## Topological Geometrodynamics: What Might Be the First Principles?

**Authors:** Matti Pitkänen

A brief summary of various competing visions about the basic principles of quantum Topological
Geometrodynamics (TGD) and about tensions between them is given with emphasis on the recent
developments. These visions are following. Quantum physics as as classical spinor field geometry of the "world of
classical worlds" consisting or light-like 3-surfaces of the 8-D imbedding space H = M4xCP2; zero energy
ontology in which physical states correspond to physical events; TGD as almost topological quantum field
theory for light-like 3-surfaces; physics as a generalized number theory with associativity defining the
fundamental dynamical principle and involving a generalization of the number concept based on the fusion of
real and p-adic number fields to a larger book like structure, the identification of real and various p-adic
physics as algebraic completions of rational physics, and the notion of infinite prime; the identification of
configuration space Clifford algebra elements as hyper-octonionic conformal fields with associativity
condition implying what might be called number theoretic compacticitation; a generalization of quantum theory
based on the introduction of hierarchy of Planck constants realized geometrically via a generalization of
the notion of imbedding space H to a book like structure with pages which are coverings and orbifolds
of H; the notion of finite measurement resolution realized in terms of inclusions of hyperfinite factors
as the fundamental dynamical principle implying a generalization of S-matrix to M-matrix identified as
Connes tensor product for positive and negative energy parts of zero energy states; two different kinds
of extended super-conformal symmetries assignable to the light-cone of H and to the light-like 3-surfaces
leading to a concrete construction recipe of M-matrix in terms of generalized Feynman diagrams having
light-like 3-surfaces as lines and allowing to formulate generalized Einstein's equations in terms of coset
construction.

**Comments:** recovered from sciprint.org

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### Submission history

[v1] 26 Oct 2008

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