Summary of Topological Geometrodynamics

Abstract

Topological Geometrodynamics is a proposal for a unification of fundamental interactions with which  I have worked for 42 years. It is based on a new view regarding space-time inspired by the problem of General Relativity Theory with classical conservation laws (energy problem). Matter makes the flat Minkowski space M⁴ of Special Relativity Theory curved leading to the loss of its symmetries. Poincare invariance implies the conservation laws of energy, momentum, and angular momentum via Noether's theorem so that they are lost in GRT. If space-time is a 4-surface in space of form H= M⁴ x S, S some compact space with very small size, space-time isometries are lifted to those of H and Poincare symmetries are not lost. The geometry of S =CP₂ codes for the symmetries of standard model. Topological Geometrodynamics decomposes to two basic threads: physics as geometry and physics as number theory. These complementary approaches related by M⁸ - H duality are discussed in this article. TGD is compared with GRT and standard model and the applications of TGD - also those to quantum biology, consciousness and technology - are briefly summarized.