Hi Joy,

I will frame my point about separate occurrences of S3 and S7 in terms of the classic EPR scenario of correlated spin states between 2 particles, which without special characters I will denote as e^|e_ for electron spin up e^ and electron spin down e_ .

My point is that this is just quantum mechanics, think quantum field theory. Just as the emission of a photon converts e^ to e_ the emission of a W-boson converts an electron into an neutrino, an up quark into a down quark etc. and there are also inter-family conversion reactions. Such interactions mean that the most general EPR 2 particle scenario in QFT is *not* of the form A^|A_ but A^|B_ where particles A and B can be of any type; A=B is just a special case in QFT.

The observables to consider in the correlation analysis are both the spin eigenvalues of the rotation group SU(2) - group space S3 - and the particle types which are eigenvalues of some 'particle space'. I use this term in place of particle symmetry group, because grand unified theories assumed that it was going to be a group - a hidden assumption I could have raised in my essay - whereas my work says that it is the quotient group SU(4)/SU(3) isomorphic to S7. So there are 2 sets of observables with quantum correlations {^,_} and {A,B,...} where the values of the first set are the eigenvalues of the rotation group with space S3. In my case the second set contains eigenvalues of SU(4)/SU(3) ~ S7 (after the symmetry has been broken) and the S3 is clearly distinct from this S7.

Your analysis should also apply to the quantum correlations between the observables in each of the 2 sets {^,_} and {A,B,...} for the most general EPR 2 particle scenario A^|B_ in the Standard Model QFT. Ultimately my question is whether there is a way to use your analysis in reverse to place a constraint on the origin of these observables?

I.e. some argument of the form

Parallelised S3 => group space S3 for the observables {^, _}

Parallelised S7 => 'group space' S7 for the observables {A,B,...}

A straightforward argument doesn't seem to work, which is why I am asking :-)

Michael

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  • Post #39

Hi Michael,

You have framed your question very clearly. It reminds me of some passionate discussions I had last year on these pages with Ray B. Munroe, who is sadly no longer with us. He was a supporter of my use of 7-sphere, but he also saw things from the particle physics perspective and I had to explain my foundational perspective to him from scratch. Please allow me to do the same here, if not for you, at least for other readers who might to be interested.

The issue at heart is local causality. This concept has been crystallized by various people over the years, starting with Einstein in his special relativity, and culminating in Bell's analysis of the EPR scenario. Bell used some earlier ideas of von Neumann to frame the concept for any realistic theory, and made it independent of any specific theory of physics, including quantum theory or quantum field theory, and independent even of the specifics of special and general relativities. He thus provided a very general, very reasonable classical, local-realistic framework, which does not depend on the specifics of a given set of observables. It depends only on the yes/no questions the experimentalists may ask and answer. Thus, for example, for the classic EPR-Bohm scenario involving a joint observable AB for observing spin up and spin down at two remote ends of the experiment, he formulated local causality in terms of the following factorizability condition:

AB(a, b, L) = A(a, L) x B(b, L),

where A(a, L) is independent of the remote context b as well as the remote result B, and likewise B(b, L) is independent of the remote context a as well as the remote result A. That is it. As you can see, his formulation of local causality only involves the measurement results A = yes/no and B = yes/no, apart from the measurement contexts a and b (such as the directions of the local polarizers), and the common cause L, which is the "hidden" variable or a complete EPR state.

It should now be clear why the kind of details you have spelt out for more general scenarios involving particle productions etc are irrelevant for the central concerns of local causality. All that matters is how the yes/no answers to relevant questions are correlated, because any experiment in physics can always be reduced to a series of questions that can be answered in a "yes" or "no."

Nevertheless, let us look at things from your perspective. Let us consider a scenario where an EPR 2-particle state is not of the form P^|P_ (in a variant of your notation) but of the form P^|Q _, where Q =/= P. For you, then, there are two sets of observables with quantum correlations, {^,_} and {P,Q,...}, where the first set contains eigenvalues of the rotation group S3, and the second set contains eigenvalues of SU(4)/SU(3) ~ S7. The question then is: Is Bell's local-realistic analysis applicable to this situation? Yes, absolutely. Is my topological correction to Bell's analysis applicable to this situation? Again, yes, absolutely.

But here is a difficulty for you: Your set {^, _} is restricted to S3. It is, however, not possible in general to reproduce quantum correlations using my framework within S3 if the corresponding quantum systems have the spectrum of eigenvalues (or measurement results) more general than that of a 2-level system. So, ironically, there is no problem for the exotic set {P,Q,...}, for which the "group space" within your framework is S7, which is the most general available within my framework. It is the set {^, _} that will cause a locality problem for you, because, for a general quantum field, the spectrum of eigenvalues within {^, _} would be highly nontrivial. Within my framework, on the other hand, both {P,Q,...} and {^, _} fall under the same "group space" S7, and so there is no problem.

So my framework does put the following constraint on the observables: If one restricts to the group space S3, then the only quantum systems for which local causality can be maintained are the 2-level systems. For more general systems S7 is inevitable.

Best,

Joy

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  • Post #41

Dear Michael James Goodband,

I see a wide gap between you, Joy Christan, Thomas Ray, Lawrence Crowell and others on one hand and likewise qualified experts like Alain Kadin who do not restrict to a mathematical approach on the other hand. Edwin Eugene Klingman seem to be almost the only one who is anchored in both areas.

May I hope for your readiness to seriously deal with and even eventually accept interdisciplinary arguments and for your efforts to present your most important arguments as easily understandable as possible to those who are laymen in your branch of modern mathematics?

While I dislike the concept of transfinite cardinality, I agree on that the rational numbers are as countable as are the natural ones. They are said to have the same cardinality aleph_0. So it's amazing to me that the difference between them is as important as you are claiming.

You wrote: "the particle/anti-particle space being S^0={-1,1} and the space of cyclic waves being S^1". Did you discuss this with Kadin and Klingman?

I anticipate that you feel hurt by many statements in my essay. May I ask you for on open discussion before prejudice. My position roughly corresponds to that by Detlef D. Spalt who only published in German with one exception (La Continu de l'Analyse Classique dans la Perspective du Résultatisme et du Genésiologisme) and is perhaps unknown to you.

Regards,

Eckard

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  • Post #42

" ... the particle/anti-particle space being S^0={-1,1} and the space of cyclic waves being S^1". Did you discuss this with Kadin and Klingman?"

Eckard, that's a very straightforward statement. The 1-dimension S^0 (which Bell-Aspect take as the measure space {-1, 1} or {- oo, oo} ) does not have enough degrees of freedom to accommodate the wave function. Joy recognized the contradiction here, because quantum mechanics cannot survive without a wave function -- and so assigns the function a probabilistic interpretation in the Hilbert space, dragging the notion of nonlocality along. No matter how many ways one slices it, the standard intepretation of quantum mechanics is not coherent without nonlocality.

By changing to a topological framework, nonlocality is obviated.

Tom

Thanks Tom. I'm still having problems with Amazon not displaying the correct stock and shipping settings. Just in case it takes a while, I'm setting up the option of making Agent Physics available from my website http://www.mjgoodband.co.uk at the same shipping rates as Amazon. This may take a day or two (will update). In the meantime there's more about Agent Physics on http://www.agentphysics.org

I think your comments pointing out that Christian's framework "breaks down the distinction between local and global ... in an extended universal domain unrestricted by classical mechanics" points at the core of the issue. In conceptual terms, I see Joy's analysis in terms of initial and final conditions about observations and what correlations there can be between them. However, one of the consequences of transcending classical mechanics is that there is inevitably no discussion of dynamics, and so there is no discussion of *how* these conditions are met. I note that terms like 'entanglement' are implicitly about dynamics.

The point about Gödel's incompleteness theorem is strictly in his original context, where the local-global structure issue appears to arise in terms of discrete and continuous valued arithmetic systems. The collection of statements expressed within some system of integer arithmetic could be viewed as a linked network of nodes spread out in a space, where the links are steps of logical deduction. In conceptual terms, Gödel proved that the discrete character of integer arithmetic is such that there can exist closed loops of nodes in this network which are stated in the same terms as the axioms of the mathematical system, but cannot be reached from the axioms. However, Gödel's proof is explicitly dependent upon the discrete character of numbers *and* number-theoretic functions over the integers. Switch from discrete integers to the continuous reals and Gödel's incompleteness proof no longer holds in this context, almost certainly because of the far richer structure of functions over the reals. This could be viewed in terms of the 'global' structure of functions over the reals being richer than the 'local' structure of functions over the integers, such that the 'global' case doesn't suffer the incompleteness of the 'local'. Conceptually this is because it can fill in the gaps between the discrete nodes of the network in the integer case. This switch from discrete terms counting the numbers of objects in classical physics to continuous real-number description of the same objects in a scientific theory in order to escape the 'local' restriction of Gödel's incompleteness is a far more generic point in science that applies beyond particle physics, as is discussed in http://www.mjgoodband.co.uk/papers/Godel-science-theory.pdf (http://vixra.org/abs/1208.0010).

In general conceptual terms, I see Joy's functional analysis showing that 'global' functional structure can account for observable correlations in a way that 'local' functional structure cannot. But this still leaves the question, where's the physics? By this we generally mean the dynamics, which means locally tracking the causation as we do in classical mechanics. I show that the above switch from discrete terms to continuous terms gives all the features of Quantum Theory. However, a consequence of this switch appears to be that the underlying 'global' functional structure appears as non-local identity in the dynamics of the quantum field terms (wave-function). The descriptive issues of QT appear to arise in resolving the underlying 'global' functional structure back to the 'local' terms of strictly countable discrete particles.

The philosophical point is that realism in terms of observational predictions is retained, but at the expense of the descriptive realism of the dynamics being compromised.

Best,

Michael

Hi Joy,

Thanks. I was getting the impression that the functional spaces of your analysis wasn't going to match up with the group spaces and particle symmetry spaces of particle physics. Although such a functional analysis appears non-contextual, the particle physics perspective spots that local causation over observables has the context of special relativity (SR). This brings with it features that look like they should be more than just coincidence, as the spinor representation of the Poincare group of SR is SU(2)*SU(2) where the group space of SU(2) is S3, and the spin eigenvalues form an S0 space. This structure is linked to local causation of fermionic objects in SR, and so forms the particle physics context for the analysis of correlations between observables. From the particle physics side, it is very hard to get past the idea that this isn't of significance - even if it really is irrelevant!

Best,

Michael

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  • Post #45

Dang it -- I messed up cutting and pasting. I will repost correctly here, and hope I can get the last version deleted. Sorry.

Michael,

I am so grateful -- as I expect Joy is as well -- to be able to have meaningful dialogue on the real issues. For so long, and for Joy many years longer than I, we've been forced to respond to straw man arguments. Very debilitating and demoralizing.

One of those persistent straw men describes Joy's model as algebraic (though one has to be innocent of what "geometric algebra" really means, to think that way), when of course a topological framework can't be other than analytical. The detractor then proceeds to identify a nonexistent "algebraic error" and dismiss the whole argument.

Anyway:

I think it fruitful to approach the subject the way you're doing, because the issues do go deep into FOM as well as physics -- and actually, as you imply, have to do so -- in order to reconcile local discrete measures with globally continuous functions.

Key to the structure is orientability, that only a topological model can supply. I really only became aware of this about a year ago -- when I read a 30 year old unpublished paper by the eminent computer scientist Leslie Lamport titled "Buridan's Principle." His analysis of the Stern-Gerlach apparatus convinced me that the principle ("A discrete decision based upon an input having a continuous range of values cannot be made within a bounded length of time") really does generalize, as a physical law, to all measurement functions continuous from an initial condition. I suggested to him that the paper really needed to be published, and fortunately, the medium I suggested -- Foundations of Physics -- accepted and published it in the April 2012 issue.

I've filled 3 notebooks with arguments and equations in the last year and half, and I'm itching to get it into publishable form -- back in 2 March I wrote " ... the continuous range of measurement results are recorded -- not on unit S^0 as Bell assumed by the functions A(a,l) = 1 or - 1, but on S^1, a unit 2-sphere. As Joy Christian explains, 'After all, no one has ever observed a 'click' in an experiment other than about some experimental direction a. With this simple change in the function A now takes on values in a topological 2-sphere, not the real line, thereby correctly representing the EPR elements of reality. The values of the spin components are still 1 or - 1, but they now reside on the surface of a unit ball.'" Orientability matters. It matters, though, over the whole range of parallelizable spheres, which are simply connected and therefore accommodate the flatness condition.

Like you, I have tended to translate Joy's research into my own familiar terms of complex analysis, information theory and number theory. I have tried not to do that, though without complete success. In any case, we bump up against your conclusion: "The philosophical point is that realism in terms of observational predictions is retained, but at the expense of the descriptive realism of the dynamics being compromised." And that is why, as I think you'll see is obvious, that I apply the criterion of Godel completeness rather than the incompleteness theorem. It meets Popper falsifiability, in the context of Tarski correspondence theory of truth, and it satisfies metaphysical realism. In other words, we recover the dynamics in a continuous function model of argument and value -- I characterize Joy's correlation result, E(a,b) = - a.b as the input argument to a continuous range of values, which generalize Buridan's Principle to the topological limit.

I hope you get a chance to visit my essay site, where some of these same issues are discussed in a different way.

All best,

Tom

(P.S. I trust that you got my email reply with my mailing address. Looking forward to reading your book!)

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  • Post #46

Fixing the link (hopefully):

Leslie Lamport

http://research.microsoft.com/enus/um/people/lamport/pubs/pubs.html#buridan

Hi Michael,

If I understand your comments correctly, here is what I think is your worry:

What I have dealt with in my work is the issue of no-signalling non-locality of the orthodox quantum theory. I have used Bell's local-realistic framework which carefully separates this type of non-locality out from a possible signalling non-locality that would actually violate special-relativistic causality (as is well known, no-signalling non-locality does not). My analysis deals with both types of non-localities in a clear-cut manner, at least at a formal level. However, since I am using functional spaces like S3 and S7 in the context that is unusual from the particle physics perspective, it is unclear whether this would not lead to some signalling-type causality violations when my framework is eventually turned into a proper theory.

This is a justified concern. Eventually my framework will have to be properly relativized, or at least made compatible with some representation of the Poincare group. Fortunately there exists a mathematical framework for doing this. It is an extension of the algebra I have used in my work, known as the Spacetime Algebra. At the moment, however, relativizing my framework is not my primary concern. All I can say at the moment is that I think it can be done. We shall see.

Best,

Joy

Hi Michael,

You have raised a key question: "...where's the physics? By this we generally mean the dynamics, which means locally tracking the causation as we do in classical mechanics."

You have correctly recognized that my framework is entirely kinematical as it stands. A fully local-realistic theory based on it would inevitably have to postulate dynamics, and this dynamics must match with that of quantum theory (if not quantum gravity). My latest mini-grant from FQXi is precisely for investigating this issue of dynamics. I have some preliminary ideas about this, but I am not yet ready to discuss them in public.

Best,

Joy

Hi Joy and Tom,

I too am grateful to you for engaging in meaningful discussion. I was previously unaware of Joy's work (and Buridan's principle ) and your comments have advanced my thinking to the point where I am certain that the key issue really is a mathematics description problem in trying "to reconcile local discrete measures with globally continuous functions".

In the spirit of the essay contest of questioning assumptions, I realised I have been making an assumption about Joy's work. This is partly because the initial point of comparison was the dependence on the 4 spheres S0, S1, S3, S7. In my case, these are physical spaces in a classical metric field theory where the Relativity meta-principle - make no preference - selects them all, and the unification principle gives only one possible unification which yields these spaces (STUFT). The fact that the dimensionally reduced version of this KKT derives the Standard Model Lagrangian with the correct electroweak vacuum (and Weinberg angle) and spectrum of 12 fermionic particle-like objects in classical physics is a nice feature (and the coupling constants, including the Higgs scalar coupling which predicted the classical Higgs boson mass to be 123GeV). Then comes the *real issue*, what is Quantum Theory all about?

I think this is the real point of comparison of my work (primarily in Agent Physics but also as presented in Science Theories) with Joy's, where the QT context for Bell's analysis has distracted me from Joy's functional analysis of hidden variable theories being more general than *just* QT. Bell's analysis started from the existence of QT and asked whether there exist a hidden variable theory that can account for the same correlations between observables as QT. However, a functional analysis whose only conditions are local causation and correlations between observables can surely be applied to any assumption of a hidden variable theory in science (ie. without the pre-condition that is replacing QT)?

The reason for considering this possibility is that my physics-based analysis of numerous physical systems identifies a recurring feature of a self-consistent (causally closed) dynamic state residing on the giant connected component of some physical network. Any physically-real theory of these systems can be proven to be incomplete because of the discrete character of the dynamics of the network - this specifically includes the classical physics of particles, as in my essay. It seems to only make sense for the possible undecidable proposition in the physically-real theory to describe a collective property of the dynamic state residing on the giant connected component. This can potentially give a description problem in physically-real terms, because the inputs to the network cause discrete changes to propagate through the giant network component, with its undecidable feature, to the outputs. Encountering a network state with undecidable properties would surely have some effect on the outputs, such as altering the correlations between the outputs observed?

Joy's functional analysis of correlations between observables in a non-relativistic context would seem to be wholly appropriate to this situation. The combination of my work and Joy's functional analysis leads me to the proposition: the presence of the undecidable property on the core network component causes correlations between the network outputs that cannot be accounted for in a discrete theory in physically-real terms. Assuming that the correlations can be accounted for if only we knew some extra missing terms constitutes an assumption of a hidden variable theory. The follow on from the above proposition is that the richer functional structure of continuous functions can account for the correlations in output, where such terms do not directly correspond to the inherently discrete physical components of the network system and so are non-physically-real terms (like the wave-function of QT).

Extending the functional analysis to this scenario could potentially provide a mathematical proof (or disproof) of my proposition that the presence of an undecidable feature on a discrete network system is the *cause* of the correlations that cannot be accounted for by a discrete hidden variable theory. I show that the required network conditions can occur in biology, psychology and economics ... with the prediction following on from this proposition that there will exist correlations between observables in these system which cannot be accounted for by a physically-real scientific theory. These disciplines implicitly make the assumption that there will exist a hidden variable theory that will account for all experimental observations. It seems to me that Joy's work provides the basis for the construction of experimental tests of these assumptions throughout science.

Best

Michael

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  • Post #50

Dear Michael:

The conclusion of your paper that QM is not a fundamental theory is vindicated in my paper - " From Absurd to Elegant Universe". My paper also provides evidence to what is fundamental universal reality and how to explain the inner workings of quantum mechanics (including wave-particle duality) and resolve its paradoxes.

I would greatly appreciate your comments on my paper.

Best of Luck & Regards

Avtar Singh

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  • Post #51

CORRECTION - Reposting the above under my name:

Dear Michael:

The conclusion of your paper that QM is not a fundamental theory is vindicated in my paper - " From Absurd to Elegant Universe". My paper also provides evidence to what is fundamental universal reality and how to explain the inner workings of quantum mechanics (including wave-particle duality) and resolve its paradoxes.

I would greatly appreciate your comments on my paper.

Best of Luck & Regards

Avtar Singh

    their heart is not even sincere and pure.

    this world does not turn correctly just due to these persons of bad.In fact we see only with our heart, the essential is invisible for eyes....don't lie about my faith.you do not even imagine my universal faith. I love Jesus Christ ok.

    A real bad band in fact you are .like what , the habit does not make the monk.

    You can lie for several but not for the real universalists understanding the sciences and its determinism, pure and simple.

    you do not imrpove and your mathematical language is weak !

    The team is knew since the begining. ahahah until soon at New york or pay people to kill me.

    5 days later

    Hello Michael,

    I greatly enjoyed reading your essay, and I find myself almost completely in agreement with your thesis. Well done! Edwin Eugene had made a recommendation a while back, but then when I read your comments on Vladimir's essay page, I knew I had to find time to read your essay immediately.

    You have put some of the pieces together nicely. I like your STUFT theory rather well. And it further explains some of what I found interesting and intriguing in Joy Christian's work.

    Like Tom Ray, I've got notebooks full of ideas after finding inspiration there. I like your response to Tom's comments, regarding global and local functional structure, though, and your comments to Joy above resonate with me also. I guess it is a matter of perspective or emphasis, in some measure, depending on what you are trying to show.

    I have much to learn, but I expect I'll find some interesting insights in the comments on this page. I've had an interest in related topics for some time, and you will find mention thereof in my essay "Cherished Assumptions and the Progress of Physics."

    But for now, I must sleep.

    all the best,

    Jonathan

    Hello again Michael,

    I have given considerable thought to what is implied by living inside a 3-sphere, what is seen by folks who reside inside a set of 'compact' dimensions, and so on. We might not notice. Size is relative, not absolute, and interiority/exteriority may be too, if we entertain higher order dimensions where geometry may be non-commutative or even non-associative.

    That was part of what I was getting at, in my essay, when I was talking about the universe being inside out of the way we perceive it. We think we are pointing to an edge, or a spot on the universe's periphery, and yet we point at the center.

    However; when we think we are pointing directly at the center of the planet, we are only getting the Schwarzschild radius away. This I see as related to the interlocking keyring example used to depict Hopf fibrations of S3. The actual center of the Earth is behind the event horizon, induced by the parallelization of the fiber bundle, it would seem.

    My guess is the reason we don't 'see' space as octonionic, but appear to be inside the quaternionic space of S3 relates to the decoupling of matter and energy - which sets a time and distance scale for the universe, as a whole. More later in another missive.

    Regards,

    Jonathan

      Michael,

      I forgot to mention that is does appear that you have successfully sketched out how Quantum Mechanics could be an emergent theory, rather than fundamental. Since that is the question you ask in your title, I thought I should let you know that it looks like you have indeed proved feasibility for your topological solution, and made significant progress toward a robust formulation.

      Regards,

      Jonathan