A generalization of intrinsic geometry and a new framework for the unification of fundamental physics

Abstract

First, we show a generalization of the intrinsic differential geometry, hence the Riemannian geometry becomes its subgeometry. In such a new geometry, there exists a new connection, which reflects some more intrinsic properties of manifold than the Levi-Civita connection. These properties are closely related to gauge fields and elementary particles. Then, we apply such a generalized intrinsic geometry to establishing a new framework for the unification of fundamental physics. (1) Principles, postulates and artificially introduced equations of fundamental physics are turned into theorems based on a unique fundamental axiom, hence they obtain a common origination at a deeper level. (2) It is proposed that the time should be regarded as the total metric with respect to all internal and external spacial dimensions, and the actual evolution should be regarded as a gradient direction field, and moreover the quantum theory should be regarded as a theory of distribution of gradient directions. The above ideas make gravitational theory and quantum theory become coordinated, so they have the same view of time and space and a unified description of evolution. (3) The generalized intrinsic geometry makes the gravitational field and the gauge field unified both in form and in connotation. The intrinsic geometry of external space describes the gravitational field, and the intrinsic geometry of internal space describes the typical gauge field. They are unified into the same coordinate representation. (4) The generalized intrinsic geometry makes the gauge field and the elementary particle field originate from the same geometric construction at a deeper level. Many postulates of the Standard Model are turned into theorems in the new framework. Moreover, there are some reasonable properties beyond the Standard Model.