Tuesday, November 29, 2005

Good ideas are published sooner or later

Risto Raitio told in his blog about a paper titled as Differential Structures - the Geometrization of Quantum Mechanics by Torsten Asselmeyer-Maluga and Helge Rose'.

I looked the introduction of the paper and the basic physical ideas turned out to be very familiar from my own homepage! Kind of dejavu experience, definitely! Although authors do not refer to my work, I am happy that these ideas finally begin to find their way to physics archives. Personally I am not allowed to add anything to archives although American Mathematical Society has a link to my homepage in subject classification tables. This is of course understandable: since M theory is the theory of everything there is no need to publish or even archive anything not consistent with M theory.

Only few weeks ago Lubos Motl told in this article A Hagedorn alternative to inflation? about a proposal of A. Nayeri, R. H. Brandenberger, and C. Vafa for a cosmology with Hagedorn temperature as a limiting temperature titled as Producing a Scale-Invariant Spectrum of Perturbations in a Hagedorn Phase of String Cosmology. Cosmology with Hagedorn temperature as a primordial temperature is now more than ten year old piece of TGD: dejavu again! Also these authors forgot to mention my work or they have not yet learned to use internet but this does not spoil my happy mood of mind. It is nice to see that good ideas find their publishers sooner or later.

Returning to the original topic, the authors introduce 3-dimensional singularities of space-time as particles and propose that fields in the interior of space-time and these singularities correspond basically to wave particle duality. In TGD framework partons are identified as lightlike causal horizons of space-time surface and the interior of space-time surface corresponds to field description. In particular, zero modes of configuration space metric defining classical macroscopic degrees of freedom in TGD based generalization of quantum measurement theory are assignable to the interior of space-time.

What is especially nice that the light-like 3-surfaces representing partons allow generalized conformal invariance by their metric 2-dimensionality. Hence 4-dimensional space-time completely unique in that it allows superconformal invariance. This also leads naturally to the Temperley-Lieb algebras and von Neumann algbras known as hyperfinite factors of type II1 appearing in conformal field theories. My sincere but perhaps unrealistic dream is that someone could some day communicate this discovery to people from Harward and Princeton (not an easy task knowing the uni-directional communication abilities of this arrogantzia) since it would put end to the long lasting state of stagnation in theoretical physics.

These factors (as opposed to factors of type I and II appearing in QM and 4-D quantum field theories) emerge also automatically from the construction of the spinor structure in the infinite-dimensional configuration space of 3-surfaces (the "world of classical worlds"), and in their very basic structure code for instance minimal conformal field theories, braid group representations, quantum groups, etc...

One can say that single concept: the "world of classical worlds" with metric fixed uniquely by the mathematical existence requirement and possessing spinor structure determined by this metric implies the basic mathematical structures characterizing conformal field theories and topological quantum field theories.

Even more, hyperfinite type II1 quantum theory leads the elimination of infinities of quantum field theories, and one ends up to a generalized Feynman diagrammatics based on the generalization of braid diagrams and duality as it was defined in the original string models. The generalization of this duality eliminates the mathematically non-existent path integral and thus corresponding infinities.

The detailed summary of this general picture can be found in the first four parts of TGD at my homepage.


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