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

Dear Joy,

I am still digesting your results (I am almost done), but my understanding of your position already benefitted greatly from the past exchanges. For example I see now I was naively tying your approach to Hilbert spaces. Your approach to local realism is much more subtle. As such, my earlier objections about division are void and I withdraw them. I think that the real debate should be around EPR and the meaning of local realism. At core is your mixing of factuals and counterfactuals to get the new topology. I have to think before formulating a for or against position at this time. Hopefuly I will have a position within a few days. I will try to see if I can obtain a meaningful distinction between traditional local realism and "factorizable completness" besides factual-conterfactual.

A few other side remarks. Let me repeat that I was not influenced in any shape or form by Grangier's comments. I did not fully agree with him, but his ideas resonated with mine. Also, QM is incomplete as it cannot account for non-interacting separated systems. I urge you to read Aerts' analasys, it is well worth it.

You say "We know that QM cannot be interpreted as a complete, local, and realistic theory (we know this since EPR)."

I don't know where you have seen that but if it's your line of reasoning, thus I am understanding your confusions.Deatils falses ...thus globality false.

The realism is not there.Copenaghen probably can help you but apparently the rationalism is not loved by all.

PS YOUR ALGEBRAS ARE BAD USED, YOUR INFINITIES AND LIMITS ALSO.....THUS YOUR PROPORTIONALITIES WITH THE NEWTONIAN FRACTALIZATION HAS NO SENSE.Your causalities are not locals and rational simply.The realism is objective and all is relativistically the same.

Sincerely

Steve

Dear Florin,

Thank you for your reply. I am familiar with Aerts's work since my student days (I have a copy of his PhD thesis). But I have not read his more recent work. It sounds consistent with my position. In fact it sounds like a restatement of the so-called "measurement problem." I will read his analysis when time permits.

Dear Edwin,

Thank you for your support. As you can see, Florin and I are making progress in understanding each other's position.

Dear Joy,

I think I figured out what is going on. The EPR completness criterion simply means that one gets the entire state space, be it phase space, Hilbert space, or other spaces. By considering actuals al well as counterfactulas you are then in fact ignoring the time evolution and get the entire state space. In general, any state space will obey EPR's completness criterion. (Try your approach on classical mechanics for a hypothetical hidden variable theory.)

Local realism in your approach is only factorizability. Factorizability is the opposite of entangelment and this gives the approach its classical intuition. Factorizability is not local realism as locality was considered by Einstein and Bell to mean just that: spatial separation. So is Bell's theorem invalid? No, because a Hilbert space dimension is N^2 for N psi(s) and it is not always separable. Still, you manage to arrive at separability. But this is not done directly in the original Hilbert space. For example you need to embed Bloch sphere in S3. S3 becomes then a different kind of state space and in fact you are rewriting QM in a diferent state space with a different formalism. But wait a minute. Is QM not supposed to be uniquely written in Hilbert space formalism? How about Piron's result of recovering Hilbert space over division algebras from propositional logic? The answer is no as there is a counterexample to that: QM in phase space via Moyal bracket.

So your prescription for separability is embedding (if possible) the Hilbert space inside S0, S1, S3, or S7 to achieve parallelizability. Because this contradicts the nonseparability of the standard Hilbert space, this means that QM over S0..S7 is something qualitatively different than a standard Hilbert space formulation. (And indeed, in your formalism you use different mathematical objects.)

Also it is not clear if this formulation of QM goes beyond QM or not. In other words, can you always succeed in embedding any Hilbert space in S0..S7? Probably not based on dimensional analasys for higher dimensions.

Another issue. If Bloch sphere is embedded in S3, would not this mean that we still deal with traditional complex QM? Let's look at another example first. Real quantum mechanics can be embeded in complex QM, but the meaning of the wavefunctions is qualitatively different. Probably something along similar lines is happenning here, I don't know. To get a better grip, an analasys of time evolution might clarify things as time tends to dissapear from the picture as both actuals and counterfactuals are considered. Maybe this analasys will show that you are still in a traditional Hilbert space (the spin factor case), and that the Killing flow is what you traditionally obtain in the original embedded space.

If I were to venture a guess, in S3 the time flow is not the same as in Bloch sphere and the meaning of psi does not stay the same. For if they do stay the same, all possible time evolution in Bloch sphere would be enough to achieve EPR completness which is not the same as S3 is needed.

the fermi diracv statistics and the BEC statistics are bad utilized simply.....If it's frozen that' doesn't turn,, thus no mass!!!...false all that....you confound a graphene in 2d(which is really in 3d furthermore)and a real system of analyzes.

The spin is not explained.....

Sincerely

Steve

Hi,

Parallelizable and where is the cause of mass, aswer ...anywhere.

The spinning spheres, entangled, turning are proportional with mass....it's the volumes which must be parallelizables, the volumes of these entangled spheres.Now if you do not insert a correct finite serie for the ultim universal fractal,never the proportions of the local realism shall be found.

The gravitational stability is implied by these rotating sphericl volumes.The mass increases at all moment of evolution.

A real parallelization must be rational for the real interpretation of our localities and globalities.

Regards

Steve

seriously, if the formalism, axiomatic, permits to harmonie the errors of paradoxs,it's interesting for the proportionalities, but all is in 3d and a time duration correlated with spinning spheres, that's why the frozzen time is bizare with its 2d.The parallelization as a translation of the 3d foundamentalism.If not it's a pure joke.

Newton can be understood with The real sense of harmonious series of convergences,Hamilton and lagrange in the same proportional relativistic vues and analyzes.

It's true what!!!, when you apply a BEC,how can you have a duration and a mass without rotations orbitals and spinals which are in logic proportionals respecting Newton and its friends.That's has no sense in a real physical logic.

Steve

even for light, only hv turns and has no mass.

Steve

Dear Joy,

Let me correct one mistake in my last post. I got the embedding backwards. S3 comes from SU(2) as a double cover and the meaning of psi stays the same. However, your beable \mu * n is part of S2 and as such they have different meaning. Also their time evolution is trivial.

As I was saying earlier, the real contention is with the interpretation of your results. Is entagelment real or not? Is Bell's theorem valid or not? In standard formulation entangelment exists, in your bivector formulation does not. This only shows that the concept is formalism dependent, and so there is no universal meaning attached to entangelment and the interpretation of Bell's theorem.

So in this sense, you are justified to attack the usual importance given to Bell's theorem as a sacred cow that settled the local realism issue for good.

On the other hand, this separation property of your new formalism workes so far only in limited circumstances. (It would also be interesting to see what happens in the case of the K-S theorem in the new formalism.) If so, the defenders of Bell's theorem do have a valid claim for its importance within the usual meaning attached to the standard formalism.

To kill Bell's theorem importance for good, you have to prove that separability is always possible, and I am not convinced that this is true.

In your papers I disagree with several points of view: separability=local realism, "topological naive assumption", disproof of Bell's theorem. Separability gives the approach clasical intuition, but locality referes to spatial separation and direct experimental results: correlations between clicks. The distiction is illegally blurred when counterfactuals are introduced. "topological naive assumption" has the "naive" word which introduces considerations outside math. An assumpton is only that, an assumption, and mathematical consequances follows from that. Talking about "naive" assumptions has a major turn-off effect on readers who work in the standard paradigm. Last, the disproof of Bell's theorem is wrong, as you start with a different assumption.

To end on a positive note, I do like the new point of view which is always welcome in understanding QM. The meaning of Cirelson's bound as maximal torsion is very interesting.

Dear Florin,

Thank you for another set of your extensive comments. I would like to respond to them as soon as possible, but I have been distracted by various other things at the moment. Needless to say, I do not agree with everything you have written. But I do appreciate your efforts. More soon.

Dear Joy,

I am looking forward to your reply. I too am very busy during the week, and my posts are usually rushed part due to the lack of time, and part of the excitement of the discussion. Therefore sometime I am making sloppy mistakes, (which I subsequently try to correct them).

By the way, I will attend this conference in April-May: http://carnap.umd.edu/philphysics/conference.html (which is local for me) and if you will be there, I would love to talk to you in person.

hihihi amen .it's cool they are civilized.lol

hihihi and now they are flying in a boeing for a conference about determinism of the locality, financed by who, still the government dear all ..REVOLUTION ? HIHIHIH LOL

but it's true it's cool these deterministic realisms......after all.

sorry for my parano(i see the word sphere and hop ...I take my meds), sincerely sorry , after rereading and without parano, it's a cool work, I like the determinism.Thus the 4 spheres are relevant...ps change the sense of one of these 4 spheres relativelly proportional....their rotations are the secret and their polarity and sort and synchro are with volumes also and the sense of rotation,main/center of our universe.

Say hello to han gueurdes it seems cool,

Steve

the volumes of entangled spheres can be inserted also, that becomes relevant there.

These 4 parall spheres(virtual or imaginaries) are relevant considering the 4 forces, but there is a problem aboutt the gravitational stability and the linearity. The fact that the volumes permit to differenciate even inside a virtual sphere of fields for example the forces become interesting considering the encoding with sort.and syncho.Now the sense of rotation seems the best explaination about this difefrence between mass and light and thus gravity and electromagnetism...the rotating volumes of entangled spheres and two main senses of Rotation shows the road.That explains many things this simple evidence.Now of course the real problem is the real inetractions between the 4 spheres and the external informations.It's a real puzzle of interations between rotating spheers and their fusion relativistically and thermodynamically proportional.The real ask is thus the volumes or this main senses, or the 2 or even more about the sortings and synchro.But it's an other question.How can we class thus the 4 interactions correctly....fascinating all that.The determinism is the sister of the rationalism after all.This Universe is wonderful and that evolves , they fuse still and always these spheres.....

4 spheres parall...and inside the entangled spheres and their pure finite serie, volumes correlated of course.That becomes relevant ....rotations helping.

Regards

Steve,parano but I evolve.

Dear Florin I am persuaded you'll change your point of vue about Bell's theorem....the determinisn is better, you are intelligent thus you shall change at my humble opinion.In all case you Th Lawrence Ray are skillings but you lack of rationalism about our real numbers and its continuity and discretness.You play so easely with maths but you make badly your domains of references, that's why your symmetries are imaginaries, the infinities also are bad used about the entropy and its distribution on the time constant of evolution due to motions(rotations).In fact it's an pure ocean of confusions.

Best Regards

Steve

Dear Joy,

I found a reference to your interest in Bell's Theorem in the fqxi discussions of Eugene Klingman's paper in the Digital/Analog essay contest. I have not read your papers yet but I wonder if you are aware of the ideas on the subject of my late friend Caroline Thompson . At the time she has flatly rejected my 2005 Beautiful Universe TOE on which my present fqxi paper is based, but in that paper I essentially explain away EQR and Bell by my premise of rejecting quantum probability as a physical reality - hence the two photons and electrons are identical and measurement differences in the sensors is responsible for subsequent effects.

With all best wishes, Vladimir