational periodicity....

Please supply relevant link(s)! [and assuming YouTube, the relevant time(s) into lecture(s)]

[Gordon Watson]

Hi Gordon.

Some posts back, you mentioned Pisa and Paris to me. Coincidentally, last month I was in Pisa for a break and I flew over Paris to get there. Very nice, too! And when I was over Paris I was not in Pisa and when I was in Pisa I was not over Paris.

I cannot see why you deny the use of A(λ)squared = 1 in the formula, as A(λParis)squared = 1 and A(λPisa)squared = 1. The fact that maybe A(λparis) x A(λPisa) = -1 is wholly irrelevant to the integration.

I agree with Michel's point in his latest post. I think that he stated that there was no error in the formula so long as one realises that the range of λs is over all possible values. This would match Michel's "strong" condition. And if you take that over an infinity of all possible λ values you have Richard's population case.

As Michel often notes, no experiment can sample over an infinity of λ values, nor get anywhere near a matching of the λ values in the run for Alice and the run for Bob. So experiments necessarily only use a "weak" condition. A weak condition is not matching the conditions of the Bell formula and so can break the Bell limits. And that can also be described as experiments use samples rather than a population, also allowing a breaking of Bell limits.

But all that is in flatland where rotations have periodicity 2pi. Joy is making use of a rotational periodicity of 4pi, which Richard wrote that is something with which most experimenters would disagree. That is strange as I have heard Leonard Susskind in an online lecture say that he has done the experiment himself (as long ago as 1967) showing 4pi rotational periodicity.

This is a just an analogy, but may correspond to your Paris/Pisa explanation. If A(λPisa) = -1 or +1 because space is 'double covered' ie 4pi periodicity rather than 2pi periodicity. Then it may be possible for A(λPisa)squared to be -1*1 = -1. That would ruin the integration. However, if one believes in a double cover of space then one would not be using flatland algebra in the first place but start again from scratch using geometric algebra.

Hi Ben,

So, to have you dine out on your great story in the history of physics -- "How I saw the light on a Paris-Pisa flight" -- we need to get you converted to the right side of this Bellian stuff.

1. Say we tested for <AiBi> in Paris (i = 1,2,.., N) and for <AjCj> (j = 1,2,.., N) in Pisa, wanting to have (like Bell in his (14a)): <AiBi> - <AjCj>.

Then it would be a bit rough to expect AiAj = +1. Yet isn't that what Bell expects in his (14b)? Remembering that we can pin-point the erroneous equation as follows:

His (14a) is experimentally validated. His (15) is NOT, so his (14c) is NOT. And he uses his (1) to justify (14b).

Now, with tests as above (Ai)(Ai) = (Aj)(Aj) = 1, but Bell is amalgamating via (Ai)(Aj) which may or may not = 1. Isn't that what he does? If not, where else is the ERROR that MUST BE in his move from correct-(14a) to incorrect-(14b)?

NB: Bell's equation (14b) is valid for classical things like Bertlmann's socks because they can be tested and retested non-destructively. That is, he could send the i-coded and tested socks from Paris to Pisa for the new set of tests. (But he cannot do that with photons, etc.) The fact that Bell thinks this way is seen in his support for the naive-realism of d'Espagnat (in his "Bertlmann's socks" essay)!

2. Re Michel vs Richard. There is no need to experimentally integrate over an infinity of tests because a much smaller number will give us adequate accuracy. By which I mean, if theory says we should get X = 0.5 and we get X = 0.499 after 10,000 tests, is that not OK?

3. Re 4π, YES, for sure: that is what I integrate over because EPRB and Aspect's experiments have spherical symmetry. But note that the maths does not change since, if you integrate dλ over 0-4π, then you average via ρ(λ)= 1/4π. (Integrating over 0-2π you have the compensating 1/2π.)

Experimentalists would not dispute the validity of using 4π. They simply find it difficult to have their magnets etc. maintain line-of-flight alignment when moving them in 3-dimensions. So we all gladly settle for 2π (in most cases); happily knowing that the likes of (say) Susskind have gone to the extra (though not essential) trouble re 4π.

With best regards; Gordon

[Heinera]

I'm an engineer who claims that quantum physics is true (in its calculations) and that quantum entanglement experiments can be explained by a classically realistic and locally causal model.
.

And we are just mathematicians and statisticians humbly suggesting that you actually produce such a model. It would make further discussions much more fruitful.

[Joy Christian]

And we are just mathematicians and statisticians humbly suggesting that you actually produce such a model. It would make further discussions much more fruitful.

One has to be totally blind and dogmatic to not see that such a model already exists:

(1) http://arxiv.org/abs/1405.2355

(2) http://libertesphilosophica.info/blog/

(3) http://arxiv.org/abs/1301.1653

(4) http://arxiv.org/abs/1211.0784

(5) http://rpubs.com/jjc/16567

(6) http://rpubs.com/jjc/19298

Sorry, perhaps one does not have to be blind and dogmatic. Perhaps one has to be just mathematicians and statisticians to not see that such a model already exists.

[Heinera]

Yes, both mathematicians and staticians understand that Pearle's model already exists, and has been doing so for about 40 years. And they also understand that this model is in no way in conflict with Bell's theorem.

[Joy Christian]

Yes, both mathematicians and statisticians understand that Pearle's model already exists, and has been doing so for about 40 years. And they also understand that this model is in no way in conflict with Bell's theorem.

Evidently mathematicians and statisticians do not seem to understand either Pearle's model based on data rejection or my model based on the 3-sphere topology.

But let me enlighten them:

Pearle’s model is a static model, based on SO(3). My model is a dynamic model, based on SU(2). Mathematicians and statisticians have not understood the difference.

The distribution function I have used in recent simulations is a result of the SU(2) dynamics, not the SO(3) statics.

The link between Pearle's static model and my dynamic model has been explained in detail in this paper: http://arxiv.org/abs/1405.2355.

[Heinera]

Yes, both mathematicians and statisticians understand that Pearle's model already exists, and has been doing so for about 40 years. And they also understand that this model is in no way in conflict with Bell's theorem.

Evidently mathematicians and statisticians do not seem to understand either Pearle's model based on data rejection or my model based on the 3-sphere topology.

Oh, we have no trouble with the first one. But you are certainly correct about us not understanding the second one...

[Joy Christian]

Yes, both mathematicians and statisticians understand that Pearle's model already exists, and has been doing so for about 40 years. And they also understand that this model is in no way in conflict with Bell's theorem.

Evidently mathematicians and statisticians do not seem to understand either Pearle's model based on data rejection or my model based on the 3-sphere topology.

Oh, we have no trouble with the first one. But you are certainly correct about us not understanding the second one...

Ignorance is indeed bliss...

[Heinera]

Ignorance is indeed bliss...

Indeed. And given the amount of ignorance there is in the world, not to mention all the bullsh*t, I'm soon taking a summer vacation. (OK, I would be doing that anyway).

Fantastic summer reading for everyone: The booklet "On Bullsh*t" by Princeton philosophy professor Harry G. Frankfurt. It's absolutely hilariously good and funny. They sell it on Amazon.

(And the book title should obviously be the word spelled correctly; politically correct forum software forced me to replace the "i" with a star. Anyway, the Amazon servers are not that politically correct, so you can search using the precise title.)

[FrediFizzx]

Guys, you are off topic; let's get back on topic.

[minkwe]

One of the other posters have suggested that we can assume that the three sets are the same since according to him "Nature is the one picking lambda, and we can assume that nature picks the same set of lambda everytime". Of course, such an assumption will allow the derivation to proceed but is such an assumption reasonable? Definitely not. In any case, even if you disagree that such an assumption is silly, it is one more candidate for rejection when the inequality so-derived is violated. There is nothing about local hidden variable theories that implies nature must pick the exact same set of lambdas every time -- none whatsoever.

Bell's derivation indeed assumes that Nature is picking from the same set of lambda every time. Not only does he assume that the three sets are the same, he also assumes that the probability distribution rho(lambda) is the same too.

If that is the case then it must be a fatal failure on Bell's part not to put forth that assumption as the most likely candidate to be rejected on violation. Violation of the inequality implies that nature does not pick the exact same set of lambda every time, obviously.

So if you you want to violate the inequality by a local hidden variables theory, you have to change the sets, or at least, change the distribution.

If you want to model the EPRB experiment or simulate it, you MUST do it on disjoint sets (aka different set of lambda every time, just like the real experiment). Some people have a very hard time understanding this. They point of QRC and all other fake challenges which involve calculating nonsensical correlations on the same set thinking they are doing anything relevant to EPRB. I laugh everytime I hear someone say, "if you believe Bell is wrong, win the QRC". It is similar to saying, "If Bell's inequality does not apply to disjoint sets of actual experiments, then prove that Bell's inequality does not apply to the single set on which it is derived, by winning the QRC". Disingenuous to say the least. QRC is a silly rigged challenge with no relevance to EPRB or QM.

[minkwe]

As Michel often notes, no experiment can sample over an infinity of λ values, nor get anywhere near a matching of the λ values in the run for Alice and the run for Bob. So experiments necessarily only use a "weak" condition. A weak condition is not matching the conditions of the Bell formula and so can break the Bell limits. And that can also be described as experiments use samples rather than a population, also allowing a breaking of Bell limits.

Do not forget the very important point that upper bound for the weakly objective expectation values is 4, and that the QM expectation values are weakly objective.

But all that is in flatland where rotations have periodicity 2pi.

The above does not care about flatness of the land, it is algebra. The main thing to realize is that once it is clearly understood that there is no discrepancy between LHV and QM, we can then focus on finding LHV which reproduce the QM correlations. This is where Joy's model comes in IMHO. The double cover is not very relevant to the discussion of the derivation of the inequalities themselves and the undeniable conclusion is that if the inequalities are correctly derived, then they are irrelevant to EPRB, and if the inequalities are relevant to EPRB then they are incorrectly derived. LHV models do not have to care about the inequalities, they just have to reproduce the QM correlations. Admittedly, there will be QRC choir members pushing inequalities in the face of anyone who attempts a LHV model. They will place silly demands which amount forcing calculation of correlations on a single set, because that is the only scenario under which the inequalities are relevant. It is just a distraction IMHO. It is not possible to comply with the demands of the QRC type challenges and stay relevant to EPRB.

[Joy Christian]

But all that is in flatland where rotations have periodicity 2pi.

The above does not care about flatness of the land, it is algebra. The main thing to realize is that once it is clearly understood that there is no discrepancy between LHV and QM, we can then focus on finding LHV which reproduce the QM correlations. This is where Joy's model comes in IMHO. The double cover is not very relevant to the discussion of the derivation of the inequalities themselves and the undeniable conclusion is that if the inequalities are correctly derived, then they are irrelevant to EPRB, and if the inequalities are relevant to EPRB then they are incorrectly derived. LHV models do not have to care about the inequalities, they just have to reproduce the QM correlations.

Ben,

I agree with Michel here. It is important to distinguish between Bell's irrelevant tautology and the actual physics and mathematics of the EPRB type experiments.

[FrediFizzx]

Yes, very good synopsis Michel. I was going to warn Gordon about the rigged challenges but you did it better than I would have.

[gill1109]

Gordon, if Bell is wrong, you should be able to win the quantum Randi challenge http://www.science20.com/alpha_meme/official_quantum_randi_challenge-80168. Or mine http://arxiv.org/pdf/quant-ph/0110137v4.pdf. That will make you famous, and destroy Bell for ever.

Why has no-one been able to do so? Who will be first?

Richard,

IF Bell is wrong??

...

Which brings us nicely to the double-speak in the QRC challenge:

"The Quantum Randi Challenge, hence forth QRC, challenges any pseudo-scientist who claims that quantum physics is not true and that quantum entanglement experiments can be explained by a classically realistic and locally causal model."

I'm an engineer who claims that quantum physics is true (in its calculations) and that quantum entanglement experiments can be explained by a classically realistic and locally causal model.

Am I allowed to enter? I'm guessing you have some escape-clauses re the direct-quotation above?

Further: Re your challenge: Since Bell IS wrong, what stops you winning QRC?

This is a serious question. So maybe you'll be more comfortable telling me why Bell is right and what, exactly, he is right about?

PS: Truly, I have no clue as to where you think my essay is flawed.

How about referring to specific paragraphs and equations, please? They are numbered for that very purpose.
.

You are allowed to enter, Gordon. Let's remove the double-speak:

The Quantum Randi Challenge, hence forth QRC, challenges any scientist who claims that quantum entanglement experiments can be explained by a classically realistic and locally causal model.

Yes I know you have no idea why your essay is flawed. Various people have repeatedly explained, with reference to specific paragraphs and equations, but it seems you have some kind of mental block. Actually I think you are missing basic understanding of probability and statistics. I suggest you study John Rice's excellent text book "Introduction to Mathematical Statistics and Data Analysis".

But in the meantime, I think it is a good idea to look for common ground. Let's study this issues in a simple, concrete, context. Simple computer experiments which we both in principle could do, which we both can understand.

Can you win the QRC? Or can you win my challenge to Accardi?

[Heinera]

If you want to model the EPRB experiment or simulate it, you MUST do it on disjoint sets (aka different set of lambda every time, just like the real experiment). Some people have a very hard time understanding this. They point of QRC and all other fake challenges which involve calculating nonsensical correlations on the same set thinking they are doing anything relevant to EPRB. I laugh everytime I hear someone say, "if you believe Bell is wrong, win the QRC". It is similar to saying, "If Bell's inequality does not apply to disjoint sets of actual experiments, then prove that Bell's inequality does not apply to the single set on which it is derived, by winning the QRC". Disingenuous to say the least. QRC is a silly rigged challenge with no relevance to EPRB or QM.

The QRC does not require that the correlations must be calculated on the same set. On the contrary, correlations are computed on disjoint sets picked randomly.

[gill1109]

The Quantum Randi Challenge, hence forth QRC, challenges any scientist who claims that quantum entanglement experiments can be explained by a classically realistic and locally causal model.

...

But in the meantime, I think it is a good idea to look for common ground. Let's study this issues in a simple, concrete, context. Simple computer experiments which we both in principle could do, which we both can understand.

Can you win the QRC? Or can you win my challenge to Accardi?

I should emphasize that both QRC and my Accardi challenge are concerned with an ideal experiment. An experiment of the kind envisaged by Bell himself (see "Bertlman's socks"). An experiment with "event ready detectors" and with "delayed choice randomly picked settings". An experiment without detection loophole.

The QRC, and my challenge, both pertain to a thought experiment, an experiment which is still in the future. They do not pertain to experiments done in the past.

Gordon should be happy with that idea, but Michel is certainly not. He's only interested in showing that experiments done to date (i.e. in the past) can be explained by LHV theories. A fact which ought to be well-known. It is well-known among the experts in the field, but apparently not well known in the broader community.