Hi Michael,

Thanks again for your comments on my thread. They definitely helped my 2nd reading of your essay.

Like Joy I had noted your mention of S0, S1, S3, and S7 as the only normed division algebras, a point that Joy has repeatedly remarked on. This time I was particularly fascinated by your view of black holes as Kaluza-Klein 'particles' with empty S2 interior and 'real physical surface' as event horizon, and no singularity.

You indicate also that you derive values close to the Standard Model "despite being derived solely within classical physics." I plan to look at that reference. In the first page or so you remark there is no means in classical mechanics for a single particle to travel as a wave. Of course my model is based on the particle always traveling 'with' a wave. It is this linked state that you seem to view as a causal linkage leading to Bell-type non-locality issues. With inherently unknowable phase the abstraction 'causal' may be stronger than is actually the case, as there is also a self-interacting aspect of the C-field that may or may not allow physically real solutions to be derivable. In other words I am uncertain, according to your definition, whether to consider my wave property of the particle 'derivable' or not. [By the way, I tried to get your book Agent Physics on Amazon, with no success. Any ideas?]

Another point I did not fully appreciate the first time I read your essay is this: "Conservation laws applying to charges of particles mean that no real-number valued variables could be the cause of changes in particles numbers [with implications for incompleteness proof]." And this time through I did like your conserved charge as a limit to black hole self-immolation.

The following section on Non-physically-real terms is a tough nut to crack. I read and understood the words, but it doesn't jell. Partly because I believe particles derive from physical processes, not symmetry. Perhaps I'll understand this better after reading your reference [15]. I do agree with you about physics unification without quantum mechanics being fundamental.

In studying your 'twist' in S7, it does not sound the same as Joy's torsional twist. Is it? I did not interpret your change in metric in the ergo-region to be equivalent to Joy's change in handedness, but do you believe your solution is isomorphic to his?

I hope to have a few new questions after another reading or so.

Best,

Edwin Eugene Klingman

    Michael,

    Nine pages is just not enough! I doubt that anyone can understand your essay with one or two readings. I would advise anyone who wishes to better understand what you are doing to read your reference [15].

    Edwin Eugene Klingman

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    • Post #14

    Hi Joy,

    Fascinating paper! It looks very much like you've got the other side of the story I have presented in the context of extended GR.

    In my Agent Physics book - and in the review paper of the chapter presenting the theory http://www.mjgoodband.co.uk/papers/STUFT.pdf - I proposed the following meta-principle:

    Physical causation will only be consistent and complete if it realises all the manifolds S0, S1, S3 and S7.

    I assume that this applies to a real physical manifold - as in a real fabric of reality like the fabric concept of space-time - which when read off directly in the context of extended GR specifies a closed S3 universe with particle dimensions S7. Such a universe is necessarily cyclical S1 and to obtain the manifold S0 as physical objects requires topological monopoles - hence the given pattern S10 -> S3*S7 with the formation of a physical twist in the fabric of space which breaks the S7 symmetry in a suitable way. This gives monopoles and anti-monopoles - giving a realisation of S0 - which must be in a representation of the rotation group - with group manifold S3 - and particle symmetry representation of the manifold S7. The S1 representation would come from the monopoles having a wave property, which I have to add from observation as my derivation of QFT is based on the wave property being non-derivable.

    Unless I'm much mistaken, it looks as though your work could be stated as the meta-principle:

    Physically-real representation of reality (in the sense of ERP) will only be consistent and complete if it involves all the manifolds S0, S1, S3 and S7.

    Would this be correct? Such a condition on mathematical representation would be the other side to the equivalent condition being applied to a real physical fabric of reality. However, the consequence of this restriction is that the symmetry breaking required to give topological monopoles must be of the form:

    S7 = SU(4)/SU(3) -> (Spin(3) * SU(2) * U(1))/Z3

    Which would imply that the local colour group HAS to be SO(3) and not SU(3). Once the significance of the manifolds S0, S1, S3 and S7 is recognised there doesn't seem to be a way of avoiding this conclusion. Does this seem correct to you?

    Michael

    Hi Michael,

    You wrote: "Fascinating paper! It looks very much like you've got the other side of the story I have presented in the context of extended GR."

    Yes, it does seem like our two respective approaches are flip sides of the same coin. I have arrived at the parallelized spheres via an analysis of EPR and Bell, whereas you have arrived at them (it seems) more from the particle physics side. But the conclusion seems inevitable:

    "Physical causation will only be consistent and complete if it realises all the manifolds S0, S1, S3 and S7."

    By the way, we are not the only ones who have recognized the significance of these manifolds for fundamental physics. Geoffrey Dixon, Rick Lockyer, and Michael Atiyah (to name just a few) also seem to share our conviction.

    I also agree with your proposed meta-principle for my work, although I would use a slightly different language:

    "Locally causal representation of reality (in the senses of EPR and Bell) can only be consistent and complete (in the sense of Einstein and EPR) if it is based on a parallelized 7-sphere, S^7, which contains S^3, S^1, and S^0 as nested submanifolds, in the manner of Hopf."

    This is more mouthful than what you have suggested, but it describes what I am proposing more accurately.

    I am not sure how to answer your other question:

    "However, the consequence of this restriction is that the symmetry breaking required to give topological monopoles must be of the form:

    S7 = SU(4)/SU(3) -> (Spin(3) * SU(2) * U(1))/Z3

    Which would imply that the local colour group HAS to be SO(3) and not SU(3). Once the significance of the manifolds S0, S1, S3 and S7 is recognised there doesn't seem to be a way of avoiding this conclusion. Does this seem correct to you?"

    I am not sure about this, mainly because I am not a particle physicist. What I am 100% sure about is the significance of the manifolds S^0, S^1, S^3, and S^7. If this implies what you think it implies, then I would put my last penny on it.

    Best,

    Joy

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    • Post #16

    Edwin is probably right. There are two interlinked parts in my essay which are both quite involved, and have been discussed carefully as they suggest a model for physics unification. See

    1) http://vixra.org/abs/1208.0010

    2) [15] http://www.mjgoodband.co.uk/papers/QFT_KK.pdf

    The first part is about the physical conditions under which Gödel's incompleteness theorem can apply to science theories constructed in strictly physically-real terms, and how this is not the end of the story as you can change the mathematical representation - to non-physically-real terms - to escape from Göde's proof. This is discussed in more general terms in a philosophy of science paper that I have posted on http://vixra.org/abs/1208.0010 to make it more available. The issues raised here are those of the relationship between physical reality and mathematical representation - as also discussed by Roger Schlafly and mentioned by others e.g. Dan Bruiger - especially how it can become problematic when a physical system forms a closed cycle of cause and effect. The problem here is specifically with the top-down causation part of the closed cycle, from effect back to cause - George Ellis discusses how we might be under-estimating all such top-down causation in science.

    The second part of my essay is specifically identifying a scenario which realises the conditions needed for Gödel's incompleteness theorem to apply to a particle-like object within classical physics. This is specifically identified in a rotating black hole of the Planck scale, as the rotation drags space-time such that there-exists a region where any radiation in it would be of the form of the virtual-radiation of Quantum Theory. The calculation of the effect this virtual-radiation has in reducing the rest mass of the particle-like black hole is shown to be subject to Gödel's incompleteness theorem. The Planck mass of the object is reduced by the virtual-radiation field around it, but the reduced mass cannot be calculated in classical physics. Heuristic arguments imply that the mass reduction effect can be almost total, giving an almost massless particle-like black hole with a radius of the Planck length and angular momentum of ½ the Planck constant - such an object looks suspiciously like a real particle. I then assume that a non-derivable feature in this theory is that this object possesses a wave property, and use the change in mathematical representation discussed above to show that these objects would then be described by a Quantum Field Theory. Since QFT can be derived by a change in mathematical representation QFT cannot be fundamental; this is expanded upon in detail in [15] http://www.mjgoodband.co.uk/papers/QFT_KK.pdf.

    The final part of the essay then discusses how this all adds up in being able to derive both General Relativity for space-time and a Quantum Field Theory for 12 topological monopoles with the same charges as the 12 fundamental particles, where the Lagrangian has the same mathematical form as that of the Standard Model. The points discussed above with Joy Christian about the spaces S0, S1, S3 and S7 being special, imply that the extended GR model of the essay - S10 unified field theory - is uniquely characterised for the assumption that the fabric of space is a real physical surface. The theory has 2 potential conflicts: it says that the local colour group HAS to be SO(3), not SU(3); and the universe HAS to closed (S3). If these are true, and the mathematical representation change is the origin of Quantum Theory that it appears to be, then S10 unified field theory would seem to be viable a candidate for physics unification.

    Michael James Goodband

    Michael,

    It's a breath of fresh air to see some serious understanding of modern topology, when these forums have been full of serious misunderstandings the last couple of years. Where were you when we needed you? :-)

    Also, I for one very much appreciate your organization -- building from classical black hole relativity to quantum theory. Nice.

    I don't think Joy Christian's mathematically complete framework has the problem of demanding a closed universe; parallelization of S^1, S^3, S^7 gives us a flat space to work in, so that conformal mapping guarantees angle preservation to infinity even in a curved space, and simple connectedness does the rest. I.e., because all real functions are continuous, and because the octonionic space of S^7 allows the geometric algebra to return all real values, the set of complete measurement results on S^3 constitutes a closed logical judgment on all the local physics, even in an open universe. (There's some peripheral discussion of this issue in my essay "The perfect first question," that I hope you get a chance to visit.) I'm not familiar with the term "particle space" that you apply to S^7; however, it seems to fit with my informal characterization of Christian's S^7 structure as "physical space" in concert with S^3 as "measure space."

    Really, you've done a crackerjack job. Thanks for sharing and best wishes in the competition.

    Tom

    Michael,

    For me the significance, or rather the inevitability of the manifolds S^0, S^1, S^3, and S^7 is necessitated by a rather innocent looking algebraic identity (cf. equation 1.53 of the attached paper). I am sure you are more than acquainted with this identity, but for a summary of my perspective on the matter please have a look at sections 1.4 and 1.5 of the attached paper.

    Best,

    JoyAttachment #1: 9_Origins.pdf

    Edwin

    I am glad that my comments were helpful.

    On the issue of a black hole being a hollow S2 in my Kaluza-Klein theory, Johann Weiser presents results of numerical calculations in GR with a relativistic ideal gas model, which shows the metric of a black hole as being a hollow mass shell. The particles of the Weiser solutions all reside just outside the event horizon radius, the inside is hollow and there is no physical singularity at the centre. In section 3 of ref [15] http://www.mjgoodband.co.uk/papers/QFT_KK.pdf. I also give a simple thermodynamic analysis which yields the temperature and entropy expressions for a black hole, but without using the Quantum Theory of Hawking radiation.

    My usage of the word 'twist' refers to a physical twist in the higher dimensional torus S3*S7 with 'outer circle' S3 of the spatial universe and 'inner circle' S7 of compactified dimensions associated with particle symmetries in KKT. In visual terms, imagine a ball of dough and poke a hole through it to get a doughnut or the torus S1*S1. This is the analogy of imagining the universe as a closed surface and then registering that the operative word in wormhole is 'hole' - a hole in a sphere gives a torus whatever the number of dimensions. However, a normal sphere is the odd one out of spheres S^N, as it is possible to poke a hole through all higher dimensional spheres to get a torus with a twist in it. For the doughnut we have to break the loop, twist one end relative to the other and stick it back together again. This is the sort of physical twist I mean, resulting from poking a wormhole through S10 to give the 'torus' S3*S7 with a twist in it - this twist has the properties of the electroweak vacuum, including giving a closed formula for the Weinberg angle (in the technical notes of the essay) which is within the experimental range.

    Joy's torsion refers to the twisted structure of the fibre bundles S3 and S7. Wikipedia has a stab at giving a visualisation of the torsion of the S1 fibre in going around the S2 base-space of S3 on http://en.wikipedia.org/wiki/Hopf_bundle, but I can't say that it helps me much. With my QFT background I tend to visualise the topological monopole ('t Hooft-Polyakov monopole) you get when the S2 base-space and S1 fibre of S3 are in a sense unwrapped. A simple visualisation of this is given by imagining poking cocktail sticks into an orange and then slotting Hula-Hoops onto the sticks - the circle S1 of the Hula-Hoop gives the S1 fibre and the surface of the orange gives the S2. The change in orientation of the cocktail sticks going around the orange gives a sense of the fibre-bundle torsion, but this configuration has the symmetry of the sphere S2 whereas the torsion of the fibre-bundle gives S3.

    Best,

    Michael

    The Agent Physics book is available from UK Amazon, or I can supply it direct via the UK Amazon marketplace. The Amazon stock numbers are not correct; hopefully that will be sorted out soon.

    Given the prior discussion of Joy Christian's work on FQXi I thought it might help to clarify how my S10 unified field theory arrives at the same conclusion: it is all about the Hopf spheres S0, S1, S3 and S7. This might initially look like yet another case of putting mathematics before physics - the cart before the horse - that many of the essay entrants have pointed at as being a problem with physics. However, I arrive at this conclusion from the physics side, where the crux is identifying the form of Quantum Theory as being that due to a change in mathematical representation from natural-number terms denoting particle numbers, to real-number terms denoting particle numbers, in order to escape Gödel's incompleteness theorem where the wave property of a particle is the non-derivable feature in classical physics. This would mean that the matter fields of Quantum Theory are not fundamental and so cannot be just introduced into a unified theory of physics - matter must originate by some other means. This suggests re-considering extensions to GR, but not to forget the physics!

    The metric of GR is conceptually a grid laid out over a surface in order to define distance measurements. An example which grounds the physics is to imagine an inflated party balloon and drawing lines of latitude and longitude on the balloon with a felt tip pen. This grid defines a metric field for the surface which expands and contracts as the balloon inflates and deflates. The Einstein tensor gives how this metric field changes with the volume of the balloon, where the form of the Einstein tensor is based upon the physical assumptions that the space is both homogeneous and isotropic. Add the physical conditions that the space is finite but without a boundary, and spheres are the simplest surfaces meeting these conditions. Now to say that there is no space-time in GR is analogous to imagining that the balloon blinks out of existence leaving the ink of the pen lines hanging in thin air - a mathematical map without its physical territory!

    So we leave the territory where it is, keep the physical conditions specifying spheres, and then remember that Kaluza and Klein successfully unified gravity and electromagnetism by extending the number of dimensions with a closed S1 dimension associated with the U(1) symmetry group of electromagnetism. The condition of space being a closed sphere S^N and the S1 group space of electromagnetism gives the key to particles, as any theory where a symmetric space S^N is broken in some way to give a space containing S1 will give rise to topological monopoles. Such particle-like objects would be of the form of a hole in the space, like an air bubble in water.

    In the same way the U(1) electromagnetic group space S1 corresponds to a compactified dimension in the orginal Kaluza-Klein theory, the S3 group space of the SU(2) isospin group would also correspond to compactified dimensions. There is the apparent problem that the colour group SU(3) doesn't have a simple correspondence to some space, so we will just denote it X for now. If the operative 'hole' of a wormhole is inserted into some sphere S^N it will change the topology to that of a higher dimensional torus S^3*S^M where the form of the closed spatial universe is the sphere S3. The problem is then to solve for S^M to get the particles as topological defects and for the colour space X to be something sensible - the solution is S^7 for which the colour space X = S^3 corresponds to colour group SO(3). As the space of monopoles and anti-monopoles is S^0 = {-1, 1} the Hopf spheres S0, S1, S3 and S7 are all physically realised. So physics arrives at the mathematical condition, it is just then a lot simpler to say it as the meta-principle: it is all about the Hopf spheres!

    The S3 is the physical space of a closed universe and S7 consists of the compactified dimensions of a Kaluza-Klein theory, which I refer to as the particle space as it gives the properties of the topological monopoles as particles. The S^3 closed universe is locally flat R^3 and has S^7 particle dimensions at every point x. However, to get the conditions for particles as topological monopoles, there must exist a non-trivial global map from S7 to the spatial S3 universe. In local terms in R^3, this means that the orientation of S7 changes between two spatial points x1 and x2; in GR this change would be denoted by the metric, whereas in the dimensionally reduced theory it would be called the Higgs field. This physical S^7 space at every point x in the locally flat R^3 space apears to give the point at which to start considering comparisons with Joy's work.

    Michael James Goodband

      Hi Michael,

      Nice summary. As Tom says: Where were you when we needed you? :-)

      The discussion of my work, both here at FQXi and elsewhere, is usually at a very superficial level. Most people seem to get stuck at the most basic EPR correlation, when I want to talk about local causality of any conceivable quantum correlations, no matter what the underling quantum state. This can *only* be done by recognizing the exceptional properties of the parallelized 7-sphere---especially its closed-ness under multiplication, as well as that of its fibres, S^3, S^1, and S^0.

      This is perhaps *the* fundamental conceptual difference between our respective uses of these spheres. While I too arrived at them through physical considerations (by analysing the conceptual arguments of Einstein, EPR, and Bell), what I ended up with are the *parallelized* spheres, which are---so to speak---as flat as a sheet of paper. More precisely, their curvature tensors vanish identically, while torsions within them remaining non-zero. Thus the theory of gravity more appropriate in the context of my work is the teleparallel gravity, not the usual general relativity. It turns out that without parallelization local causality cannot be maintained for all conceivable quantum correlations, or even for the basic EPR correlation. Parallelization is the *only* way to meet Bell's challenge. Unfortunately this fact is not yet widely appreciated, even by some supporters of my work.

      Best,

      Joy

      As the potential skunk at the picnic, and the possibly alluded to deluded 'supporter' and one who is minimally familiar with both of your work, it is not clear to me that a shared appreciation of S0, S1, S3, and S7 doth a marriage make. I too believe that these normed division algebras are important and, with Rick Lockyer's view of Octonions, see them as applying to my own work. Just sayin'.

      Hello Professor Mickael from UK,

      Ok let's play, they need help :)

      Your essay shows us a very good knowledge of several theories, existings.But I see several irrationalities. Why BH particules ? the derivations cannot give us a quantum BH, a BH is a sphere , with a volume, central to galaxies, with rotations. So indeed Godel is right, but his reasoning is subtle, indeed a lot of people confound the theorems of uncompleteness of Godel with the physical axiomatizations. the axiom of truth becomes an essential. Is it important to insert not coherent derivations or superimposings for a kind of confusions.

      My perception is that a lot of persons utilize this uncompleteness of Godel to imply an, ocean of confusions. In fact, the coherences must be formalized with a kind of universal wisdom !!! Is it necessary to imply the confusions when the truth is so evident and simple? it is the question after all.

      The Uncompleteness is simple in its pure meaning.

      until soon and spherically yours of course.

      Hi Edwin,

      My comments were by no means an attack on you (there are supporters of my work outside FQXi and the cyberspace, including within the main-stream Bell community). But, yes, as I have said before, you are among those who have not yet understood my argument.

      I have nothing against your own ideas as long as you acknowledge that your model is manifestly non-local and it can never be local. But you are unlikely to acknowledge this because you are unable to see the blatant non-locality of your model. I thought we had agreed to disagree about this.

      In any case, both Michael's work and mine stand on its own. They neither need to be married, nor stand in conflict. At this stage I am as curious as Michael to witness some of the same broad conclusions emerging from two very different explorations.

      Best,

      Joy

      Hi Joy,

      That was tongue-in-cheek and not to be taken seriously, but I don't think that Michael's approach to normed division algebras bears much relation to yours. I believe that he and I see SO(3) as more appropriate to our theories than SU(3) but his theory and mine are very far apart in other ways. But you are correct, that it is interesting that normed division algebras are becoming significant in this fashion. And I do not think your theories are either married or in conflict. I really don't see much overlap except for the shared appreciation of this topology. My remark was spurred by Tom's "where were you?" with the implication that his use of Sn spheres would have helped your case. Perhaps, but I doubt it. Although there was a period about 18 months ago when you and others were arguing about the definitions of particular topologies when Michael would probably have been on your side. And he does agree with you that I haven't solved the non-locality problem.

      I'll bow out of this discussion with the best wishes for your model and for Michael's theory. Both are very impressive. The problem with both is their complexity, requiring so much effort to comprehend. They are beautiful accomplishments. Congratulations to both of you. I truly admire you both for the obvious intellectual effort required to produce these works.

      Best,

      Edwin Eugene Klingman

      Hi Joy (Part 1),

      I have been contemplating your work in the links you gave. My slip in saying the Hopf spheres I think was my subconscious trying to get my attention: with the particle/anti-particle space being S^0={-1,1} and the space of cyclic waves being S^1, the existence of wave-particle duality seems to be saying the fibre-bundle of the first Hopf sphere. This implies that the first Hopf sphere provides an underlying context for an analysis of Quantum Theory, such as yours.

      I think that you short-changed yourself with the meta-principle you gave earlier. Although in mathematical terms the S^7 case (eqn 1.32 of your 9_Origins.pdf attachment) is more general than the S^3 case (eqn 1.28) as S^7 contains S^3 subspace, the assertion of S^7 ONLY precludes the possibility in physics that the two spaces have different origins such that the S^3 is not a physical subspace of S^7. A real sphere example is where the space of the particle symmetries is S^7 - as in my S10 unified field theory (STUFT for short) - and the space of the rotation group is S^3. The rotation group is not a subgroup of the particle symmetries and so BOTH S^3 and S^7 occur as they have a different origin. So the most general statement of your work is not solely in terms of S^7, but S^3 (1.28) AND S^7 (1.32). With the first Hopf sphere providing an underlying context for the wave-particle duality of Quantum Theory, your work would then seem to independently contain S0, S1, S3, S7 and not just as subspaces of S7 (as parallized spheres).

      In the context of the spheres being real physical surfaces, the presence of BOTH S^7 and S^3 is critical as the homotopy group for the map S^7 -> S^3 shows that it just involves the S^4 base-space PI_7(S^3) = PI_4(S^3) = Z_2 and gives a chiral non-trivial vacuum looking for all the world like the electroweak vacuum and gives the correct value of the Weinberg angle just in geometric terms. This breaks the symmetry of the S^7 and gives a 3 by 4 table of topological monopoles looking like the particles.

      In metric field terms, your eqn 1.53 together with the closure condition of eqn 1.55 specify the spheres S0, S1, S3, S7 as a collection of closed spaces. The principles of GR seem to be captured by the meta-principle: make no preference. This means no preferred speed, ie. the speed of light is always the same, no preferred location (homogeneity) and no preferred direction (isotropy) - these also say no boundary to the space. Applying this no preference condition to the 4 spheres, says all of them. With space being S^3 and the 'particle space' being S^7 the above map S^7 -> S^3 gives a non-trivial vacuum winding and topological monopoles and anti-monopoles with space S^0. The pre-condition of the S^7 -> S^3 map and the lack of an independent S^1 are both addressed by the unification principle: the S^3 of space and the S^7 'particle space' are unified in a sphere S^10 which then has a hole inserted to give S^3*S^7 with the above mapping. In GR, such a scenario would be cyclical between the unified S^10 phase and the 'broken' S^3 * S^7 phase, thus giving the independent occurrence of S^1 in a 10+1 dimensional extension to GR.

      This gives the physically-real side I address in extended GR where spheres are spheres, particles are particles and waves are waves.

      Michael

        Joy (Part 2),

        There is a critical dividing line between your work and mine which doesn't seem to have been fully appreciated yet: essentially my extended GR is on the physically-real side and your work is on the non-physically-real side - as in QT. Although the physically-real side of extended GR is consistent I prove that it is incomplete because the calculation of the mass reduction of the topological monopoles as Planck scale rotating black holes is subject to Gödel's incompleteness theorem. This both means that the reduced masses of the particle-like objects cannot be calculated from classical physics, and that the self-consistent dynamic state of the particle-like objects can possess a non-derivable feature.

        Assuming that this feature is a wave property, Gödel's proof can be circumvented by changing from physically-real terms denoting the countable number of particles at specific points in space, to non-physically-real terms denoting them as real-number valued fields spread throughout space with a wave property, ie. a wave function. The mathematical conditions of Gödel's proof can then be used to prove no hidden variable theory and the mathematical conversion from wave function to particle number cannot be derived in classical physics - hence has 'weird' descriptions like 'collapse of the wave-function' which make little physical sense.

        However, in the switch in integrals from physically-real terms to the non-physically-real term of the wave function there is a critical flatness condition. The problematic expansion is about a black hole, and the event horizon and ergo-region *cannot* be denoted by a continuous field term in space, so the replacement which derives QFT *only* holds in flat space away from the black hole. This firstly means that QFT *cannot* be unified with GR. But there is a further problem with this approximation of QFT, in that it excludes the ergo-region with its sign reversal of the metric term gtt that allows apparently non-local causation to make sense in physical causation terms. In an approximation that excludes this ergo-region, you *are* going to have a causation issue. The purpose of the representational change to the non-physically-real wave function and QT is to get a consistent and complete theory, but the represenational replacement doesn't even consider this causation issue.

        It would seem that my flat space condition on the representational replacement was just the beginning of the 'flattening' required to get QT fully consistent and complete. There is going to have to be some condition in QT to resolve this causation issue, but I currently don't understand the parallelization of S0, S1,S3 and S7 well enough to understand how it does it.

        Best,

        Michael

          • [deleted]

          • Post #30

          Joy wrote, " ... what I ended up with are the *parallelized* spheres, which are---so to speak---as flat as a sheet of paper. More precisely, their curvature tensors vanish identically, while torsions within them remaining non-zero."

          This seminal point really isn't easy to grasp, but grasped it must be. I think what Michael says below, "The pre-condition of the S^7 -> S^3 map and the lack of an independent S^1 are both addressed by the unification principle" -- i.e., the "no preference" principle necessitated by general relativity (nice, Michael) -- nails down why Riemann curvature vanishes everywhere while torsion is preserved in the 2-dimensions of S^1 as a twist, which demands such a nonorientable surface embedded in the orientable measure space. Classical orientation entanglement is preserved, as in spinor theory.

          I realize that Michael continues with S^3 X S^7 to S^10, but we don't need it for the present discussion, because the limit of parellizability is S^7. (I would comment, though, that an earlier topology paper of mine concluded that the 10-dimension limit is identical to the 4-dimension horizon but that is also, no pun intended, outside the scope of this discussion.)

          Yeah, I'm shooting from the hip. It looks like something important is going to start percolating here very quickly, though.

          Tom

          • [deleted]

          • Post #31

          Michael,

          Quick reply, while I am still digesting ...

          Truncate your theory to the S^7 limit, and I think you will find that Joy's framework satisifies both the completeness criterion for a physical theory (as described by EPR) and Godel completeness.

          Tom