Ein klassisches Teilchenmodell mit variablem Gravitationskoeffizienter

1962 ◽  
Vol 17 (7) ◽  
pp. 554-558
Author(s):  
Jochen Lindner
Keyword(s):  
Coulomb Field ◽  
Coulomb Force ◽  
Equation Of Motion ◽  
Great Distance ◽  
Classical Particle ◽  
Unified Theory ◽  
Specific Charge ◽  
Field Function ◽  
Typical Function ◽  
Theory Of Gravitation

The unified theory of gravitation and the electromagnetic field in the form suggested by BECHERT 1 has solutions which correspond to the model of a classical particle of mass Moo and charge Q. We shall assume that the coefficient of gravitation χ is not a constant but a field function. The equation of motion is derived for this case. It shows that a suitable choice of the field function χ leads to a correct COULOMB field as well as to a correct gravitational field (corresponding to Q and Mo) in great distance from the particle. The extension of the particle is characterized by the classical radius L=Q2/Moc2 of the particle, it holds together by the balance between COULOMB force and gravitation. The specific charge turns out to be a typical function of the distance from the center of the particle.

The equations of motion in the non-symmetric unified field theory

1954 ◽  
Vol 226 (1166) ◽  
pp. 366-377 ◽  
Keyword(s):  
Equations Of Motion ◽  
Coulomb Force ◽  
Unified Field Theory ◽  
Field Equations ◽  
Original Theory ◽  
Unified Field ◽  
Theory Of Gravitation ◽  
The One ◽  
A Charge ◽  
Weak Fields

The field equations of the non-symmetric unified theory of gravitation and electromagnetism are changed so that they imply the existence of the Coulomb force between electric charges. It is shown that the equations of motion of charged masses then follow correctly to the order of approximation considered. The equations for weak fields in the modified theory are derived and shown to lead to Maxwell’s equations together with a restriction on the current density. This restriction is different from that in the original theory, and in the static, spherically symmetric case permits a charge distribution more likely to correspond to a particle. The failure of the original theory to lead to the equations of motion is related to the structure of the quantities appearing in it, and reasons are given for supposing that no nonsymmetric theory simpler than the one put forward is likely to give these equations in their conventional form.

scholarly journals An attempt to geometrize electromagnetism

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 848-853
Author(s):  
XiuLin Huang ◽  
Yan Xu ◽  
ChengZhi Liu
Keyword(s):  
Reference Frames ◽  
World Line ◽  
Equation Of Motion ◽  
Unified Theory ◽  
Mass Ratio ◽  
Classical Electromagnetism ◽  
Lorentz Covariance ◽  
Flat Spacetime ◽  
Lorentz Equation ◽  
Equivalent Equation

AbstractThis study investigates the curved worldline of a charged particle accelerated by an electromagnetic field in flat spacetime. A new metric, which dependes on the charge-to-mass ratio and electromagnetic potential, is proposed to describe the curve characteristic of the world-line. The main result of this paper is that an equivalent equation of the Lorentz equation of motion is put forward based on a 4-dimensional Riemannian manifold defined by the metric. Using the Ricci rotation coefficients, the equivalent equation is self-consistently constructed. Additionally, the Lorentz equation of motion in the non-inertial reference frames is studied with the local Lorentz covariance of the equivalent equation. The model attempts to geometrize classical electromagnetism in the absence of the other interactions, and it is conducive to the establishment of the unified theory between electromagnetism and gravitation.

Relativistische Verallgemeinerung des Lenzschen Vektors (I) / Relativistic generalisation of the Lenz vector (I)

1984 ◽  
Vol 39 (8) ◽  
pp. 720-732
Author(s):  
Eberhard Kern
Keyword(s):  
Angular Momentum ◽  
Kepler Problem ◽  
Coulomb Field ◽  
Equation Of Motion ◽  
Central Field ◽  
Relativistic Energy ◽  
Geometric Meaning ◽  
Type Curves ◽  
Relativistic Problem ◽  
Charged Nucleus

The non-relativistic motion of a particle in a central field with 1/r potential, e.g. the motion of an electron in the Coulomb field of a charged nucleus at rest, is described by the equation of motion (non-relativistic Kepler problem) m x″ = α · x /r3 with α = ez e (product of the charges of the central body ez and the electron e). From this equation of motion, three statements of conservation can be derived: in respect of the energy E, of the angular momentum L and of the Lenz vector Λ = m {x′× L + α ·x/r}. The geometric meaning of Λ is that of a vector pointing in the direction of the perihelion of the particle orbits (conic sections). It will be demonstrated that also at the relativistic Kepler problem, which is based on the equation of motion an analogous Lenz vector exists. It represents a quantity of conservation - in the same way as the relativistic energy and the relativistic angular momentum. For the transitional case → ∞, where the relativistic problem turns into the non-relativistic problem, the relativistic Lenz vector also turns into the non-relativistic Lenz vector. The generalised (relativistic) Lenz vector has also a geometric meaning. Its direction coincides with the oriented axis of symmetry of the orbits (rosettes, spirals, hyperbola-type curves etc.). The quantity of conservation Λ occupies a special position in respect of the quantities of conservation energy and angular momentum. Whereas the energy and the angular momentum correspond with a symmetry of time and space, the Lenz quantity of conservation corresponds with a symmetry of the orbits. The fact that the Lenz vector can relativistically be generalised touches thereby on principal aspects.

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