Matter and Space. New Theory of Fields and Particles

The paper presents a theory giving a unified geometric description of space and matter on the basis of a new concept related to general relativity (GR). The theory is built on the basis of a critical analysis of GR. The principle of materiality of space is introduced. The description of matter is based on the idea of space as a three-dimensional material hypersurface embedded in a four-dimensional Euclidean space. Matter particles are associated with extended areas of the material hypersurface, and their properties, such as charge and mass, with topological and geometric properties of this hypersurface. The central place in the mathematical apparatus for describing the material hypersurface itself and matter particles is played by marker fields, which are similar in essence to hydrodynamic markers used in classical hydrodynamics. Based on the theory of marker fields, questions of the topological structure of particles and connection between the electric charge and the topology of a material hypersurface are discussed. The mass of particles is represented as a property of the material hypersurface itself and has the meaning of gravitational and inertial mass at the same time. The fields, gravitational and electromagnetic, are properties of the material hypersurface geometry expressed in terms of marker fields. To describe the dynamics of particles, the geometric principle of averaging is introduced, which, as a result, leads to the equations of Newtonian mechanics and quantum theory.