Model of embedded spaces: Peculiarities of dynamical embedding and geometry

Vitaly I. Noskov1

Abstract

The paper is devoted to construction of a geometry of 4D space-time arising from geometrization of classical electrodynamics and associated with the Model of Embedding Spaces (MES). The basic premise of the model is the assumption that each element of matter has an eigenspace, and the spacetime of the Universe is a result of mutual dynamic embedding of these spaces, such that the magnitude of partial embedding is determined by the relative Lagrangian density of the element interactions. It is shown that the required geometry of the MES is qualified as an inhomogeneous Finsler geometry (the metric is an arbitrary function of [dot]x); the basic variant of the geometry (the unique law of parallel shift of metric and non-metric tensor quantities) is obtained as a differential generalization of the Riemannian geometry by the formal replacement ∂/∂xi → ∂/∂xi + 2uk2/∂x[ixk], u = dx/ds; and the dynamic embedding provides linearity of this generalization. Additionally, some features ofMES cosmology, which can be caused by the natural electromagnetism of the Universe, are discussed.

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