Progress in TGD: Physics as Geometry & Number Theory

Abstract

This article is the first one in a series of 3 articles, trying to give a rough overall view about Topological Geometrodynamics (TGD) as it is towards the end of 2021. The preparation of this article series led to considerable progress in several aspects of TGD. In the first article the two views about TGD are discussed at the general level:

The first view generalizes Einstein's program for the geometrization of physics. Entire quantum physics is geometrized in terms of the notion of "world of classical worlds" (WCW), which by its infinite dimension has unique Kahler geometry. Physical states correspond to WCW spinor fields. WCW consists of space-time surfaces, which are minimal surfaces in H=M⁴ x CP₂ analogous to Bohr orbits so that they realize holography forced by general coordinate invariance. H is fixed uniquely by standard model symmetries and quantum numbers and also by the twistor lift of TGD.

Second vision reduces physics to number theory. Classical number fields (reals, complex numbers, quaternions, and octonions) are central as also p-adic number fields and extensions of rationals. The physics is classically coded by algebraic 4-surfaces in complexified M⁸ having octonionic structure and "roots" of octonionic polynomials obtained as algebraic continuations of real polynomials with rational coefficients. M⁸_c has an interpretation as an analog of momentum space.