Sunday, August 28, 2011
Simplex Virtual Chirality
Simplex Virtual Chirality Unifying the QFT and Diracian Views of Quantum Theory L. Edgar Otto Aug.28, 2011
I spent a lot of time trying to draw some things I realized could not be done (I do not mean as some sort of projection of axes or actual space models.) The problem was to make a clear representation and graph of the unfolding of the 5-cell. Whatever way this was done there was always an opposition of the orientation of the triangular faces that could not be arranged as say the moving of congruent drawn objects on a plane. So I had nothing to say really today until I realized that this was nature's problem too. The quaternions and like can be viewed as indicating the physical or they cannot. We can imagine the interchange of charge and mass for example. Why are there two such views of Quantum theory, QFT and Dirac? Where in Dirac there is negative energy possible (thus anti-particles yet no firm foundation for this theory is there short of the actual prediction and finding of them). The virtual sea of particles and the filling of that sea- where all is positive or not or where we see there can be left and non-right in issues of the ultimate mixing and reaching of some remote limit or not in the still not integrated into the other laws that third thermodynamic one.
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From an overview, as we probe new levels of physics and review some of the earlier levels and scope of the technology in new light, it should be expected that we will find conflicting and reversals of what we think as physical and the proper interpretation of the data. For what we discover is after all concepts and facts we have to deal with which ground our ideas of science itself and how well it works as to its uniformity of laws and reasonable certainty of predictions. So the data and the conflict to resolve them into the older views, which can be almost a religious faith in our familiar systems as if on the level of not so much a conflict of cultures as the fronts of conflict between civilizations, should be no surprise. For after all in the new physics we have not had to press the issue as far as the anomalies that now show up while the methods were but a matter of taste and worked will enough within their compass so far from the remote and foundational encounters.
There are analogs of complexity in time of course, the wave or the matrix formulations shown the same and yet so different in what we choose to define as the weirdness or the physical in the quantum theory. I am not sure this analog has been realized yet so as to be put in a form where we can synthesize and transcend the current conflict.
What after all in terms of physical theory and how that relates to the raw and abstract geometry of things, that of 256 chiral forms of the carbon only one is recognized by the body. The solution to this, as with all things that catalyze these new hidden analogs to higher symmetries, a focusing really, a science really of cataloging and exploring the reactions, is in our time just how seriously we take the idea of higher dimensions as real, physical- an issue some feel is obviously the case or not still in our day. It is not enough to push the idea of such symmetry which at times is stronger in theory than physics or as the pendulum of philosophies swing the physics is primary again, into realms of concepts of Dark Matter or Energy and its varieties. But it is clear that since there are a few independent but equal descriptions of the Casmir like forces including its possible reach into cosmology, that here we need a closer scrutiny and period of unification into a more general theory. Yet, I find it hard to maintain some averaging, some quasi-reality that half persists, without a solid understanding of measure, that the universe is that abstract and relaxed in its sciences, and not find a little unity, verification, and certainty that while these in theory might totally vanish can still explain the whole. These clashes of notions by our theorist, a see of real but fanciful preon-like scales of continuity, can collectively and individual risk the board and the game and it is not easy for them to see what they have not developed the clarity of intuition, the creativity, and the tools to do so that they so perish along with their world view. As Napoleon once observed in his games in Corsica as a child that lead to the great changes in the history of Europe, on the chance or fate of his role in law and war, "It is but a small step from the sublime to the ridiculous."
But in some ways what cannot be done in the physical world can certainly be imagined and sometimes done, with vision.
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I find it most interesting, and what should be obvious but hard to see for some reason, that the centers of these structures if they exist in the next space do after all embed the tetrahedron (self dual) into the four space analog of the octahedron (not the 24 cell). While in normal space we can connect polyhedra by extending the connection between two faces by a prism or an anti-prism, the connection between these two faces can do neither if either is tried. This is a basic observation of Kepler and the count of regular and vertical solids. But in the extension of this idea it is clear that such considerations that involve the icosahedral (even the deltahedral symmetries- for are there not 18 faces of the corner tetracube? each of which might be considered a triangle?) is also and intelligible count of how these subdivide hyperstructures into these simplexes. I wonder if the magic sequence of electron configuration is correct after 50? In any case the inclusion or not in the duality of regular and vertical solids do seem to have a pattern where the surface count of the nodes may be two more and so on. Then again some of these considerations have been intuitively explored on this blog before these proven a deeper theory- yet when we apply this to say the structure of DNA as if there is only a positive direction (no negative anti-state) many are still operating on metaphors and intuition, and some strive to only see it positive on one side of these important duality lattices. Certainly the fivefold-ness and how the signs interchange- say + + + - - to - - - + + should be explored where there are variations in say relativistic invariance that strives to interchange space and time as if these were always distinct concepts foundationally. What is confusing in the relativistic theories is similar to that of the quantum theories for a corresponding ambiguity of separate theories.
Even if it could be shown there is no supersymmetry, then the restrictions such ideas would impose can still be there in the abstract virtual forms of such symmetry regardless of the underlying nature of the prevailing quantum or qlassical theories.
The remarkable consideration of symmetries applied in depth to the polytopes in four space and its wide variety of structures- and these intelligibly related to the simplex count, 120 and 600 and so on... that these are shadowed in the ten fold symmetry radially or elongated as in a spiral of such polytopes or tetrahedra, that we have a cycle of duality of five levels in the flat highest Euclidean space (see Coxeter) I not only find intelligibly as geometry but that such shadows can in fact be seen in a few varieties of ways, sidewinding to what we imagine the limit of such shadows.
Of course it would be nice to pin down the values of mass and energy and so on- something I am not trained to do- with these new considerations.
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Principle of Squaring the Oblong Numbers:
One problem with the labeling approach is not the confusion of the labels, for it is a great advantage having a rapidly recalled system of symbol substitution, is simply that I run our of terse labels. Although formulas are an advantage in the simplification of logical systems, these too have their own limitation of labels. It is hard to reduce them into simplicity at times without a focused and clear reduction which in effect narrows the scope of explanation and information.
So, with another set of alphanumeric labels, for the 21 items before of 5-cell simplexes, A to U, I attempted another layer of color. (this I call 7-arcolour, 7-arc) yet it is in a sense like the Conway matrix where we place the 21 and the mirror of the 21, triangular numbers, to form a square number. Apparently this can go to wide complexity. But the value of these matrix like items is that we should keep in mind that it is representing doorways to hyperdimensional structures in some sort of plane theory. But at what point will the picture be the minimum complexity of the labels?
Nevertheless, such a doubling of the notations, informationally, can make the overall picture of color lattices much clearer where the confusion is a result of the different interdimensional "unlattices" is the issue and not the color as seen from some perspective of the priviliged or prefered lattice- not to mention the reduction forced of such seemingly lost paths to follow of the system itself when in fact the restrictions over the totality are not to be assumed as free as that in these ideas of hyperdimensional symmetries of which we explore at first by play and tinkering before we sense a path to breakthrough to an intelligible general theory.
Also, I have been under the weather again lately, not severe as last month but a recurence of minor flu or alergy like symptoms- and a diet change. But this idea comes from a nice day at the picnic table by the pavilion outside to where I slowed down enough to find something interesting without that much strain on mental labour.
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