On the geometrization of electrodynamics

Journal Article · Mon Apr 01 04:00:00 EST 1991 · Foundations of Physics; (United States)

DOI:https://doi.org/10.1007/BF00733354· OSTI ID:5305410

Vargas, J G ^[1]

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1. Univ. of Alabama, Huntsville (United States)

This paper develops the conjecture that the electromagnetic interaction is the manifestation of the torsion {Omega}{sup {mu}} of spacetime. This conjecture is made feasible by the natural separation of the convection {omega}{sub {mu}}{sup v} into gravitational and electromagnetic parts {alpha}{sub {mu}}{sup v} and {beta}{sub {mu}}{sup v}, respectively, related to the metric and to the torsion. When {alpha}{sub {mu}}{sup v} is neglected in front of {beta}{sub {mu}}{sup v}, the affine geodesics are shown to become the equations of motion of charged particles with Lorentz force, for an appropriate choice of {Omega}{sup {mu}}. Since {beta}{sub {mu}}{sup v} contained the factor q/m, neutral particles do not see the torsional part of the connection and behave as if {Omega}{sup {mu}} were zero, i.e., as in Einstein's theory of gravity. In addition to the factor q/m, the velocity of the test particle appears in {Omega}{sup {mu}}. This indicates that the appropriate context for this problem is to be found in velocity-dependent connections. The velocities are now coordinates and become the actual velocities of the test particles only in the system of equations that one solves for obtaining the affine geodesics in connections of this type. When written with differential forms, the combination of Maxwell's equations and of the pertinent form of the torsion suggests geometric field equations for electrodynamics. As for the gravitational part of the connection, it can be made to obey equations similar in form to the Einstein field equations. A unified geometric theory of electrodynamics and gravitation spontaneously emerges. The present state of theory does not yet permit us to ascertain whether the right-hand side of the fully geometric, gravitational field equations corresponds to the energy-momentum tensor.

• OSTI ID: 5305410
• Journal Information: Foundations of Physics; (United States), Journal Name: Foundations of Physics; (United States) Vol. 21:4; ISSN FNDPA; ISSN 0015-9018
• Country of Publication: United States
• Language: English

Related Subjects

662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BASIC INTERACTIONS
CHARGED PARTICLES
COORDINATES
DIFFERENTIAL EQUATIONS
ELECTRODYNAMICS
ELECTROMAGNETIC INTERACTIONS
EQUATIONS
EQUATIONS OF MOTION
FIELD EQUATIONS
FIELD THEORIES
GENERAL RELATIVITY THEORY
GEODESICS
GEOMETRY
GRAVITATION
INTERACTIONS
LORENTZ FORCE
MATHEMATICS
MAXWELL EQUATIONS
METRICS
PARTIAL DIFFERENTIAL EQUATIONS
SPACE-TIME
TEST PARTICLES
TORSION
UNIFIED-FIELD THEORIES
VELOCITY