New Approach to Geometrization of Electromagnetic Field

O A Olkhov

doi:10.11648/j.ajpa.20150306.16

Abstract

The new approach to geometrization of electromagnetic field is suggested, where previous author’s results on geometrical interpretation of quantum objects are taken into account. These results can be considered as a justification for considering of spaces with higher dimensions for geometrization of electromagnetic field. Electromagnetic fields and potentials are considered here as components of torsion tensor in 5-dimensional affinely connected space where the usual 4-space-time is a pseudo-Euclidean hyperplane. Electromagnetic potentials and tensor of electromagnetic field are represented by different components of the torsion tensor as it should be for the notions of different physical meaning. Suggested geometrization is free of such disadvantages of the known 5-dimensional Kaluza’s theory as the absence of physical foundations for introduction of additional spatial dimensions and the lack of any relationship with quantum mechanics.

Highlights

Geometrization of electromagnetic field is one of the problems on the way of establishing the geometrical paradigm in physics where all mater is considered as some deformation of the space
At first this work was directed to finding such non-Euclidean geometry of physical 4-space whose geometrical characteristics could be identified with electromagnetic fields and potentials, but all attempts on this way have failed
We show that electromagnetic fields and potentials can be represented as different components of torsion tensor of the 5-dimentional affinely-connected space where the usual 4space-time is a pseudo-Euclidean hyperplane

Summary

Introduction

Geometrization of electromagnetic field is one of the problems on the way of establishing the geometrical paradigm in physics where all mater is considered as some deformation of the space This idea was suggested in 19 century by mathematicians Clifford and Riemann, and the first confirmation of this idea was obtained by Einstein who showed that in general relativity gravitational field can be interpreted as some distortion of the space geometry. At first this work was directed to finding such non-Euclidean geometry of physical 4-space whose geometrical characteristics could be identified with electromagnetic fields and potentials, but all attempts on this way have failed Another approach was proposed by Kaluza who assumed that geometrical meaning of electromagnetism can be connected with geometrical properties of 5-dimensional Riemannian space-time [1]. Olkhov: New Approach to Geometrization of Electromagnetic Field considered as geometrization of the fermi-field, and we start with presentation of the main points of this geometrization [4,5,6,7,8,9]

Geometrization of Quantum Particles

Geometrization of Classical Electromagnetic Field

Results

Conclusion