Wednesday, April 21, 2010
The Chiral Theorem
Wed. April 21, 2010
The Chiral Theorem
Not much on my mind today save a vague plan to map some chiral coordinates and wondering about the Conway idea of abstraction R and L and 0 and 1 as a sort of surreal calculus (where the square root of two is a rational number?) I guess I only had a vague idea of what such calculus was but it is sort of a philosophy. But in those terms and reading last night on this in Rowlands it is clear to me that my quasic system meets all the demands of nilpotent system ideas intuitively assumed and developed, and even further developed than the nil, or double naught counting. I am amazed the weak force ideas would be taken at the state they are in now and directly applied to gene chemistry by some authors. I still am thinking a out the circle and line thing in all aspects- including the deeper sense I feel I have for chiral ideas than what I see said about them.
* * *
Later today: It turns out I do have an original thought today about aspects of what I called a decade ago The Chiral Theorem. I had not thought about it since then but sometimes, as my work is decidedly finite compared with the standard terminology of Lie groups (and the usual terms of quantum mechanics and so on). As such one does not always see what is so intimate that underlies a concept so familiar to ones own system. I imagined the chiral theorem as really that aspect of math or physics intuitively that was there as a fundamental principle which would better explain the evolution of galaxies.
What I have called inversion say through the center of a solid cube in effect can be seen more simply than I imagined of the more general case. Given t xyz the xy and z are all made negative, if only the x is that is the simple geometric idea of parity. If we apply this then clearly it relates to the foundational ideas applied other places like the vectors out of a sphere in all directions where some of the modern authors use this to derive holographic and conservation interpretations of the underlying space. In a sense then the chiral question seems a deeper foundation than where it is applied and extended especially as a measure of mass and so on. Is it after all a driving force in life- and can we say clearly just how similiar or identical the Casmir force is to the Vanderalls force and yes the idea of some sort of mirror supersymmetry and dark matter concepts and so on.
In a way, as strange and beautiful as the bra ket quantum formalism is it reads to me as a mere descriptive symbology rather than say something to compute within itself. So I can imagine that inside the bra and ket being the input and output of things where again this idea of a biased weak force violation of C P is thought a dynamic thing for life force rather than a casual result of the models of math and the consequent spaces. Quantum is not enough, between the bra ket we may find other input and outputs as a description, as linear as this seems and as collapsed in relation to some space it certainly would expand our description of what are the levels of processes in an organic system. The chiral theorem asserts then that it is a primary principle and physical principle that organizes the geometry and physics and will intimately correspond to the math, algebras involved. Things like the string theories are also a product of this, the math and physics a product of the more fundamental reality. It also has the ability to limit and extend things beyond the raw information contained in handedness and the binary symbols in not just a casual sequencing without an organizing purpose and principle. But I should map some of the examples, perhaps using the results of genetics (for example in newscientist today the relation of the sense of smell (aromatics) and lifespan in some animals may be more significant than what I got out of the article.
In the accompanying illustration I have the six dimensional structure and the 32 tetracubes- we desire to double them in some mirror situations but we can oversimplify the idea of chirality by regarding two of them as the same where we may not distinguish the handedness- not to mention the relation of chirality to the various ways of seeing the dimensionality.
In my old manuscript I used the old pi symbol for chirality- which is interesting in Rowlands treatment of the e and pi which once used the mirrors of those symbols.
* * *
Still a little later today while waiting for a ride to the grocery store: I begin to think about what I had in mind in mapping some extended chiral strucures as having to work within my own quasic system awhile, and looking as some rather basic and possibly trivial principles.
Developed further in my philosophychatforum days was the principle I called the Fundamental Theorem, which states that things change and things do not on the most basic level. It is as if to say, seemingly illogically, one of the most early of my enigmatic musings that all things have an opposite and all things do not. 1960.
But our modern forms are really an elaboration on such abstract principles and we should keep that in mind on the back burner of concrete seeking speculations.
The fundamental theorems in math are appealed to and most certainly at some point should be questioned and reconsidered. For one thing what goes through or into a boundary may not necessarily be what comes out- no zero sum. To say chirality is balanced with anti particles or extending the scope of symmetry may tell us little decisively concrete about the physics of it all. Mathematics and its analogies are of the nature that small errors may be guaranteed to affect the whole edifice of the complexity. In fact consider amplification from small regions based on the imaginary numbers or of small chaoscience (for chaos as kaos I will distinguish the ideas in spelling, not the assumed more modern meaning)changes leading to great ones and maybe at a distance and maybe what is not there influence thru no distance our eventual result of choices.
So as overly simple as this may be let us consider this- the handedness may be at a higher level of the discernibly of that indiscernible. I can image being in a higher space of some sorts where I have to distinguish six hands of distinct and equivalent symmetry. Now there is nothing wrong with the idea of what comes in or goes out being a zero sum but this idea of a boundary could be everywhere throughout the continuous space and it may be wrong to only see it as a localized phenomenon or one that by this principle extends it to the bounds of the entirety of the universe. It is equivalent to the idea that we can imagine a space where every point in it is everywhere a singularity.
So, let us make a positive finite quasic distinction that may apply to those motion functions described from a cell in that space in all directions of a square or from say the bounded corner of a square. We could say there are the motions of a queen and a knight that either way make the difference of particles- we can even say that without a true zero or axis as if zero that what intuitively seems the case in more than just an Euclidean space the zero is not in that space but at distance from it and thus we have the irregularity of placement of points in the complex plane. We do indeed have to return to consolidate the wisdom of earilier geometries and not be so bewitched by the new and more complicated ones and the philosophy of science and arrogance of the "obsolete" the new ideas or change of ideas fundamentally inspires. We can imagine the unity of the knight moves as designated imaginary. In no case do we overwork the distinction of the use of e translated into trigonometry.
Our most general spaces, Hilbert, Phase, Configuration, Fourier Analysis, Lorentz, quaternions and so on are not comprehensive enough for intelligible unification of physics.
We can imagine the space of a quasic grid ascending or descending on any level to some order of dimensionality and we can follow the sequence thru a cell at a point or between cells in the quasic ordering. (we might also have intuitions that we can shift between such spaces or even between systems of such spaces or even entire systems in systems as some near or singular point of such spaces an so on into them. So the quasic space of some level grid as Q nay in a distant null point meet say R S T or four equivalent or different ones in a greater plane and we may also if we want make complex space mirrors of these.
But the null distant points can be thought of as everywhere, and a quasic cell needs not be seen as a point but as a possible minimum or maximum of a grid state and may actually be so perhaps or some quasi-continuous place in between.
But I have to get back to the hand computations again, that hard work which only the reward is that in the end numbers fit together- but there is no guarantee that the use of the time and effort results immediately or ever, especially if we are starting from such trivial points of departure.
While many suggest the observed non-conservation of fermions in the weak force is the drive of say organic things with the creation of its own gaps of vacuum and how the basic numbers also partake of the fundamental paradoxical theorem, we have to have a wider overview which may have clear micro steps of computation beyond just casual principles that work. The observed exceptions are really the rule and not just a casual statement of the rule based thus on very rare evidence.
* * *
And about 8:30 pm - from the corner thing as partial radial symmetry of a quasic motion we can do a sort of differentiation by subtraction which results in the difference of say 1 + 1 to the nth and the orthogonal 1 + 2 to the nth. In a metaphorical sense a "field theory" is the difference of local and nonlocal quasic motions. A cubic structure for example breaks down into 8 1+1 functions and 5 1+2 functions which also makes from a flat space a spherical space- in a sense then at the very heart of enumerable finite structures we have the first idea of symmetry breaking as a general and not just cosmic dimensionality phenomenon which does indeed relate to decoherence quasinonlocally and treats the realizable energy in terms of information and fundamental zero sum boundaries as if the realization of the limits in the universe of discourse in question of the Carnot engine, quantum or otherwise. Next we think about this as the magnetic and electric differences in the interpretation of the usual Maxwell like formulas and that of the relative or absolute nature of mass and space. Now to actually map the various natural dimensional (time like) distinguished senses of chiral jumps information notated. In a higher level sense most students have to understand things like heat and energy on its first conception as a poetic (hmmmm what is the origin of that word?) metaphor.
* * *