Classical Spheres, Division Algebras, and the Illusion of Quantum Non-locality:

Joy Christian,

First, let me say, you have a beautiful name.

You also have a beautiful mind. I've well over a dozen QM text books, all of which I have studied to some degree, and, in a few pages of '...the Illusion of Entanglement' you've clarified things that have confused me for decades.

Thank you.

Since my theory presumes local realism, with a particle plus pilot-wave, I've encountered rejection based on entanglement issues that you treat so well. If you succeed in rescuing physics from this illusion, we will all be indebted to you.

Best of luck to you.

Edwin Eugene Klingman

A slight correction. I said we'll all be indebted to you. Not quite so. As Tolstoy said:

"I know that most men, including those at ease with problems of the greatest complexity, can seldom accept even the simplest and most obvious truth if it be such as would oblige them to admit the falsity of conclusions which they have delighted in explaining to colleagues, which they have proudly taught to others, and which they have woven, thread by thread, into the fabric of their lives."

Being an expert on 'spooky' and 'weird' quantum mechanics is fun. To have to retract all the fascinating things, said to so many rapt audiences is no fun. And will probably be resisted to the grave.

Edwin Eugene Klingman

Thank you for your kind words. The person who rescued us from the illusion of entanglement was Einstein, not me. My aim is to simply demonstrate that Bell's theorem does not undermine Einstein's position, because the theorem is simply wrong. To be sure, Bell's argument is very simple and convincing at first sight, not to mention instructive, and for these reasons it will continue to appeal to many people.

The key to understanding Bell's error is to recognize that his very first equation is not as innocent as it seems. It smuggles-in incompleteness in the accounting of measurement results from the start, by oversimplifying the topology of the measurement events. His argument thus commits to a classic error of circularity in logic, by *not* satisfying the completeness criterion of EPR. This is not easy to see, however, and has led many brilliant minds in physics astray.

Dear Joy Christian,

your papers are very technical, so i have to ask explicitely my question here.

Does your arguments refuting Bell's theorem rely on the fact that for example in the EPR-Bohm experiment the two particles are "born" out of the same source and with properties that depend on the conservation of spin?

No.

Dear Joy Christian,

thank you for your quick response that lead me to another question.

If there's no dependence between the two EPR-Bohm particles and their subsequently measurements, shouldn't we observe the same statistics also with "unentangled" particles? The latter could be conducted via 2 EPR-Bohm sources, the first source emitting particles 1 and 2, the second source emitting particles 3 and 4. Particles 2 and 4 fly northwards, the particles 1 and 3 fly southwards and are measured in the same fashion like in the original EPR-Bohm setup.

What's the reason according to your hypothesis that this experiment will output a different statistics than the original EPR-Bohm setup?

Regardless of my work, the difference between the two scenarios you describe---the standard scenario and the un-entangled or product-state scenario---is what Bell calls the existence of a "common cause." In any local realistic theory the standard EPR-Bohm systems do what they do because there has been a common cause linking them (i.e., they have interacted in the past). This common cause is also known as "a complete state" or "a hidden variable." Within my model this common cause is the handedness of the physical space within which the EPR-Bohm experiment takes place. It is represented by a trivector mu, which is a non-trivial geometric object, and provides a pre-established harmony among the remote observations. For the un-entangled scenario you describe there would be no common handedness of the physical space for each run of the experiment (no common mu), and hence there would be no correlations among the remote observations.

Dear Joy Christian,

thank you for your reply.

I ask myself if it could be possible to superpose the particles 2 and 4 (for example by a Mach-Zehnder-Interferometer or a similar setup) of my example and therefore force the particles 1 and 3 to be "entangled" and hence to reproduce the results of the standard scenario.

Does quantum mechanics allow such a kind of "entanglement" (i do ask because i am not firm enough with the QM-Maths to deduce this question by myself)? I suppose that due to your hypothesis, this scenario wouldn't be possible, but what does QM say to such an experiment?

My local-realistic framework reproduces quantum mechanical expectation values (at least in principle) for all conceivable physical scenarios.

As for your question about what quantum mechanics would predict for your thought experiment, this is not the right forum for such a basic question. I suggest you first learn quantum mechanics elsewhere before trying to understand Bell's theorem or my work.

Dear Joy,

Edwin Eugene Klingman just made me aware of your post here. This is very exciting because I followed your archive papers and I would love to debate them with you. I need to understand 1101.1958 first, though.

As a disclaimer, I found the prior papers incomplete in their arguments, and on the recent comments, I am very skeptical about octonions and QM because of their lack of associativity. However, this all is very thought provoking and I really look forward to studying your paper in detail and asking you questions about it.

AHAHAHA LIKE IF YOUR WORKS WERE DIFFICULT ahahah I will say AHAHAHA

First it's not difficult and furthermore false.

Still a comic or a vanitious hihihi

signed steve the humble arrogant. 3 and 7 spheres ahahah no but what after a nobel prize perhaps ahahaha

Laugh is good for health no?

Congratulations

Steve

Joy,

I like your paper and I love your method. I agree with you on the infinite measurability of S^2 S^2 over the S^3 manifold. I derived the same result in my ICCS 2006 paper, 3.2, et seq.

I don't follow, however, why you consider J.S. Bell's choice of local configuration space naive, much less simpleminded. You write:

"In the light of these extraordinary features of S^3, the reader ought to be struck by the naivety of Bell's choice of a local prescription. Clearly, no simpleminded function like (1) with a totally disconnected codomain S^0 can provide a complete account of all possible measurement results constituting S^3."

(Ref 1 is Bell's mapping of quantum configuration space to physical space.)

Of course, Bell's choice is "topologically naive" as you earlier write, because he wasn't doing topology. And yes of course, the zero sphere S^0 is a totally disconnected set in the context of simply connected spaces. However, Bell's choice does include the two simple poles at infinity required by classical time reversed symmetry; one could not speak of reconciling physical space with quantum mechanical results without this closed algebra on C, because locality implicitly demands that local realism be time symmetric. Generalizing to C*, with the one simple pole at infinity, conectivity is restored with equatorial results that are not just ( 1, - 1) but ( 1, - 1, i) such that points that go off to infinity are lodged in the n-dimensional Hilbert space, which is consistent with Bell's demonstration that quantum configuration space cannot map to physical space without a nonlocal model.

I don't quite understand the value you invest in parallelizability (2, 4, 8 dimension spheres). I know vector spaces are useful for calculation, but I can't see the foundational significance. I'll work on it.

It is important to know that I do not write to be contrary, and certainly not to be adversarial. We share more similarities than differences, notoably the topological approach and enthusiasm for the unique properties of S^3. I hope you feel disposed to engage in dialogue.

All best,

Tom

Thank you for your comments. Bell's choice of a 0-sphere for the co-domain of his local-realistic functions is extraordinarily naive. Recall that Bell's goal, and indeed the goal of any Bell-type theorem, is to demonstrate that no *complete* theory (in the sense of EPR) can be locally causal. Indeed, without completeness there is no theorem. But it is clear from the detailed discussions in my papers that the choice of a 0-sphere in his functions can never fulfil the completeness criterion. Thus by making this choice Bell forfeits his game from the start. This is the main message of my papers. Bell's theorem (and indeed all Bell-type theorems) is a non-starter.

The parallelizable spheres are fundamentally important for several reasons. First, without the parallelizability the completeness criterion cannot be satisfied (as already mentioned). Second, quantum correlations are what they are *because* of the discipline of parallelization, as extensively demonstrated in my papers. Third, without parallelization the factorizability or locality condition of Bell is not satisfied. Thus parallelizability of the four spheres is fundamentally important.

I fail to see how one can maintain the Bell-type party line in the face of detailed and explicit local-realistic counterexamples I have produced---not only for the original EPR-Bohm state, but also for the Hardy and GHZ type rotationally non-invariant entangled states. Moreover, I have the basic framework in place for reproducing *any* quantum mechanical correlations purely local-realistically. So I am puzzled by your comments.

Dear Joy,

Don't be surprised, I am just a little crazzy and sphericentrist.

Hihihhi I love this platform

Steve

you are comic the moderator with under review, it could be well if you insert a programm hihih ok I have a better idea, I say you whan I have taken my meds, as that I will be quiet and civilized.

Hihihih dear Brendan Foster it's you no I think

Regards

Steve

Frankly dear scientists, pseudos sceinces and pseudos dimensions of nothing for nothing......you try to make similiraties and details ,but you don't understand the generality, thus frankly it's ironic.

A real global irony.and what after the fear of the truth also no and the crezdibility which falls down ....a real comedy.

ps can I speak with rationalists please, if it's possible.

Steve

Hi all,Tom,Joy,

Have you seen my posts, hihihi they are under review, incredible tom I am always nice no? hihiih

Well well well , I recome quickly with some details of some errors.With humility of course, you are comics in fact and funny.

The spheres and the sphere ....and THE SPHERE!!! 3d of course even if they think that they can invent pseudosimilarities in extradimensions ,ahahaha incredible irony for a specific road of strategy, I am not parano it's God who said me that, hihihihi crazzy this belgian,crazzy.

Regards dear scientists

Steve

Using the broad brush, I hear you say that you respect ithe results of quantum mechanics, and yet preserve local realism. Surely you realize that "quantum locality" makes no sense at all -- you're puzzled at the reaction you get? I'm puzzled by your reaction to the reaction. :-)

Tom

Dear Joy,

Let me start with a disclaimer, please excuse the typos below as I did not write this in Word and I am addicted to Word's check spelling.

I am am still digesting 1101.1958 along with its introductory ideas from 0806.3078. However, before I fully understand those papers, I want to discuss your earlier disproof papers, the responses from the critics, and my prior incompletness claim. I'll start with the simplest topic, the critics. quant-ph/0703218 is obviously flawed. 0704.2038 is not an air tight counter argument. 0712.1637 is not valid as I do have myself a concrete counter argument for 0712.1637. However, I do mostly agree with Grangier. I would like to argue along the lines of this quote "So the proposed model [1] cannot be a local realistic model, it could at best be an alternative formulation of quantum mechanics [4], like Bohm's theory is." Now let me set the preparatory stage.

What captures best the spirit of QM? I can argue (following the lines of research of Emile Grgin) that the most important property of nature (and in particular of classical and quantum mechanics) is its invariance of the physical laws to composing two systems: put any 2 QM systems together and the composed system is still described by QM. In terms of abstract properties of QM, QM is described by two products: an anti-symmetric Lie algebra and a symmetric Jordan algebra. The rule of invariance under composition (the requirement to be able to construct a tensor product) demands three algebraic identities: Lie, Leibnitz (leading to the introduction of derivation) and a compatibility condition between Lie and Jordan algebras. Physically this corresponds to a 1-to-1 mapping between observables and generators, or in Alfsen and Shultz lingo, a "dynamic correspondence". Going from the algebraic approach to QM state spaces, one introduces an associative product by combinning the Lie and Jordan products using sqrt(-1). However, the 3 algebraic identities lead to a more general approach to QM than a simple standard C* algebra because there is no positivity condition associated with it. (Landsman for example works along similar lines when he talks about a Lie-Jordan algebra, but he incorporates the positivity condition by demanding an additional rule.) At this stage the plot one can look for example at the Cartan classification of Lie algebras and adding the 2 additional algebraic constraints would restrict the available realization of the usual Lie algebra classification. First one gets the usual su(N) associated with complex QM, but there are also exceptional solutions: so(1,2), so(3), so(6), so(1,5), so(2,4), so(3,3).

In general, from the classification of Jordan algebras, one get the standard NxN matrices over the division algebras, the spin factors, (and the Albert algebra). Geometrically, ignoring octonions, in state space this corresponds to cones and spheres (or hemisperes). All spheres can be easily described in terms of geometric algebras. Long story short, your counter-argument to Bell is based on one of the exceptional cases, the so(3), and this can actually be shown to be a limiting case of so(2,4)~su(2,2) corresponding to a "fermionization" of twistor theory when a twistor is considerd to represent the observable of the theory. (now some people became interested in the plain so(2,4) case-Bars, Segal). All the other exceptional cases can be easily cast in a geometric algebra formalism, but what you loose at this time is the physical justification for your topological argument. This does not make the math invalid, but so(3) was just a lucky coincidence which can be interpreted along your arguments for justifying bivectors because of the gimbal lock problem in the standard approach. In this sense your proof was incomplete. If there were no other exceptional solutions except so(3) allowing unrestricted composability (arguably a major requirement for any sensible physical theory), the argument against Bell would have been complete and irefutable. The presence of the other solutions opens the door for other interpretations as well. Because all the other cases are not fully investigated at this time, I cannot conclude with 100% certainty that your proof is right or wrong in imposing your particular topological interpretation.

However, I strongly feel that your topologial completness argument, while fully working in the so(3) case may not hold in general in QM based on other spin factors. (If I can prove it one way or the other, I would certantly publish it.) I am saying this because at least in one particular case based on so(2,4) one gets a different geometric phase which may kill any hope of natural justification of beables, unless the beables display a Yang-Mills gauge freedom-a completely non-classical behavior.

Moreover, your bivector beable interpretation does not work in the self-dual cone case (plain QM with no spin) =because this is not well suited for the geometric algebra formalism= but arguably there is no Bell inequality there, (and your example was intended as a counter example).

You may counter my incompletness claim by saying that your example is just a counter example and you only need one right? Not quite. If the aim was to mathematically disproof Bell's theorem, this is not achieved as you start with a different assumption. If the aim is to demolish the philosphical pedestal and the importance of Bell's theorem in justifying the opposition to local realism, then a simple counter eample is not enough. Either your interpretation is natural and the only one possible, or you find an actual mathematical flaw in Bell's proof. There are no flaws in proving Bell's theorem, and your interpretation IS natural. I am not convinced it is the only one possible.

Maybe you would not agree on imposing the requirement for a unique interpretation. Fine then. But I do know the origin of your counterexample: the spin factor state space geometry. As there are only a handful type of Jordan algebras, this limits the kind/type of possible beables. It is conceivable to be able to systematically categorize all beables and if there are cases where they only display non-classical behaviors, the argument against local realism still stands. You may claim then that Bell's theorem is incomplete in its broader aim of killing local classical realism and this hypothetical future results strenghtens it making it air tight. (You may actually claim that Bell's theorem is undeserving its reputation right now,but I am not clear on your stance on local realism.)

But although I am not convinced you can successfuly kill's Bell's theorem importance for QM, your approach has excellent merits. Your upper bound correlations interpretations based on maximum torsion is a wonderful result which I plan to understend in depth. And if this leads to a sensible octonionic QM, this would be a crowning victory and suddenly everyone will start paying attention. Let me read yor result some more, and I'll be back with questions and coments.