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

Dear Joy,

Let me start here a new thread so we can simplify the exchange.

I re-read the papers you suggested. I also revisites your FQXi talk. I think that the key sentences are as follows:

1"Such a naive map would therefore necessarily fail to satisfy the completeness criterion of EPR."

2."Every element of the physical reality must

have a counterpart in the physical theory. (EPR)"

3. "in each case we began by noting that a Hilbert space in general is a topological vector space whose topology is given by a norm. Then, by using the normalization condition on its elements we recognized--say, for the two-level system--that the corresponding Hilbert space has the topology of a 3-sphere."

So I do get your points. Fully. But I don't think you get my argument. Let's do a little game and apply your program on a toy example. Let's apply statement 2 on classical mechanics, and let's say on phase space. Then analyze its topology. Here you cannot claim you get local realism because the symplectic space defines only volumes and there are no local invariants possible. Local realism means somerthing more. And let's forget Grangier and address my criticism instead. The disagreement is not on your math results, or on your method, or on your usage of geometric algebra. The disagreement is on the interpretation of your results. Specifically on what you call local realism. The gimbal lock argument shows that in the original example you are indeed justified to call it local realism. But I do not believe this justification works in general. Granted, I did not give you an example from QM, but I feel that something along the same lines can happen there as well. So if demanding that every element of the physical reality must

have a counterpart in the physical theory (agreed) and analysing correctly the topology as you are doing (agreed again), do you *always* get local realism? Here I say no. And the answer depends on what do you mean by local realism. For me local realism is fundamentally tied with spacetime. As spacetime cannot be always linked with state spaces, local realism is doomed by QM in general.

You say: "The dismissal a la Grangier of my work is thus fundamentally invalid, because it surreptitiously brings us back to the flawed first equation of Bell." That is correct on the part of "because it surreptitiously brings us back to the flawed first equation of Bell". So let's not make it so surreptitiously and let's bring it back front and center.

Indeed, the core disagreement comes back to the topological arguments. If realism is tied with spacetime, than you are forced to discuss only the final outcome of experiments, or the topology {-1, +1}. If realism is tied with the notion of a complete theory, than your full topology argument is valid. For the singlet state, because of su(2)~so(3) we are in a degenerate case: the two distinct interpretations are actually compatible.

On the completeness of QM, based on the EPR analasys I agree with Aerts and Einstein, QM is incomplete (here I am too in the minority view). But local realists are wrong, and Bell's theorem is valid in killing their case BECAUSE THEY ALSO SHARE THE SAME TOPOLOGICAL FLAW THAT YOU DISCOVERED. Therefore while killing Bell's faulty assumption, you did not killed its importance and Bell's result remains very relevant.

What I do not find justified in your analasys is the implicit extention of realism definition based on completness of the theory instead of spacetime and the experimental outcomes. To me, EPR's logic was not that impecable, and I can debate this point more if you like.

Granted, you may call completness of the theory realism, but this is not everyone else thinks realism is, or what I think it should be.

Dear Joy, I started a new thread for simplifying the exchange. Please se my answer below. Thanks, FLorin

I am waiting an answer, but apparently it's not possible.Transparence my friend.ahahah 4 spheres classical and 7 and after how many ahahah learn the 3d polarity please hhihii the arrogance and the humility are so humans.

On that regards

SPHERICALLY YOURS

Steve THE THEORY OF SPHERIZATION A GUT TOE OF SPINNING(ROTATING)SPHERES,a beautiful gauge no hihiih QUANTUM SPHERES....COSMOLOGICAL SPHERES....UNIVERSAL SPHERE.

oh yes still one thing EUREKA with humility and arrogance.

ps2 you speak a lot dear friends but where are your real innovations, answer nowhere simply....

Best Regards

Steve

God(creates and improves a sphere, yes my friend) bless you ....sincerelly.

GOD BLESS YOU .

Steve

Dear Florin,

To tie local realism with spacetime is to make a serious category error. We do not know the true nature of spacetime. We do not know what is happening at the Planck scale. We do not even know the correct dimensionality of spacetime. I am not a big fan of string theory, but it has taught us some lessons about the dimensionality of spacetime that cannot be unlearned. At any rate, none of the masters---Einstein, EPR, von Neumann, or Bell---made such a category error. The reality criterion of EPR, for example, is quite minimalist: "If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity." There is no commitment here, of any kind, to spacetime. Bell is even more careful. His locality condition depends only on the idea of factorizability of his beables. Again, no commitment to spacetime. And von Neumann's masterful systematization of the hidden variables program too is extremely minimalist. He recognized that no matter which model of physics one is concerned with--the quantum mechanical model, the hidden variables model, or any other--for theoretical purposes all one needs to consider are the expectation values of the observables measured in various states of the physical system. Thus all of the pioneering masters---Einstein, EPR, von Neumann, and Bell---are very careful to avoid any excessive commitment to a contingent notion like "spacetime." And in my work I follow the works of these masters. But you want to tie local realism to spacetime, and that is surely a grave mistake.

So what I call local realism is not some ad hoc idea. It is what is defined by these masters, and it is what I learned from Shimony and Bell as a young student (yes, I have been very privileged in that respect---and, by the way, Bell was one of the least dogmatic physicists I have ever met). To be sure, there is nothing wrong with having some intuitive ideas about spacetime when we are in our workingman's clothes. But one shouldn't forget the lessons of the masters when the most general idea of local realism is being discussed---for not everything they have said is wrong. Thus my entire program is based on von Neumann's and Bell's systematizations of local realism. This amounts to reproducing every quantum mechanically predicted expectation value in a dispersion-free manner. Since expectation values are independent of the spacetime structure, spacetime does not constrain the von Neumann-Bell program in any way, and yet it is capable of accommodating any notion of spacetime required by the future theory of physics (i.e., the future "quantum gravity").

There is another conceptual flaw in your whole outlook. I think your thinking is derived from your mistaken perception that my framework is somehow a reformulation of quantum mechanics. That this cannot be the case can be seen easily. We know that QM cannot be interpreted as a complete, local, and realistic theory (we know this since EPR). One of the three must be sacrificed in any interpretation, baring many worlds. But my framework is complete, local, and realistic, and since everything is definite in this framework there is not even an option for any many world interpretation. So my framework cannot possibly be a mere reformulation of QM. Now I think some of your views of my work are due to the confusion about this issue that you have inherited from Grangier. This is also related to your comments about my use of division algebras (from your other post today). You are still thinking in terms of reformulating QM using a division or non-division algebra. But I am concerned about local realism, and hence about preserving local causality, and yet reproducing strong, quantum correlations within my local realistic framework (which is derived from the von Neumann-Bell program). And for this, division algebras are not only inevitable, but very natural. One does not need Dixon's book to realize that without parallelizability and a divisor the points of a sphere cannot be closed under multiplication, and without the latter there is no infinite factorizability of every conceivable point of a sphere, and without factorizability there is no local causality (even a single non-local point would kill local causality---that is why so many claims of local-realistic models are invalid). I have discussed this in greater detail in my latest paper. A casual thinking about these issues will not do. A deep reflection on this matter, and a deep appreciation of the well known topological theorems, is essential.

I hope these comments makes it clear why I am doing what I am doing, and why I think you are wrong about some of your assertions. To be sure, I see value in your investigations too, but not within my program.

I discuss with one of your friend The Dr Santuary,apparently he makes a pub for a 2d anyon on linkedin aps.What is this anyon? A CIRCLE hihihh thus you begin with a 1 d after a 2 d and hop an other there ahaahaha interesting.Ironic but interesting.

It could be well if they were here with you.because Han Geurdes is there also.We are going to laugh in live.

well tried.

Sicerelly

Steve

Perhaps, since this whole thing started with Einstein, it is appropriate to see what he says about spacetime. Peter Jackson quotes Einstein as saying in 1952 that:

"The concept of space as something existing objectively and independent of things belongs to pre-scientific thought, but not so the idea of the existence of an infinite number of spaces in motion relative to each other."

Jackson claims:

"We view Cartesian coordinates as a 'frame', and refer to inertial frame, yet Einstein referred to a body, or coordinate system rigidly connected to a body."

Local gravito-magnetic or C-fields take the form of induced circulation 'rigidly connected to a body' with momentum. The connection is the '=' sign connecting the C-field circulation to momentum: del cross C = p.

Momentum also allows us to treat entities that have zero rest mass, such as photons. Two such entities forming 'discrete fields' each centered on matter in relative motion are shown in the figure on page 6 of my essay.

I believe that this is in support of Joy Christian's points on space-time and I believe it supports local realism.

I also wish to convey to Joy and Florin my appreciation for their exchanges. I'm sure I speak for all of us.

Edwin Eugene Klingman

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 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