Wednesday, July 07, 2010

Article series about TGD in Prespacetime journal

I have worked out during last two months an article series to Prespacetime Journal. It covers the two basic mathematical approaches to quantum TGD and their interconnections. Physics as infinite-dimensional geometry of "world of classical worlds" (just WCW among friends) and physics as a generalized number theory. These are the two great visions.

One could of course raise also some other principle at a special status. The notion of finite measurement resolution or the reduction to almost topological quantum field theory could be taken as a basic principle. Or one could talk about hyper-finite factors as really fundamental structures. Somehow however these two approaches seem to be the most natural ones and the basic vision is that they are more or less equivalent.

The writing process was very fruitful for the simple reason that it forced to print out most of the material from the two books devoted to these approaches and to perform painstaking comparisons to identify all inconsistencies. The visual feedback led to the realization of a large number of new interconnections between various approaches. Perhaps the most important outcome was the re-incarnation of the old idea of electric-magnetic duality as something which I re-christened as weak form of electric-magnetic duality. This turned out to be a Golden Road to an integration of the existing mathematical understanding of the theory.

The basic outcome was the reduction of Kahler function to Chern-Simons term subject to the constraint given by electric-magnetic duality. This meant that the reduction to almost topological QFT- to which I had already lost my belief- had been implicitly present in quantum TGD for more than five years. The condition guaranteing the reduction was the propoportionality of the conserved Kähler current to instanton current that I had proposed more than five years ago to characterize general solution ansatz to the classical field equations: at that time the motivation was the vanishing of Lorentz force guaranteed by this condition. At that time I did not realize that the Coulomb interaction term in Kähler action also vanishes so that it reduces to a boundary term and by the weak form of electric magnetic duality to Chern-Simons term.

A much more detailed form of the solution ansatz emerged: all conserved Noether currents are proportional to the same current which by integrability conditions must be what is known as Beltrami field. The hydrodynamical interpretation is that the flow parameters associated with flow lines integrate to a global coordinate. For this kind of hydrodynamic flows one can assign to each flow line conserved quantities and the flow apparently decomposes from separate independent flow lines: the interpretation is in terms of separation of degrees of freedom. Quantum field theorists speak about integrable quantum field theories in this kind of situation.

The solutions to the Beltrami conditions have beautiful dual interpretations in terms of hydrodynamics and as modes massless radiation fields. A beautiful realization of quantum classical correspondence realizing the idea about space-time surface as a generalized Bohr orbit emerges: one obtains only the generalization of plane waves but not their superpositions. This is what QFT predicts and experiment verifies but linear Maxwell's electrodynamics fails to give!

The ansatz generalized also to the Kähler Dirac equation in the interior of space-time sheet and generalized eigenvalue equation for Chern-Simons Dirac action. Even braids and number theoretic braids pop up automatically from the modified Dirac equation: periodic boundary conditions force the basic solutions of Chern-Simons Dirac equation to concentrate at discrete sets of flow lines of the Beltrami flow defining the braidingof topological QFT. Also connections between p-adic length scale hypothesis and infinite primes and corresponding arithemetic quantum field theory emerged but this is more speculative "must-be-true" stuff. An important outcome was an explicit expression for Dirac determinant in terms of geometric data characterizing the orbits of partonic 2-surfaces giving an alternative formula for the Kähler function of WCW. The second expression is as an exponent of Chern-Simons term. The basic problem of calculating the WCW Kähler function is therefore solved at certain level of details.

This kind of process is of course dangerous since it generates also not too long-lived ideas and my proof readers must have had moments of horror (apologies and thanks to them). One such one-night adventure was indeed generated by a rather delicate error in certain mathematical statement. I spoke about Kähler function as "Chern-Simons term" instead of "Chern-Simons term subject to constraint given by the weak form of electric-magnetic duality". The shocking conclusion was that the metric of WCW seems to be trivial in Minkowski degrees of freedom in contrast to all physical and mathematical intuitions. This mistake forced to consider a modification of Kähler action by an additional term in the induced Kähler form which in principle is possible but which I had for a long time ago tested and given up for reasons forgotten. It however looked mathematically extremely beautiful since the vacuum degeneracy of Kähler action was extended dramatically. It however turned out to lead to a non-acceptable long length scale limit for gravitation. I managed to kill the idea two days before deadline and also to notice my mistake!

The birth of TGD is a holistic process taking place in the time span of 32 years involving all physics related things from Planck length scale to quantum biology to cosmology and therefore a diametric opposite of the usual scientific work in which one has a precisely defined problem and method and one can forget everything else in the Universe and be fully left-brained and extremely reductive, precise, and analytic. Therefore it is obvious that I will probably remain the only one who understands what TGD is in this left-brained scientific community. Despite this I am happy and proud albeit somewhat frustrated. Who wants to be a musician playing music which sounds heavenly in his own ears but whom no one bothers to listen? A lonely millionaire is not a happy millionaire. But maybe- someday when I have gone TGD will be standard stuff of theoretical physics;-)!

Anyone interested about TGD even when I am still here, can find the articles here.


At 11:38 PM, Blogger Ulla said...

This post made me happy. Congratulations.

I have got some glimpse of that music :) It is fabulous and so beutiful. Thanks.

But to me it is still misty, and I feel like a child that just has learned to walk. But I can walk now, although stumbling around :) I would want to could dance. Your teachings was not in vain :)

When you say nobody listen you are wrong, and it hurts. I and a few else listen, but we are no physicians. You should say no physician listen :) But they are too restrictive in many other ways too. Think, over 20 theories of QFT, and they bother of only their own theory!!! It is unbelievable. Something has gone very wrong there.

The way to the new physics goes through the biology, because living things are different, more quantal, than ordinary matter. So biology is very important, and even more so in the future.

I told you some time ago about emotions and negentropy, that emotions must be shared to fully experience them. I know how it feels to meet ignorance and no interest. So frustrating.

The boy will survive.

At 3:02 AM, Blogger Ulla said...

A good quote:

What I am going to tell you about is what we teach our physics students in the third or fourth year of graduate school... It is my task to convince you not to turn away because you don't understand it. You see my physics students don't understand it. ... That is because I don't understand it. Nobody does.
(Feynman, Richard P. Nobel Lecture, 1966, 1918-1988, QED, The Strange Theory of Light and Matter)

At 7:44 AM, Anonymous kavak yelleri 127. bölüm fragmanı said...

thank you

At 2:07 PM, Blogger Ulla said...


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