Monday, June 16, 2008

What goes wrong with string models?

Something certainly goes wrong with super-string models and M-theory. But what this something is? One could of course make the usual list involving spontaneous compactification, landscape, non-predictivity, and all that. The point I however want to make relates to the relationship of string models to quantum field theories.

The basic wisdom has been that when Feynman graphs of quantum field theories are replaced by their stringy variants everything is nice and finite. The problem is that stringy diagrams do not describe what elementary particles are doing and quantum field theory limit is required at low energies. This non-renormalizable QFT limit is obtained by the ad hoc procedure called spontaneous compactification, and leads to all this misery that spoils the quality of our life nowadays.

My intention is not to ridicule or accuse string theorists. I feel also myself very very stupid since I realized only now what the relationship between super-conformal and super-symplectic QFTs and generalized Feynman diagrams is in TGD framework: I described this already in the previous posting but did not want to make noise of my stupidity. This discovery (discovery only at level of my own subjective experience) was just becoming aware about something which should have been absolutely obvious for anyone with IQ above 20;-).

A very brief summary goes as follows.

  1. M-matrix elements characterize the time like entanglement between positive and negative energy parts of zero energy states. The positive/negative energy part can be localized to the boundary of past/future directed light-cone and these light-cones form a causal diamond.

  2. M-matrix elements can be expressed in terms of generalized Feynman diagrams with the lines of Feynman diagrams replaced with light-like 3-surfaces glued together along their 2-D ends representing vertices. For a given Feynman diagram of this kind one assigns an n-point function with additional intermediate points coming from the generalized vertices. In hyper-octonionic conformal field theory approach these vertices are fixed uniquely.

  3. The amplitude associated with a given generalized Feynman diagram is calculated by a recursive procedure using the fusion rules of a combination of conformal and symplectic QFT:s as described in the previous posting.

What this means that a fusion of generalizations of stringy conformal QFT to conformal-symplectic QFT and of ordinary QFT gives M-matrix elements. Feynman diagrams are not given up! Only the manner how they are computed is completely new: instead of the iterative approach one uses recursive approach based on fusion rules and involving automatically the cutoff which has interpretation in terms of finite measurement resolution.

For more details see the previous posting, the chapter Construction of Quantum Theory: Symmetries of "Towards S-matrix", and the article Topological Geometrodynamics: What Might Be the First Principles?.

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