The 5-dimensional model for electromagnetism and gravity

V A Andreev,D Yu Tsipenyuk

doi:10.4236/ns.2014.64028

Abstract

The generalization of Einstein’s special theory of relativity (SRT) is proposed. In this model, the possibility of unification of scalar gravity and electromagnetism into a single unified field is considered. Formally, the generalization of the SRT is that instead of (1+3)-dimensional Minkowski space the (1+4)-dimensional extension G is considered. As the fifth additional coordinate the interval S is used. This value is saved under the usual Lorentz transformations in Minkowski space M, but it changes when the transformations in the extended space G are used. We call this model the extended space model (ESM). From a physical point of view, our expansion means that processes in which the rest mass of the particles changes are acceptable now. If the rest mass of a particle does not change and the physical quantities do not depend on an additional variable S, then the electromagnetic and gravitational fields exist independently of each other. But if the rest mass is variable and there is a dependence on S, then these two fields are combined into a single unified field. In the extended space model a photon can have a nonzero mass and this mass can be either positive or negative. In this model the 5- vectors which components correspond to energy, pulse and mass of a particle are isotropic both for massive and massless particles. The rotations in the (1+4) dimensional extended space G can transform massive particles into massless and vice versa.

Highlights

We consider a generalization of Einstein’s special theory of relativity (STR) on a 5-dimensional space, or on a (1+4)-dimensional space with a metric (+ − − − −)
It is well known that the photon can be considered as a massless particle, and described by the plane wave only in an infinite empty space [1,2]
We can consider the process of changing the mass of other particles, such as electrons, assuming that it depends on external conditions and influences

Summary

INTRODUCTION

We consider a generalization of Einstein’s special theory of relativity (STR) on a 5-dimensional space, or on a (1+4)-dimensional space with a metric (+ − − − −). We assume that in the extended space model (ESM) a rest mass m may vary in some processes. Such a change of a rest mass is the result of external influences. When photon falls into a medium, or in an external field, its velocity ν becomes smaller than c, and the mass becomes nonzero In this case, we assume that the non-zero mass can be both positive and negative. In the dual space with coordinates ( E, p, m) , the Lorentz transformations act in the subspace ( E, p) These transformations don’t change a value of mass m. In the ESM electric charge is a constant and does not change under transformations of the group O (1, 4)

THE STRUCTURE OF THE EXTENDED SPACE

THE VECTORS OF THE FREE PARTICLES

ELECTRODYNAMICS AND GRAVITATION IN THE EXTENDED SPACE