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%% 6.1 Interaction
% There are several ways to describe interaction.
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% (6-1)
% The connection of the interaction with the momentum gradient in electrodynamics and space curvature will be considered in more detail below.
% In our conscious experience of the world, we constantly observe a change of momentum. This change is described physically by a momentum gradient. This gradient must be subject to a clear law, otherwise the change is scientifically or consciously intangible. All basic laws of electrodynamics and gravitation can be explained by the continuity of the momentum gradients.
% Comparison of the interaction with the water outflow
% Water flows out of a tap and spreads evenly on a surface, the electric field flows from a source and spreads out spatially:
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% (6-2)
% The water flow decreases radially in two dimensions with 1/R,  and the electric field in three dimensions with$1/{R^2}$. This results in each case from the continuity equation.
% Invariant formulation of the continuity equation
% We first write the continuity equation with four-vectors:
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% (6-3)
% The potential equations for electrodynamics and gravitation
% The continuity equations for the components of the four-momentum gradient correspond to the potential equations of electrodynamics.
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% (6-4)
% However, in electrodynamics the vector potential A_\mu is introduced and linked to the momentum through what is commonly known as  'minimal substitution'. The conserved total momentum is now p_\mu - A_\mu.
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% (6-5)
% The potential equations of electrodynamics developed here from the momentum gradients are equivalent to Maxwell's equations. The electromagnetic fields\vec Eand\vec Bmust be considered as derivatives of the potentials for this purpose.
%
% (6-6)
% Example: Stationary point source at rest
% The Coulomb potential or gravitational potential results immediately for a stationary point source.
% The source emits the ability to change the momentum. This ability is distributed on the spherical surface 4\pi r^2 around the source, and is thus inversely proportional to the square of the distance to the source, just as Newton formulated it in his law of gravity.
% The difference between the various interactions is the number of charge types. In gravity it is one: the mass. In electromagnetism there are positive and negative charges, and in strong interaction there are three colors of quarks.
%
% (6-7)
% General solution for stationary currents
% Due to the linearity of the potential equations, the sources can be integrated directly. This is simple for the boundary conditions of free space $\left( {\vec r \to \infty :\quad {A_\mu } \to 0} \right)$.
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% (6-8)
% Equation of motion with field A_\mu
% The classical equations of motion of a charged particle in the electromagnetic field are given in Hamiltonian mechanics:
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% (6-9)
% Free motion in Riemannian space
% Equations of motion also arise in a space without potential A_\mu if this space is curved. The forces then result from the inertia of the body. The space curvature is described by the metric. The metric and their derivatives are summarized in the Christoffel symbol.
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% Generally, the centrifugal forces are proportional to the velocity square, as in the usual centrifugal force of a circular motion.
% Equivalence principle
% The observed quantity is always the momentum gradient. It is indistinguishable whether it is caused by a field or by inertial forces. This can be used to relate field and metric.
%
% (6-10)
% The metric can thereby be determined from the continuity of the momentum gradients. For a resting point charge, the curvature of the space around a black hole in the form of the Schwarzschild metric is provided as an example in Chap06_5.
% Christoffel symbols and metric
% The Christoffel symbols can be determined solely from the metric g_{\mu\nu} without explicit knowledge of the ground vectors \vec{g_\mu^{(4)}}:
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% (6-11)
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