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

The idea that one should expect all four division algebras to play a role in the ultimate theory of physics, on the basis that there are four fundamental forces of nature, ``allowing octonions, in particular, to account for gravitation'' sounds very convincing, were it not for the fact that according to our modern -- i.e. post-1915 -- views on gravitation, the latter is not a force at all, but rather an aspect of spacetime structure. However, if the gluons (8), resp. electroweak vector bosons (4), are somehow associated with resp. the octonions and the quaternions, one should expect that there are exactly three Higgs bosons, being associated with the remaining two normed division algebras, namely the real and complex numbers. Alternatively, since the mean dimension of the five exceptional Lie algebras is 105, and there are only 25 known fundamental particles -- one of which is still elusive -- one should expect the discovery of 80 new fundamental topologically nontrivial EPR elements of reality at LHC sometime very soon.

Your sarcasm is not entirely unjustified, but it distracts from my main point. While I wholeheartedly endorse the thesis that "gravity is not a force" (see, e.g., some of my older papers on the arXiv), to be fair to Atiyah his arguments were not as simplistic and naive as your comments seem to suggest.

But all that is beside the point. The main concern of my note is the prevalent but false belief in "quantum non-locality", not the true nature of quantum gravity. And whatever else one may discover at LHC, it certainly won't be "non-locality", unless LHC is capable of discovering figments of imagination.

Right, well I find it very amusing to read that my ``sarcasm is not entirely justified'' coming from a person with such fantastical ideas. It seems to me you are taking Feyerabend a little too seriously.

You have misread my sentence. Please read it again and recognize your error. As for my "ideas", there is nothing fantastical about correcting the incorrect mathematics used within a fallacious theorem. That is all I have done. You will recognize that if you actually read my papers.

Or worse still....you really do believe you have actually disproven Bell's theorem. As for your point about incorrect mathematics, I indeed found that to be a nuisance when attempting to read your work. For instance, in one of your more recent pamphlets you mention that ``a 2-sphere is not homeomorphic to R2 (or to R for that matter, for both R and R2 have the same cardinality)''. However, the accompanying figure which is supposed to demonstrate this only shows that stereographic projection is not a homeomorphism, not that there exists no such homeomorphism. That, in fact, there exists no homeomorphism between R2 and S2 can for instance be shown as a simple consequence of the fact that the latter space is compact, while the former is not. The fact that R2 and R have the same cardinality is completely irrelevant here. According to your reasoning, R would not be homeomorphic to itself, since it is not homeomorphic to R2 (i.e. replace S2 by R in the above quote). Now, I can go on and mention (many) other similar exmples, but perhaps some other time. Anyway, I think my point is clear. Before accusing Bell -- or anyone else -- of sloppy mathematics, please check your own.

I am sorry you found reading my work a nuisance, but I thank you for reading it in any case.

"...the latter space is compact, while the former is not."

Indeed ... my point is as trivial as that, and I have said precisely that in one of my previous "pamphlets" (see especially my talk posted on this site). But this simple point was not understood by some, prompting me to add a figure to explain the issue.

Now I have reread my sentence you have quoted, and I do not see how anyone can infer what you are inferring from it. My sentence is correct as it stands, and within the context of my paragraph it makes perfect sense. I will let the reader decide who is in error here.

In any case, it is perfectly clear from my discussion in that paragraph that the type of functions proposed by Bell are simply not capable of accounting for all possible measurement results, and hence Bell's argument does not even get off the ground.

For example I have invented a new universal equation between all physical spheres.(quant.and cosm.)

m mass V volume v1 vel.spin.of rot. v2 vel.orb.of rot. more the others rotations of the system......if you take these elements you have an universal constant....mvV= CONSTANT.............now of course all that is in 3D for the respect of our proportionalities of evolution, the SPHERIZATION OF QUANTUM SPHERES ....COSMOLOGICAL SPHERES ...INSIDE A BEAUTIFUL 3D SPHERE IN OPTIMIZATION TOWARDS THE PERFECT HARMONY BETWEEN ALL THESE SPHEERS AND LIFES AND COSCIOUSNESS.....LOGIC DEAR SCIENTISTS LOGIC......THE OCTONION AND THE QUATERNION ARE UNDER THE LAWS OF THE SPHERE!!!!!!!

Regards

Steve

I think the sentence that you seem to be confused about is quite clear. No logical inference intended, so if you choose to read it differently that is simply an error on your part.

Thanks. You have confirmed what I assumed to be the case - the simple inertia of introducing new ideas into the system. There must be a strong desire to keep hold of spookiness - it makes good stories.

However, I would have hoped that your work at Oxford Uni and the Perimiter Institute would have acorded you a little more respect than having to respond to the charges of 'fantastical ideas' below. It is hard to understand how adding a few extra dimensions to balance Bell's equation is unfavourably compared with instantaneous action at a distance.

Hopefully more people will simply read the paper for what it is, and appreciate the problem it attempts to solve. Hope you don't have to wait as long as Grete.

Dear Dr Christian,

I am a bit confused regarding your critique of Bell's theorem. While I don't claim to understand your work in detail, it appears on first sight that you allow geometries that not necessarily approximate flat metric, or any metric at all, on small scales. You bring the example of a torsion tensor, and - unless I am mistaken - one could also mention some noncommutative geometry as another example. Doesn't that mean that your work begins on a somewhat different premise as compared to conventional formulation in physics would? It appears to me that giving up "metric" as central concept to guarantee universal applicability of physical law, that indeed there will be far reaching consequences. That would make your work a very interesting opportunity for restricting validity of Bell's theorem to incomplete subspaces of a more general, "complete" geometry of nature. Am I off?

Thanks, Jens

Thank you for responding so quickly! I'll have to study this and your work a bit.

There's one more thing I'd like to ask: You mention Sir Atiyah's talk from Simons Center last year. Many people wonder about it, as do I; but beyond the slides I couldn't even find the reference list ... Since you're hinting at it, I thought I'd ask what you're referring to when you wrote about specific steps and substantiated ideas. Sorry for the indiscretion :)

Thanks, Jens

(no Dr/PhD)

Jens,

I myself was not present at Atiyah's talk and know about its contents only through secondary sources. I have written to him directly and perhaps he will respond (although he is an extraordinarily busy man, as you can imagine). Beyond that I rather not go into details about his talk, because the last thing I want to do is to misrepresent his carefully thought-out argument.

Joy

ok, thank you, I'll stay tuned. Jens

Joy

Excellent, brilliant and honest, thank you. Physics needs more prepared to let go of old myth and nonsense and develop their brains properly.

I don't pretend to follow much of the maths, but I'm among 3 who have found the same conclusion, all from slightly different routes, with essays in the current competition. It really arose from the string posts under the essays. My own is entirely logic based and maths free http://fqxi.org/community/forum/topic/803 '2020 Vision' but you'll also want to read at least Edwin Klingsman and Willards essays. Edwin is an ex NASA research scientist and handy with sums, Willards appraoch is philosophical, mine is very Reality/Locality, showing how bells inequity is completely sidelined by a local reality that should keep Roger P happy by producing his Holy Grail of giving SR a (non spooky) quantum mechanism to run it.

I would be delighted if you'd comment. The solution has also opened up many other previously obscured areas of science, and I'd like to cite your paper in the one I'm just finishing deriving a real galactic secular evolution sequence, which is quite dramatic stuff. I hope you can understand my language!

We really must start a movement to clear physics of troglodytes to let it catch up one day!

Thank you again.

Very best wishes

Peter

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.