Ghost Factorials L. Edgar Otto January 14, 2012
The quantum explanation for why there are three dimensions as if that a deep explanation of how physical particles behave in relation to dimension itself can be generalized over the structures involved to make a new representation and configuration of possible abstract quasic motions and rest- it is this sort of thing that not only suggests the idea of nuclei but that things happen or move intelligible and concretely within them. But it is not enough as Rowlands does to contrast the nipotent and indempotent- but that of unity prime and privileged in directions in itself so justified by the duality that underlies discreteness- that in a deep sense nature does not rationalize her fractions even when in all the parameters involved we call physics these are seen to have an inverse so are reduced to simple plane models and twists of so many degrees.
In the illustration I also include the break down of the 27 elements of the hypercube into three 3by3by3 cubes, the center one representing the next level of quasic motions and from this found the symmetries to rearrange sukodu permutations.
This in the ghost factorial page (I mean some lattices that are between others needs not be quasi-xtalline) is a generalization with essential and not reduced or rationalized spaces- after all the Feymann diagrams are generalized already in the idea of the quasic matrix which goes beyond the Lagraginan or H operator formulism in the philosophy underlying qm theory- we note also that this of course relates to the deep concerns on the nature of dimensionless constants and those generalized in a wider concept of space also.
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I posted to Pitkanen as some of his quantum terms in relation to what is long standing now within those terms and on my paper labeled ? in script for ghost factorials the following suggestions... How is it we imagine generations of particles that involve inverses of 2^n powers... 1/4 that for sure in mass calculations. Of course all the squaring of things is involved too in the measures.
So, Matti,
You insist on quantum descriptions- but what then is original beyond Dirac's four spinors- I mean something is generalized is these work (but only so well for these decades since him) as your last post that wants to make sense out of four waves... this four or five fold pattern in nature (recall Einstein tried 5 dimensions for one rather cylindrical unified field.)
And these can be reduced to 2+1 formulism from the 3+1, much like Feymann diagram so reduced and see as a general matrix to be expanded again into your 2x2 view (a debate of exclusion.) Now, in the quantum formulation we have different ways to view things that amount to almost the same thing- in its way it explains why we wind up with three dimensional space and two types of particles.
Mass in not in the equations- that is what some are looking for as well the nature of gravity. To base things on mass-less is merely to interpret Dirac's "nilpotent" algebra rather than "idempotent" forms of models.
If you cut a knot, as if a string, does it have more than 2 end points- if twistors are only complex duplications and numbers so to justify the 2 or 4 formulisms (of which in one form Dirac uses five...) it is not enough, qm mechanics is not enough.
Now, the Mersenne's as you use them may be enough but that is a wide field to explore- but it is to me an original approach.
I understand someone independent of the academia being creative and free to read and speculate- but I see no reason to make a great deal over idols of the day like Arkani-Hamed which all the bloggers seems to have done even when in disagreement. His is another near idea along the way like some of Hawking's.
There are other ways to explain quantization than that from Dirac in that differences in space and time and matter and charge are those of that great foundational difference between the continuous and the discontinuous in the search for some measure.
Maybe the old Egyptians had it right- we should not always rationalize our fractions- we simplify but lose information- and the lost information is not clearly lost- nor does it prove anything.
The PeSla
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Dear Pesla,
ReplyDeletesome comments. First about twistors and related things.
a) Why I appreciate Nima is that he is theoretician with a tight contact with reality. Also clarity of thinking, enthusiasm, and courage and ability o use imagine belong to his virtues. Before knowing one must imagine.
b) Second point is that the work with twistors lead to the realization of Yangian invariance and discovery of an infinite hierarchy of them. Their generalization emerges naturally in TGD framework. N=4 SYM is the most useful toy model ever discovered. If I want to formulate TGD as concrete rules some day, I must use all the wisdom that already exists.
c) The idea that all massive states have massless building bricks is extremely powerful. Much much more than "nilpotent Dirac algebra". Generalization of Yangian invariance, twistors, new view about Feynman diagrams as twistor diagrams implied by zero energy ontology,... Together with zero energy ontology this identification might resolves also the basic problems of twistor approach: how to get rid of infrared divergences, how massive states emerge and can be described, how to describe non-planar diagrams, how to understand renormalization group and coupling constant evolution...
To be continued....
Some comments about Dirac spinors.
ReplyDeletea) I - and I think all theoreticians nowadays- use the term "Dirac spinor" in more general sense than Dirac. This may or not be regarded "original": physics means to me much more than "originality". Some things have been understood and the mathematical description of spin is one of them: it is waste of time to try to invent ad hoc descriptions of spin.
Same applies to electroweak quantum numbers. The attempts to reduce them to - say - knot or braid topology is simply waste of time. There is huge data basis of empirical facts demonstrating that group theory is behind electroweak symmetries. Braids are extremely interesting part of also TGD but in the case of elementary particles (1 or two braids only) they do not bring in anything interesting. The interesting new things emerge at the level anyonic physics involving braids with more than two strands. They define new kind of entities not identifiable as elementary particles since the propagators from these states do not behave like they should behave for elementary particles.
b) Dirac spinors in TGD framework are 8+8-component spinors of M^4xCP_2 and describe electroweak isospin besides spin and give automatically rise to quarks and leptons with correct electroweak quantum numbers. At the level of "world of classical worlds" - WCW- the counterparts of Dirac spinors are fermionic Fock states and spinor fields in WCW describe all quantum states. Fermi statistics finds a geometrization in terms of WCW gamma matrices expressible as combinations of fermionic oscillator operators. Quite a leap conceptually but mathematically very natural.
c) Mersenne primes are only specific p-adic primes which are of special importance in p-adic physics. What is important are the p-adic topologies as the natural topologies for the correlates of cognition. They have also deep connection with particle physics and number theoretical universality based on quantum arithmetics becomes the deep principle posing constraints on quantum physics. These specific primes give only grasp to the reality via applications. Twistorial approach allows imagine to see how the number theoretically universal amplitudes should be constructed using quantum arithmetics.
To be continued...
And few words about four wave interaction.
ReplyDeletea) Four-wave interaction is nonlinear interaction of laser waves - as such it is not something that unified theorists is usually interested in. Modulation is second non-linear interaction involving two waves familiar from first year courses in physics.
b) Why I am talking about this kind of basic things is that the linear superposition of fields corresponds in TGD only to the superposition of their effects: particle has topological sum contacts to the two or more space-time sheets and experiences the sum of the fields carried by them.
This is a profound difference at the basic ontological level, and it is more than interesting to see whether it really works: can one describe effects like amplitude modulation and four-wave interaction in this framework? One can!
Cheers,
Matti
Matti,
DeleteThank you very much for the clarification and dialog. Amplitude certainly relates to interpretations of some physical things in the complex number field- Are we trying to see more than the generalization by p-adic numbers? I think we certainly can and would like to see this approach developed more.
I have mixed feelings about the term non-linear unless it means simply a statement of powers greater than one (conceptually) for how these linear things relate is certainly the stuff of higher geometry. SO(32) may finally unify gravity and electromagnetism along Einstein's early hopes but his 5D solution was after all cylindrical, curve and line. I am wanting to probe deeper into the meaning of this idea of intrinsic curvature.
I am wondering in fact if there is really anything original anywhere- that is I am worried we all get caught up in the mood of the times that delay progress of enquiry- so I have psychological concerns here as philosophy more than physics per se. I ask you outright- do our struggles with city hall, even Leonardo did that, and wounds retard our discoveries? I wonder too, if knowing such physics and philosophical systems we can see beyond the visions and intelligibility of our own theories so as to recognize that say Mine are an illusion or fantasy hardly the standard accepted fantasy. How can I support an alternative and creative work if there is such a disconnect between how we separately view things? To that end my next post goes back to my own developmental influences in childhood.
Can we not have laser planes? Or even laser sphere as in Californium on the surface of the sun? What sort of topology are we missing here? Certainly there can be a generalization beyond twistor theory that is self restrained- but I do not see why, metaphorically speaking, God would cop out to choose ad hoc restraints on any design including the vague idea of cosmic censorship.
Does anything happen or is actually there between the mouths of wormholes and how do these fit into the multi-plane scheme of things? What is the stuff such strings are made from in order to interact- as in my next post, the more poetic one of childhood thought experiments, I see my view intuitively moved toward the discrete rather than the wave forms and it is very good my practical (too practical really) father discussed things with combined or different answers. By wormhole do you mean the standard view of the ideas? Also, I have shown the 6D manifolds are only a stepping stone to a more coherent picture. (continued, interesting html not accepted > 4096 characters)
How is it we human theorists are so smart but our methods and mathematics are not powerful enough to solve some things? If the error is mine, and Lubos could see something more generalized to call me than "crackpot" hehe I must outrank you on at least that- Well, in our blog world of hopeful free enquiry for you especially, and with hope for him- should I prove adding to the dialog something of value- I just wanted to raise the bar of your goals and efforts. Your summations lately were helpful. Originality in the end, and that we can claim as shared, is emotional and artistic only. We all understand what can be original intuitively and want so to be the first in new lands and frontiers and can actually explore and be so- but all the wishes in the world may not make it so, for somewhere there is only so much sand in the flow of our hourglass. Of course on some level that is a closed system- we braid our own permutations of our dreams.
DeleteIn the end, as in brane theory, our dreams of dimensions connects to eight or more sheets- and with my idea, a rather vague one in my last post of "ghost factorials" are we not concerned with say 2n! and associhedra in divisions that seem to dimensionally cancel out as you see the p-adics and limits or restraints of the values to 512 integrated elements- but one thing for sure you seek the right questions. Not so sure what it fundamentally means to say of some view or project we are "wasting our time".
As I child with a measuring tape my father had me compare the diameter of the coffee table to the circumferance- my child hands on the first try said Three. What sort of science is it that from some view of generalizing things, beyond the metaphysics of fermions and so on- the Bible says it is this rational number? Again, the old saying- we have mastered the infinite but the finite will take us a little while longer.
I am quite honored to have your posting here... But what does this virtual world mean anyway? We have a generation addicted to this light and who is to say that is not what we all want and evolve to in the end? I find your trying to match the theory to genetics and consciousness worth the speculation.
The PeSla