## Wednesday, 10 June 2015

### A flatlanders view on Joy Christian's simulations

Flatlanders living in the plane below are witnessing something strange. Normally any object of any form that rotates in their world spans the surface of a perfect circle. But in the current experiment they measure something rotating in their world that spans an oval instead. So in their 2d system they try to simulate what they see to understand the process. But they don't succeed unless, for example, they use a loophole where they change the size of the object during rotation.

For us being privileged 3d persons it is easy to understand that the flatlanders are witnessing a projected effect from our world.

This example illustrates the discussions about Joy Christian's theory and simulations. In a nutshell Joy's theory postulates that an object has to undergo a 4pi rotation  to return to its original state (1) (and not 2pi). Currently all attempts to simulate this in an event by event Monte Carlo simulation have been done in an algebraic system that doesn't support this 4pi constraint. The simulations that have been carried out by Joy (2) and others are based on the analytic proof of the theory. But transferred our 'flat' 3d space algebra this means that results falling into the 'green area' should be rejected, because, like in the flatlander's case, these outcomes do not exist.

Joy might be right. But to completely support this by an event by event simulation, I think the total EPR process should be calculated using an algebra that naturally incorporates this 4pi feature. Quaternions? Multivectors? Or maybe yet something else?

1. Macroscopic Observability of Spinorial Sign Changes under 2π Rotation, Joy Christian, http://link.springer.com/article/10.1007/s10773-014-2412-2 The arxiv text: http://arxiv.org/pdf/1211.0784.pdf
2. Joy about his latest simulation: http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=168&p=4172#p4172

1. Albert Jan,

In this context you may find the following animation interesting:

https://johncarlosbaez.wordpress.com/2015/03/17/planets_in_the_4th_dimension/

1. I have now included calculations for the violations of both the CHSH and the more general CH inequalities in this simulation:

http://rpubs.com/jjc/84238 .

This completes the numerical, event-by-event verification of the local-realistic model presented in this paper:

http://arxiv.org/abs/1405.2355 .

2. Proofs of "no 0 outcomes" added: http://rpubs.com/jjc/84238 .

2. Nice post, Albert Jan! Problem is, an event-by-event simulation (without loopholes) on classical computers is by definition a simulation of a flatland world. Even if the computer incorporate quaternions or multivectors, the computers are just Turing machines.

Now things would be different if we could use quantum computers. But then we are doing our simulation using the resources of the 4d spherical world, of which our 3d world is merely a projection.

1. What a mind-numbingly flat comment.

2. I don't think we have constrained our classical computers to only calculate what we currently consider our reality, But as stated in the post it might be the mathematical system we use in these calculations that holds us back.

3. Dear Albert Jan, You are missing the point. But it is a subtle point, which many people do not grasp.

Consider an event-by-event digital digitally networked digital computer simulation of a loophole free CHSH experiment. It consists of five computers (Alice setting device, Alice measurement device, Source, Bob measurement device, Bob setting device) connected linearly. The computers are just heaps of logic gates. Everything is deterministic (all needed "random numbers" have been pre-stored on the five computers). The only thing that happens is that bits are fed into classical logic gates. The whole system is a completely deterministic physical system in a universe with one discrete spatial dimension and one discrete time dimension.

Of course you can "simulate" any exotic physics using any exotic mathematics that takes your fancy on a single computer. But that is not the issue here.

4. PS, of course, if we had quantum computers and quantum network connections, we would be able to do it. But Joy Christian has argued that this is impossible, because the whole idea of quantum entanglement is an illusion.

5. PS it's like Gödel's incompleteness theorems, and everything that grew from them (model theory, non-standard calculus, etc). We can write down the standard axioms of set theory (ZFC). In ZFC we can define the natural numbers, define the real numbers and prove that the real numbers are uncountable - there is no bijection between the natural numbers and the real numbers. Yet it is a theorem that there exists a countable model for ZFC. In other words: a list of objects which (internally) satisfy the axioms, hence such that there is no bijection in the list between the item in the list representing the set of natural numbers and the item in the list representing the set of real numbers.

One can use this construction to do cool things like prove the indepence of the continuum hypothesis from the other axioms. And to do non-standard analysis: calculus with infinitesimals etc etc.

3. The event-by-event simulation cited by Albert Jan as ref. (2) in his post, namely

http://rpubs.com/jjc/84238 ,

is a perfectly satisfactory event-by-event simulation of my 3-sphere model.

To be sure, a pre-ensemble M of the pre-states u has been used to build this simulation, but such scaffolding mathematical structures are routinely used in modern physics --- for example, in gauge field theories. The scaffolding structures are eventually "gauged out" to extract the correct physics out of the auxiliary mathematics. Similarly, the true ensemble N of the true states (u, s) has been extracted in my simulation from the pre-ensemble M of the pre-states u, thereby reducing the auxiliary pre-pair {M, u} to the true pair {N, (u, s)}, just as in any modern gauge theory.

1. Unfortunately, what Christian says here is false. I believe he does not understand his R code very well.

The simulation he refers to (his adaptation of my simulation of the Pearle model) generates a different "true" ensemble for each pair of measurement settings (a, b). This flatly contradicts the claim in (B10) of Christian's latest paper that a single ensemble of size N directions u^k can be extracted from a given ensemble of size N of bivectorial outcome pairs.

Christian has elsewhere explicitly acknowledged that "he doesn't know how to do this yet". See his recent postings on Albert Jan's blog of last month.

2. Fortunately, what Gill says here is worse than false. It is quite evident that Gill does not have a clue what he is talking about. He is mixing several different things without understanding a single one of them correctly. For example, he is confusing the Clifford-algebraic representation of the 3-sphere in my latest paper with the non-Clifford-algebraic representation of the 3-sphere presented in this simulation: http://rpubs.com/jjc/84238 (this simulation, by the way, has nothing much to do with the simulation of the Pearle's detection loophole model pioneered by Michel Fodje, to which Gill later made a very minute correction with much help from me and many others).

The reader is urged to read the preamble of the above simulation for details rather than being hoodwinked by Gill's attempted misrepresentation of it.

3. The reader is urged to study the code and think for him or herself! Regarding Pearle's model, see http://arxiv.org/abs/1505.04431

4. The simulation of the Pearle's detection loophole model was pioneered by Michel Fodje, to which Gill later made a very minute correction,with much help from me and many others. For more details, the reader is urged to check out these facts:

http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=66&start=10#p3054

http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=111&start=20#p4032

4. PS "IJoy's theory postulates that an object has to undergo a 4pi rotation to return to its original state (1) (and not 2pi)". Well, this idea has a long history in quantum mechanics and even in our own familiar 3d world: cf. Dirac's string trick. https://en.wikipedia.org/wiki/Plate_trick The clue is that it is not an object on its own, but the object in relation to its surroundings, which needs a 4 pi rotation to "return home". And the amazing thing is not that the answer is not 2 pi, but that that the strings magically untangle at 4 pi.

5. "The plate trick, also known as Dirac's string trick, the belt trick, Balinese cup trick, is any of several demonstrations of the mathematical theorem that SU(2) (which double-covers SO(3)) is simply connected. To say that SU(2) double-covers SO(3) essentially means that the unit quaternions represent the group of rotations twice over."

So in fact we do already have a highly suitable mathematical framework with the required framework. Indeed, Doran and Lasenby have two chapters in their book re-writing conventional quantum theory in the language of Clifford algebras.

The barrier to an event-by-event simulation lies elsewhere ... it lies with Bell's theorem. And by the definition of event-by-event simulation: it needs to generate *events*. Detector clicks.

1. It is time for Gill and his fellow believers to wake up and smell the coffee. Bell's theorem is as dead as the blue parrot:

2. I see that Gill is still struggling with trying to understand geometric algebra.

6. Hi Albert Jan,

Excellent post! That really illustrates what is going on with the complete states concept and that it is possible to simulate it as Joy has done.

1. To answer your questions, it can be simulated with +/- 1 outcomes with regular algebra. Pearle stumbled upon the answer long ago but had the wrong interpretation of what was going on. Joy found the right interpretation using 3-sphere topology. I think we are done.

2. We are done except for a proper macroscopic singlet experiment to see if the model holds macroscopically.

3. You haven't yet simulated a proper macroscopic experiment. If you can't even simulate one, I doubt you can perform one in the lab either.

4. Many good simulations have been done. You just don't accept them because then you would have to pay the bet you lost.

5. This has not happened yet. The jury at Växjö adjudicated that Christian's submission last year did not win the bet.

I am happy to make a new bet with you, Fred, if you like. We would have to enter into negotiations as to the conditions. Do you want to go for my old challenge to Luigi Accardi? http://arxiv.org/abs/quant-ph/0301059

5000 Euro's says you can't do it.

6. Gill: "The jury at Växjö adjudicated that Christian's submission last year did not win the bet."

Christian: A shameless lie. There was no such jury. Gill owes me 10,000 euros + interest + inflation + profuse apology for writing a series of malicious letters about me to the President of my college at Oxford (as a diversionary tactic to avoid paying me).

The truth can be found at the following link

http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=66#p3030 ,

or at the bottom of my blog: http://libertesphilosophica.info/blog/

7. The jury consisted of Gregor Weihs and Hans de Raedt. Andrei Khrennikov dropped out because of unexpected conference organisational difficulties (a train strike caused a lot of difficulties for a lot of participants).

I complained to the president of Wolfson College about the continuing verbal abuse and lies which Joy Christian heaped upon myself and indeed anyone who dared to point out mistakes in his work.

It all goes to show that in science one should stay polite and respectful even to people who disagree with you. Descending into childish temper tantrums when you don't get your own way is unwise.

8. Yes Fred, many good simulations were done, all of which confirmed Bell's theorem. What the theorem has to say about physics is a nice point for discussion, but one thing is for sure: it is a true theorem about distributed computing (with classical computers and a classical communication network).

That's why one can very safely make bets about the results of such simulations. Now physical reality, that is a much more difficult matter.

9. Bell's theorem and inequality have absolutely nothing to do with physics. It is all pure math. Nothing physical can violate the inequality; not even QM. It is plain nonsense. So it is ridiculous to play by Bell's rules and conditions.

Joy's simulations are about classical local realistic physics in S^3 topology. Something your right handed only flatland brain will never be able to understand.

10. The only thing that matters in science is the Truth.

But truth is not something you will find either in Gill's words or in his deeds.

I will continue to expose the truth about Gill, at whatever cost, as I have done at the bottom of my blog page linked above.

7. FediFizzx "Bell didn't even realize his own mistake that QM can't even violate the inequality."

Rosinger: "It was shown in [1], cited in the sequel as DRHM, that upon a correct use of the respective statistical data, the celebrated Bell inequalities cannot be violated by quantum systems."

de Raedt: " A violation of these inequalities is at odds with the commonly accepted rules of arithmetic or, in the case of quantum theory, with the commonly accepted postulates of quantum theory"

So Joy Christian's simulations depend on incorrect use of statistical data in order to fake violation of Bell inequalities?

1. More rubbish and nonsense. Nothing can violate Bell's inequality; not even QM. You lose the debate. Get over it.

2. You lost the debate; get over it. Thank you very much.

3. How do you explain that Michel Fodje's simulations appear to violate Bell?

4. epr-simple doesn't violate Bell; it produces the same result as QM.

5. Michel's point is that his simulations *do* violate Bell. *And* reproduce the quantum correlations pretty well indeed. Please take a look at his own descriptions of his programs:

Long ago, I used the word "clocked" in correspondence with Michel, intending to refer to *pulsed* experiments. Michel uses the word "clocked" in a very different sense. He is thinking of coincidence-window post-selection in continuous time, un-pulsed experiments.

epr-simple exploits the detection loohole (Pearle, 1970)

epr-clocked exploits the coincidence loophole (Larsson and Gill, 2004); de Raedt, Hess and Michielsen (2011), J. Comp. Theor. Nanosci. 8, 1011 - 1039 (2011); http://arxiv.org/abs/0901.2546 . Notice that de Raedt et al explicitly cite Larsson and Gill in this respect "Recalling that the dichotomic character of the variables was essential for the derivation of the Boole inequalities, it is unlikely that similar inequalities hold for the raw data Eq. (126), for an exception see Ref. 58".

Later, Hess in his book suggests that the earlier Hess-Phillips papers were actually about the coincidence loophole all along, and cite a much earlier researcher who had already pointed out this problem: Pascazio, 1986, Physics Letters A.

6. Nothing physical can violate Bell's inequality since it is pure math; not even QM. You lost the debate. Get over it.

8. The quotes are from http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=75&start=250#p4491

9. The initially refreshing discussion "Thoughts about Bell, Bohm, Christian, et al" at sciphysicforums.com/Sci.Physics.Foundations is degenerating into deeper and deeper idiocy... nobody seems to realise that all the "issues" with Bell (1964) had been resolved within a few years. Nobody wants to admit the existence of Bell (1981).

See
http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=75&start=260#p4504
for an example of what I mean.

1. LOL! Nothing physical can violate Bell's inequality since it is pure math; not even QM. Michel has clearly shown that. You lost the debate. Get over it.

2. Michel has shown an amazing disregard for logic and ignorance of the literature.

[quote="minkwe"]
Bottom line:
1) There is no locality assumption required to in the derivation inequalities, despite claims (See de Raedt et al, and Rosinger's paper for details).
2) The CFD assumption, required to derive the inequalities also applies to QM and is used by Bell himself.
3) The use of counterfactual outcomes in the inequalities precludes experimental tests, and make them inapplicable to the predictions of QM for this experiment.
4) Either the inequalities forbid time dependent functions $$A(t), B(t)$$ or time dependent hidden variables $$\lambda(t)$$, or they require that all measurements be performed at the same time.

Each of these points by itself is fatal to Bell's theorem but together, they simply shatter it to smithereens. Nothing substantial arguing against these points has been presented by you or anyone else, no doubt you want to focus instead on irrelevant nonsense about QM and SR time-coordinate. No reasonable person can continue to Believe Bell's theorem is true.
[/quote]

Interesting summary.

Point 3 is solved by statistics: it tells us how far a sample average might deviate from a population expectation value. Standard errors, error bars, p-values? See Bell 1981.

Point 4 is addressed by Bell 1981, where the focus is on a time-slot within which various processes take place, not specific time points at which things happen.

Point 1 is irrelevant. If *weaker* assumptions than locality imply Bell's inequality, then violation of Bell implies even more. Those "weaker still" assumptions are not true.

Point 2 is irrelevant. Minkwe thinks QM is true and thinks it implies CFD? So why does he have a problem with it?

3. "Point 1 is irrelevant. If *weaker* assumptions than locality imply Bell's inequality, then violation of Bell implies even more. Those "weaker still" assumptions are not true."

Triple LOL! NOTHING PHYSICAL CAN VIOLATE BELL'S INEQUALITY. IT IS PURE MATH. Not even QM. You really lost the debate for sure now. Get over it.

4. This is really amazing. Michel Fodje has two simulations showing violation of Bell, and he claims that they are "physical". The simulations imitate real experiments. The simulation results and the experimental results are very close. Hans de Raedt and co-authors have published such simulation models many times in the past.

I get the impression that some person is really badly mixed up here.

In fact that person is actually contradicting his hero Joy Christian who says that Bell's theorem is *not* pure math: it is a false theorem.

You guys had better get your act together. Also please, coordinate a bit with Michel Fodje. He's a very good programmer. A professional biochemist (originally from Cameroun, now at "Canadian Light Source") https://www.youtube.com/watch?v=Ir_Yj4PameM

6. I'm pointing out that Michel is really smart and that he is saying things which contradict what Fred says and what Christian says!

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9. Fred, Gill, please....

10. Thanks, Albert Jan.

11. Michel Fodje has seen my comments above and he has followed the discussion about my work on the Internet for many years. He is laughing at Gill's laughable response to my comments. I have documentary evidence of everything I have claimed. I have submitted this evidence to appropriate parties.

12. Michel is a great guy and moreover has published more than Fred and Joy together. Christian has told his lies so many times that he now even believes them himself.

13. This comment has been removed by a blog administrator.

14. Gill says "Michel is a great guy..." Interesting. Michel seems to have quite the opposite opinion of Gill:

http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=52&p=2159#p2159 .

15. Here's Michel's latest: http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=75&start=270#p4528

He says "Where is the counter-argument?" (to his four point "bottom line"). The answer is: it was censored by Fred Diether!

10. What Pearle (1970) and Pascazio (1986) do is show that it is not difficult to write programs like epr-simple and epr-clocked. Bell's (1981) strict experimental protocol would rule out the detection loophole and the coincidence loophole. So far (50 years on!) nobody has been able both to violated CHSH *and* at the same time adhere to a strict experimental ("loophole-free") protocol.

Maybe this is about to change. We live in interesting times.

1. Double LOL! You will never understand. Bell's work is irrelevant for physics since it is pure math.

2. It takes no more than half a page of calculations to see that Bell's so-called theorem is a worthless piece of junk:

http://arxiv.org/abs/1103.1879 .

Any precocious schoolboy can verify the calculations in the above paper in less than 20 minutes to see that Bell's so-called theorem is a worthless piece of junk.

3. Lot of precocious schoolboys around here ... think they know everything. Totally ignorant of almost everything. Bell '64 is superceded by Bell '81. Read it!!!

4. Bell's '81 is also a piece of junk. It takes no more than half a page of calculation to see that Bell's so-called theorem --- in its '64 version, or '81 version, or '91 version --- is a piece of junk:

http://arxiv.org/abs/1103.1879 .

Any precocious schoolboy can verify the calculations in the above paper in less than 20 minutes to verify this trivial fact.

11. Let's get this clear. Fred thinks that nothing can violate Bell's inequality, not even QM.

Christian thinks that reality follows his model, and that violation of Bell's inequality is even possible in the macroscopic domain.

Christian has also proved that (in our regular space time) the correct bound is S < = 2 sqrt 2 (also known as the Tsirelson bound).

So Fred also believes that the Christian-Tsirelson bound is incorrect?

1. Here we go again; constant attempts at misrepresentation by Gill. I do believe that Michel, Joy and I are all on the same page. Nothing can violate Bell's inequality since it is pure math. Therefore Bell's theorem is pure junk as far as physics is concerned.

2. But Michel's simulations do violate Bell's inequality?

3. Though, by the way, Michel's epr-clocked does not violate Larsson-Gill's corrected CHSH for coincidence sampled data, just as the detection loophole simulation epr-simple does not violate Larsson's corrected CHSH for data obtained by post-selection caused by the detection loophole. The corrected Bell inequalities certainly do apply to all simulations of LHV models, to date.

4. epr-simple and epr-clocked do not violate the inequalities if you look very carefully. They reproduce the results of QM experiments. It is about time that you figure that out. BTW, your eq. (6) is still wrong.

5. Exactly, Fred. epr-simple and epr-clocked do not violate the correct inequalities, if you look carefully. They indeed reproduce the results of QM experiments which, as is well known, to date all do have a local realist explanation. So far there has been no experiment done following the loophole-free experimental protocol of Bell (1981). All experiments have had to introduce experimental loopholes, since otherwise the experimenters wouldn't have had any exciting news to publish. In other words: to date, all experiments have been analysed with the incorrect inequalities. Supplementary un-testable assumptions have to be made if you want to project the observed results to the results which you would have got if you had done the experiment properly: primarily, the "fair sampling assumption".

See
http://rpubs.com/gill1109/epr-clocked-full
http://rpubs.com/gill1109/epr-clocked-core
http://rpubs.com/gill1109/epr-simple

6. BTW, your eq. (6) is still wrong.

7. Well, at least I do have an equation! But ... equation (6) ... in which of my many masterpieces, dear friend?

12. For a state of the art overview of the loophole question, see http://arxiv.org/abs/1407.0363
Loopholes in Bell Inequality Tests of Local Realism
J. Phys. A 47 424003 (2014)

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14. PS Bell's theorem might be pure maths and its relevance to physics is therefore up to debate, but sure as hell it is a true theorem about distributed classical computing. See for instance Steve Gull's proof using Fourier analysis which he often uses as an exam question in Cambridge. (This is the proof which left Jaynes speechless). http://www.mrao.cam.ac.uk/~steve/maxent2009/
http://www.mrao.cam.ac.uk/~steve/maxent2009/images/bell.pdf

1. If you define "physics" in the broadest sense as the study of the observable behavior of physical entities qua physical entities (no humanities or social science, please), the application of the Wigner-d'Espagnat inequality, which is pristine set algebra, to groups or sets of macroscopic objects takes the mathematics entirely out of the "pure" realm into that gnarly domain of the kind of stuff which, if its mass is sufficient, would induce pain were you to drop it on your foot.

In addition, re: another contention herein, one has been under the impression that Joy's proposed experiment involves physical objects and that it would, if successful, violate CHSH ... and that CHSH is a Bell-type inequality. Ergo if Bell cannot be violated because it's pure mathematics (or mathematical logic) then Joy's experiment can never succeed.

It's kind of like the upcoming referendum in Greece. If you want to keep the Euro you'll need to put up with austerity, and if you want to get rid of austerity you'll have to go back to the drachma. Life is hell.

15. Analysis of Michel Fodje's "epr-simple" and "epr-clocked": http://rpubs.com/gill1109/minkwe

16. http://arxiv.org/abs/1507.00106

Event based simulation of an EPR-B experiment by local hidden variables: epr-simple and epr-clocked

Richard D. Gill

In this note, I analyse the data generated by M. Fodje's simulation programs "epr-simple" and "epr-clocked" using appropriate modified Bell-CHSH type inequalities: the Larsson detection loophole adjusted CHSH, and the Larsson-Gill coincidence loophole adjusted CHSH. The experimental efficiencies turn out to be approximately beta = 80% and gamma = 55% respectively, and the observed value of CHSH is (of course) well within the adjusted bounds.

17. http://arxiv.org/abs/1507.00106 and http://rpubs.com/gill1109/minkwe are now both revised and extended.

18. Revision 3 will appear tomorrow, with improvements of epr-clocked which should delight Michel

19. The third version shows that epr-clocked is actually a disguised epr-simple; and that since we now know how to improve epr-simple, we can similarly improve epr-clocked.

Of course these two simulations, one using the detection loophole and the other the coincidence loophole, do not violate the *correct* bound, which is 4/eta - 2 in the detection loophole case, and 6/gamma - 4 in the coincidence loophole case (note: eta = 1 = 100% detection efficiency gives the usual bound 2; similarly gamma = 1 = 100% pairing efficiency gives the usual bound 2).

However it should be noted that because epr-clocked is "just" a disguised epr-simple, it does not get optimal results. For a given (same) efficiciencies, the LHV bound in the coincidence loophole case is larger than that in the detection loophole case. And both those bounds are sharp. That means to say, it ought to be possible already to "fake" the quantum correlations at higher efficiency in the coincidence loophole case, than in the detection loophole case. One has more room to maneuvre in! Michel is not making any use of that extra room.

20. Here is the latest news on Joy Christian's simulations: please compare http://rpubs.com/jjc/84238 and http://rpubs.com/gill1109/joy

Joy claims there are no "zero" outcomes in his model. He performs this check for just one pair of angles: alpha = beta = 360 degrees. No zero outcomes. I copy-pasted his code and did the check for a pretty random other pair. Lots of zero outcomes.

Joy still has quite a lot to learn about programming.

1. It is true: I still have quite a lot to learn about programming.

However, there are no “zero” outcomes in this 3-sphere model:

http://arxiv.org/abs/1405.2355 .

Nor are there zero outcomes in my simulation of the above 3-sphere model:

http://rpubs.com/jjc/84238 .

To be fair to Gill, I have revised the simulation slightly to address his latest concern.

It is now easy to check that for any pair of angles there are no zero outcomes in the simulation.

The down side is that it now takes forever to run the simulation.

2. Dear Joy,

Good try. But you are now calculating Cou, Cod etc *inside* a double loop, but only printing out the result just once. You print it out, once, after you have exited the loop. Which means that you still only print out those numbers for the special case i = j = K.

If you want to see the results for other values of i and j you should save them in some suitable matrix. Like you save the correlations and the N's.

3. Or one can check one pair of angles at a time, as demonstrated here:

http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=179&p=4847#p4847

4. You really need some lessons in programming. For instance: do not calculate the same thing again and again. Each time you do it, it costs you a lot of time. Calculate it once, save in a suitable variable. No wonder the code takes such a long time to run! Things like g(a, e, s) are being computed again and again and again, but with the same values of a, e and s each time.

5. And in the present code, you calculate Cou etc etc for every single value of i and j between 1 and K, but only print out the values they got on the last iteration!!! (when i = j = K which is rather a special case...)

6. The bottom line is that there are no "0 outcomes", either in the theoretical 3-sphere model, or in its latest simulation. This can be verified by anyone, for any given pair of fixed angles alpha and beta, chosen freely by Alice and Bob, as demonstrated here:

http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=179&p=4847#p4847

Bell "theorem" is thus a blue parrot. It ain't just restin... It is theorem no more. It is an EX theorem.

7. What Christian needs to do is to plot the size of the sample (A != 0 and B != 0) as a function of the angles alpha and beta. That simple graphic would dispel all doubt. But no way that Christian is going to add it to his R script ...

Still I think it is really cute how Christian keeps on trying and keeps on believing, with the support of his little band of cargo-cult believers, n particular his chaperone Fred Diether, who is perpetually vigilant in order to protect the readers of his forum from dangerous ideas. Just writing "Bell, 1980" on sciphysicsforums.com will get the posting erased and the poster banned. I'm reminded of Hitler's Third Reich and Stalin's Russia. Though this verges more on the ridiculous than on the sinister.

It is truly the cause of a great deal of amusement. A lot of laughs for a lot of people!

8. So, Gill, since you are so clever and all, why don't *you* plot for us all to see the size of the sample (A != 0 and B != 0) as a function of the angles alpha and beta? Are you afraid that your graphic might dispel the myth that the blue parrot is just resting?

9. Yes, I just did this: http://rpubs.com/gill1109/pearle2

10. LOL!

That has nothing whatsoever to do with my 3-sphere model. :-)

See the first plot in this simulation: http://rpubs.com/jjc/84238 .

This is the correct plot of the size of the sample (A !=0 and B !=0) as a function of the angles alpha and beta for my model.

All I did was to add the following two lines to make you happy:

P = length((A*B)[A != 0 & B != 0])

Ns[i,j] = P.

So the original Ns[i, j] = N and the new Ns[i,j] = P are the same thing in my model.

This proves, without any shadow of doubt, that there are no "0 outcomes", either in my theoretical 3-sphere model, or in its simulation above.

So your blue parrot is still very much dead, not just resting.

11. That first plot is so funny!

You are plotting the ratio of Ns[i, j] to Ns[i, j] which of course is rather constant ...

Try plotting Ns[i, j], if you can, and if you dare.

Here I plot Ns / M for you: http://rpubs.com/gill1109/joy1

12. Your claim is false, and you know it.

I am plotting Ns / Ls, where Ns counts number of simultaneous events A and B, and Ls counts number of initial states (e,s) within S^3. FYI: A and B is not the same as (e, s).

But I forget. You are a flatlander living in R^3, with no intellectual capacity to comprehend what it is like to live in S^3, which is a well known solution of Einstein's field equations of general relativity. So I should be kind to you and pity you, rather than ridicule you for the flatness of your brain.

In any case, what you have plotted, Ns / M, has nothing to do with my 3-sphere model. But to understand this statement one has to actually read the full commentary in my simulation:

http://rpubs.com/jjc/84238 .

Unless of course you have no intention of admitting that Bell's so-called theorem is as dead as the blue parrot. It is theorem no more. It is an EX theorem. :-)

13. Your definitions of Ns and Ls make them identical. They both vary with the settings alpha, beta. Which contradicts the claims in your theoretical papers. Which are therefore proved to be wrong by your own computer simulation.

Fred would say "LOL".

14. I am afraid that Joy Christian's model is the only dead parrot around these parts. But who cares ...

15. To a flatlander everything looks "identical", including Ns and Ls.

To a flatlander anything that "varies with the settings alpha, beta" is "identical."

Both Alice's results and Bob's results "vary with the settings alpha, beta", so to a flatlander they are "identical."

16. I think the almost completely dead parrot is having a last squawk ...

17. I think so too, but there no need for "almost." Bell's "theorem" is dead, period.

21. This comment has been removed by the author.

22. Open letter to Michel Fodje ("minkwe"):

“Jochen” apologizes that he cannot answer your latest because he has been banned from Fred Diether's forum. The reason: being disrespectful to the admin and lying.

I suppose the definition of “lying” is “contradicting Joy Christian, Fred Diether or Michel Fodje”.

And it is hard to be respectful of an admin who is more interested in promoting his own point of view than ensuring a comfortable environment for challenging scientific discourse.

Richard

PS regarding

http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=168&start=260#p4806

"Minkwe" says "Your example misses the mark. My point (3) remains valid <= 4, even better I would say there is a non-zero probability that >= 2 for 4 independent particle pairs.”

I agree that in a loophole free experiment and with LHV true, there is 50% chance that the *observed* value of S will be bigger than 2. However the chance that it is bigger than 2.001 is less than about 10^{-15} if the total number of trials N is larger than 10^9. (I’m assuming a variance of 16 / N and and approximately normal distribution of the "sampling error”).

How do I get 16/N ? There are four subsamples each of size roughly n = N / 4. The variance of an estimated correlation based on n pairs of binary outcomes occurs is maximally 1/n (rho = 0 is the worst case; the variance converges to zero as rho converges to +/- 1). We add three such correlations and subtract the fourth. The variance of a sum of independent variables is the sum of the variances. Hence we get a worst case variance of 4 x 4 / N = 16 / N.

Now use the cumulative normal distribution. If N = 10^9 then sqrt(16 / N) = 0.0001264911. An observed deviation of S from 2 of 0.001 is therefore 0.001 / 0.0001264911 = 7.905695 standard deviations. The chance a normally distributed variable is more than 8 standard deviations about its mean is 6 * 10^{-16}

1. I have replied to the above "open letter" by Gill on behalf of Michel Fodje. My reply has been posted here:

http://vixra.org/abs/1504.0102#comment-2135491333 .

2. Big deal, Joy. Has Michel seen my open letter? Did you forward it to him? I am not interested in your opinion. I am interested in Michel's own opinion (not about my personality, but about the science) because he is pretty smart, but a little bit trapped in his own ignorance and prejudices. But he certainly learnt a great deal from those discussions which Fred locked down, when it became clear that the wrong side was winning them. I noticed that he was beginning to realise that there were some things that he didn't know about, but ought to. So there's hope for him. He has no interest at all in Joy's model, as far as I know ... the only thing you have in common is your belief that Bell was mistaken.

23. My analysis of Michel Fodje's simulation models epr-simple and epr-clocked is now also posted on viXra (so as to facilitate discussion): http://vixra.org/abs/1508.0015

24. New challenge to Bell-deniers: a local hidden variables simulation of the results of this experiment: http://arxiv.org/abs/1508.05949 Hensen et al "Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km"

1. Who was Bell that Nature should be mindful of him?

But good to know that an experiment has been finally done that rigorously confirms the predictions of my 3-sphere model of the EPR-Bohm correlation. It is also good to know that Einstein has been proven right about physics and Nature once again:

http://rpubs.com/jjc/84238

http://rpubs.com/jjc/99993

http://rpubs.com/jjc/105450

http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=188&p=5318#p5316

http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=188

25. Joy is so funny!!! :-)

This is what he wrote in 2013 about computer simulations:

Reply to John Reed in the usenet group sci.physics.foundations (2013) when he tried to event-by-event simulate his theory:

Hi John,

I do not wish to discourage you, but this will be a rather negative
comment. Regardless of the details of your simulation, I can guarantee
you that you will not be able to get either the sin^2 curve for the probabilities or the cosine curve for the correlations in your simulation.
The reason is pure and simple: Bell's theorem. It is a mathematical
theorem that proves, ones and for all, that no procedure like what you
are considering will ever produce the cosine correlation. There are also
some corollaries of Bell's theorem, specifically aimed at simulation
attempts of the kind you are considering, which prove that you will not
be able to generate correlations or probabilities stronger than the
straight line you are getting. Of course, if you somehow let some
information pass on from one side to the other non-locally, or exploit
some kind of a loophole like the detector loophole, then you will be
able to get stronger correlations. One such example which exploits the
time-window loophole can be found here: http://rugth30.phys.rug.nl/eprbdemo/simulation.php

Best,

Joy

Seems that Joy has radically changed his mind. So has Fred Diether. For a long time he has been saying that the only good CHSH bound is 4 but now he is following his master in trying to establish the Tsirelson bound 2 sqrt 2.

http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=196

Seems these guys are impervious to *science*. Everything confirms Joy's theory, nothing contradicts it. They can change their mind 100% every year or so without their supporters noticing. It ain't physics. it really is a cargo cult. Pretty much marginalised, so physics does not have to fear.

26. Dear Guys,

may i comment to some aspects of wether reality is "non-local" or "not"?

I followed this discussion time by time and it strongly seems to me that implementing whatever into a computer program cannot answer questions about physical reality other than those their answers we already know.

We already know that nature gives us certain statistical packages of data as output - called correlations - when executing certain experiments (quantum optics experiments like the ones by Aspect, Weihs, Zeilinger etc. etc.).

Having a theory about reality that is implemented into computercode, by letting this code run and gaining the QM-correlations at the end of the experimental runs, what does this say about nature?

Let me articulate here my humble opinion: It does not say anything about nature, at least nothing we aren't aware of yet.

One cannot get more information out of a computersimulation that was put into it from the very start.

No simulation, be it a computersimulation or a simulation in one's own imagination, can prove something to be right or wrong, concerning nature's behaviour.

Only real physical experiments can decide between one or the other theory about nature.

So even the mentioned experiments by Aspect, Weihs, Zeilinger et. al cannot prove that QM is the foundational basis of reality. These experiments only confirm that they confirm the quantitative predictions Bell once made. But that doesn't mean that any theory that reproduces this predictions - be it by computersimulation or by physical experiment - does describe nature's behaviour in a true and complete manner.

It is true that any theory who wants to replace QM, must forecast the mentioned QM-correlations (we can also use the word "Data" instead of "correlations"). But this necessary ingredient of such a theory is by no means also sufficient. A new theory must make *new* predictions about nature's behaviour which are in opposition to those of the old theory.

So, pondering about wether some mental construct (which is then formalized into mathematical language) matches the Data of already made QM-experiments (concerning "entanglement"), is lost time.

One should not mistake the answers of a computerprogram for the answers coming from nature. The most what one can say about the computerprogram's underlying theory (in the case that it can reproduce the correlation-data) is, that it might or might not be a proper theory about how nature works.

So the whole discussion is somewhat useless, because one always can presuppose some "facts" about nature which are in perfect congruence with the computerprogram's structure, but aren't proven yet by real experiment. Computersimulations are only "real experiments" insofar as they implement circumstances that have been already proven by physical experiments. What leads again to the statement that one cannot get out more information of a computerprogram than one has put in in the first place.

Greetings
Stefan Weckbach

1. Stefan, thank you for your post. I personally think most of the contributors of this blog - either by posts or comments - are well aware of the limitations of physical models and simulations.

However, the main stream interpretation of QM is that at some level, it is no longer possible to have a descriptive model for nature, and it can only be treated stochastically.

In laymen’s terms the Bell-EPR experiment is said to be a proof for that, because according to Bell the observed effect cannot be explained ‘logically’.

This no-go theorem makes the dispute special, because only one counter example is needed to show that nature could be described classically. This doesn’t necessarily mean this counter example describes nature correctly.

2. "Only real physical experiments can decide between one or the other theory about nature."

Not always. The quantum experiments validate quantum theory but they also validate Joy Christian's classical local realistic theory that matches the predictions of quantum theory for the EPRB type scenarios. So which one is right? Most probably they are both right. Just different ways of describing the same reality.

3. Thanks for the replies. I did not comment to criticise Joy Christians Work. I only wanted to mention that maybe both theories, Joy's and QM, could be false (incorrect) and with the aim of wanting to achieve a simulation of a tiny part of those theories, one would be on an incorrect pathway. Even if one of these theories matches reality, you cannot prove this with computer simulations. Even if one is convinced to 100% that one of the theories completely match reality, this would be in my opinion not sufficient to claim it to be the right one. Only the experiment could do this - in cooperation with a prediction of the theory that would be confirmed by the experiment.

I hope that there are some aspects in Joy's theory that can be tested experimentally to be present in nature or not and for which QM either has nothing to say or makes a different prediction. I see no other way to settle this discussion, which makes me somewhat sad. But i think the burdon of proof is at the side of Joy and by focusing on other aspects of his theory than this EPRB-thing, he would have the chance to settle the discussion. Maybe his is working this way, i don't know, but i wish him good luck. I think it is needless to say that for Joy's theory to be a real competitor to QM, it must explain all the other already experimentally confirmed predictions of QM as well, or at least a part of it.

4. Thank you, Stefan, for your comments.

Simulations are valuable on their own right, but let me leave that argument aside.

You are right about a need for a decisive experiment to settle the issue, and I have proposed one such experiment since 2008. You can find the details at the following link, including some improvements on my initial proposal in 2008:

http://libertesphilosophica.info/blog/experimental-metaphysics/

You are right also about the need to explain all of the other experimentally confirmed predictions of QM. All one needs for that is to reproduce all QM correlations predicted by any arbitrary quantum (or entangled) state. I have already achieved that in a comprehensive theorem on the page 12 of the following paper:

http://arxiv.org/pdf/1201.0775.pdf

Note, however, that this theorem is a formal theorem only. It is of course impossible for me and my small number of supporters to reproduce every detail of all of the vast number of QM experiments. But the theorem provides a proof that we can do that in principle. :-)

5. Bell's theorem is a very simple theorem saying that a certain kind of computer programme (actually: a suite of programs running on three computers) cannot generate certain data sets. Christian has not denied the truth of that theorem, he has only disputed the physical relevance of it. He proposes to replace the binary outcomes +/- 1 by bivectors and to redefine "correlation" accordingly. So far, no physicists have taken any notice of these proposals. His "model" is moreover incomplete. Look at formula (16) of his first publication http://arxiv.org/pdf/quant-ph/0703179v3.pdf and tell me what mapping has to be used to associate the bivectors mu . a and mu . b with the numbers +/-1. It's missing! There is no model!!!

The recent experiment in Delft has binary settings and binary outcomes and computes correlations in the classical way, obtaining results which violate "local realism" but which are allowed by quantum mechanics.

Congratulations to Albert Jan Wonnink for having plugged the algebraic holes in Christian’s math. I have a proposal to make it even better. It's been noticed that the model doesn't exactly reproduce the negative cosine, but only approximately. In GAViewer terms, referring to today's developments:

http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=200#p5516

My proposal: put N = 1 and have the line q = (v w + w v) / 2 instead of the lines:

if(lambda==1)
{
q=v w;
}
else
{
q=w v;
}

Now it is time to take a look at the physical content. Is there any? It’s also time for Joy Christian to revise his papers and his book. Yes - the guy is human after all. He not only makes mistakes from time to time … he even admits that! (Would be nice if it were true …)

I posted this as "Guest" today but of course I have been censored by the thought-police.

6. My model is X.

Gill wants to look at "the physical content" of his own model Y.

He is free to look at "the physical content" of his own model Y until his face turns blue.

No one cares.

7. Hmm....
mean_mu_a_mu_b = -1.000000
mean_mu_a_mu_b = -0.987688 + 0.000000*e2^e3 + 0.000000*e3^e1 + 0.002640*e1^e2
mean_mu_a_mu_b = -0.951057 + 0.000000*e2^e3 + -0.000000*e3^e1 + 0.004952*e1^e2
mean_mu_a_mu_b = -0.891007 + 0.000000*e2^e3 + -0.000000*e3^e1 + -0.006571*e1^e2
mean_mu_a_mu_b = -0.809017 + 0.000000*e2^e3 + 0.000000*e3^e1 + -0.006752*e1^e2
mean_mu_a_mu_b = -0.707107 + -0.000000*e2^e3 + 0.000000*e3^e1 + 0.007857*e1^e2
mean_mu_a_mu_b = -0.587785 + 0.000000*e2^e3 + -0.000000*e3^e1 + -0.005201*e1^e2
mean_mu_a_mu_b = -0.453990 + 0.000000*e2^e3 + -0.000000*e3^e1 + 0.001310*e1^e2
mean_mu_a_mu_b = -0.309017 + -0.000000*e2^e3 + -0.000000*e3^e1 + 0.015851*e1^e2
mean_mu_a_mu_b = -0.156434 + -0.000000*e2^e3 + -0.000000*e3^e1 + -0.003858*e1^e2
mean_mu_a_mu_b = -0.000000 + 0.000000*e2^e3 + 0.000000*e3^e1 + 0.028226*e1^e2
mean_mu_a_mu_b = 0.156434 + 0.000000*e2^e3 + 0.000000*e3^e1 + -0.010700*e1^e2
mean_mu_a_mu_b = 0.309017 + -0.000000*e2^e3 + -0.000000*e3^e1 + -0.022137*e1^e2
mean_mu_a_mu_b = 0.453990 + -0.000000*e2^e3 + -0.000000*e3^e1 + -0.019889*e1^e2
mean_mu_a_mu_b = 0.587785 + -0.000000*e2^e3 + -0.000000*e3^e1 + -0.016480*e1^e2
mean_mu_a_mu_b = 0.707107 + -0.000000*e2^e3 + -0.000000*e3^e1 + -0.008159*e1^e2
mean_mu_a_mu_b = 0.809017 + 0.000000*e2^e3 + -0.000000*e3^e1 + -0.001176*e1^e2
mean_mu_a_mu_b = 0.891007 + 0.000000*e2^e3 + 0.000000*e3^e1 + 0.007094*e1^e2
mean_mu_a_mu_b = 0.951057 + 0.000000*e2^e3 + -0.000000*e3^e1 + -0.011756*e1^e2
mean_mu_a_mu_b = 0.987688 + -0.000000*e2^e3 + 0.000000*e3^e1 + 0.000356*e1^e2
mean_mu_a_mu_b = 1.000000 + -0.000000*e2^e3 + 0.000000*e3^e1
mean_mu_a_mu_b = 0.987688 + 0.000000*e2^e3 + 0.000000*e3^e1 + -0.003129*e1^e2
mean_mu_a_mu_b = 0.951057 + 0.000000*e2^e3 + -0.000000*e3^e1 + 0.000813*e1^e2
mean_mu_a_mu_b = 0.891007 + -0.000000*e2^e3 + -0.000000*e3^e1 + -0.003153*e1^e2
mean_mu_a_mu_b = 0.809017 + -0.000000*e2^e3 + 0.000000*e3^e1 + -0.018152*e1^e2
mean_mu_a_mu_b = 0.707107 + -0.000000*e2^e3 + -0.000000*e3^e1 + 0.005524*e1^e2
mean_mu_a_mu_b = 0.587785 + -0.000000*e2^e3 + -0.000000*e3^e1 + 0.040451*e1^e2
mean_mu_a_mu_b = 0.453990 + -0.000000*e2^e3 + -0.000000*e3^e1 + 0.006364*e1^e2
mean_mu_a_mu_b = 0.309017 + -0.000000*e2^e3 + -0.000000*e3^e1 + 0.043895*e1^e2
mean_mu_a_mu_b = 0.156434 + -0.000000*e2^e3 + -0.000000*e3^e1 + 0.016461*e1^e2
mean_mu_a_mu_b = -0.000000 + 0.000000*e2^e3 + 0.000000*e3^e1 + -0.020455*e1^e2
mean_mu_a_mu_b = -0.156434 + 0.000000*e2^e3 + 0.000000*e3^e1 + -0.041977*e1^e2
mean_mu_a_mu_b = -0.309017 + -0.000000*e2^e3 + 0.000000*e3^e1 + -0.036986*e1^e2
mean_mu_a_mu_b = -0.453990 + -0.000000*e2^e3 + 0.000000*e3^e1 + -0.038982*e1^e2
mean_mu_a_mu_b = -0.587785 + -0.000000*e2^e3 + 0.000000*e3^e1 + -0.028893*e1^e2
mean_mu_a_mu_b = -0.707107 + 0.000000*e2^e3 + 0.000000*e3^e1 + -0.058926*e1^e2
mean_mu_a_mu_b = -0.809017 + 0.000000*e2^e3 + 0.000000*e3^e1 + -0.008817*e1^e2
mean_mu_a_mu_b = -0.891007 + -0.000000*e2^e3 + 0.000000*e3^e1 + -0.028374*e1^e2
mean_mu_a_mu_b = -0.951057 + -0.000000*e2^e3 + 0.000000*e3^e1 + -0.005150*e1^e2
mean_mu_a_mu_b = -0.987688 + -0.000000*e2^e3 + 0.000000*e3^e1 + -0.007822*e1^e2
mean_mu_a_mu_b = -1.000000

Scalar values are exact to negative cosine to 6 decimal places for 9 degree increments.

8. Of course the scalar values are essentially exact. GAViewer knows how to compute (I.a)(I.b) and it also knows how to compute (I.b)(I.a). They have the same scalar part a.b but their non-scalar parts are equal and opposite. Moreover, since a and b are in the plane generated by e1 and e2, the non-scalar part is perpendicular to it, that's why you only have non-zero e1^e2 terms.

Increase N, and it'll get smaller. Or better still, have exactly as many positive as negative lambda's, instead of only approximately as many.

9. And let me repeat this: look at formula (16) of Christian's first (2007) publication http://arxiv.org/pdf/quant-ph/0703179v3.pdf and tell me what mapping has to be used to associate the bivectors mu . a and mu . b with the numbers +/-1. It's missing, there is no complete model; at least, not in 2007!

But I can give you a hint. Take a look at the one-page paper from 2011. http://arxiv.org/pdf/1103.1879v1.pdf. Formulas (1) and (2) do define measurement outcomes +/-1 and formula (5) *redefines* E(a, b) as a Pearson-Christian correlation: divide the raw product moment on the left by the bivectorial standard error of A and on the right by the bivectorial standard error of B.

10. My papers are not written for those who cannot understand elementary mathematics and basic physics. But I have been generous enough to explain things in baby terms when needed,
as, for example, in this paper: http://arxiv.org/abs/1501.03393

11. This is the baby language explanation: "In practice the above dynamical variables are supposed to be measured in the proposed experiment by directly observing the polar vectors s^k dual to the random bivectors L(s, lambda^k). It is only after all the runs of the experiment are completed and the vectors s^k are fully recorded, the traditional dynamical variables sign ( + s^k · a) and sign ( − s^k · b) supposed by Bell are to be calculated, by an algorithm extraneous to the actual experiment. These calculations may be done, for example, years after the experiment has been completed. Thus they are not supposed to be an integral part of the physical experiment itself, and this fact must be accounted for in the ensuing statistical analysis of data."

So did the guys in Delft analyse their data in the wrong way? What algorithm should they have used to compute the s^k and to compute the values of sign ( + s^k · a) and sign ( − s^k · b) ? They don't refer to any works of Christian so they surely did not use the algorithms which he has so kindly made available to us. How can their experiment confirm his theory when in fact they did the statistical computations completely wrongly?

12. As I said, my papers are not written for those who cannot understand elementary mathematics and basic physics:

http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=183&p=5421#p5421

27. The present GAViewer code uses N independent trials in each of which lambda = +/-1 completely at random. So there will be about about N/2 trials with lambda = +1 and about N/2 with lambda = -1. But those numbers will vary (by amounts of the order of +/- sqrt N).

But: take N to be even and arrange that lambda is exactly equally often +1 as -1 and there will be no statistical variation in the results at all. In fact they won't depend on N anymore. You might as well take N = 2 and have lambda = -1 once, and lambda = +1 once. Try it and see! You'll get an exact fit to the cosine and the code will run a lot faster, too. No random variation in the results.

Of course the problem of how to associate actual measurement outcomes taking the value +/-1 with your bivectorial hidden variables, and whether to compute correlations in the orthodox way or in some novel way, is a problem which Joy has to resolve. I am glad that his explanation in http://arxiv.org/abs/1501.03393 is so clear that anyone with just an understanding of elementary mathematics and basic physics can easily follow it. Then we should not have long to wait for the successful completion of the research programme, since there must be a lot of people around who are smart enough to do this.

1. Same old story. Joy's model is X.

"Gill wants to look at "the physical content" of his own model Y."

2. Joy's model says "lim as N tends to infinity". I'm telling you how to compute the limit as N tends to infinity. Wake up.

I'm a mathematician and I study the mathematical content of what Joy has written in various papers on arXiv.

I also point out that there is a gap. The "baby talk" paper http://arxiv.org/abs/1501.03393 does not explain what algorithm to use to determine the actual measurement outcomes of Joy's model.

Clearly Fred Diether has no clue either.

3. Joy's local realistic model for EPR-B predicts E(a, b) = -a.b.

Quantum theory for EPR-B predicts E(a, b) = -a.b.
https://en.wikipedia.org/wiki/Quantum_mechanical_Bell_test_prediction

No measurement outcomes are required for the prediction as clearly seen by the article at the link. The measurement outcomes are done in experiments which by the way validate both quantum theory and Joy's model. You lost the debate. You really should get over it. Don't you think it is time already?

4. The wikipedia article you refer to is based on Abner Shimony's article on the Stanford Encyclopedia of Philosophy http://plato.stanford.edu/archives/sum2005/entries/bell-theorem/ . You'll notice that he computes the value of the correlation function E(a, b) by first computing the probabities of the four possible outcome pairs +/-1, +/-1 which are predicted by quantum mechanics. See formulas (20a), (20b), (20c) and (21).

5. My local-realistic 3-sphere model reproduces all 13 of the EPR-Bohm probabilities predicted by quantum mechanics *exactly*:

http://arxiv.org/abs/1405.2355 .

The correlation function E(a, b) computed in Eq. (42) of the above paper is exactly the same as the correlation function E(a, b) computed event-by-event in Eq. (B10) of this paper:

http://arxiv.org/abs/1501.03393 .

There are no more "problems" to be resolved. All of the bogus issues raised about my model by some dishonest, ignorant, and incompetent people like Gill have been comprehensively debunked by explicit demonstrations by me and others, both analytically and numerically.

All that remains for Gill to do is eat his hat publicly, and pay up 10,000 euros he owes me + interest + inflation. Since this is unlikely to happen, I am seeking donations from other interested parties to continue my work. If you are interested in helping me with my work, then please go to my blog and donate generously:

http://libertesphilosophica.info/blog/ .

6. Pity that the jury Hans de Raedt, Gregor Weihs and Andrei Khrennikov were not impressed by your submission, Joy Christian. We had negotiated the conditions of the bet together, and you had agreed to them in public. Pity I didn't insist on you putting your money where your mouth was. I was much too nice.

But anytime you are interested in setting up a new bet, just let me know. I propose we combine it with a workshop / public debate. In Oxford or Leiden, just as you prefer.

7. Gill is lying again:

http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=66#p3030

He lost the bet, but refused to pay up.

8. @gill1109
So what. They are using the law of Malus to get the prediction. It is not the same as what you keep trying to impose on Joy's prediction. They don't actually use any "measurement outcomes" for the prediction. Neither does Joy. In fact, Joy's local realistic model prediction is more simple and more elegant.

9. The law of Malus *follows* from the standard quantum mechanical treatment. Shimony uses quantum mechanics to predict the probabilties of ++, +-, -+, --. Then he uses common sense to derive from this the correlation = expectation of product = prob(++ or --) - prob(+- or -+). Ballentine does it in the same way. Peres in his book too. Everybody does it the same way.

10. And so do I:

http://arxiv.org/abs/1405.2355

http://arxiv.org/abs/1301.1653

http://arxiv.org/abs/1501.03393

Stop the bogus claims about my work.

11. Christian's theory is certain very simple and very elegant. It can be summarised as following:

E(a, b) = 1/2 (a b + b a), because Christian says so.

Since a b = a.b + a ^ b and ba = a.b - a ^b (geometric algebra) it follows that E(a, b) = a.b. (Doran and Lasenby's book, (2.1)).

There is a dual version of the theory which we obtain by introducing I = e1 ^ e2 ^e3 and A = I a, B = I b. Notice that the trivector I commutes with the vectors a and b. Hence, multiplying left and right hand sides of the equation E(a, b) = 1/2 (a b + b a) by I^2 = -1 and using the commutation of I with a and b, we find E(a, b) = - 1.2 (A B + B A).

This is the equality which is nicely confirmed by the package GAViewer.

I would say that the weak point of the theory is the fact that it defines E(a, b) by something like Papal decree rather than from any pre-accepted physical or mathematical principles.

12. @gill1109
And again I say; So What? No actual measurement outcomes were used in the prediction. Joy's model predicts the result of -a.b without having to predict the expectation of the outcome pairs individually. One simple hidden variable and one simple physical postulate is all it takes. It really is quite elegant.

13. And I would add that once again Gill is being dishonest, ignorant, and incompetent. His goal has always been to deliberately mislead the scientific community to protect his own vested interests. He has succeeded in the past in doing so, but the scientific community is not going to be hoodwinked by him forever.

14. I see that Gill is still having some trouble understanding GA and how it exactly works with Joy's physics postulate. Still stuck in right handedland.

15. Perhaps it is too much for a mathematician to understand what a physics postulate is? I bet Gill can't even state Joy's postulate in words. It is actually pretty simple to understand and makes good common sense.

16. Let me point out a very silly mathematical mistake Gill has made in *HIS* model he has described above to expose his incompetence in elementary mathematics. He has defined his measurement function as A = I.a, but this is not a two-valued function, no matter what the direction "a" is. It is a single-valued function. Moreover, there is no "hidden variable" in his model. Thus his model is a breathtakingly idiotic one. This is a very revealing mistake, because it shows that even after "studying" my model for over eight years he is totally clueless about what it is.

17. I did not define a measurement function. My model is Christian's model, reduced to mathematical essentials. It's the model simulated by the GAViewer code which Albert Jan and Fred have been working on. I simply took the expectation value over the hidden variable - a fair coin toss - that's the "1/2" in the formula. Your GAViewer code will run faster and be more accurate if you do the same thing. It's just a question of actually taking the limit as N goes to infinity.

18. No actual measurement outcomes were used in the prediction. That's the whole point. They aren't there. It leads to the ultimate in simplicity and elegance.

19. What Gill's silly model shows is his shocking incompetence in elementary mathematics and basic physics. He tries too hard to compensate for his schoolboy howlers with dishonesty, aggression, and dirty political tactics behind the scenes. He would have been a textbook case study for Sigmund Freud.

20. Yep and he doesn't even realize that he wiped out the physics of the model by what he did. Same old story; Joy's model is X and "Gill wants to look at "the physical content" of his own model Y." Except the key physics is wiped out in Y. AB and BA happen in different iterations depending on lambda.

21. With probability half, AB happens; with probability half, BA happens. What is the expectation value of the result? 1/2 (AB + BA) = - a.b

Suppose that the simulation uses N trials. Let X be the number of times lambda = +1. X is binomially distributed with parameter 1/2. X/N has expectation 1/2 and variance 1/4N. The result of the simulation is X/N AB + (1 - X/N) BA = a.b - X/N a ^ b - (1 - X/N) b ^ a = a.b + (1 - 2 X / N) a ^ b.

By the law of large numbers, the last term converges to 0 as N goes to infinity.

What's the point of verify the law of large numbers for fair coin tosses with GAViewer? Why not use some elementary mathematics to compute straight away the result of taking the limit as N goes to infinity? Christian defines E(a, b) with a limit as N goes to infinity.

22. There is no physics in this GAViewer simulation program because there are no binary measurement outcomes and there is no calculation of correlation as it is done in the laboratory: the laboratory outcome is E(a, b) = (# equal - # unequal) / (# equal + # unequal).

23. Some people have a huge self-inflicted bubble between their ears.

Those without this infliction can actually read and understand Eq. (B10) of this paper:

http://arxiv.org/pdf/1501.03393.pdf ,

and / or further explanation provided here:

http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=188#p5129

24. Again..., Gill has no clue about Joy's physics postulate and can't even state it in words. Doubtful that he will ever understand it. And it is so simple and just plain common sense.

25. Very interesting paper, http://arxiv.org/pdf/1501.03393.pdf

According to formulas (7) and (8),

sign(s_k . a) = lambda^k
sign(s_k . b) = - lambda^k

where lambda^k = +/-1 is a fair coin toss.

Thus making E(a, b), according to the left hand side of (B1), identically equal to -1.

By the way the paper also has formula (A8) which is exactly what I proposed as a way to get the GAViewer simulation faster and more accurate. Take the limit as N goes to infinity by using the law of large numbers.

The paper seem to be missing definitions of D(a) and D(b). And also, as I have remarked before, of s^k (k = 1...N)

26. The paper, http://arxiv.org/pdf/1501.03393.pdf, is not missing definitions of anything. The problem is that Gill cannot read. He cannot even read equations as simple as equations (7) and (8) (which he has stated incorrectly) let alone the more sophisticated concepts discussed in the paper. One has to be extraordinarily stupid to think that the expectation value E(a, b) of the product of the functions A and B is anything but -a.b.

27. Someone is messing around with the wikipedia link above for the QM derivation showing that no measurement outcomes are used for the prediction. Here it is straight from the horse's mouth.

http://plato.stanford.edu/entries/bell-theorem/#3

28. Actually should be this link. Scroll down a bit.

http://plato.stanford.edu/entries/bell-theorem/#2

28. Might S^3 throw light on a "problem" which still bothers some people (most recently the philosopher Colin McGinn): the relativity of simultaneity in SR? Could S^3 allow discovery of a preferred reference frame in which a "single fact of the matter" can be established in the case of disparate observations produced by moving versus stationary reference frames? Isn't it plausible that this effect too is a product of our disadvantaged flatlander perspective?

1. S^3 has nothing to do with a preferred reference frame. S^3 is a well known solution of Einstein's field equations of general relativity:

http://arxiv.org/abs/1405.2355

2. Is your solution really that well known? Possibly not as well known as Gödel's. Perhaps in time.

S^3 assumes something suspiciously like a God's-Eye perspective. Your ally Tom Ray believes it's the key to resolving the P vs. NP question (cite available upon request) which is nothing if not all-encompassing. So why should it be irrelevant to the relativity of simultaneity? You seem to love the flatland metaphor, by the way.

3. http://arxiv.org/pdf/1505.05920.pdf
"Numerical solutions of Einstein’s equations for cosmological
spacetimes with spatial topology S^3 and symmetry group U(1)"

4. It is not my solution. It was discovered long before I was born:

https://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric

Have you heard of cosmology or universe by any chance?

29. According to equation (7) of http://arxiv.org/pdf/1501.03393.pdf,

A(a, lambda^k) = +1 if lambda^k = +1,
A(a, lambda^k) = -1 if lambda^k = -1,

while according to equation (8),

B(b, lambda^k) = -1 if lambda^k = +1,
B(b, lambda^k) = +1 if lambda^k = -1.

It is also stated that lambda is a random variable with 50/50 chance of being +/- 1, thus other possible values of lambda are excluded.

It follows that E(a, b) defined in equation (11) is identically equal to -1.

Side note on typography: in the formulas I refer to, Christian uses a script capital A and script capital B; later he also introduces "standardized" variables for which he uses plain capitals.

1. I see that Gill is still stuck in flat right-handedland.

2. Nowhere in any of my papers, on any subject, do I have written down the following set of equations:

A(a, lambda^k) = +1 if lambda^k = +1,
A(a, lambda^k) = -1 if lambda^k = -1,

B(b, lambda^k) = -1 if lambda^k = +1,
B(b, lambda^k) = +1 if lambda^k = -1.

These equations are a total fabrication by Gill to hoodwink the scientific community. I think he has forgotten to take his meds again.

30. Oh, Christian is so clever! This is actually what he wrote in http://arxiv.org/pdf/1501.03393.pdf , formulas (7) and (8):

\begin{align}
S^3\ni\pm1\,=\,{sign}\,(\,+\,{\bf s}^k\cdot{\bf a})\,\equiv\,
{\mathscr A}({\bf a},\,{\lambda^k})\,&=\,\lim_{{\bf s}\,\rightarrow\,{\bf a}}\left\{\,-\,{\bf D}({\bf a})\,{\bf L}({\bf s},\,\lambda^k)\right\}
=\,
\begin{cases}
+\,1\;\;\;\;\;{\rm if} &\lambda^k\,=\,+\,1 \\
-\,1\;\;\;\;\;{\rm if} &\lambda^k\,=\,-\,1
\end{cases} \label{88-oi}
\end{align}

\begin{align}
S^3\ni\mp1\,=\,{sign}\,(\,-\,{\bf s}^k\cdot{\bf b})\,\equiv\,
{\mathscr B}({\bf b},\,{\lambda^k})\,&=\,\lim_{{\bf s}\,\rightarrow\,{\bf b}}\left\{\,+\,{\bf D}({\bf b})\,{\bf L}({\bf s},\,\lambda^k)\right\}
=\,
\begin{cases}
-\,1\;\;\;\;\;{\rm if} &\lambda^k\,=\,+\,1 \\
+\,1\;\;\;\;\;{\rm if} &\lambda^k\,=\,-\,1\,,
\end{cases} \label{99-oi}

According to these equations,

{+1 if lambda^k = +1,
A(a, lambda^k) = {
{-1 if lambda^k = -1,

{ -1 if lambda^k = +1,
B(b, lambda^k) = {
{+1 if lambda^k = -1.

1. Another try:

............................{+1 if lambda^k = +1,
A(a, lambda^k) = {
............................{-1 if lambda^k = -1,

............................{ -1 if lambda^k = +1,
B(b, lambda^k) = {
............................{+1 if lambda^k = -1.

2. Anyone *not* desperate to be hoodwinked by Gill would be better off reading what I have actually written in this paper:

http://arxiv.org/pdf/1501.03393v4.pdf

3. Yes, do please read http://arxiv.org/pdf/1501.03393v4.pdf, and take a close look at equations (7) and (8). They seem to state

A(a, lambda^k) = +1 if lambda^k = +1, -1 if lambda^k = -1

B(b, lambda^k) = -1 if lambda^k = +1, +1 if lambda^k = -1

This would seem to imply that A(a, lambda^k) B(b, lambda^k) = -1 whatever value is taken by lambda^k, from which it would follow that E(a, b) = -1.

4. http://challengingbell.blogspot.co.uk/2015/06/a-flatlanders-view-on-joy-christians.html?showComment=1442307125863#c1149185565469822053

5. Just for the record, it is very easy to prove that for A and B defined in my paper

A(a, lambda^k) B(b, lambda^k) = +1 or -1,

and

E(a, b) = -a.b.

I have proved both of these equations in several of my papers, such as, for example, in the appendices of these two papers:

http://arxiv.org/abs/1201.0775

http://arxiv.org/abs/1301.1653

One has to be extraordinarily incompetent in mathematics to not be able to recognize this form my explicit derivations.

6. So there is a contradiction between (7) and (8) of http://arxiv.org/pdf/1501.03393v4.pdf and results claimed in http://arxiv.org/abs/1201.0775 and http://arxiv.org/abs/1301.1653

Perhaps Albert Jan Woninck will be interested to add computation of A(a, lambda) and B(B, lambda) according to (7) and (8) to his GAViewer script, and find out whether E(a, b) as defined in (11) equals -1 or - a . b

According to (7) and (8),

A(a, lambda^k) = +1 if lambda^k = +1, -1 if lambda^k = -1

B(b, lambda^k) = -1 if lambda^k = +1, +1 if lambda^k = -1

7. There is no "contradiction" in any of my papers.

The contradictions are only in the huge bubble between Gill's ears.

Gill is clearly trolling, knowing full well that Albert Jan is too nice a person to kick him out of here.

8. He lost the debate and won't admit to it. What else can he do except for being hung up on measurement outcomes? Also, this is what happens when a person gets stuck in flat right-handedland. :-)

9. Probably, Albert Jan is too nice a person to write that he agrees that equations (7) and (8) of http://arxiv.org/pdf/1501.03393v4.pdfv4 seem to state

A(a, lambda^k) = +1 if lambda^k = +1, -1 if lambda^k = -1

B(b, lambda^k) = -1 if lambda^k = +1, +1 if lambda^k = -1,

and that this would seem to imply that A(a, lambda^k) B(b, lambda^k) = -1 whatever value is taken by lambda^k ... from which it would follow from (11) that E(a, b) = -1.

10. Anyone but Gill can see from equations (7) and (8) of

http://arxiv.org/abs/1501.03393

that

A(a, lambda^k) B(b, lambda^k) = +1 or -1.

And anyone but Gill can see from equation (B10) of that paper that

E(a, b) = -a.b.

11. From (9), L(a, lambda) = lambda D(a)
From (5), L(a, lambda) = lambda I a
So D(a) = I a and lim_{s to a} -D(s)L(a, lambda) = - lambda I^2 a^2 = lambda confirming (7), and similarly (8) is correct.

We find sign(s . a) = script A(a, lambda) = lambda and
sign(- s . b) = script B(b, lambda) = - lambda

leading to E(a, b) = -1

Certainly, anyone can see this.

12. Is Gill really this stupid, or is he just pretending to be this stupid?

13. His usual MO; distraction by spamming a topic to death. He lost the debate but will never admit to it. Obsessed with measurement outcomes. But a theory doesn't have to use measurement outcomes for a prediction as we have seen above. Here is another QM prediction for EPRB that doesn't use outcomes.

14. Yes, it is repetitious, isn't it? All this hammering away at (7), (8) and (11) of http://arxiv.org/pdf/1501.03393v4.pdf is making an important point, which I hope that readers of Albert Jan's blog take good notice of: Joy Christian and Fred Diether have *no* mathematical answer whatsoever to well-founded mathematical criticicism. None at all. Christian starts being rude, Diether shows how mixed up he is.

Christian's paper introduces measurement outcomes. In formulas (7) and (8).

Diether's reference is to a standard computation of the expectation value of outcome of measuring an observable. Yes one can get the expectation value in QM directly without going via the probability distribution. Both ways give the same answer, of course.

15. http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&p=5609#p5609
And the result is,
Joy_CHSH = 2.828427

16. This comment has been removed by the author.

17. Do you think, Fred, that your explicit, computed demonstration will shut Gill up? I doubt it. For the only "important point" he is making here is that he can neither read English nor do math.

All of Gill's so called "important points" have been debunked in this two arXiv replies to him by me:

http://arxiv.org/abs/1203.2529 (this was three years ago!!!)

http://arxiv.org/abs/1501.03393

Anyone but Gill can see from equations (7) and (8) of the second reply that

A(a, lambda^k) B(b, lambda^k) = +1 or -1 (just do the math).

And anyone but Gill can see from equations (11) and (B10) of the same paper that

E(a, b) = -a.b,

computed event-by-event, as demonstrated by Fred and Albert Jan here and elsewhere.

But Gill will keep throwing stink bombs at my work, because that is the only way he can continue to mislead the scientific community. He is simply protecting his vested and political interests.

31. Nice to see all you fine folks on this blog. Maybe it would be even better if Richard was allowed access to Fred's site. The editing has many more options. What are you afraid of? In the meantime, let me add my comments about equations (7) and (8). If they are interpreted as written, I don't see any way that you can get anything other than -1. It's trivial and as Richard says, anyone can see it.

Your good friend, jreed

1. We all know how *your* mathematics works, John Reed. We all know that in your mathematics factoring out zero and dividing by zero are legitimate operations:

http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=199&start=20#p5537

You should have followed the advice given to you by Michel Fodje and recognize your place:

http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=199&start=40#p5582

Instead, you have decided to continue to make a fool of yourself. Well, that is just fine with me.

32. Let's talk about mistakes. I admitted that I made a mistake in that posting. I was wrong. Unlike you, I admit my mistakes and move on. Now, let's talk about some of your mistakes:

(1) Equations (7) and (8) above. You haven't made a reply about why they will always give -1. That's a mistake, isn't it? Why not admit you're wrong. It shouldn't be difficult for anyone to see this mistake.

(2) Loopholes in your simulation. It's obvious that you exploit loopholes to violate CHSH, yet refuse to admit this. I don't know what to think about this. Either you are too ignorant about programming to understand your program (most of which was written by Richard), or you are dishonest. Which is it? In fact, you still make references to this simulation as proof of your theory, and state that anyone who believes that there's a loophole here isn't thinking in 3D, whatever that means.

(3) Now for your biggest mistake of all. In your paper 1203.2529 you show formula (8) for a right hand frame is:

(I . a)(I . b) = - a . b - I . (a x b)

and then state for the left hand frame this formula is:

(I . a)(I . b) = - a . b + I . (a x b)

I decided to see if I could verify this. I set up Mathematica with two frames, right and left handed. Then I generated vectors a and b along with (I . a) and (I . b), in both right and left frames. Now I took the product,

(I . a)(I . b) = - a . b - a ^ b in both frames.

This product is the same in either frame. Since a ^ b = I . a x b there is something wrong with your derivation. Here's your mistake:

I have the little book "Space-Time Algebra" by David Hestenes. On page 22 he says in a space inversion transformation (right to left frame transformation) the cross product a x b CHANGES SIGN. You missed that. All your work that uses this cross product to prove the vector part of this product is zero is wrong. That nonsense about the coordinate system flipping from right to left hand is all wrong. Why did you use I (a x b) instead of the easier to use form a ^ b? Is it because a ^ b didn't give you the answer you needed?

1. Very good. Now go and read my replies to Gill, Moldoveanu, and Weatherall in the following papers and links:

http://arxiv.org/pdf/1203.2529.pdf

http://arxiv.org/pdf/1501.03393.pdf

http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=183

http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=188#p5129

Until you have done your homework there is no point in my trying to make you see the light. In fact I doubt that you ever will see the light.

2. "I have the little book "Space-Time Algebra" by David Hestenes. On page 22 he says in a space inversion transformation (right to left frame transformation) the cross product a x b CHANGES SIGN."

Amazing! He found the clue and can't figure it out.

3. Thanks Joy for those references. I have figured it out! Here's the solution:

In your paper "Refutation of Richard Gill's Argument Against my Disproof of Bell's Theorem" you write equation (8) :

(I . a)(I . b) = - a . b - I.(a x b)

representing the product of two bivectors in the right hand coordinate system. Later you write equation (14):

(I . a)(I . b) = - a . b + I. (a x b)

representing this product in the left hand coordinate system. Now here's what you missed. You call the trivector I in each of these equations "the standard trivector". The problem is that there's no standard trivector. When you change over from the right to left hand coordinate system, you have to also change the trivector. Since it's the product of the three basis vectors, and these all change sign, the left hand trivector has a minus sign. This changes the + sign in equation (14) to a minus sign and now everything works out correctly. Your problem is this correction does away with your changing lambda in switching frames. It doesn't change, and your idea of averaging the non-scaler term won't work.

4. John Reed, let me break it to you as gently as possible. You have no idea what you are talking about. Please read my paper again. If you still don't understand what has been explained to you so clearly, then have a look at this simplified explanation:

http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=183&start=80#p5064

Please note also that I have no interest in convincing you about anything. If you wish to learn, then all my papers are at your disposal.

5. Let's look at your derivation of the left to right equation again. Here's the starting point:

(I.a)(I.b) = -a.b - (a^b)

or using the duality relation a x b = -I(a^b):

(I.a)(I.b) = a.b - I(a x b) correct?

Now, if we do the left-right conversion (space inversion) according to you this turns out to be:

(-I.a)(-I.b) = a.b + I(a x b)

But you missed something here. Under space inversion:
I -> -I
and using the duality relation ( a x b = -I(a^b)), we must have a x b -> -(a x b). Your transformed equation should read:

(-I.a)(-I.b) = a.b - I(a x b)

as it must, since the transformed equation using inner and outer products is unchanged by space inversion.

6. John,

Please stop making a fool of yourself all over again.

You wrote:

" Here's the starting point:

(I.a)(I.b) = -a.b - (a^b)

or using the duality relation a x b = -I(a^b):

(I.a)(I.b) = a.b - I(a x b) correct? "

The last equation is wrong. You can't even do simple algebra correctly.

The rest of what you have written is garbage.

I don't have time for such nonsense. I will not be responding to your junk anymore.

Anyone else reading this can find my correct model in my papers, for example in this one: http://arxiv.org/abs/1203.2529

7. ooops, I did make a small mistake. It's difficult to math on this site. Sorry about that. Here's a corrected version:

Let's look at your derivation of the right to left equation again. Here's the starting point:

(I.a)(I.b) = -a.b - (a^b)

or using the duality relation a x b = -I(a^b):

(I.a)(I.b) =- a.b - I(a x b) correct?

Now, if we do the right-left conversion (space inversion) according to you this turns out to be:

(-I.a)(-I.b) = -a.b + I(a x b)

But you missed something here. Under space inversion:
I -> -I
and using the duality relation ( a x b = -I(a^b)), we must have a x b -> -(a x b). Your transformed equation should read:

(-I.a)(-I.b) = -a.b - I(a x b)

as it must, since the transformed equation using inner and outer products is unchanged by space inversion.

There now, that's better, isn't it?
Thanks for correcting this, and do you see any further errors?
You are complaining about my junk? Remember your incorrect equation:

(-I.a)(-I.b) = -a.b + I(a x b)

Which is the starting point of your theory. Since this is incorrect, the rest of your theory is nonsense.

You can choose not to respond, but we both know who's right, don't we? If you do choose not to respond, I'll be left wondering if you're just too stupid to understand this, or you're dishonest. I prefer the latter, because I think that's why you chose to go with (a x b) rather than (a ^ b). With this sign error in your equation, you could create your nonsense theory about flipping coordinate systems. Come on Joy, let's be honest here.

8. Your last paragraph is a classic strategy often employed by trolls. I will, however, break the first rule of internet and respond to it, because it gives me the perfect opportunity to expose your ignorance and incompetence in elementary mathematics.

You wrote:

" You are complaining about my junk? Remember your incorrect equation:

(-I.a)(-I.b) = -a.b + I(a x b)

Which is the starting point of your theory. Since this is incorrect, the rest of your theory is nonsense. "

I am sorry to say it is not my equation. It is the equation William Rowan Hamilton wrote down more than 150 years ago. You have just insulted one of the towering figures of physics and mathematics. Well done!

9. It is easy for those stuck in flat right-handedland to get confused. Thankfully GAViewer made it so simple to understand. But they still have trouble even when it is made so simple for them. ???

http://challengingbell.blogspot.com/2015/05/further-numerical-validation-of-joy.html

10. Joy, I understand you wanting to attack me. I truly feel sorry for you. How many years, how many papers and how much work have you spent all based on an incorrect equation? You should have seen a problem when the original equation, correctly expressed as inner, a.b and outer products a ^ b was invariant under space inversion, and yet your incorrect version of this equation, now expressed in terms of inner a.b and cross products, a x b was not invariant under space inversion. That should have been a clue that there's a problem somewhere. Yet you went full speed ahead with that equation in terms of inner and cross products without investigating this difference. In fact you made this error the basis of your theory.

Fred: Every time Joy has a problem you always come up with the same old story: Flatlanders can't figure it out or you can't think in 3-D. It's easy to see what the GAViewer program is doing. A random variable is generated with values +1 or -1. Then the geometric product is taken between two vectors a and b: If the random variable is +1, the product is ab, if -1, the product is ba. These products are summed. Think about what happens: The geometric product of ab = a.b + a^b and the geometric product of ba = a.b - a^b When this is summed, a.b always sums, but the bivector products will cancel out. This has nothing to do with right hand coordinate systems or flatland. In fact I don't see what it has to do with much of anything.

11. John Reed,

You are still unable to recognize your mistakes. You made an idiotic claim that Hamilton's equation,

(-I.a)(-I.b) = -a.b + I(a x b) ,

is incorrect, when this equation is found in every good textbook on classical mechanics. You should be ashamed of yourself for claiming that the standard equation for angular momenta is wrong. You made a silly mistake, just like your many other silly mistakes (such as factoring out zero). And yet you exhibit no shame in attacking me and my impeccable work. I am not attacking you. You have been attacking me for the past several months, despite having no intellectual capacity of understanding my work. I have repeatedly exposed your silly mistakes here and elsewhere. It is now up to you to learn from your mistakes. But somehow I doubt that you will.

12. Yep, poor John is badly stuck in right-handedland and doesn't understand what a left handed system looks like from a right handed only perspective. And it is so simple. a x b in a left handed system is b x a from a right handed only perspective (GAViewer confirms this).

Plus you can see from what he wrote above, he still has no clue how your model works in GA.

13. Here's what Doran and Lasenby in their book have to say about quaternions on page 34:

"This shows that the quaternions are a left-handed set of bivectors, whereas Hamilton and others attempted to view the i, j, k as a right-handed set of vectors. Not surprisingly, this was a potential source of great confusion and meant one had to be extremely careful when applying quaternions in vector algebra."

It looks like you were not extremely careful when you assumed that his equation was correct for your coordinate system. It looks like Hamilton's equation gives the cross product in the wrong direction. This makes sense, since the quaternions are bivectors in a left hand system, and Hamilton assumed that the cross product should obey the right hand rule. I think it's best not to get sidetracked into quaternions.

My derivation of the correct equation is easy and correct. Please outline how you arrived at the cross product in the left-hand frame. I'll help you find your error.

14. LOL! What do you think Joy's coordinate system is?

15. John Reed, you are the one in a desperate need of help. Get some.

16. It is truly amazing that something so simple can be mangled so much. And I already told John the simple answer. He must just be trolling now is all I can figure.

17. Thanks for your helpful reply. I'll use your derivation of this equation from your paper 1203.2529, reply to Richard Gill. More on your error in this derivation later.

Fred, too bad you can't ban me on this forum. You would have done that long ago on your forum, I'm sure. When we get through here, I'll go on your forum and go through this derivation again and again, so you can ban me. I look forward to being banned. It's a sign of true intellect and a badge of honor.

18. John Reed,

I have never been intimidated by threats, blackmails, bullying, and online harassment, especially when they are coming from ignorant fools. So keep factoring out zeros as much as you like.

33. Well, thanks to Albert Jan and GAViewer you managed to fix one line of the derivation. One line in the middle. It now leads to the right answer at the end. Unfortunately, it now no longer matches the starting point.

See the text around formulas (A6) to (A8) of http://arxiv.org/pdf/1501.03393.pdf

It is not a coincidence, Fred, that you still haven't programmed formulas (7) and (8) of http://arxiv.org/pdf/1501.03393.pdf in GAViewer. You are scared of what you will find. (I guess: you have tried, but you are not going to tell the world what you saw. Because it would mean the end of the party). I'm afraid that Albert Jan can't save you, this time.

1. Fred has programed precisely the formulas (7) and (8) of

http://arxiv.org/pdf/1501.03393.pdf

The results are E(a, b) = -a.b and "CHSH" = 2.828427.

The two GAviewer codes are available here:

http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=200&p=5628#p5627

The flatlander Gill, on the other hand, is incapable of doing elementary calculation to see that equations (7) and (8) of the above paper give

A(a, lambda^k) B(b, lambda^k) = +1 or -1.

Just do the math yourself. If you are too lazy to do the math yourself, then you can find it done for you in this paper:

See the appendix of this paper.

2. Yes I have done the maths myself. I hope everyone else does, too.

I have also checked the computer code myself. I hope everyone else does, too.

Indeed, A(a, lambda^k) B(b, lambda^k) = +1 or -1

Because, in fact, A(a, lambda^k) B(b, lambda^k) = -1, always. ie, both when lambda^k = +1 and when lambda^k = -1.

Fred did not program formulas (7) and (8) of http://arxiv.org/pdf/1501.03393.pdf and it is plain to see why not ... Instead he makes lame remarks like "a theory doesn't have to use measurement outcomes for a prediction as we have seen above".

Christian's theory *defines* E(a, b) = -0.5 (ab + ba). It follows by a standard result from GA that E(a, b) = -a . b.

Yes, I hope everyone is able to do the math for themselves.

3. One has to be mind-blowingly stupid to think that equations (7) and (8) of my "Reply to Gill" implies

A(a, lambda^k) B(b, lambda^k) = -1, always.

Gill has repeatedly made this mind-blowingly stupid claim. He must have heavily bribed, bullied, or blackmailed someone to nab his academic position.

4. It seems that Gill doesn't understand what the definition symbol means in math. Kind of strange for a mathematician not to understand it. We already know he is not capable of understanding your model. And... it is really not that complicated at all.

5. Are you talking about the symbol ":=", Fred? It appears in equations (21) and (22) of http://arxiv.org/pdf/1501.03393.pdf

Or are you talking about the definition (A1)? Which needs to be understood with the help of the new geometric products introduced in (A2) and (A3). The law of large numbers then gives us (A8).

6. PS that's what I mean by saying "Christian's theory *defines* E(a, b) = -0.5 (ab + ba). It follows by a standard result from GA that E(a, b) = -a . b". Please compare with Christian's (A8). If you can read math you can see that I am just paraphrasing Christian's derivation.

34. Nobody ever answered my request for a definition of D(a). However, we can deduce what it should be from http://arxiv.org/pdf/1501.03393.pdf

Please confirm or deny:

From (9), L(a, lambda) = lambda D(a)
From (5), L(a, lambda) = lambda I a
So D(a) = I a
where
I = e_ x ^ e_y ^ e_z