Thought, Experiment, and Mathematical Physics

Thought, Experiment, and Mathematical Physics

I still have some loose ends from these blog encounters, a creative blog after all perhaps should make no apology for speculation.

The first book of poems, Forever, My Sphere beginning in high school with a interest in physics in the general series Spheredream is found here: https://picasaweb.google.com/100378441531961948209

Kea has linked to three rather advanced papers concerning knots and other issues. One clearly states that we cannot distinguish in the math if the trifoil knot is right or left handed. One suggests a way to sort these in a notation for braids and loops to which a third paper suggests these can be addressed by computational methods and matrix methods seeing the underlying stratum of data as a sort of quantum cosmic computation.

The issue for me, as issues of momenta, certainly does face the question of chirality in general and to what extent it can be a creative or physical force of evolving things in the cosmos. I find no problem with computation from such algebraic topology or informational computation from the bottom up or from the top down as the ground of departure for more complex systems and explanations. But is it here that some of our disputes begin to border on the speculative- after all we are limited to the quality of experiments in our age and time and time again the data has derailed the theoretician (including Einstein and the Hubble values) from wider considerations. Of course going so far we cannot blame the theoretician for the desire to apply what has been learned to the ultimate questions of cosmology.

One issue that occurs to me is the fact that B is more fundamental than H in electro-dynamics including issues of symmetry. Still, we experimentally have to deal with the values associated with them, real but not as fundamental constants involving induction, permeability and so on. We ask when Maxwell observes B = 0 , what is the nature of this zero or vacuum and could it be part of a greater symmetry or understanding of chirality and that in relation to momenta?

We can say there is shell of something with an electric charge and somewhere in the space measure that charge until close to the surface, as with all concepts of the maximum curvature of such spheres- things become flat and infinite. Only later do we find the earth and universe round, and then apparently flat again. (that analogy to show science has progressed was not a good one in light of new understanding of the dimensions)

From a centered roundness we can imagine the higher dimensional symmetrical structures or we can imagine them directional and linear to an indefinite extent. We can also imagine them multiply connected back again. But in space we still have the issue of a choice of the common helical or solenoid form being bidirectional.

Now, configuration space as a way to define a path at a point of so many dimensions for the degrees of freedom, 3n at the most then, what does it mean to say we have higher n-adic degrees of freedom possible? 9n of some sort of higher systems of symmetry? What after all would this do to better understand the n-body problem (that is from the top down of computations)?

The idea of braiding, just as in the equator of Euclidean polytopes we can imagine a Pietrie polygon to define some properties and symmetries, can be a ring or an extension into space of some such ring- I vaguely imagine such an extension as what the associahedra are or could be applied to. I also note that these need not be a ring in the sense of braiding strings (but to distinguish them I called them dreads and certainly there are other forms of braiding). Experiments moreover have shown that in steams of electrons we can twist them with respect to the equipment sensors so as to imply the can be or reach the point of linear braiding.

These mathematical ideas come together in the questions of life and cosmology. But let us consider, think about, polarized photons. We know that if we separate them and take a beam of say the left handed ones and shine it on a disk with a center to spin around (in a frictionless setting) they will cause the disc to spin. But the unpolarized photon stream will not. No momentum is transferred. (in a sense this is like an ideal radiometer in a vacuum not in fact dependent upon the darker and lighter parts of the vane moved by heated traces of air molecules).

But more to the point, as if we imagine centripetal force in relation to material that can vary in its ability to adsorb impulse (as if darker) a recent report from a random motion of ball bearings (photons unpolarized by analogy) can cause the windmill structure to spin.

Thus momenta as well as chirality can as well be described by statistical processes and this is often a matter of physical and philosophical debates for all models.

If something can be conceived in the abstract in some remote past or future time and place - it logically may apply in some respects to the spacious present here and now.

This seems true for example as perhaps diminishing but ongoing star creation- to find one explanation does not always show there are not other explanations that may be obvious from a more general perspective. Yet:

The Cosmic Calypso

I can conceive of a universe, where in its totality there is across all scales (an internal computational solution unto the utmost trace of continuity) where non-linearity and thus disorder can be ruled out as not thermodynamically decreasing, thus a conservation of entropy even while energy concepts (diluted or in a deeper flux of singularity, infinite) breaks down - this would be (and could stabilize calyptic models of various descriptions) in favor of NP and a result of Riemann's hypothesis multidimensionally in the affirmative only. Ponclaire's conjecture and even ultimate braids inverse to these internal symmetries would vanish as an issue or conjecture. this multiverse and multidimensionality seemingly if not absolutely disproved in a scientific sense. This applies also to oscillating models of cosmology and the new steady state like idea of stars renewed by black hole jet creation even if in some pure geometric models (let us not forget that DeSitter's was a redshift by geometry alone and no matter), no minimal size black holes would endure expansion (pre-inflation and inflation) as any sort of restraint or acceleration save as in reference to the creative scales, eternal by varying dimensionless wholes. But I must wonder at the idea, easily observed in the existential case of falling rows of dominos, that gravity is an endless source of renewal of energy (that is the work in the universes)- and this a direct unification with the other forces- the separation must be of a greater concept of broken symmetry.

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In a few millenia to come the people of the virtual book looked back at Holy Hoyle forgiving him of his lapse of reductionism by invoking to the superstitious the idea that life arose from beyond the sky as strains of matter and aliens.

For he was the last great prophet of the Citadel of Science and its cultural wars that bespoke of what was creation at some beginning of the "Let there Be Light" and like Spinoza before him he was called an atheist and even an infidel against the evidence of the discerned sky of the redness of the heaven.

Into the dark matter wherein the old science followed religion into the bottomless pit no one cared to gaze, following his spirit in this world of life abundant and forever with room enough for endless souls.

And the wordless wild card joker in the deck said- let there be neutrinos, and he knew as they made the earth shake passing thru it but infinitely far away that it was good as he faced the east and west, the north and south, the zenith and the nadir in right angle jumps doing his dervish dancing or making that done of the world while he stayed the center of things.

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I can only admire Lubos writing over and over Einstein's equation, near its final form but not as complete to his desires for a final description- an inspiration really of faith in what may come as a final reference frame. But how can I forget as a child the force of the great magnet in the shortwave radio orienting my compass from anywhere in my yard- the physical sense of it pulling, the ongoing strength of it suspending coins on a string, the apparent focus of motion that seemed perpetual from spirals dangling and winding up cut from old beer cans- how solid seemed the experience of something not seen- and even more, the glass and wool and pith and the electrostatic too invisible save for an occasional spark or so.

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So from a Philosophic standpoint what can our enquire's teach us for the prospects of knowing and learning in at least the near future?

In the end the ultimate topological units, from the most general stance, have a state of all possible functions and shapes at once of their possibilities to which we may observe at time the dominance of some forms over the others. We are caught in these times between the realm of thought and of physicality (experiment and experience) to which either we may view and extend to reality as fundamental. Not to say this is a Platonic stance- which we could also state as fundamental - that given the widest compass and proper tools and methods that mathematical methods in the physics is more fundamental than chance place in the physis or that all things contain a vague idea of mind. But who by taken thought can add one qubit to his stature? Our choices of what to develop and emphasize can commit us to some path of which in the short run there may be no cure or return to wholeness.

Thought then in a sense can be seen as not fundamental but an afterthought really of which it is as familiar so intelligible as much as the physical in our experience. It has been said that both descriptions of the world, from a quantum standpoint are equally valid descriptions in the interpretation of quantum theory. Yet the idea of a general and comprehensive mathematical approach as fundamental is as much an afterthought and chance encounter also. While we may find certain algebraic structures of things like least action and a more general context of coordinates and even arrange these into equations by our matrix and diagonal methods, this is only as good as our symbol system with all the paradoxes involved in describing them in a world equally discrete and continuous where in time the distinction blurs.

For no other reason needed then is the pursuit of these fundamental mathematics for the sake of clarity in reason and power over our physical needs a matter of the most worthwhile of human investment in our futures, and a source of pride and wonder at our achievements. But of course I speak of but the beginnings of a better philosophy to come by which we in our day heroically face our species's prospects and general uplifting in our collective enterprise racing toward and not shunning from the unknown even thinking this is all there is to come but what comes at least in this world is yet we are not quite sure what.

Thought, experiment, and mathematical physics will meet in a theory higher than we presently view any of them thus far. It is no less physics than what physics is today, and as science will seem we had false visions of what in uncertainty has stiffed enquiry.

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