On the Logical Models of Coherent Particle Systems

On the Logical Models of Coherent Particle Systems L. Edgar Otto 03-03-11

In our ever focusing interpretations of particle physics by theory and experiment we find unexpected choices on how to define fundamental ideas like mass or the adjustment of values for it. We try to do this without full knowledge of the context of a deeper theory. Also, without full knowledge such theoretical contexts we are apt to imagine partial ideas, comprehensive on their own level of relevance be it of defining matter or space in ways that suggest notions of things, words like selectron which then applies throughout the context. Some such values and theoretical notions have found very close or exact agreement, some show systems cannot be logically coherent for the state it is in- not a standard one. This in itself is an achievement as science. We suspect a more coherent generalization from our attempts no longer technically right but of course morally so in the spirit of these theories. If it matters, we know how little credit or false credit has been given to those who stumble on or reach for the grail of the Nobel Prize. Our progress is rapid in these times and in retrospect one must wonder if such theories were suggested today would they still be considered worthy of that prize. In the wee hours of last night I imagined a better overview of what is happening with such particle physics models from recent realizations of the scope and possibilities of abstract motions and representations, numbers and groups. In particular I applied the notations of rotating or moving orthogons to the quasic grid and asked of the logic of it- as if a music based on quadraphonics- what sort of physical interpretation might I imagine from this. The ideas of quaternions and so on, complex numbers in general seems to apply- indeed to be better grounded when we see all coherent and decoherent systems in an overview.

The illustration today is of the horse head so as to consider the surprising ideas of knight motion in arrangements of numbers and space in the multidimensional chessboards. With a little further insights one can see that the four fold properties of numbers, and here I use a poetic metaphor, the missing knights of our decks of cards used in entertainment, predictability, and shear counting of what seems physicality in allegory. These with the four suits came from other civilizations than Europe so being unfamiliar with the hockey stick it was changed to gnarly or sleek clubs or batons. This reminds us culture has its influence of coloring our notions as we borrow or claim the ideas back and forth. In the standard chessboard when a piece is in some center its possibilities of motion do not cover all the chessboard. What the queen misses the knight finds symmetrically. But the knight has its own surprising jumps and tours. When we find certain representations in higher space, it the stuff or carrier of physical identity as an element to return or complete a cycle again, the context of space itself in its ill defined concept of dimensions can have global properties of shape that seem symmetric only to the mover or that it flattens and centers its compass of potential and kinetic abstract motion.

This overview shows that we cannot just assert some hierarchy of particles or say of sheets of topological realms- for if the dimensions are not defined how can we expect to so define and contain the notions of such particle motions? If in doing this in some way and adopting standard model terms- like Higgs, then we may adjust not only the values these have but have to redefine fundamentally what we mean by mass. We can envision for example, in the next level of speculation on such a particle, that these too obey the general ideas of so many generations of matter or we may think that such things can be interpreted as a sort of super-dark matter.

This will not be surprising really for we return again to our familiar notion of the states of matter- the solid, liquid and gas (and beyond as in plasma and so on) to which we try to find therein simpler models to apply to the general physics of the universe or say to the nature of what happens in the extreme states of stars. How then do we decide if a theory is logical when in the partial chaos of things in which we can only fix certain ideas or parameters as controlled experiments up to the level of our achievements and fine tuning of technology?

I suggest to some extent we take the permutations of the orthogons and their spinning as a model when there are distinct sets of meaningful pairs of binary numbers- a different way to pair them does not detract from that some series is meaningful. For this purpose we can see the usual labeling of he 24 cubes in my illustrations of yesterday and arrange them (these are half the picture as they could be labeled with their mirror symmetry but not the global arrangement itself) so as to state that these valid positions in the quasic board of 4 6 or 8 as four colored. A system can be valid in four space or its representation as 6 space.

This gives some justification too for ideas of which I am doubtful like trying to find the local shapes of six dimensional compactified space. It also establishes the foundations behind the error correction and gray codes in a more general sense.

Now, since the abstract coordinates and motions can be 4D or 6D the same sort of motion thru say a square in a lattice is so described by 6 or 8 coordinate numbers. Thus an absolute change in six space of 4 coordinates thru a square is an axiom of the intersection of planes in a point for 4 space but a little more generalized and if we keep in mind the coherence of it we will not get lost in notions and notations.



We then label those distinct 24 points in the quasic plane with the order and 24 group notation as on those cubes- for we have a coordinate notation of 6 by 4 where the four seems to mean the rotation 1, i, -1, -1 on a face (in fact by these considerations I see where I have not made the best choices of certain labels as to the subscripts and on this level of thinking these might matter and should be standardized.) But that leaves six of them in the other direction. Because of this we can further generalize the space (to perhaps a more truly fourth generation of matter- again we have to stretch our notions here) so as to apply to 15 colors for even further reaches into real dimensions of physicality- the 16D seems natural but for particles we do indeed have to think about at least the 64D but in the sense of which I speak about dimensions here. The quasic extent would have 4096 squares. A quasic twelve dimensions.

So clearly we can move in six space thru square planes which exist as the 8 cubes of a four dimensional hypercube- an these can be linear or circular going in the three positive or negative directions of the natural three space axes. (These by the way given four colors and my Conway 6 color labeling say seven objects around a central one "I" or the excluded orange-violet which of course also have 15 possibilities as does the four, for the series DIJ CIK BIM.)

It may be of interest to take the cubes as the four colors of the edges and stacking them for we will find the linear motion of four of them repeating in a line. On the other hand if we match the edges only in a 3 x 3 cube of them we find we can put six of them in a ring that slices the cube- in fact, in this one side of a mirror representation we recover all four sets of them. Interestingly as all axes are represented one at a time per cube there is indeed room in the center for another one.

What does it mean in 8 space that there is a motion thru a hypercube? It could mean that a particle moves thru a lattice of hypercubes. But as 4 space it is already a centered object so where could it move in this respect? One thing would be if we imagine this embedded in the 24 cell. Clearly the motion thru a hyper-lattice is the same as some sort of identity change or motion thru 4 space- that is as if a fixed unfolding or rotation. The particle moves thru the three hypercube of 8 cubes of the twenty-four cell.

This could be interpreted as the model of a proton, then the deuteron or tritium of one two or three of them. We further can add them as five or 8 and so on and eventually 26 or so of Iron and so on. Here we begin to find a better relation between the boson and fermion distinction. We can go further in that there are polynomials in which we can relate to 80 of these.

I wish Pitkanen were more specific as to his use of 89 in the number theory- for one thing in relation to it as the 11th such number, and a prime, this idea seems to me to be parallel in some respects to my own but not central- nor can I see primes as such, independent in physicality anymore. Nor can symmetry breaking just be a question of Fibonacci numbers only. The new clarity with our own theories we strive to clear up also applies to other theories as we understand and reevaluate them.

There is a whole new world to explore, but we need not get lost in it- nature does preserve its coherence's when it can and does not when that is natural and helpful.

Nature acts at times at the local real position or wildcard singularity and we might consider these like tidal forces. In such abstract coordinates and mirrors and seeing nature the way she sees it- not just our thought this is an illusion, we may have just upgraded what we mean by mass and gravity here, a higher level in the topological background that are and where particles act. P-adic is part of the view but not the theory of everything- the difference in the octonian and quaternion like numbers also are but part of the view while still a more general and truer one than our still earthbound old physics.

I had a poetic thought, perhaps to name elements 119 and 120 not as I have done with Terranium but less worship of our great men and more along the lines of the planets for the essentially 3D transuranium elements. Just as Uranoid suggests Neptunoid and Plutoid these I considered for poetic titles of this paper- maybe name them following the planets as my chem professor lady suggested we continue the planet names in high school. Welcome then, Erisium and Quaoaurium. But the naming of things, the terms we use or symbols we use is often a matter of our identity and claim to priority of discovery and perhaps all the reward we have beyond forgotten biography behind our empty names. Such symbols seem to endure, in that any such symbol might endure so many thousands of years.

The measure of the power of a new generalization- if it is coherent and has some of the logic of it all- is perhaps our need for replete new terms running out of old ones. But alas, one can feel life too short staring at the first drawing of a computer chip and being young enough to have such wide dreams.

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It may be of interest to view my sketch notes in the middle of the night with low light. The labeling of this occurred to me in a flash but not a dream- perhaps it was enough in that most questionable state bordering on sleep to awaken me enough to get up and scribble by the light of the television screen.




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The search for cultural prescient and interpretation of current discoveries:

On the frontier we look for fundamental notions that have come before us- in general we do not stray to far from our familiar symbols- say in science or in something social like national flags (the first Confederate one the most obvious example).

Or, to remain intelligible and appear scientific in our enterprises we use the current terms or try to show where our pet theory relates to some recent fact or that we could have foreseen such a fact from the personal perspective. I hope I am not making that natural process as a minor local mistake- but I should try to relate this again for emphasis to the life sciences.

http://www.sciencedaily.com/releases/2011/03/110302131842.htm today strikes me as a working example of these dynamic topological ideas. To start with we justify physically the ideas of duplication of systems usually justified by merging of complex number systems. The quaterions as numbers are intimately related to other systems of numbers and not distance or that different from vectors and counting numbers and so on. Clearly on this simpler level (after all the fano plane is the simplest of such planes) We observe the rotation of a natural cube 180 degrees in the general description of such rotations. We also note that we establish relative to our own perspective not only a center of things but the orientation to what we consider as up- perhaps this was just an evolutionary development, perhaps it is intrinsic to evolving notions and matter in nature.

In a sense the chromosomes (and I mention the four fold hexagons in the quasic planes as natural variations in the maintenance and structure of chromosomes) as such a generational generalization of these sorts of topologies with their rules of restrictions as occur and are observed in numbers.) is a duplication of DNA strands. Thus, since DNA can be read as if there are in fact, as discovered and as was in fact predicted before that fact by these binary notions, that these sorts of geometry operations apply on the chromosome level in terms of such logical systems. We have not looked to far beyond this as to how much more complicated and deeper the structure of the physical biological organisms apply- nor if there are any significant artificial systems constructable and viable. This hints at the possibility of new experiments and predictions.

In terms of what we consider natural or artificial, it seems to me that the description of things- as powerful as they are, in matters of computation machines, using terms like inheritance algorithms, where they just use a coordinate of the computational space as a linear address and not the more matrix or even string-like variety of notations of the vacuum or singularity- is a limitation of what we can say of visualization of what space is. For example, there should be no problem in an animation and analog in the virtual programming (indeed, what we may not do yet in physical space- say in quantum computing- we certainly might do in mental or virtual space models) to make four dimensional fractals. This would be a step up from the taffy like early three space ones, or the new analogs to more shapely pictures in three space of the various fractals. The programming should be highly linear in this sense provided we know the general context of such spaces. Moreover where it is not so we can let the program find its paths of intelligible decoherences where we may reach an analog level to what seems discrete and not continuous in a non-linear sense of the term. To this end the statistical methods and grounding of a theory, and the proper limits of computing as modeled in the two space of mathematical programs such as Conway's game of Life, proves rather powerful and rapid in the execution of the programs as in fact Dawkins early on pointed out.

This would perhaps amount to an actual visualization of gene processes- and moreover make some predictions as to the possible tendencies in them as simulations. But the intelligibility and unity of such new physics tells us that any new and truly radical departure from our core structure that is viable cannot be that different from what we have evolved to already- unless reality itself is made even more radical so transcended in a sense. As a part of the intelligible cosmos it will be a matter of programming to show the effects and side effects of inorganic chemicals introduced to the organic environs. Perhaps too, instead of actual DNA used as a rapid computation tool the innate programing itself in the DNA can be used- this could help with material science and obvious links to the nanotech as today a lady discovered that bacteria can communicate even across species with nanotubes.
http://www.sciencedaily.com/releases/2011/03/110302080003.htm

This too is worth mentioning when local things in space reach or extend outward once we determine at zero or infinity which direction is up:
http://www.newscientist.com/article/dn20193-treklike-tractor-beam-is-possible.html

See this 3D programed fractal animation:
http://www.newscientist.com/blogs/nstv/2011/03/travel-into-3d-fractals.html

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http://www.superliminal.com/cube/cube.htm

http://www.gravitation3d.com/magiccube5d/ found this, new to me, looking for an online model of the 4D one

http://christophersisk.com/tag/rubiks-cube/ and I thought I was already dealing with very high numbers!

Well, if your java works or you can download the 4D cube you will see seven cubes in it at a time- it does not really matter how we divide each cube for the more general idea. I imagined this long before I had a computer in the early 80's. I feel a little obsolete as our explorations so wonderfully progress. And I thought this post was a little too difficult to read and grasp :-)

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